Pandian VasantPetronas University of Technology, Malaysia Nader Barsoum Curtin University, Malaysia Jeffrey Webb Swinburne University of Technology, Malaysia Innovation in Power, Control, and Optimization: Emerging Energy Technologies Innovation in power, control, and optimization: emerging energy technologies / Pandian Vasant, Nader Barsoum, and Jeffrey Webb, editors. p. cm. Summary: “This book unites research on the development of techniques and methodologies to improve the performance of power systems, energy planning and environments, controllers and robotics, operation research, and modern artificial computational intelligent techniques”-- Provided by publisher. Includes index. ISBN 978-1-61350-138-2 (hardcover) -- ISBN 978-1-61350-139-9 (ebook) -- ISBN 978-1-61350-140-5 (print & perpetual access) 1. Electric power system stability. 2. Power resources--Research. 3. Power resources--Economic aspects. I. Vasant, Pandian. II. Barsoum, Nader N. III. Webb, Jeffrey, 1963- TK1010.I45 2012 621.31--dc23 2011026251 British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the authors, but not necessarily of the publisher. Senior Editorial Director: Kristin Klinger Director of Book Publications: Julia Mosemann Editorial Director: Lindsay Johnston Acquisitions Editor: Erika Carter Development Editor: Myla Harty Production Editor: Sean Woznicki Typesetters: Jennifer Romanchak, Chris Shearer Print Coordinator: Jamie Snavely Cover Design: Nick Newcomer Published in the United States of America by Engineering Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue Hershey PA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail:
[email protected] Web site: http://www.igi-global.com Copyright © 2012 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Editorial Advisory Board Milorad Bojic, University of Kragujevac, Serbia Gianfranco Rizzo, University of Salerno, Italy Janos Sebestyen Janosy, KFKI Atomic Energy Research Institute, Hungary Ivan Zelinka, Thomas Bata University in Zlin, Czech Republic Davor Skrlec, University of Zagreb, Croatia Nikolai I. Voropai, Energy Systems Institute, Russia Monica Chis, Siemens Program and System Engineering, Romania Cengiz Kahraman, İstanbul Technical University, Turkey Valentina E. Balas, “Aurel Vlaicu” University of Arad, Romania Arturo Suman Bretas, Universidade Federal do Rio Grande do Sul, Brazil Etienne Kerre, Ghent University, Belgium Radu Emil Precup, “Politehnica” University of Timisoara, Romania Gerardo Maximiliano Mendez, Instituto Tecnologico de Nuevo Leon, Mexico Table of Contents Foreword by Ivan Zelinka .................................................................................................................. vii Foreword by Igor Tyukhov ................................................................................................................. ix Preface .................................................................................................................................................... x Acknowledgment ................................................................................................................................xiii Chapter 1 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems ........................ 1 Nicolay Voropai, Energy Systems Institute, Russia Irina Kolosok, Energy Systems Institute, Russia Elena Korkina, Energy Systems Institute, Russia Alexey Paltsev, Energy Systems Institute, Russia Anna Glazunova, Energy Systems Institute, Russia Victor Kurbatsky, Energy Systems Institute, Russia Nikita Tomin, Energy Systems Institute, Russia Alexander Gamm, Energy Systems Institute, Russia Irina Golub, Energy Systems Institute, Russia Roman Bershansky, Energy Systems Institute, Russia Daniil Panasetsky, Energy Systems Institute, Russia Dmitry Efmov, Energy Systems Institute, Russia Dmitry Popov, Energy Systems Institute, Russia Christian Rehtanz, University of Dortmund, Germany Ulf Häger, University of Dortmund, Germany Chapter 2 Hopfeld Lagrange Network for Economic Load Dispatch .................................................................. 57 Vo Ngoc Dieu, Asian Institute of Technology, Thailand Weerakorn Ongsakul, Asian Institute of Technology, Thailand Chapter 3 Renewable Energy and Sustainable Development................................................................................ 95 Abdeen Mustafa Omer, Energy Research Institute, UK Chapter 4 Demand-Side Response Smart Grid Technique for Optimized Energy Use ....................................... 137 Fouad Kamel, University of Southern Queensland, Australia Marwan Marwan, Queensland University of Technology, Australia Chapter 5 Soft Computing and Computational Intelligent Techniques in the Evaluation of Emerging Energy Technologies ....................................................................................................................................... 164 Selcuk Cebi, Karadeniz Technical University, Turkey Cengiz Kahraman, Istanbul Technical University, Turkey İhsan Kaya, Yıldız Technical University, Turkey Chapter 6 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms: Kurdistan Electric Network Case Study ............................................................................................. 198 Mohammad Saleh, University of Kurdistan, Iran Hassan Bevrani, University of Kurdistan, Iran Chapter 7 Many-to-Many Assignment Problems: Lagrangian Bounds and Heuristic ........................................ 220 Igor Litvinchev, Nuevo Leon State University, Mexico Socorro Rangel, São Paulo State University, Brazil Chapter 8 Power Systems Investments: A Real Options Analysis ...................................................................... 248 João Zambujal-Oliveira, Instituto Superior Técnico & Technical University of Lisbon, Portugal Chapter 9 Optimal Confguration and Reconfguration of Electric Distribution Networks ................................ 268 Armin Ebrahimi Milani, Islamic Azad University, Iran Mahmood Reza Haghifam, Tarbiat Modares University, Iran Chapter 10 A Descriptive Approach for Power System Stability and Security Assessment ................................. 293 A. G. Tikdari, University of Kurdistan, Iran H. Bevrani, University of Kurdistan, Iran G. Ledwich, Queensland University of Technology, Australia Chapter 11 Analyses and Monitoring of Power Grid ............................................................................................ 315 Rana A. Jabbar, Rachna College of Engineering and Technology, Pakistan Muhammad Junaid, Rachna College of Engineering and Technology, Pakistan M. A. Masood, Rachna College of Engineering and Technology, Pakistan A. Bashir, Rachna College of Engineering and Technology, Pakistan M. Mansoor, Rachna College of Engineering and Technology, Pakistan Chapter 12 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms and Hybrid Genetic Algorithms Pattern Search Approaches .......................................... 344 Pandian Vasant, University Technology Petronas, Malaysia About the Contributors .................................................................................................................... 369 Index ................................................................................................................................................... 377 vii Foreword Since the beginning of our civilization, the human race has had to confront numerous technological challenges such as finding the optimal solution of various problems including control technologies, power sources construction, and energy distribution, amongst others. These examples encompass both ancient as well as modern technologies like automatic theatre controlled by special programmes in ancient Greece, the first electrical energy distribution network in USA, mechanical, electronical, as well as computational controllers, et cetera. Technology development of those and related areas has had and continues to have a profound impact on our civilization and lifestyle. The topics discussed in this book are of these mentioned areas and mutually joined into a compre- hensive text, which while discussing the specific selected topics, give a deeper insight to the interdis- ciplinary fusion of those modern and promising areas of emerging technologies. This book discusses the mutual intersection of interesting fields of research, as hybrid renewable energy and energy saving, solar and fuel cells, power systems, chaos and power quality, soft computing, simulators, and software engineering, amongst others. Novel techniques are also discussed in this book, which are able to handle tasks such as control of various technological and energetical systems, optimization by means standard, as well as novel methods. Together with many interesting emerging technologies, a reader will also find in the book various mathematical and algorithmical methods used for proposed technologies including models like fuzzy logic, neural network, evolutionary algorithms, or Hybrid System Optimization. Therefore, this book titled “Innovation in Power, Control and Optimization: Emerging Energy Technologies,” edited by Pandian Vasant, Nader Barsoum, and Jeffrey Webb, is a timely volume to be welcomed by the community focused on power control and optimization as well as computational intel- ligence community and beyond. This book is devoted to the studies of common and related subjects in intensive research fields of emerging technologies. For these reasons, I enthusiastically recommend this book to our scientists and engineers working in the above mentioned fields of research and applications. Ivan Zelinka Czech Republic January 2011 Ivan Zelinka (born 1965) is currently working at the Technical University of Ostrava (VSB-TU), Faculty of Electrical Engi- neering and Computer Science. He graduated consequently at Technical University in Brno (1995 – MSc.), UTB in Zlin (2001 – Ph.D.) and again at Technical University in Brno (2004 – assoc. prof.) and VSB-TU (2010 - professor). Before academic career he was an employed as TELECOM technician, computer specialist (HW+SW) and Commercial Bank (computer and LAN supervisor). During his career at UTB he proposed and opened 7 different lectures. He also has been invited for lectures at 7 universities in different EU countries plus role of the keynote speaker at the Global Conference on Power, Control and viii Optimization in Bali, Indonesia (2009) and Interdisciplinary Symposium on Complex Systems (2011), Halkidiki, Greece. He is responsible supervisor of grant research of Czech grant agency GAČR named Softcomputing methods in control, co- supervisor of grant FRVŠ - Laboratory of parallel computing. He was also working on numerous grants and two EU project like member of team (FP5 - RESTORM) and supervisor (FP7 - PROMOEVO) of the Czech team. Currently he is a head of Department of Applied Informatics and in total he has been supervisor of more than 27 MSc. and 19 Bc. diploma theses. Ivan Zelinka is also supervisor of doctoral students including students from the abroad. He was awarded by Siemens Award for his Ph.D. thesis, as well as by journal Software news for his book about artificial intelligence. Ivan Zelinka is a member of British Computer Socciety, Machine Intelligence Research Labs (MIR Labs - http://www.mirlabs.org/czech.php), member of expert team of company DaySpring Global Multinational Inc., division Knowledge Management & Mining division (see also http:// www.dsgm.ca/consulting.asp), IEEE (committee of Czech section of Computational Intelligence), a few international program committees of various conferences and three international journals (Associate Editor of MSE, Hindawi, http://www.hindawi. com/journals/mse/editors.html, Editorial Council of Security Revue, http://www.securityrevue.com/editorial-council/, Edito- rial board - Journal of Computer Science, Riga, Latvia). He is author of journal articles as well as of 5 books in Czech and 8 chapters in 6 books in English language. ix Foreword This book is a challenge! The challenge to a reader, who is interested in new power technologies, but does not have a solid technical background. Possibly, reader has to have the technical skills. This book does not look like a fiction, but it is a scientific fiction which is becoming a reality! To read fiction or scientific fiction is much easier than to read scientific books. It reminded me my story about reading books on hard sciences, such as quantum mechanics. When I was the first year student at the Moscow Power Engineering Institute, the Russian transla- tion of famous American Physicists Richard Feynman Physics Course became available in our student bookstore. There were many complicated concepts and formulas over there but I enjoyed this book because between the formulas I could find very exciting belletristic. I hope the reader will find here the exciting belletristic pieces with combination of strict technical approaches and formulas describing various hot topics. The reader will find answers to the question: what is happening in new emerging power technologies? This book is a challenge because it covers a wide spectrum of problems from optimal configuration of electric distribution networks to smart grids, and from monitoring power grid to renewable energy technologies. The energy market, as you know, is on the verge of a vast transformation. Just take a look at this book and see what kind of energy innovation is appearing! Igor Tyukhov Moscow State University of Environmental Engineering, Russia Igor I. Tyukhov is Executive Director of UNESCO Chair “Ecologically clean engineering” at the Moscow State University of Environmental Engineering (MSUEE) and Deputy Chair Holder of the UNESCO Chair “Renewable Energy and Rural Elec- trification” (part time) at the All-Russian Research Institute for Electrification of Agriculture (VIESH), member of the Interna- tional Solar Energy Society, and Associate Editor of Solar Energy Journal. He graduated from the Moscow Power Engineering Institute, V. A. Fabrikant Physics Department, 1972. He got degree “kandidat technicheskikh nauk” (Ph.D.) at 1979. He has been with the Moscow Power Engineering Institute for more than 30 years teaching various physics disciplines and conduct- ing research work on solar energy, solar concentrators, optical metrology, and semiconductor technology . Dr. Tyukhov was visiting scholar at George Mason University (GFDP, 1999/200 academic year), at University of Oregon (Fulbright Program, 2002/2003), and at the Oregon Institute of Technology (2003). Dr. Tyukhov is expert in the field of photovoltaics and renewable energy. He is author more than 200 papers, more than 20 patents, several chapters in the books and coauthor of monograph. x Preface Many engineering systems and science problems suffer from the issue of developing a system that can cope with variations of system or control parameters, measurements uncertainty, and complex multi- objective optimization criteria. The need for a priori knowledge and the inability to learn from past experience make the design of robust, adaptive, and stable systems a difficult task. Currently, research on energy resources is of great importance for future oil replacements, particularly in vehicles and other transportation. Computational intelligence has been proven to provide successful solution of com- plex optimization problems by fuzzy logic, neural networks, evolutionary algorithms, and genetic algo- rithms. They include system identification, parameter estimation, multi-objective optimization, robust solutions, adaptive systems, self-organization, and failure analysis. This book aims to provide relevant theoretical frameworks and the latest empirical research findings in these areas. It is written for professionals who want to improve their understanding of the strategic role in the area of power, control, and optimization. Each book chapter is written by experts in their particular field of expertise. Chapter 1 of this text describes coordinated intelligent operation and emergency control of electric power systems. In Chapter 2 a Hopfield Lagrange network (HLN) is proposed for solving economic load dispatch (ELD) problem. HLN is a combination of Lagrangian function and continuous Hopfield neural network where the Lagrangian function is directly used as the energy function for the continuous Hopfield neural network. The increased availability of reliable and efficient energy services that stimulates new develop- ment alternatives such as solar, wind, et cetera is discussed in Chapter 3. This chapter elaborates on the potential for such integrated systems in the stationary and portable power market in response to the critical need for a cleaner energy technology. Anticipated patterns of future energy use and consequent environmental impacts (acid precipitation, ozone depletion, and the greenhouse effect or global warm- ing) are comprehensively discussed in this chapter. Chapter 4 describes a dynamic smart Grid concept which enables electricity end-users to be acting on controlling, shifting, or curtailing own demand to avoid peak-demand conditions according to infor- mation received about electricity market conditions over the Internet. The global warming and energy need requires developing emerging energy technologies for the electricity, heat, and transport markets are subject of discussion in Chapter 5. In this chapter are also discussed in great detail the emerging energy technologies that aim at increasing efficiency of energy utilization processes from energy sources and diminish CO 2 exhalation. The main aim of the chapter is to exhaustively present soft computing and computational intelligent techniques in the evaluation of emerging energy technologies. xi Chapter 6 presents an overview of key issues and technical challenges in a regional electric net- work, following the integration of a considerable amount of wind power. A brief survey on wind power system, the present status of wind energy worldwide, common dynamic models, and control loops for wind turbines is given. Modified Lagrangian bounds and a greedy heuristic are proposed and discussed in Chapter 7 for many-to-many assignment problems taking into account capacity limits for tasks and agents. A feasible solution recovered by the heuristic shown to speed up the subgradient technique to solve the modified Lagrangian dual. A numerical study is presented to compare the quality of the bounds and to demonstrate the efficiency of the overall approach. Energy projects with extended life cycles and initial investments can be unprofitable under discount cash flow methods. Therefore, real options analysis has become relevant as a pricing technique for these types of projects, with private risks and high investment levels. Following this question, the work pre- sented in Chapter 8 analyses different real options approaches to select the most acceptable for investing decisions in the energy sector. Power loss reduction is considered as one of the main purposes for a distribution system’s design- ers and operators especially for recent non-governmental networks. Moreover, the nature of power loss challenges different methods to solve this problem, while various studies indicate effectiveness of reconfiguration and its high portion for this case. Thus, “reconfiguration” can be introduced as an optimization procedure to obtain economical high quality operation by changing the status of sectional- izing switches in these networks. Some major points, such as using different switch types, considering number of switching, and time varying loads which are almost neglected or not applied simultaneously in most pervious essays are discussed in Chapter 9. In Chapter 10, the power system is considered as a continuum, and the propagated electromechani- cal waves initiated by faults and other random events are studied to provide a new scheme for stability investigation of a large dimensional system. For this purpose, the measured electrical indices (such as rotor angle and bus voltage) following a fault in different points among the network are used, and the behavior of the propagated waves through the lines, nodes, and buses is analyzed. The impact of weak transmission links on a progressive electromechanical wave using energy function concept is addressed. In Chapter 11 analyses and monitoring of the power grid in Pakistan is presented. Finally, in Chapter 12, a solution is proposed to a certain nonlinear programming difficulties related to the presence of uncertain technological coefficients represented by vague numbers. Only vague numbers with modified s-curve membership functions are considered. The proposed methodology consists of novel genetic algorithms and a hybrid genetic algorithm pattern search (Vasant, 2008) for nonlinear program- ming for solving problems that arise in industrial production planning in uncertain environments. Real life application examples in production planning and their numerical solutions are analyzed in detail. The new method suggested has produced good results in finding globally near-optimal solutions for the objective function under consideration. xii The editors of this text want to thank all the contributors to this text for their time, energy and invalu- able expertise that we believe will make this book a success and extremely valuable resource in the area of power management, control and optimization of engineering problems. Pandian Vasant Petronas University of Technology, Malaysia Nader Barsoum Curtin University, Malaysia Jeffrey Webb Swinburne University of Technology, Malaysia xiii Acknowledgment We would like to this golden opportunity to sincerely thank the following friends and colleagues of us for their valuable help and strong support of book chapters of the manuscript. Their marvelous feedback, opinion, constructive comments, and suggestions for the improvement of the overall outstanding qual- ity of the book chapters are gratefully acknowledged. Nikolai Voropai, Energy Systems Institute, Russia Dragica Vasileska, Arizona State University Tempe, USA Igor Litvinchev, Nuevo Leon State University, Mexico Hassan Bevrani, Kumamoto University, Japan Cengiz Kahraman, Istanbul Technical University, Turkey Rainer Burkard Graz, University Of Technology, Austria Milorad Bojic, University of Kragujevac, Serbia Gerardo M. Mendez, Instituto Technologico de Nuevo Leon, Mexico Blanca Pérez Gladish, Universidad de Oviedo, Spain Furthermore, we sincerely thank the group of IGI Global at Hershey PA, USA, for their great help and excellent support on this book project. In particular, special thanks go to Ms. Jan Travers, Ms. Myla Harty, and Mr. Dave De Ricco of IGI Global for their great help. Last but not least, we sincerely express our sincere thanks and appreciation to members of PCO Global for their great support. Pandian Vasant, Nader Barsoum, Jeffrey Webb January 2011 1 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 1 DOI: 10.4018/978-1-61350-138-2.ch001 Nicolay Voropai Energy Systems Institute, Russia Irina Kolosok Energy Systems Institute, Russia Elena Korkina Energy Systems Institute, Russia Alexey Paltsev Energy Systems Institute, Russia Anna Glazunova Energy Systems Institute, Russia Victor Kurbatsky Energy Systems Institute, Russia Nikita Tomin Energy Systems Institute, Russia Alexander Gamm Energy Systems Institute, Russia Irina Golub Energy Systems Institute, Russia Roman Bershansky Energy Systems Institute, Russia Daniil Panasetsky Energy Systems Institute, Russia Dmitry Efmov Energy Systems Institute, Russia Dmitry Popov Energy Systems Institute, Russia Christian Rehtanz University of Dortmund, Germany Ulf Häger University of Dortmund, Germany Coordinated Intelligent Operation and Emergency Control of Electric Power Systems ABSTRACT This chapter presents the following approaches and developments: (1) the approach to power system state estimation based on structural and functional decomposition. PMU measurements are used to coordinate the solutions obtained in individual areas; (2) a non-iterative method to calculate voltage 2 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems INTRODUCTION Last decade’s electric power industry is being lib- eralized and restructured in many countries. This process forces governments and science to learn what market structures are the most efficient and how regulation methods influence the industry and welfare of the people. Consumers are interested in optimizing their activity in a new environment and investors tend to accurately forecast the pros- pects of companies in electric power industry and related industries. The growing interest in this field generates necessity to exchange ideas and research results. The trends in expansion of electric power systems and changes in the conditions of their operation have led to complicate power system operation, increased its changeability and unpre- dictability that call for prompter and more adequate response of controls systems. Operational management deals with emer- gency state prediction concept (probability of emergency state occurrence). Prediction functions can be realized by means of different advice-giver software. But anyway, the final decision (control action) is realized by a system operator who for a variety of reasons is not able to realize rapid and economically ineffective control actions that would prevent an accident development. In such a manner, emergency control schemes do not predict the possible development of the normal, emergency or postemergency states but operate only when the disturbance has occurred. It is possible to suppose that there are two main disadvantages of the existing control ideology. First disadvantage is the absence of fast control actions realization in operational management. And the second one is the absence of prediction procedures in emergency control. According to the authors’ opinion, these dis- advantages may have been one of the causes of the blackouts that took place all over the world over the last several decades. Describing the disadvantages authors suggest a possible ways of developing and improving of the existent control systems (Panasetsky, 2009). The main idea is that the new methods that deal with voltage instability and cascade line tripping must complement and do not contradict to the existing ideology. The new control system can be built by using distributed intelligence principles. The distributed intelligence is taken to mean the multi-agent systems. Development of systems and devices for monitoring the state of energy and electrical equipment (devices and systems of diagnostics) and also monitoring the Electric Power System (EPS) operation conditions seems to be highly important because of radically changed develop- ment trends and complicated operating conditions of large-scale Interconnected Power Systems (IPSs) (Kurbatsky, 2009; Voropai, 2010). Modern systems for measurement of power system state variables and their control, new communication and information processing systems, etc. allow creation on a new basis and with essentially higher efficiency one of the most important stages of power system control – their operation and emergency control. magnitude and phase at all the buses, allowing the state parameters of EPS to be obtained fast enough; (3) the approach to the super short-term forecasting of state variables on the basis of neural network technologies and algorithms of nonlinear optimization that is realized in the ANAPRO software; (4) an analysis of the possibility of determining weak ties and cut sets in EPS; (5) a control system based on the multi-agent technique; (6) the development of selective automatic systems intended to prevent and eliminate out-of-step operation on the basis of synchronized voltage phase measurements obtained from Phasor Measurement Units. 3 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems The chapter includes: new conditions and requirements for power system monitoring and control; wide area monitoring of power system state using new technologies and tools; compre- hensive emergency control systems and defense plans for large power systems; coordinated con- cepts and control systems for improving stability and security of power systems; coordinated wide area monitoring and control of large power sys- tems; development of computer technologies and modern tools towards smart power grids The Problem of Monitoring, Forecasting and Control in Electric Power System The trends in expansion of EPSs and changes in the conditions of their operation have led to considerable transformations in their structure and operation. These transformations are conditioned by the following factors: • Increase in scale, expansion of territories to be serviced, interconnection of dif- ferent power systems for joint operation which results in creation of interregion- al, interstate and intercontinental power interconnections; • Decentralization of power supply due to a wider use of distributed generation sources that are connected to the distribution net- work nodes; • Restructuring of power industry, which of- ten makes its structure drastically different from the technological structure of EPS as a technically single unit and from its con- trol structure; • Liberalization of relationships in the elec- tric power industry which leads to many participants of relationships with different, often opposing, interests, in the course of expansion, operation and control of power system. All these factors essentially complicate power system operation, increase its changeability and unpredictability, raise danger of severe emergen- cies with undesirable development and massive consequences for a system and consumers and, therefore, call for prompter and more adequate response of control systems. This generates the need to improve and develop principles and sys- tems of power system operation control which can be based on: • New systems for measurement of operat- ing parameters (PMU) and their control (FACTS, energy storage devices etc.) that signifcantly improve EPS observability and controllability; • Modern communication systems, new in- formation technologies and artifcial intel- ligence methods, highly effcient comput- ers, which totally change the processes of acquisition, transmission, presentation (visualization) and use of information on power systems; • Effcient mathematical control theory methods in multicriteria non-coincident conditions. Based on the above circumstances the so called Smart Grid concept was developed (Of- fice, 2003 and European, 2006). This problem is very often associated with the integration of renewable energy sources in EPS as well as with distribution electric network based on the informa- tion technologies and artificial intelligence in the distributed control systems of power supply and power consumption (Chuang et al. 2004; Amin et al. 2005). The most comprehensive understanding of the Smart Grid concept to date has been given by Shahidehpour (2009). In general the Smart Grid concept can be represented as a set of the following components: • Generation (enhancement of reliability and economic effciency of electric ener- 4 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems gy production through the use of modern highly intelligent systems for monitor- ing and control, integration of renewable sources, distributed generation and energy storage devices on the basis of the Internet technologies); • Electric transmission network (wide scale monitoring of operating conditions and their control with the help of new devices and technologies (FACTS, PMU, artifcial intelligence, etc.) in order to provide pow- er supply reliability and electric network controllability); • Substations (automation of substations that are based on the advanced electric equip- ment by using modern systems for diag- nosing, monitoring and control on the basis of information and computer technologies in order to provide reliability and control- lability of substations); • Distribution electric network (a radical increase in its controllability and reliabil- ity through introduction of distributed mi- croprocessor-based control and protection systems with the use of new information, computer and Internet technologies); • Consumers (equipping them with highly intelligent systems intended for electricity control and metering, demand-side man- agement and load control in emergency situations). In Russia power industry reforms and new methods and technical tools of control have also encouraged the development of principles and methods of EPS dispatching and emergency con- trol (Ayuev et al, 2008; Voropai, 2008). Let us consider the problems of improving the principles and enhancing the efficiency of systems intended for EPS operation and emergency control. The most important directions here include an increase in control adaptability and expansion of coordination among control stages, devices and systems. For this purpose it is necessary to develop an efficient system of wide scale monitoring and forecasting of operating conditions and control of EPS. Figure 1 shows power system states and the blocks of problems on monitoring, forecasting and control that correspond to these states. The blocks of monitoring and forecasting of the EPS normal, pre-emergency and post-emer- Figure 1. Time diagram of events in the system for monitoring, forecasting and control in EPS 5 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems gency operating conditions include the following problems: • System state estimation; • Forecasting the parameters of expected operating conditions. Forecasting is nec- essary because during the state estimation procedure current state is estimated with some delay, while monitoring and control problems require some advance estimation of system state (“to control is to foresee”); let us note that for these two blocks of problems the advance time can vary; • Detection of weak points in the system in the expected operating conditions; • Determination of margins for transfer ca- pabilities of ties in the expected condi- tions; This is necessary to effciently use the margins in the operating conditions and automatic control through appropriate con- trol actions; • Visualization of the expected conditions; • Determination of indices and criteria for transition from normal to pre-emergency conditions and, vice versa, from post- emergency to normal conditions. A special explanation should be given concern- ing the last problem. It relates to the following basic principles of power system operation control in a market environment: • under normal operating conditions – ef- fcient contract relationships among the participants of the wholesale markets for electricity, capacity and ancillary services, that are coordinated on a market basis; • under a threat of emergency conditions – a transition from market criteria of operation control to the centralized principles of dis- patching control; • under emergency and post-emergency con- ditions – the use of strictly centralized dis- patching and automatic emergency control. The enumerated problems have certain specificity when applied to normal conditions, on the one hand, and to pre-emergency and post-emergency conditions, on the other hand. Pre-emergency and post-emergency conditions (at system restoration) require higher speed of algorithm operation and smaller time intervals between individual states for which the problems of operation monitoring and control are solved. A separate problem is monitoring of emergency conditions. Dynamic nature of emergency condi- tions requires that the results of monitoring be promptly transferred to dispatcher. They should have an integrated form and indicate dangerous points in the system in terms of undesirable de- velopment of emergency. The primary informa- tion, however, obtained as a result of emergency conditions monitoring, should arrive at the auto- matic control devices and systems with the view of their adaptation to the current power system emergency state. In addition to monitoring and forecasting of the operating conditions the efficient adaptive methods and algorithms for choosing the points of control action application and adjustments on the basis of advanced achievements of the control theory and artificial intelligence play an important part in increasing the adaptability of control. The methods and algorithms are implemented by dis- patcher and automatic control systems and provide adaptation of controls to the current system state and possible disturbances. It is necessary to considerably expand and improve coordination of control. This can be done in the following directions: 1. Expansion of EPS operation control coordination: A. In terms of time - from coordinated design of control systems to their implementation through dispatching and automatic devices; 6 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems B. In terms of situation – coordination of on-line dispatching, continuous auto- matic and discrete emergency control. 2. Extension of a range of devices intended for coordinated control of EPS operating conditions: A. Development of traditional systems, including automatic voltage regulators (AVR) and speed governors of synchro- nous machines, automatic emergency control devices, etc.; B. Use of new devices for measurement and control – PMU, FACTS, energy storage systems, etc. 3. Development and extension of principles and systems for coordinated online dispatching and emergency control to distribution electric networks with distributed generation. 4. Harmonization of commercial interests of participants in the markets for electricity, capacity and ancillary services and the need to provide EPS reliability and survivability. 5. Development of new criteria and new methods for monitoring, forecasting and control of operating conditions in order to provide effective coordinated control for all participants of the wholesale market, power system reliability and survivability. Implementation of the foregoing positions will allow one to considerably enhance the operation efficiency, controllability, reli- ability and survivability of modern power systems. Decomposition of Power System State Estimation Problem with the Use of PMU Data for Large Dimension Schemes State estimation (SE) of electric power systems is an important procedure that allows on-line cal- culation of state variables for a current scheme of electric network on the basis of Tele-Information. The obtained calculated model of power system is then used to solve various technological problems to effectively control electric power system. Currently the System Operator - Central Dispatching Office of Russia’s UES is creating an integrated computational model that reflects most completely the topology and operation of UES, to solve a set of online dispatching control problems instead of previous models that varied in degree of detail and were applied to solve individual problems. The single computational model of UES/RPS covers the entire backbone network of 220 kV and higher; the lines of lower voltage classes, that are important for market participants in terms of correct description of power supply volumes, boundaries of federal network company, interstate power flows, electricity outputs of power plants; and power plants with an installed capacity above 5 MW and large consumption nodes (Ayuyev, 2005). Currently the single computational model includes about 7000 nodes, 10000 branches and 800 generators. Similar situation is observed in the dispatching practices in other countries. Creation of Western European Union for the Coordination of Transmis- sion of Electricity (UCTE), North American Elec- tric Reliability Corporation (NERC) that embraces most of the North-American power systems, etc. has lead to the necessity to make calculations for very large and sophisticated systems. The calculations for a large system encounter the problems related to the un-homogeneity of calculated schemes, large volumes of various data to be processed and the requirement for high speed software. Besides, the need for online state estimation of such systems increases the burden on the available computing resources in the EPS Control Center. The distributed data processing at decomposi- tion of the state estimation problem is an effective method of solving these problems. Decomposi- tion of power system state estimation problem is addressed in a great number of scientific papers in Russia (Gamm, 1983; Gamm, 1995) and other 7 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems countries (Clements, 1972; El-Kleib, 1992; Iwa- moto, 1989 and others). Until recently state estimation in EPS was mainly based on the SCADA measurements: volt- age magnitudes, branch power flow, nodal power injections and, occasionally, current magnitudes. The advent of WAMS (Wide-Area Measurement System) that contains phasor measurement units (PMU) as the main measurement equipment (Phadke, 2002) makes it possible to synchro- nously and accurately control the EPS state and essentially improve the results of state estimation (Gamm, 1997). The use of PMU measurements offers new possibilities in decomposition of the state estimation problem. The paper considers the algorithm of state esti- mation by the test equation technique (Clements, 1972) that employs structural decomposition of state estimation problem, i.e. division of the cal- culated scheme into subsystems, and functional decomposition of the SE problem (detection of bad data, state estimation on the basis of quadratic and robust criteria). The two-level algorithm is proposed to divide the calculated scheme into subsystems for state estimation by the test equa- tion technique. Application of the test equation technique that allows the values of measured variables to be fixed by setting zero variances for them, and placement of Phasor Measurements Units at boundary nodes (El-Kleib, 1992) make it possible to essentially simplify the procedure of coordinating the solutions obtained for separate subsystems. In addition the paper presents the algorithm of PMU placement at boundary nodes. The example of calculation for a fragment of real power system is given. Decomposition of State Estimation Problem Decomposition of the state estimation problem is based on structural (by subsystems) and func- tional (by the problems solved) decomposition. The structural decomposition is made by dividing the calculated scheme into subsystems by one or another method (Gamm, 2007). The functional decomposition is made in accordance with the problems solved within the SE procedure. The main of them are: analysis of network topology (formation of current calculated scheme); analysis of observability; analysis of bad data; calculation of estimates and calculation of steady state with regard to the estimates obtained. Methods of Structural Decomposition The calculated scheme can be divided into subsys- tems by the following techniques: decomposition utilizing geographical characteristics (Gamm, 1995; Falcao, 1995), decomposition by boundary nodes (Gamm, 1983; Clements, 1972), by tie-lines (Gamm, 1983; Gamm, 1995; Abdel-Rahman, 2001), based on the structure of gain matrix (Wallach, 1981), by Danzig-Wolf decomposition algorithm (El-Kleib, 1992), and others. The main algorithms of SE problem decompo- sition suggest dividing the calculated scheme into subsystems whose boundaries are either nodes or branches. In this case the SE problem is solved iteratively unless the boundary conditions are met. The method of decomposition with bound- ary nodes has been chosen for realization in the offered algorithm. In this case the equality of voltage magnitudes and phases at the boundary nodes should be met [2]: U U U i j k = = = ... ; (1) δ δ δ i j k = = = ... ; (2) Besides the boundary balance relationships should be met. For example for boundary node l, common for the i, j, …, k-th subsystems P P U U l lm l l m m m s i j k s + = ∈ = ∑ ∑ ( , , , ) , ,..., δ δ ω 0 ; (3) 8 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Q Q U U l lm l l m m m s i j k s + = ∈ = ∑ ∑ ( , , , ) , ,..., δ δ ω 0 , (4) where ω s - a set of nodes of the s-th subsystem, that are adjacent to the l-th node. The Use of PMU Data in Structural Decomposition Development and improvement of software for monitoring and control of power systems at a qualitatively new level have become possible ow- ing to WAMS (Wide-Area Measurement System) that allows the EPS state to be controlled synchro- nously and accurately. The devices for measuring phasors (Phasor Measurement Units) are the basic measurement equipment in this system. The results of solving the state estimation problem can be essentially improved by using the PMU data. As compared to the standard set of measurements received from SCADA system PMUs placed at a node provide accurate (the error is 0.2-0.5%) measurements of voltage magnitude and phase at this node as well as the magnitudes and phases of currents in the branches adjacent to this node. The possibilities of using synchronized pha- sor measurements for distributed state estimation were discussed in (Zhao, 2005; Jiang, 2007; Jang, 2008 and others). In (Zhao, 2005) the method is suggested to decompose the calculated scheme into the areas with PMU to be installed in each area. The data from these PMU are then used to solve a coordination problem. In (Jiang, 2007) the authors suggest placing PMU at a basic node of each area. The PMU measurements coordinate the SE problem solution of each area. (Jang, 2008) presents a diakoptic-based distributed SE algorithm, in which PMUs are used to coordinate voltage angles of each area SE solution. The chapter suggests the use of PMU measure- ments for distributed state estimation to coordinate the solutions obtained for individual areas. For PMU placement under SE problem decomposi- tion the algorithm based on the annealing method was developed. They will be presented in Section 4. Compared to the PMU-based decomposition methods proposed in (Zhao, 2005; Jiang, 2007; Jang, 2008) the number of PMUs in our case study did not increase, yet made it possible to perform parallel state estimation by subsystems, to solve coordination problem without iteration and obtain an optimal but not pseudo-optimal, as in (Zhao, 2005), solution that coincides with the solution for the entire network. Placement of PMUs at boundary nodes makes it possible to register boundary variables U and δ measured highly accurately. In this case the operating conditions of some subsystems can be calculated independently of one another and solution of the coordinated problem consists in calculating nodal injections by (3), (4) using the estimates of power flows. Algorithm of Structural Decomposition Using Test Equations The idea of decomposing the state estimation problem with PMU placement at boundary nodes is rather attractive. In reality, however, due to high cost of PMUs they can only be used when the number of boundary nodes is small. To calculate large inhomogeneous schemes the authors propose a method of dividing the calculated scheme with respect to voltage levels (Wallach, 1981). This method decreases essen- tially a negative impact of un-homogeneity of calculated scheme and telemetric information in calculation of subsystems of one voltage class but for the complex scheme inevitably leads to a large number of boundary nodes. Therefore, the paper proposes a two-stage algorithm to decompose the calculated scheme into subsystems that combines the positive features of both approaches. At the first stage the scheme is divided into rather large areas with minimum number of inter- system ties and boundary nodes. This decomposi- tion can be made on the basis of administrative 9 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems division, for example, the entire scheme of Russia’s UES is decomposed into regional power subsys- tems of large regions in the country that operate in parallel or it can be decomposed artificially into separate areas by special algorithms (Gamm, 1995). PMUs are placed at the boundary nodes of the areas. Highly accurate measurements obtained from PMU make it possible to register the values of magnitudes and phases of nodal voltages at the boundary nodes and make calculations for the areas in parallel. At the second stage the calculated scheme of each area in turn is divided into subsystems that correspond to the levels of nodal voltages. The calculations start with the subsystem of the highest voltage level (750-500 kV). Normally this part of the scheme is well provided with highly accurate telemetry and contains a basic node. Then the calculations are made successively for the rest of the subsystems. The subsystems are ranked by voltage levels (220 kV, 110 kV, etc.). Every time the node bordering the subsystem of higher voltage level is chosen as a basic one. After the calculation of the low level sub- systems a coordination problem is solved for all areas. In this case boundary conditions (1), (2) are met automatically, and the coordination problem implies calculation of nodal injections at the boundary nodes on the basis of power flow estimates obtained for each area (Equations (3) and (4)). Functional Decomposition The functional decomposition of the SE problem is performed in accordance with the problems solved within the state estimation procedure. The main of them are: analysis of network topology; analysis of observability; analysis of bad data; calculation of estimates and steady state by the estimates obtained. The current calculated scheme is formed for the entire scheme. Bad data analysis and calcula- tion of estimates and steady state are performed by the test equation technique for each subsystem of a certain voltage class before solving the state estimation problem (Gamm, 2007). State estimation is made according to two criteria: the method of weighted least squares and the robust criterion that allows the estimates to be obtained and bad data to be suppressed simultaneously. Control is transferred to one or another state estimation program depending on operation of the bad data detection program. In case of bad data detection or their absence the program for calculation of estimates operates on the basis of the least squares method. However, if it is im- possible to detect erroneous measurements and, hence, identify bad data the program operates according to the robust criterion (Gamm, 2005). State estimation is made starting at the upper level of the structural decomposition. Full Algorithm The full algorithm for solving the state estima- tion problem based on structural and functional decomposition is as follows. 1. The complete calculated scheme of EPS is decomposed into rather large areas. Phasor measurement units are placed at the boundary nodes of subsystems. In the subsystems that have no basic node of the complete scheme one of the boundary nodes with PMU of the highest voltage class is chosen as a basic one. Measurements of nodal injections at boundary nodes are excluded from the vector of measurements. 2. At the second stage of decomposition the calculated scheme of each area is divided into subsystems that correspond to the levels of nodal voltages. The boundaries of the sub- systems are the nodes adjacent to the nodes of the voltage class of this subsystem. For example for the 750-500 kV voltage class subsystem the nodes with the voltage of 220 kV are boundary nodes and vice-versa. 10 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems 3. The calculation starts with the subsystem of the highest voltage level (750-500 kV) for each subsystem. Normally this part of the scheme is well provided with highly accurate measurements and contains a basic node. The state estimation algorithm for subsystems with boundary nodes is as follows: A. For each subsystem that contains boundary nodes the problem of bad data detection is solved by the test equation technique. B. In case of bad data detection or their absence the state estimation is made according to least squares method. C. In the event that erroneous measure- ments cannot be detected and hence it is impossible to detect bad data, the state estimation is made according to the robust criterion (bad data suppression). 4. The rest of the subsystems in the scheme are successively calculated. They are ranked by voltage level (220 kV, 110 kV, etc.). Every time the node bordering the subsystem of higher voltage level is chosen as a basic node. The estimates of the boundary variables of the state vector that are obtained at the upper level of decomposition are registered. 5. The injections at boundary nodes between the subsystems of different voltage class are calculated. 6. After all subsystems of the first level of decomposition have been calculated similar problem is solved for the boundary nodes with PMU. Placement of PMU at Decomposition of the State Estimation Problem For decomposition of power system state estima- tion problem it is necessary to maintain accurate values of voltage magnitudes and phases at boundary nodes of subsystems for iteration-free solution of coordination problem. A simple but not an optimal solution is placement of PMUs at all boundary nodes. Based on the measurements to be received from the placed PMUs the voltage magnitude and phase at a neighboring node can be calculated using the electrical circuit equations. In the paper the vector voltage measurement obtained by the equations is called the “calculated” PMU. The study shows that the accuracy of parameters of the calculated PMU practically equals the ac- curacy of measurements of the physical PMU (Kolosok, 2009). With an optimal combination of physical and calculated PMU at all boundary nodes of subsystems it is possible to determine voltage magnitudes and phases required to coordinate the solutions obtained for individual subsystems. In order to minimize the number of PMUs we analyze not only the list of boundary nodes but the list of internal lines within subsystems that are incident to these nodes as well. The bound- ary nodes may happen to belong to one and the same subsystem and bound one and the same line. Then it is enough to place a physical PMU at one end of the line and a “calculated” PMU at the other. To choose the optimal PMU placement the algorithm based on the simulated annealing method was developed. A fragment of a real scheme divided into 3 subsystems (Figure 2 and Figure 3) will be con- sidered for illustration of the algorithm operation. Figures 2 and 3 show a variant of system divi- sion into subsystems with boundary lines: between subsystems I and II - lines 2-5 and 4-7, between subsystems I and III – lines 3-9 and 4-9, and between subsystems II and III – lines 7-10. The objective function of the annealing method in this problem has the form: min var E K K K K PMU iants calculated subsystems = + + 1 2 3 4 , (5) where • K PMU 1 – the number of placed PMUs; 11 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems • K iants 2 var – the number of calculated PMU variants, their existence implies that there are redundant PMUs in the scheme. • K calculated 3 – the maximum number of cal- culated PMUs enabling one to obtain ac- curateδ,U ; • K subsystems 4 – the number of subsystems with PMUs. It is desirable that every sub- system has at least one PMU. The problem starts with the choice of random nodes, preferably those with maximum connectiv- ity, and with the assignment of PMUs with accurate measurements of δ φ pmu pmu ij ij U I pmu pmu , , , to these nodes. Further the possibility of obtaining the calculated PMU at the ends of incident branches is determined. At each step the objective function is calculated. If the result E new , obtained by (5) after some iteration is less than the previously as- sumed optimal result ( E E new opt < ), a new variant of assignment is taken E E opt new = , if the result is not less - whether or not the return to the previous step occurs depends on the value of wrong decision probability P E e E k T b ( ) /( ) ∆ ∆ = − , where ∆E k T b – the Metropolis criterion, an analog of Boltzmann factor. Figure 2. Placement of PMUs in intersystem lines. PMUs at nodes 4,6,12 Figure 3. Placement of PMUs at boundary nodes. PMU at node 7 12 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems The criterion of operation completion is min E . The practical result of searching and obtain- ing the optimal placement of PMU at division of system into subsystems with boundary lines is given in Table 1, line 1. Figures 2 and 3 show that with an account taken of the calculated scheme topology the optimal result is given by PMUs (black squares) placed at boundary node 4 and nodes 6 and 12 which are adjacent to the bound- ary ones. The circles denote the nodes for which the “calculated” PMUs are obtained. Figure 3 presents the variant of dividing system into subsystems by boundary nodes: between subsystems I and II - nodes 5 and 7, between subsystems I and III – nodes 4 and 7, between subsystems II and III – boundary node 7. Table 1, line 2, shows the optimal PMU placement under the following division into subsystems: the optimal result E opt = 0 14 . is given by the PMU (black square), installed at boundary node 7 which is common for all subsystems, the “calculated” PMUs provide pseudo-measurements at nodes 4,5,8,10, which are adjacent to the boundary ones (denoted by circles). The calculations show that the number of PMUs placed at decomposition of the scheme is consider- ably lower than the number of boundary nodes. Calculation Example In order to test the efficiency of the suggested decomposition algorithm of state estimation the calculations were made for a real scheme consisting of 107 nodes and 175 branches. The calculations were based on real measurements. The efficiency of the algorithm was assessed by comparing the results of calculations made for subsystems to the results of the calculation made for the entire scheme. At the first stage the Genetic Algorithm (Ko- losok, 2003) was used to divide the entire scheme into two subsystems containing 55 and 52 nodes including 6 boundary nodes in which the PMU data (measurements of magnitudes and phases of nodal voltages) were modeled. The calculations of these subsystems were carried out in parallel which reduced the time of solving the SE problem almost twice: from 0.49 s to 0.27 s. At the second stage of decomposition each of the subsystems in turn was decomposed into three subsystems corresponding to the voltage levels of 500 kV, 220 kV, 110 kV and lower. The calculation of these subsystems according to the above algorithm was made successively; therefore the full time of solution could increase. However, owing to the improved convergence of the iteration processes in the calculation of subsystems of the same voltage class the total time of the calcula- tion for all the three subsystems practically did not change. More efficient operation of bad data detection algorithm and application of the robust criterion of SE (Kolosok, 2003) for two of six subsystems improved considerably the results of state estima- tion: the value of the SE objective function at the point of solution decreased almost by a factor Table 1. The practical result of searching and obtaining the optimal placement of PMU at division of system into subsystems with boundary lines Division into subsist. PMU placement at nodes, K PMU 1 Variants of calculated PMU, K iants 2 var Calculated nodes, K calculated 3 The number of subsist. K4 Function Е By lines 4,6 and 12 0 2,3,5,7,8,9,10,11 3 0,27 By nodes 7 0 4,5,8,10 3 0,14 13 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems of 6 and the estimates at boundary nodes were noticeably improved. Structural and functional decomposition of state estimation problem is an effective method to solve the problems arising during calculation of large schemes. The proposed two-level algorithm for structural decomposition of the SE problem allows one to simultaneously process the data for local sub- systems of considerably smaller dimensionality; decrease the adverse impact of un-homogeneity of the calculated scheme and telemetric information when calculating one-voltage-class subsystems; essentially simplify solution of the coordination problem which, in this case, does not require itera- tive calculations by subsystems; and reduce the time for SE problem solving for the entire scheme. Functional decomposition of the SE problem allows one to coordinate interaction between the problems solved at different levels, organize a flexible choice of the method to solve one or an- other state estimation problem for each subsystem, integrate the methods of artificial intelligence and numerical methods, accelerate the process of measurement processing, and, thus, reduce the time of system state estimation. The use of measurements from PMUs placed at boundary nodes of subsystems allows state esti- mation to be performed for individual subsystems independent of one another. Solution of coordi- nated problem in this case implies calculation of nodal injections at boundary nodes and does not require iterative calculations. The developed algorithm of placing PMU by the annealing method and the use of “calculated” PMU make it possible to reduce the number of PMUs required for solving the coordination problem which in this case is essentially lower than the number of boundary nodes. Simulation calculations as well as the calcula- tion of a real scheme demonstrate the efficiency of the suggested approach to electric power system state estimation. PMU for Fast Calculation of Steady State in Electric Power Systems The current state of an electric power system (EPS) can be properly determined by a minimum set of state variables that will make it possible to uniquely determine all the rest of state variables. Such a set of variables is called a state vector. As a rule it is voltage magnitudes and phases x = { , } δ U . The speed of determining the current system state depends on the speed of calculating all state vector components. As a rule the state vector components are calculated in the process of state estimation problem solution by the iterative methods. In emergency situations the speed of achieving the result can prove to be insufficient. Measurement of these components by using PMU is the most attractive method. PMU installed at the bus provides measurements of voltage mag- nitude U i and phase δ i at this bus, current mag- nitude and angle value between voltage and current φ ij in the entire branches incident to this bus or in some of them subject to transmission capacity of communication channels (Phadke, 2002). In practice, however, installation of PMU at each bus is impossible. The paper presents a non-iterative method to calculate voltage magnitude and phase at all the buses, allowing the state parameters of EPS to be obtained fast enough. Problem Statement To calculate load flow in EPS fast, the complex network configurations are reduced to a radial form and the voltage magnitude and phase at all buses are calculated directly. For this purpose an optimal set of measurements from the SCADA system and PMU and the known relations between the state variables in EPS are applied. The calculated PMU is installed at bus j. Instal- lation of the calculated PMU means calculation of 14 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems voltage magnitude and phase at the neighboring buses by the formulas: U U I R X j i ij ij ij = − + ( cos sin ) φ φ , (6) δ δ φ φ φ φ j i ij i arctg I X R U R X = − − − − ( cos sin ) cos sin . (7) The phases δ k at bus k are calculated through measurements of ( U P Q k k j k j , , − − ). To do this, the active and reactive voltage drops ( , ) ' '' ∆ ∆ U U are calculated by the expressions ∆U P R Q X U k j k j k ' = + − − (8) ∆U P X Q R U k j k j k '' = − − − (9) then δ k is determined δ δ k j j arctg U U U = − − ∆ ∆ '' ' . (10) With the measurements shown in Figure 3 the voltage magnitude at the bus k is calculated by the formula: U U U U k k = − + ( ) ( ) ' '' ∆ ∆ 2 2 . (11) δ k is calculated by expression (5), where ( , ) ' '' ∆ ∆ U U are determined through P Q U j k j k k − − , , . Calculation of δ, U at all EPS Buses Calculation of δ, U starts with the reference bus that is determined in accordance with (Glazu- nova, 2009). PMU is installed at the reference bus. The process of searching for the reference bus reveals buses and branches with insufficient measurements for determination of δ, U at the next bus. Their calculation can be continued by installation of additional PMUs. These buses are also called reference buses. Algorithm for Calculation of δ, U 1. Reduction of the scheme to a radial form (removal from the network graph of buses forming loops). 2. Determination of reference buses, from which the voltages are calculated in each radial scheme. Installation of PMUs at the reference buses. 3. Installation of the calculated PMUs at the buses adjacent to the reference ones. 4. Calculation of voltage magnitude and phase at all buses of each radial scheme. 5. Calculation of voltages at the removed buses. To do this, the state estimation of each scheme is performed, with the number of buses equal to m+1, where m – number of branches adjacent to the removed one. 6. Comparison of values of voltage phasors that are obtained at point 4 with the values calculated at point 5. If the difference is less than the threshold d, then go to point 7, otherwise to point 11. The threshold is determined by the formula: d = 3σ , where σ - variance of measurements. For voltage σ u 2 2 = ; d Bm u = = ± 3 2 4 24 * . Κ ; 15 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems d o δ = ±0 2 . . 7. Calculation of the values of power flows in the branches, limited by the buses where voltage is corrected. 8. Adjustment of the injection values at the buses, where voltage is corrected and at the adjacent buses. 9. Calculation of the values of power flows in the boundary branches, i.e. those connect two radial schemes. 10. Analysis of the obtained results. Comparison of the calculated values of power flows with measurements. If the difference is less than the threshold d, then go to point 11. Where d MW p = = ± 3 25 15 * , d MVAr q = = ± 3 100 30 * . 11. Generation of the signal on the error in measurements. 12. End of the algorithm work. Practical Results Examples of the 13-bus and 14-bus schemes il- lustrate the possibility for non-iterative calcula- tion of load flow by the measurements from the SCADA system and data of PMU. 13-Bus Scheme The states of the 13-bus scheme (Figure 4) were calculated on the basis of real data. Figure 4. Fragment of a real scheme 16 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems The given network scheme is reduced to the radial form by removal from the graph of bus 3 as the most connected (Figure 4). The dashed lines show branches adjacent to the removed bus. Bus 13 is a reference bus. For the non-iterative calcu- lation of load flow to be made on the basis of measurements presented in Figure 4 an addi- tional PMU should be installed at bus 10. Branch 7-8 becomes a boundary one. As a result the transformed scheme has two radial schemes with the vertex at bus 13 (13-1- 11; 13-2; 13-12-5-4-6-7), and the vertex at bus 10 (10-8; 10-9), one boundary branch (7-8), four branches adjacent to the removed bus. PMUs are installed at buses 13, 10. Voltage magnitudes and phases are calculated at the neighboring buses 1, 2, 12, 8, 9 by using the data of PMU from Equations (6), (7). Voltage magnitudes (if it is needed) and phases for other buses are calculated by the following measurements from the SCADA system: At buses 4, 6 – by the active and reactive power flows at the beginning of the branch (10), (11). At buses 11, 5, 7 – by the active and reactive power flows at the end of branch and voltage in the following succession: 1. Calculation of voltage drop from (8), (9); 2. Calculation of δ k by Equations (10), where k=5, 7, 11. Voltage at the bus removed from the scheme shown in Figure 4 is calculated by separation of the 5-bus scheme (Figure 5). For the obtained scheme the state estimation is performed based on available measurements by the algorithm described in (Gamm, 2007). Figure 5. Fragment of a real scheme 17 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Voltages calculated by Equations (6)-(11) are applied as initial data. Here it is taken into con- sideration that the calculated PMUs are installed at buses 2, 9, 12, i.e. the voltage magnitude and phase at these buses are measured with a high degree of accuracy. Then the following condition is analyzed: U U d SE cal − < , (12) where U SE – estimated voltage values, U cal – voltages calculated in the radial scheme. If condi- tion (7) is true, it means that there are no errors in measurements and the obtained state is adequate. This condition holds true for bus 4: 509 508 4 25 SE cal − < . . (13) The values of active and reactive power flows in the branch 3–4 are calculated. Balances at buses 3, 4 are maintained by correc- tion of the injection values there. The calculation results are given in Table 2. The second column presents the values of measurements. The results of SE of the 13-bus scheme are given in column 3. The fourth column shows results of SE for the 5-bus scheme. The fifth column presents voltage values calculated by the suggested algorithm. The Table 2 indicates that the voltage phasor obtained by the non-iter- ative method coincides with SE results. The values of active and reactive power flows in the boundary branch 7-8 are calculated based on the known voltages. The values of obtained flows and the values of flows from SE, measurements of flows are shown in Table 3. Table 2. Calculation results with real data Measurement Estimate Estimate of 5-bus scheme Non-iterative method 2 3 4 5 U ˆ U − ˆ δ ˆ U − ˆ δ U cal −δ cal 753 753 0 753 0 746 747 0.103 747 0.10 747 0.103 517 503 0.118 503 0.11 502 505 0.159 506 0.16 505 0.160 505 505 0.171 505 0.173 498 500 0.153 501 0.154 497 504 0.114 504 0.117 512 507 0.104 508 0.107 515 500 0.096 500 0.09 501 0.099 515 503 0.102 503 0.102 741 743 0.193 743 0.191 512 502 0.113 502 0.11 502 0.113 785 740 0.083 740 0.083 18 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Analysis of the obtained values reveals that the power flows in the boundary branch are within the normal range: P P d meas ss − < . (14) Hence, the steady state of the 13-bus scheme is calculated. 14-Bus Scheme Figure 6 presents a 14-bus test IEEE scheme. SS of the considered scheme is calculated by using the described algorithm. 1. For reduction of scheme to the radial form 3 buses (2, 4, and 6) are removed from the network graph. Two radial schemes with the vertices at buses 9 and 5 are obtained. 2. Installation of PMUs at buses 9 and 5. 3. Installation of calculated PMUs at buses 1, 2, 4, 6, 7, 10, 14. 4. Calculation of voltages at the buses of each radial scheme: 14-13-12; 10-11; 7-8. Calculation starts with the buses, where the calculated PMUs are installed. 5. State estimation for the 3-bus scheme (2- 3-4). For the schemes with removed buses the problem of SE is not solved because of installation of the calculated PMUs there. Voltage magnitude and phase at bus 3 are calculated through SCADA measurements and the calculated PMU data. 6. Adjustment of power flows in the boundary branches 6-12; 6-11, 6-13, 4-3. The calcula- tion results are shown in Table 4. 7. Analysis of the obtained results. Table 4 shows that condition (14) for the boundary branches is true (the difference between the calculated flow and the measurement is less than the threshold equal to 15 MW and 30 MVAr). Hence, the steady state for the 14-bus scheme is calculated. The results of SE and the results obtained on the basis of the suggested technique are pre- sented in Table 5. Data of PMUs are shown by bold type and data of the calculated PMUs – by italic type. From Table 5 it is seen that the voltage values obtained by different techniques coincide. Table 3. Values of power flows in the boundary branch Ranch P Q Meas SE SS Meas SE SS 7–8 -266 -264 -258 83 80 79 Table 4. Power flow values in boundary branches Branch P Q SE SS SE SS 6 –11 6.89 7.4 11.4 9.2 6–12 8.18 8.01 9.8 2.12 6–13 17.9 21.7 22.39 10.8 3–4 -23 -27 -5 -8 19 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Determination of the Quality of Results The quality of results is determined by applying the objective function value of state estimation: ϕ σ ( ) ( (ˆ)) x y y x i i i i m = − = ∑ 2 2 1 y – vector of measurements, ˆ x – estimates (or calculated values in the radial schemes) of the state vector components, m – number of measure- ments. The values of criteria for different calculations are given in Table 6. The Table reveals that the values of criteria are almost the same for all calculation methods. It means that the EPS steady state can be calcu- lated by the non-iterative method approximately with the same accuracy as by SE. 1. The algorithm of non-iterative calculation of load flow that is based on reduction of the calculated scheme of EPS to a radial form is suggested. It applies a minimum number of PMUs and an optimal set of measurements from the SCADA system. 2. The steady states of the test 14-bus scheme and a fragment of the real scheme are cal- culated. The EPS state calculated by the suggested method is shown to coincide with the results of state estimation. Figure 6. A 14-bus IEEE scheme 20 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Artificial Intelligence Technologies for Monitoring Large Power Interconnections Implementation of market principles in planning and control of operating conditions, expansion of the area of coordinating operation control of EPSs in terms of time (from design of control systems to their realization by dispatching and automatic devices) and situation (coordination of dispatch- ing, continuous automatic and discrete emergency control) all cause fast dynamics of change in EPS operating conditions. As a result the problem on working out principles of interconnection of EPSs of different geographical length and with different structure of an electric network is considerably complicated. The principles developed apply dif- ferent norms, standards, control algorithms, etc. Development of systems and devices for moni- toring the state of energy and electrical equipment Table 5. Calculation results of steady state Nº Estimate Non-iterative method 3 5 ˆ U ˆ δ U cal δ cal 1 380 0 380 0 2 397 -0.0604 397 -0.0604 3 383 -0.12 381 -0.12 4 387 -0.1027 387 -0.1027 5 387 -0.0874 387 -0.0874 6 406 -0.1363 406 -0.1363 7 403 -0.1277 403 -0.1277 8 414 -0.1310 414 -0.1323 9 401 -0.1404 401 -0.1404 10 399 -0.1402 399 -0.1402 11 401 -0.1375 402 -0.1374 12 400 -0.1401 401 -0.1356 13 399 -0.14 402 -0.1407 14 393 -0.1423 393 -0.1423 Table 6. The values of criteria φ Scheme Real data SE Non-iterative method 13 20.35 22.70 14 20.4 25 21 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems (devices and systems of diagnostics) and also monitoring the EPS operation conditions seems to be highly important because of radically changed development trends and complicated operating conditions of large-scale IPSs. It should be underlined that in these conditions a system of operation monitoring is a powerful tool to study dynamic characteristics of EPSs in real time for different system states. The system en- hances control efficiency of normal and emergency conditions in the current market environment. Artificial Intelligence Methods in Problems of Operating Condition Monitoring Effective organization of the system of IPS operating condition monitoring is possible by an extensive involvement of new tools for the analysis and calculations of operating conditions, primarily technologies of artificial intelligence. It should be underlined that the methods of artificial intelligence have nothing to do with algo- rithmic calculations and therefore, do not require complex computational mathematical models to be constructed for an object. The artificial intelligence methods reproduce (copy) individual functions of the creative activity of human brain, which makes it possible to find optimal decisions in a large set of possible states in the shortest time. The following are primarily the main technolo- gies of artificial intelligence: • Models applying an apparatus of artifcial neural networks (ANN) (Haykin, 2006, Ossovsky, 2004) • Genetic Algorithms (Goldberg, 1989) • Hybrid and fuzzy systems (Pospelov, 1986). The Kohonen maps applied for visualization and analysis of schemes and operating conditions in EPS may be given as an example of practical use of the artificial intelligence technologies. Use a self-organizing Kohonen network in the struc- ture of the main system of data processing of the WAMS system is offered in (Handshin, 2006). The Kohonen network in this case is capable of analyzing schemes and operating conditions “on-line” and “off-line”. For the given ANN the problem is solved by division of the studied situations into clusters with close typical change of processes in EPS. Hence, the whole variety of schemes and operating conditions can be visual- ized effectively and dangerous contingencies in the studied EPSs can be detected timely. The experimental studies have shown (Kur- batsky, 2009) that the Kohonen maps applied allow an adequate detection of inadmissible combina- tions of the scheme and operating parameters and a correct choice of necessary control actions. In addition, a key monitoring problem is the problem of forecasting state variables of EPS. In this case within the system state estimation (Glazunova, 2009; Gamm, 2007) it is supposed to forecast all the state variables for a very short time span. The lead time can be from several seconds (an interval of obtaining information on EPS state variables in a unit time) to one minute. Information on the system state is obtained by us- ing the SCADA system and from PMU recorders. Normally modern monitoring systems employ for these purposes traditional forecasting models such as ARIMA and Kalman filter. These make it possible to obtain rather good forecasts pro- vided the dynamics of random variations of state variables is represented as a stationary Gaussian process. In the cases where state variables are rather variable and nonstationary it is more sensible to use neural network models. In the course of numerous studies and calculations the traditional forecasting methods have proved to be insufficiently accurate in modeling state variables of power systems as compared to the neural network methods. In spite of this fact it is necessary to emphasize that the advantage of the neural network forecast as compared, for example to ARIMA and Kalman 22 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems filter is most pronounced in the cases where the trend of analyzed time series differs from the linear one and the initial data contain a considerable value of irregular component (Borovikov, 2006). In the cases, however, where time series of the process contains a linear trend the traditional approaches practically do not differ from the neural network ones in terms of forecasting accuracy. Super Short-Term Forecasting of State Variables on the Basis of Artificial Neural Networks The authors propose the approach to super short- term forecasting of state variables on the basis of neural network technologies and nonlinear optimization algorithms. The approach is imple- mented in the ANAPRO software (Kurbatsky, 2008, Kurbatsky 2009). The use of nonlinear optimization algorithms in the approach, namely, the methods of simulated annealing (SA) and neuro-genetic input selection (NGIS) (Haykin, 2006, Ossovsky, 2004), provides the procedure of choosing the best forecasting model for each individual sampling. For example in the process of learning sampling analysis based on the NGIS algorithm individual input data can be rejected as less informative. This method represents optimization on the basis of random search techniques and combines the capabilities of GA and PNN/GRNN networks to automatically determine optimal combinations of input variables. The PNN/GRNN networks allow the best results to be “remembered”, which improves the previous results. Owing to the radial layers with Gaussian function in the structure of PNN- algorithm, bad data in the input sampling can be reduced to minimum. The SA technique makes it possible to ana- lyze the properties of the initial sampling and organize a competition-based system between different neural network forecasting models when in the process of nonlinear optimization the best forecasting model is selected. This competition procedure is based on the criterion of minimiz- ing the total risk of ANN error (Ossovsky, 2004). This allows the balance between the reliability of learning and the quality of model to be reached, thus making the neural network forecasting model generalize better. R(w)=E w (W)+Ec ( W) (15) E w (W) - standard performance measure that depends on both the network itself (model) and the input data; E c (W) - complexity penalty depends solely on the ANN itself and is determined on the basis of preliminary data on the model structure; λ – regularization parameter. The ANN types considered in the studies were: radial basis function (RBF) and general- ized regression neural network (GRNN) (Haykin, 2006, Ossovsky, 2004). They make it possible to obtain rather accurate results in super short-term forecasting. In the case of complex computational forecast- ing problem (for example when learning sample contains many additional factors) the principle of committee machine (CM) is used [Haykin, 2006] as a basis or the proposed approach. The CM represents a neural network system consisting of combination of neural networks-experts which allow one to find a general solution, y (n), which has priority over each solution of an individual expert, y k (n). The calculation practice shows that for differ- ent combinations of learning and test samples the SA procedure should be started 3-6 times to form the neural networks - experts. Experimental Calculations The calculations show (Kurbatsky, 2009) that the suggested neural network approach within the ANAPRO software makes it possible to much more efficiently solve this problem as compared to the other traditional forecasting methods. This is related to the use of nonlinear optimization 23 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems algorithms as a basis for the approach. The al- gorithms are used to analyze the time series and networks on the basis of Gaussian radial functions, in particular, the GRNN structure. The GRNN networks are learned practically in a flash, which is extremely important for on-line forecasts, and are robust to the presence of bad data. The experimental calculation results obtained while minutely forecasting active power flow in the 500 kV intersystem transmission lines that connects two large-scale interconnected power systems are presented in Figure 7 and Table 7. The calculation data show that the neural network model allows one to decrease the mi- nutely forecast error almost twice as compared to the forecast made by the ARIMA model. As it is seen from Figure 7 the time series of change in the active power flow on this section of ESR is extremely variable and non-stationary which does not allow the traditional forecasting models to be used. As is seen the neural network forecast on the basis of the proposed approach allows one to decrease the forecasting error by a factor of 2 as compared to the ARIMA model. The need for wider application of monitoring systems is growing increasingly urgent in the light of the future possibility to interconnect the main power grids of Europe and Russia. The techno- logical progress in the last decades has shown that the use of perspective information technologies, first of all ANN, can provide reliable operation of future interconnected power grids of EU and Russia, optimal use of energy resources on vast territories and mutually beneficial electricity trade between different regions in terms of market requirements. Study of the Properties of a Large Electric Power System by Using Singular Analysis Transfer capability of a tie determines the maxi- mum power which can be transmitted over this tie without deteriorating system reliability. Electric power system has so called weak ties. The transfer capabilities of these ties will be the first to achieve their limit if the changes occur in the system conditions and this limit will vary depending on the system state. Transition to market leads to the power flows close to the maximum admissible ones. Therefore it is important to find the methods to detect weak ties in electric cutsets in which stability losses are most probable and to organize monitoring of their transfer capabilities. It is also very important to study the factors that determine the weakeness of ties and their transfer capabilities and find the methods to reinforce the ties. Accurate knowledge of weak ties and their transfer capabilities is very important to plan maintenance and management of wholesale electricity markets. With gradual increase in the power transmitted along the tie line the maximum power will be reached in the end at which there is no solution to the load flow problem. This is the result of degeneration of the Jacobean matrix J. The matrix relates the changes of active ∆P and reactive ∆Q powers with changes in phases ∆δ and Table 7. Telemetry forecasting errors on the basis of ARIMA and ANN Model MAPE for interval,% 20:01 20:02 20:03 ANN of GRNN type (60-83-60) 12,5 18,1 17.1 ARIMA (2,2,0) AR(2) 32,1 57,1 49,2 24 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems magnitudes ∆U of nodal voltages in the system of linearized equations of power balances ∆ ∆ ∆ ∆ P Q J U P P U Q = = δ ∂ ∂ δ ∂ ∂ ∂ ∂ δδ ∂ ∂ δ Q U U ∆ ∆ (16) Degeneration of the Jacobi matrix in a gen- eral case, as is shown in [Venikov, 1975], is a local index of the global phenomenon related to the loss of static stability. The sign of degeneration can be closeness to zero of the determinant det( ) J , equality of the conditionality number cond J ( ) max min = σ σ to infinity, where σ max and σ min are maximum and minimum singular values of the Jacobi matrix. The minimum singular value of the Jacobi matrix is another index, since the closer σ min to zero the closer the current conditions to the limit ones in terms of static stability. In (Voitov, 2000) the authors analyze the pos- sibility of applying σ min for estimation of static stability with respect to voltage. In the paper the singular analysis technique is used to detect the ties with the parameters and/or high active power flows that lead to a considerable rise in voltage phases and deterioration of the Jacobi matrix conditionality. The study on interrelation between the Jacobi matrix conditionality and transfer capabilities of ties and cut sets employs the method of contribution factor (Bialek, 2000). Singular Decomposition of the Jacobean Matrix Singular decomposition of the n n × asymmetri- cal Jacobi matrix can be presented in the form: J W V w v T i i i n i T = = = ∑ Σ σ 1 , (17) Figure 7. Use different models for short-term forecast “60 second ahead” of active power plow 25 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems where W w w w n =( , , ..., ) 1 2 and V v v v n =( , , ..., ) 1 2 - orthogonal matrices of left and right singular vectors, σ σ σ σ 1 2 3 ≤ ≤ ≤ ≤ .... n - singular val- ues given in an ascending order. If σ σ 1 = min is considerably lower than the rest of the singular values then, all other condi- tions being equal, the least contribution to the change in phases and magnitudes of nodal volt- ages is made by the first term of the decomposi- tion (17). Taking into account the inversion of matrix J this can be written as follows: ∆ ∆ ∆ ∆ ∆ ∆ δ σ U J P Q w P Q T = = −1 1 1 (v 1 / ) . (18) I n t r o d u c t i o n o f s c a l a r v a l u e ∆ ∆ ∆ S w P Q T 1 1 1 = ( / ) σ , which is called the first generalized disturbance shows that the maximum changes in phases and magnitudes of voltage will occur at the nodes that are called sensors in (Golub, 1995) and correspond to the maximum components of the first right singular vector. Similar to the first generalized disturbance taking into account the expression (1) and decom- position (2) we can write down the scalar value of t he f i r s t ge ne r a l i z e d r e s pons e ∆ ∆ ∆ F v U T 1 1 1 = ( ) σ δ . It shows that the maximum contribution to the change in phases and magni- tudes of voltages are made by the changes in injections at the nodes that correspond to the maximum components of the left singular vector. The elements of the network scheme whose parameters change having the greatest impact on the minimum singular value σ 1 , are called weak places in (Golub, 1995). The change in the active power f l ow al ong t he t i e k - l ∆ ∆ P P kl kl kl kl = ∂ ∂ ⋅ ( ) δ δ is largely determined by the value of ∆δ kl . This value can be estimated by the difference of the components of the right first singular vector ( ) v v k l 1 1 δ δ − that correspond to the phases of nodal voltages at the k-th and l-th nodes and can be applied as an index of the tie weakness. The larger the change in ∆δ ij with increase in the flow along the tie the faster the maximum of the transmitted power will be reached in it and the Jacobi matrix will degenerate. Another index of tie weakness that allows one to determine the network parameters or state variables f, that make the greatest impact on the conditionality of the Jacobi matrix is the derivative of the minimum singular value with respect to f ∂ ∂ = ∂ ∂ σ 1 1 1 f w J f v T ( ) . For example the tie k l − can be called weak if the change in its admittance y kl leads to the maximum change in σ 1 ∂ ∂ = ∂ ∂∂ = ( ) ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ σ δ δ δ 1 1 1 1 1 2 2 2 y w J y v w w P y P U y Q kl T kl U kl kl ( ) ∂ ∂ ∂ ∂ y Q U y v v kl kl U 2 1 1 δ (19) It follows from expression (19) that the mini- mum singular value σ 1 is affected not only by the values of branch admittances but also by the parameters of current conditions which may lead to a change in ranking the ties in terms of weak- ness under varying conditions. Another possibil- ity to determine the ties whose weakness does not change or changes little under varying conditions is to study the derivative of the minimum singu- lar value of the symmetrical nodal admittance matrix with respect to admittances of ties (Golub, 1995). By changing the admittance of weak ties it is possible to increase or decrease the minimum singular values and thus to improve or deteriorate 26 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems the conditionality of the Jacobi matrix and the nodal admittance matrix. Contribution Factor of Power Transmission The contribution factor method (Bialek, 2000) makes it possible to determine for a known load flow between what ties in the electric network the power of each generator node is distributed and in what proportion. If to assume that all tie lines, along which the power is transmitted from gen- erator node j, have equal transfer capabilities then with an increase of power at the generator node power flow in the tie that has the maximum coef- ficient a kl j will reach its limit value earlier than the flows in the other ties. The algorithm (Golub, 1995; Gamm, 2003) can be used to determine the coefficients a kl j . It suggests searching for the paths from each generator on the directed graph with the orientation of branches that coincides with the direction of flows along these branches. If power of the generator node increases by the value ∆ p , the power flow in the tie k - l will increase by the value∆ ∆ p a p kl kl j = ⋅ , where a kl j is a contribution factor that determines the contribution of generator node j to the flow along the tie k - l from the node k to the node l. In the subsystem transmitting power of a specific generator, the ties ranked as weak on the basis of singular analysis may have low contribu- tion factors and vice versa the ties that are not weak may have high contribution factors. To find the compromise solution the ties of each subsys- tem can be assigned the weight equal to the product of the tie weakness index and the contri- bution factor, for example the weighting coeffi- cient for the tie k - l can be represented by ( ) v v a k l kl j 1 1 δ δ − ⋅ . The information on the maximum weighting coefficients makes it possible to detect weak cut sets in every subsystem. This procedure is rather simple and implies that the most loaded weak ties are excluded unless the studied subsystem is divided into independent subsystems. Case Study Let us consider a 14-node network scheme (see Figure 8). Nodes 1, 3, 101, 201 and 203 are gen- erating, node 101 is slack, nodes 4, 6, 100, 202 are load ones. Directions of active power flows for the base network state that is far from the steady-state stability limit are shown in the scheme by arrows. The plan for detection of weak ties and cut sets of the test scheme is the following: 1. Determination, for the base conditions by using the singular analysis, of the nodes with the maximum response to generalized disturbances, the nodes that cause maximum generalized disturbances and also the weak cut sets, the changing conditions of which have the greatest effect on the Jacobi matrix conditionality. 2. Analysis of factors influencing the transfer capability of weak ties. 3. Confirmation of the fact that with the increase in power transmitted on the path along weak ties the limit of transmitted power is reached in the most loaded weak tie. Components of the right singular vector that correspond to phases of the nodal voltages are presented in Figure 9a, curve а. They determine nodes 200-203 as nodes with sensor phases and separate two groups of coherent generators – 201, 203 and 1, 3, whose voltage phases have a similar response to external disturbances. Analysis of the components of the left singu- lar vector that correspond to nodal voltage phases, Figure 9b, curve а, reveals that generation change at nodes 201 and 203, should lead to the maximum response of voltage phases. Curves а in Figures 9c and 9d illustrate the values of difference of the right singular vector 27 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems components that correspond to node numbers at the tie ends and derivatives of the minimum sin- gular vector of the Jacobi matrix with respect to tie admittances. Analysis of the curves reveals ties 200-8, 8-5 and 202-100 as weak. The ranging of weak ties using the first and second criteria differs. Therefore, it is possible to suppose that weakness of the 202-100 depends to a greater extent on the conditions and weakness of ties 200-8, 8-5 on their admittances, the latter is proved by the studies carried out in (Golub, 1995). We will show that with the increasing active power flows on the path with loaded weak ties the limit of transmitted power is found in such ties. Let us determine by the method of contribution factor the subsystems in Figure 10 transmitting power from: • Generator nodes 1 and 3 to load node 4 - subsystem а); • Slack node 101 to load nodes 4 and 6 - sub- system b); • Generator node 201 to load nodes 4, 6 and 202 - subsystem c) that includes weak ties 200-8, 8-5 and 202-100; • Generator node 203 to load nodes 4, 6, 202 - subsystem d) that includes weak tie 202-100. The effect of the increase in power transmitted over weak ties on the Jacobi matrix conditional- ity will be illustrated by considering the simulta- neous equal increase (decrease) of active power of generation at nodes 201 and 203, whose con- tribution to the generalized disturbance is maximal, by the value ∆ p . This will lead to decrease (in- crease) of generation at base node 101 by the value 2 ⋅ ∆ p plus the changing losses. Figure 8. Scheme of the 14-node test network 28 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Figure 9. The values of components the singular vector and derivative 29 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Figure 11a shows the change of minimum singular value of the Jacobi matrix with increase and decrease in the active power of generation at nodes 201 and 203. When generation at node 201 or 203 increases by the value larger than 16 75 . ⋅ ∆ p , steady-state stability is violated with sharp decrease of conditionality number. The best conditionality of the Jacobi matrix is determined with the decreasing generation by the value 35 ⋅ ∆ p with respect to the base state denoted by null. In Figure 11b curves b are constructed for the limit conditions and characterize the in- Figure 10. Subsystems transmitting active power from certain generator to load nodes Figure 11. Change of the minimum singular value of the Jacobean matrix and the voltage phase difference 30 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems creasing sensitivity due to deterioration of the Jacobi matrix conditionality. Change in the difference of voltage phases in the ties on the path of power transmission from generator nodes 201 and 203 in subsystems с and d, Figure 11b, shows that the Jacobi matrix is degenerated, because the phase difference in the 202-100 becomes high. The weakness of the 202-100 is also confirmed by the impact of increasing admittances of weak ties on the minimum singular value of the Jacobi matrix and the limit value of generation at nodes 201 and 203 that is shown in Table 8. With practi- cally the same impact on the conditionality number the increasing admittance of tie 202—100 leads to much higher transfer capability of the network in comparison with ties 200-8, 8-5. Table 9 illustrates the change in contribution factors of ties in subsystems с and d with the increasing generation at nodes 201 and 203 and also the values of weighting coefficients in the initial and limit conditions. Weak tie 202-100 in subsystem d is the most heavily loaded. With the increase of generator node power the contribution factor of this tie also increases. Tie 202-100 in subsystem d has maxi- mum weighting coefficients in both initial and heavy conditions. In the initial and heavy conditions in subsystem с ties 200-8, 8-5 and 202-100 are the most loaded weak ties. With the change of power at node 201 the contribution factors of these ties vary insig- nificantly. When the power of node 201 changes by the value − ⋅ 35 ∆ p , at which the Jacobi matrix conditionality is the best, tie 202-100 is no longer weak and even its tripping does not lead to instability. The weak cutest is observed in the most loaded weak ties 202-100 and 8-5 of sub- system с. On the basis of the singular analysis of the Jacobi matrix and the method of contribution factors the index for determination of the most loaded weak ties is suggested. In these ties with the increase in transmitted power the limit of transfer capability is reached earlier than in other ties, which leads to steady-state stability loss. Further studies on weak ties should provide for consideration of the constraints imposed on op- erating parameters. Table 8. Impact of increasing admittances of weak ties in per cent (Y %) on the limit power ∆ p of generation at nodes 201 and 203 and the minimum singular value of the Jacobi matrix Increase of Y% ∆ p σ σ 1 = min 202-100 200-8 8-5 200-8 8-5 0 16.75 16.75 16.75 4.59 4.59 4.59 10% 19.88 18.25 18.25 4.59 4.88 4.85 20% 23.75 19.81 19.94 5.13 5.18 5.13 30% 28.63 21.56 21.69 5.43 5.53 5.43 40% 34.94 23.44 23.69 5.77 5.93 5.77 50% 43.25 25.56 25.81 6.13 6.4 6.13 31 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems T a b l e 9 . C h a n g e o f t h e c o n t r i b u t i o n f a c t o r s f o r t i e s i n s u b s y s t e m s с a n d d w i t h i n c r e a s e o f g e n e r a t i o n a t n o d e s 2 0 1 a n d 2 0 3 b y t h e v a l u e ∆ p a n d t h e w e i g h t i n g c o e f f i c i e n t s ( ) v v a k l k l j 1 1 δ δ − ⋅ s h o w n i n b o l d t y p e f o r t h e i n i t i a l a n d l i m i t c o n d i t i o n s ∆ p T i e s o f s u b s y s t e m s с d 2 0 0 - 8 8 - 5 5 - 6 5 - 2 2 - 4 1 0 0 - 6 2 0 0 - 2 0 2 2 0 2 - 1 0 0 1 0 0 - 4 2 0 2 - 1 0 0 1 0 0 - 4 1 0 0 - 6 - 4 5 . 0 0 . 9 9 9 0 . 9 8 5 0 . 8 9 6 0 . 0 7 6 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 1 0 . 0 0 1 0 . 0 0 1 - 2 5 . 0 0 . 9 5 0 0 . 9 4 0 0 . 8 1 0 0 . 1 1 1 0 . 1 1 1 0 . 0 0 2 0 . 0 4 1 0 . 0 1 1 0 . 0 0 1 0 . 2 6 0 0 . 0 2 4 0 . 0 5 3 - 1 5 . 0 0 . 9 2 9 0 . 9 0 8 0 . 7 5 0 0 . 1 3 0 0 . 1 3 0 0 . 0 0 5 0 . 0 7 1 0 . 0 3 0 0 . 0 0 2 0 . 4 2 8 0 . 0 3 5 0 . 0 5 3 - 5 . 0 0 0 . 9 0 0 0 . 8 8 4 0 . 7 1 0 0 . 1 4 2 0 . 1 4 1 0 . 0 0 7 0 . 0 4 8 0 . 0 4 8 0 . 0 0 3 0 . 5 3 0 0 . 0 3 7 0 . 0 7 5 0 . 0 0 0 . 9 0 1 0 . 8 7 3 0 . 7 0 0 0 . 1 4 6 0 . 1 4 5 0 . 0 0 7 0 . 0 9 8 0 . 0 5 7 0 . 0 0 4 0 . 5 7 0 0 . 0 3 7 0 . 0 7 3 0 . 0 0 0 . 3 5 3 0 . 4 2 5 0 . 0 0 8 0 . 0 1 4 0 . 0 0 3 0 . 0 0 2 0 . 0 0 0 0 . 0 3 6 0 . 0 0 1 0 . 3 6 5 0 . 0 1 3 0 . 0 1 8 4 . 0 0 0 . 8 9 5 0 . 8 6 5 0 . 6 8 7 0 . 1 4 8 0 . 1 4 7 0 . 0 0 7 0 . 1 0 4 0 . 0 6 3 0 . 0 0 4 0 . 6 0 0 0 . 0 3 6 0 . 0 6 9 8 . 0 0 0 . 8 8 9 0 . 8 5 6 0 . 6 7 3 0 . 1 4 9 0 . 1 4 8 0 . 0 7 2 0 . 1 1 0 0 . 0 6 9 0 . 0 0 4 0 . 6 2 0 0 . 0 3 5 0 . 0 6 5 1 2 . 0 0 0 . 8 8 2 0 . 8 4 5 0 . 6 5 0 0 . 1 4 9 0 . 1 4 8 0 . 0 0 7 0 . 1 1 7 0 . 0 7 6 0 . 0 0 4 0 . 6 4 6 0 . 0 3 4 0 . 0 6 1 1 6 . 0 0 0 . 8 6 9 0 . 8 2 3 0 . 6 3 0 0 . 1 4 5 0 . 1 4 3 0 . 0 0 8 0 . 1 3 0 0 . 0 8 7 0 . 0 0 4 0 . 6 6 8 0 . 0 3 3 0 . 0 5 8 1 6 . 7 5 0 . 8 5 0 0 . 8 0 5 0 . 6 1 3 0 . 1 3 9 0 . 1 3 6 0 . 0 0 8 0 . 1 4 1 0 . 0 9 5 0 . 0 0 5 0 . 6 7 0 0 . 0 3 3 0 . 0 6 0 1 6 . 7 5 0 . 3 3 6 0 . 3 8 7 0 . 0 0 3 0 . 0 0 2 0 . 0 0 0 0 . 0 1 4 0 . 0 0 1 0 . 0 7 3 0 . 0 0 1 0 . 5 1 3 0 . 0 0 4 0 . 0 0 6 32 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems A Multi-Agent Approach to Coordination of Different Emergency Control Devices Against Voltage Collapse Power Industry spends a lot of money to protect a power system against different severe distur- bances. Nevertheless, large interconnected Power Systems throughout the world are frequently subjected to widespread blackouts which interrupt millions of consumers and cost billions of dollars. Analysis of the recent blackouts showed, that the most severe interruptions occurred in highly loaded interconnected power systems due to EHV line disruption followed by multiple contingencies (CIGRE, 2007). These accidents highlighted the deficiency of the existing protection systems that cannot maintain the integrity of the transmission grid during multiple contingencies (Lachs, 2002). Power system behavior in an emergency state is characterized by complex interaction between dis- crete and continuous control devices. Continuous control devices are automatic voltage regulators, turbine governors, FACTS devices, etc. Discrete control devices are different pro- tection relays, under load tap changers, etc. Currently both continuous and discrete control devices substantially use local signals only and do not coordinate their actions with each other. Absence of coordination between discrete and continuous control devices is the shortcoming of the existing protection system and it may lead to blackout. This section presents a control system based on the multi agent approach. The control system provides coordination between discrete and continuous control devices to prevent volt- age instability. Voltage Instability Mechanism To understand the importance of the discrete and continuous control devices coordination, one should understand the mechanism of voltage instability that may occur any time after the first severe contingency and lead to blackout. Existing practice shows that if protection system works correctly, most power systems have sufficient stability to withstand the first heavy disturbance in EHV transmission system. The post-disturbance phase represents a deceptively calm period that lasts several minutes with a normal level of frequency and then voltage collapse that lasts seconds (Lachs, 1992). The first heavy disturbance leads to increase in the reactive power losses and reactive power out- put of rotating units in the vicinity of the affected region. So, the first disturbance effects influence only the affected region, being initially a local problem. But some time after, the lack of reac- tive power in the affected region might increase considerably, leading to voltage collapse in the neighboring regions and even in the whole system. This happens because if the disturbance is not dealt with timely, the after-effects spread out through the EHV transmission network and actuate different control devices such as automatic voltage regula- tors, automatic transformer tap changers, current protection relays, etc. These control devices act at the different speed, respond to changes in the immediate vicinity and act without coordination with one another. Their actions in response to the post-disturbance conditions are actually the main cause of power system breakdown; consequently, the timely control of the discrete and continuous control devices under the post-disturbance condi- tions is the only means to prevent voltage collapse of the whole system (Lachs, 2002). Undoubtedly, the absence of different control actions coordina- tion during the post-disturbance period can cause different types of instability. But first of all, one should cope with voltage instability because it was the main cause of the recent blackouts. New system protection system philosophy has to be proposed to prevent voltage instability during the post-disturbance period. 33 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems A Multi-Agent Approach Outlines There are a number of definitions for what an agent is. This fact testifies to the difficulty in de- fining the notion of multiagent systems (MAS). General definition says that MAS is a distributed and coupled network of intelligent hardware and software agents that work together to achieve the global goal. Agents are autonomous structures and they operate with each other through differ- ent mechanisms. MAS could have different architectures. Reac- tive architecture is one of them. It is based on a simple stimulus-response mechanism triggered by sensor data. Its advantage is a faster but not reason better response in dynamic environments. Agents in reactive architecture are also simpler in design than agents that are more intelligent. Power systems are already using many reactive agents such as protective relays, automatic volt- age regulators, etc. However, the fact that these simple reactive agents have extremely narrow knowledge about one another, results in some disadvantages, for instance, lack of coordination. Another type of the MAS architecture is layered (hybrid) architecture that allows both reactive and deliberative agent behavior. Another key component of the MAS is a com- munication principle. If agents need to cooperate and be coordinated, they have to communicate with one another by using some communication language. Currently, the most used communica- tion language is the FIPA (The Foundation for Intelligent, Physical Agents). FIPA standards can be found in [The Current]. Coordination among agents can be provided by using different ap- proaches including organizational structuring and distributed multiagent planning. Organizational structuring provides coordina- tion through the definition of roles, communication paths and authority relationship. Organizational structuring is the easiest way to resolve conflicts among agents and provide their coherent behavior. Power system control centralization is an example of organizational structuring: there is an agent (control center) which has some knowledge of the current and the prospective system states and establishes rules for other agents according to hierarchical structure of the MAS. However, such an approach sometimes is impractical, because it is hard to design such a central controller, especially when the latter has a little time for collecting a lot of information to provide control actions. Another approach to agent coordination is a distributed multi-agent planning. In order to avoid inconsistent or conflicting actions, agents can build a multi-agent plan that details all the future agent actions and interactions required to achieve their global goal. In the process of working agents communicate in order to build and correct their individual plans until all conflicts are removed. We believe that MAS that is likely to be used for protection against voltage collapse should have layered architecture and use distributed multi- agent planning approach as a perspective way to provide coordination between different control devices during the post-disturbance period. For better understanding of the multi-agent approach principles see (Bellifemine, 2007; McArthur, 2007; Taylor, 1991). System Protection Philosophy A new system protection philosophy is needed to control the post-disturbance phenomenon. A new protection system must detect the critical situa- tion and coordinate the work of control devices to exclude any possibility of voltage instability. So, how can the new protection system identify the critical situation and what kind of control actions should the system use to control the capacity of available reactive power resources? Parameters-Indicators The main symptoms that precede the voltage col- lapse are considerable reduction of transmission 34 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems voltage levels and increase of reactive power outputs on rotating units (Lachs, 2003). Reduction of voltages and increase of rotating unit excitation were proposed in different papers to indicate the proximity to voltage collapse. Thus, these two criteria may be used to detect the critical situation appearance and activate protection system. Control Actions Power industry has already used the philosophy of load shedding by selecting non-essential load to prevent frequency reduction. The analysis of recent blackouts showed that the rapid load shedding is usually the only way to prevent the collapse of the whole system (CIGRE, 2007). On the one hand, load shedding should be as fast as possible, on the other hand, it should be optimal. The optimal load shedding scheme can be realized by using different optimization procedures, but it is hard to solve optimization problem for any possible situation in advance, because the number of situations is too big. This means that some op- timization computations should be made during the post-disturbance period. In spite of the fact that there is a number of optimization techniques that can be used to calculate emergency control actions quickly, the amount of input data required to solve the problem is usually too big. The state estimation alone can take from tens of seconds to minutes. However, load shedding under the post- disturbance conditions has to work faster. Hence, load shedding procedure has to use less complex methods to control post-disturbance phenomenon. The following simple countermeasures to control post-disturbance phenomenon were proposed in (Lachs, 1992): • Countermeasure 1. Fast tap changing on transmission substation transformers. • Countermeasure 2. Raising terminal volt- age on selected synchronous condensers and hydro generators. • Countermeasure 3. Fast tap changing on selected generator transformers. • Countermeasure 4. Strategic load shed- ding at selected transmission substations only if voltage levels and reactive outputs do not meet the requirements, or some transmission lines are overloaded. • Countermeasure 5. Rearranging genera- tor MW outputs. Connecting part of the disconnected load. Countermeasures 1–3 have approximately the same execution time and their main purposes are to impede the sharp increase of series reactive power losses, to increase transmission line charg- ing and to inhibit tap changing on subtransmis- sion and distribution transformers. Load is shed (Countermeasure 4) only after countermeasures 1 – 3. This will decrease the amount of the load to be shed. Countermeasure 5 considers an opti- mization procedure. The optimization procedure takes much more time in comparison with coun- termeasures 1–4 and provides post-emergency operation optimization. Thereby, countermeasures 1–4 provide fast control of the post-disturbance phenomenon to avoid voltage collapse and countermeasure 5 pro- vides long-time-period post-emergency operation optimization. The proposed control principles can be applied to various parts of the grid that work independently. Briefly, the control actions aim to control the capacity of the available reactive power resources and do not let reactive power demand of the affected region increase beyond their sustain- able capacity to exclude the possibility of voltage instability (Bellifemine, 2000). The proposed control system can be built by using distributed intelligence principles. The distributed intelligence is taken to mean the multi- agent system. Multi-Agent Control System Structure The proposed multi-agent control system provides reactive power control to prevent generator trip- 35 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems ping and preserve load bus voltages within the normal range. A power system is used to illustrate the main principles of the proposed multi-agent approach. This power system is a part of the modified 24 bus IEEE One Area RTS-96 system (see Figure 15). It is divided into two subsystems - Subsystem A and Subsystem B that correspond to transmission and subtransmission plus distribution systems respectively. The proposed MAS consist of two types of agents: Load Agents and Generator Agents. Any agent at any time has the following set of local data: • Local state variables (primary and second- ary voltages, power fows, etc.). • Operating characteristics of the local equipment (generator terminal voltage, tap range of the tap changer, excitation current of the generator, etc.). Any agent has two goals: • Local goal. It consists in maintaining lo- cal state variables and equipment operating characteristics within the normal range. • Global goal. It consists in voltage collapse prevention. To make different parts of the proposed MAS system work independently, each agent must know only about the limited number of agents, which influence his activity most. For instance, Load Agents, installed at Bus101 – Bus103 in Subsystem A must know much about the agents in Subsystem B, because all these agents can influence them. On the other hand, in spite of the fact that agents in Subsystem B could know much about one another, they must know only about three agents in Subsystem A: Load Agents, installed at Bus101 – Bus103, because these three agents can only influence them. In this case, sub- transmission system produces minimal influence on transmission system. MAS Ontology Agents communicate with each other, by us- ing some communication language. According to FIPA standards, messages exchanged by agents have a number of fields and in particular: sender, receiver, communicative intention (also called”performative”), content, language, ontol- ogy and some fields used for control. Ontology is the vocabulary of symbols and their meanings. For the effective communication, both the sender and the receiver must ascribe the same meaning to symbols. Ontology can include different elements such as agent actions, terms, concepts, etc. Agent actions indicate actions that can be performed by some agents. Terms are expressions identifying entities (abstract or concrete) that”exist” in the world. For voltage control purposes, following the simplest Voltage Control Ontology can be proposed: Agent actions of the Voltage Control Ontology: • Increase Reactive Power. • Stop Reactive Power Increase. • Start Load Shedding. Terms of the Voltage Control Ontology: • Owner. • Voltage Rate. The Voltage Control Ontology Usage Principles will be Given further Generator Agent Generator Agent obtains local information about excitation current of the generator, primary and secondary voltages at the generating substation, active power flows and transformer tap ranges. If excitation current goes beyond of its normal range, Generator Agent tries to decrease it to exclude the possibility of the generator tripping. Generator Agent sends messages to other agents that can decrease the shortage of the reactive power in the affected region. The sent messages apply 36 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems FIPA Request Interaction Protocol and include Increase Reactive Power action of the Voltage Control Ontology. The sequence diagram for the Request Interaction protocol used by the Generator Agent is depicted in Figure 12. Before sending a message, Generator Agent could use a rule set to identify whether receiver is able to help him. In our research, we used the following simple rule: Generator Agent do not send Request message to another agent if electric coupling between them has become too weak. For instance, if Bus202 – Bus203 active power flow is equal to zero, Generator Agent at Bus 203 does not send Request message to Generator Agent at Bus 202. In response to his request, Generator Agent can receive either Refuse or Agree message. Agree message means that Request Interaction proto- col participant starts to increase reactive power. Sometime later, Generator Agent will receive Inform-Done message with Stop Reactive Power Increase action, which means that the participant stopped increasing reactive power. Thus, Gen- erator Agent always knows when reactive power increase in his subsystem is stopped. If reactive power increasing is stopped, but Generator Agent is still overexcited, it starts Load Shedding pro- cedure (see Figure 13). FIPA Contract Net Interaction Protocol is used in Load Shedding procedure. In this protocol, the initiator wishes to optimize some function that characterizes the Load Shedding Procedure. We use minimal voltage rate function, but of course, it could be function, which includes some eco- nomic aspects. Generator Agent sends n Call for Proposal messages to Load Agents and solicits from them m proposals and k refuses. The propos- als contain voltage rates at primary buses of the Load Agents. After that, Generator Agent accepts j proposals and sends j Accept-Proposal mes- sages to those Load Agents which have the low- est voltage rates at their primary buses. When Load Agent receives Accept-Proposal message it Figure 12. FIPA Request Interaction Protocol 37 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems starts to shed the load until its primary voltage will not increase up to the specified value. Now consider situation when Generator Agent receives Request message. First, it analyzes oper- ating characteristics of the generator and if they are within the normal range it starts to increase reactive power output according to the algorithm, presented in Figure 14. Load Agent Load Agent obtains local information about pri- mary and secondary voltages at the substation, transformer tap ranges and active power flows. Load Bus agent takes part in Load Shedding pro- cedure. It also can shed the load independently in case of critical voltage drop. If it is installed at transmission system substation, Load Agent can take part in reactive power regulation. In this case, Load Agent changes transmission transformer tap ratio until primary voltage will not decrease or secondary voltage will not increase up to specified values. Changing transmission transformer tap ratio, Load Bus agent must coordinate its actions with generators in transmission system. Multi-Agent Control System Implementation The success of multi-agent system mainly depends on the availability of appropriate technology (development tools, programming languages) that allows its implementation. Any kind of programming language could be used for MAS realization, but object-oriented languages are more suitable, because the concept of agent is close to the concept of object. The computer model of the proposed MAS for power system voltage stability control was implemented in JADE. JADE has become a firm favorite with researchers in power engineering in recent years. JADE implements a famous object- oriented language Java. Agents, developed for Figure 13. FIPA Contact Net Interaction Protocol 38 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems the JADE platform consist of three basic layers: a message handling layer; a behavioral layer; a functional layer. Message handling layer is respon- sible for the sending and receiving of messages from other agents. The behavioral layer provides control of when an agent has to implement some task. The functional layer embodies the action the agent can perform. JADE provides program- mers with the following ready-to-use functions: full compliance with the FIPA specifications; efficient transport of asynchronous messages; a simple agent life-cycle management; a library of interaction protocols, etc. For further information about JADE platform, see (Bellifemine, 2007), (Taylor, 1997), (Milano, 2005). Necessary power flows and time domain simulations were carried out in Matlab/PSAT environment (Milano, 2008). Java capabilities of the JADE environment were used to implement communication between Matlab/PSAT and JADE. To provide communication between Matlab and JADE, Box Agents are used. Box Agents are Java objects that contain different data structures. During Time Domain Simulation, information about power system operating conditions at each integration step passes from Matlab environment to JADE by means of Box Agents. After that, agents inside JADE environment process this information, produce control actions if needed, put information about control actions inside Box Agents and pass Box Agents back to Matlab en- vironment. Thus, there is no need to use computer hard disc during the simulation, all computations are performed inside the main memory and simu- lation process is faster. The proposed MAS software realization allows one to use complex Matlab/PSAT routines and to model complex behavior of the agents. Figure 14. Reactive power output increasing algorithm of Generator Agent 39 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Case Study The Test System Modified IEEE One Area RTS-96 system is used as a case study (see Figure 15). Initially this test power system contained 24 buses and had no dynamic elements. During modification, the following changes in the test system structure were made: • To explore the infuence of the ULTCs actions during low voltage conditions, transformers equipped with ULTCs were installed between subtransmission system and distribution system loads. • Each load was modeled as 50% constant impedance and 50% constant current for both active and reactive components. • Each generator was modeled by six order dynamic model and was equipped with Type I Turbine Governor (TG) and Type II Automatic Voltage Regulator (AVR) (see PSAT documentation). • Three machines connected to Bus201 – Bus203 in subtransmission system were equipped with over excitation limiters (OXLs) (see PSAT documentation) After modification, IEEE One Area RTS-96 system contains 42 buses. Parameters of the unmodified 24-bus test system can be found in PSAT test folder (Milano, 2008). Parameters of the modified 42-bus test system can be found in [Modified]. For better understanding of the transient process, agents were installed only at the buses depicted in Figure 15. Figure 15. A part of the modified IEEE One Area RTS-96 system 40 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Disturbance To test the proposed MAS for an extreme con- tingency, the following sequence of disturbances is examined: • 2 seconds after the simulation starts. Loss of the generator connected to the Bus 201. • 40 seconds after the simulation starts. Loss of Bus208 – Bus207 line. Preliminary Remarks to the Simulation Process During the simulation process, two types of au- tomatic systems are considered: • Automatic system based on conventional principles • Automatic system based on multi-agent principles. • Both automatic systems do not provide for decentralized Under Voltage Load Shedding (UVLS) scheme. Undoubtedly, decentral- ized ULVS scheme is an effective means of preventing voltage collapse and it should be provided for both conventional and multi- agent automatic systems. However, the main purpose of the simulation is to dem- onstrate the MAS advantages in relation to reactive power sources coordination for the purpose of generator tripping prevention. It should also be mentioned, that the proposed centralized multi-agent ULVS scheme dif- fers from conventional centralized ULVS scheme, because it is actuated without time delay in case when there is no available re- active power in a subsystem. Dynamic Simulation for Automatic System Based on Conventional Principles Conventional automatic system includes the fol- lowing set of the decentralized devices: • TG and AVR at each generator. • OXLs at the generators, connected to Bus201 – Bus203. OXLs maximum field currents for generators connected to Bus202 and Bus203 are 3 and 2.5 respectively. OXLs maximum voltage output signal is 0.1. • ULTCs are installed at the subtransmission substations Bus204 – Bus210. ULTC time delay for the frst tap movement is 20 sec- onds. ULTC time delay for subsequent tap movements is 5 seconds. ULTC tap range is ±12 steps. Voltage reductions at load substations during the simulation are shown in Figure 16a. The change of rotor currents during simulation is represented in Figure 16b. After the first disturbance, rotor current of the generator, connected to Bus203, reaches its ther- mal limit, and AVR reference voltage of the generator starts to decrease. 20 seconds after the first disturbance, ULTCs on all transformers at the affected subtransmission substations starts to work. This leads to further decrease of generator 203 AVR reference voltages. Compensating reac- tive power shortage, generator 202 increases its excitation current. After the second disturbance, rotor current of generator 202 reaches its thermal limit and rotor current of generator 203 exceeds its thermal limit. AVR reference voltages of both generators continue to decrease and after a while, this will lead to generator 203 tripping and to the voltage collapse. Dynamic Simulation for Automatic System Based on Multi-agent Principles In addition to the set of local devices, represented for conventional automatic system, multi-agent automatic system also includes ULTCs for trans- mission transformers at Bus101 – Bus103. Trying to exclude generator tripping, multiagent automatic system coordinates the work of local devices. Voltage reductions at load substations during the simulation are shown in Figure 17a. The change 41 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Figure 16. Changes of rotor current and in HV substation voltage level 42 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Figure 17. Changes of rotor current and in HV substation voltage level 43 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems of rotor currents during simulation is presented in Figure 17b. After the first disturbance, rotor current of the generator, connected to Bus203, reaches its thermal limit and the generator sends request message to generator 202 and to the transmission transformers, connected to Bus101 – Bus103. Transmission transformers at Bus101 – Bus103 as well as gen- erator 202 are trying to decrease reactive power shortage. Their joint actions decrease generator 203 excitation current. Excitation current becomes lower than its thermal limit, and generator 203 AVR reference voltages starts increase. After the second disturbance, rotor currents of both genera- tors reach their thermal limits and generators send request messages to each other and to transmis- sion transformers at Bus101 – Bus103, but in this case, the generators receive refuse messages and immediately start load shedding procedure. Thus, during the transient process, rotor currents of the generators remain within the normal range. This fact excludes the possibility of the generator tripping. The absence of the control devices coordina- tion during the post-disturbance period is one of the main causes of the voltage instability, which permanently occurs in power systems all over the world. The proposed multi-agent control system provides reactive power control by coordinating the work of different discrete and continuous control devices in a post-disturbance period. The reactive power control in a post-disturbance period prevents generator tripping and maintains load bus voltages within the normal range. The efficiency of this ap- proach has been proved by numerical simulations. Advanced Emergency Control System for Prevention and Elimination of Power System Out- Of-Step Operation Using PMU Out of-step operation in power system intercon- nections is one of the most severe emergency conditions. It is related to the loss of stability in power system interconnections which may cause damage to equipment, interruption of power supply to consumers and unwanted development of emer- gency processes with severe consequences for the entire interconnection and its parts (Sovalov, 1988; Pourbeik, 2006; Mаkаrov, 2005 et al). With the future possibility of an interconnection between UCTE and IPS/UPS power systems by use of AC tie lines the occurrence of out-of-step operation at the interface between these power systems can be dangerous for both of them and result in undesir- able consequences for the systems and consumers. Measures are therefore required to detect, prevent and eliminate out-of-step conditions. Special automatic out-of-step protection sys- tems (OSPS) have been used in electric power systems for reliable, timely and selective detec- tion and elimination of out-of-step conditions (Sovalov, 1988; Gonik, 1988; Brinkis, 1975). The most effective system is the so called selective OSPS which is based on the angle measurement (Brinkis, 1975; Quintana, 1991). Previously the difficulties of comparing angles at different po- sitions within the network made us use indirect angle calculation. Most popular methods of this calculation are based on determination of current amplitude or complex impedance at a connection point of automatic system (Brinkis, 1975). In this case the system is represented by a two-machine equivalent with regard to cutset of the ties in which the OSPS is installed. The parameters of the two-machine equivalent are determined on the assumption that the motion of generators in the initial system along both sides of the cutset at issue is coherent (Brinkis, 1975; Narovlyansky, 2005 et al). This assumption is based on the fact that kinetic energy of generators’ mutual oscilla- tions in the transient process under disturbance, in the case of out-of-step conditions, passes to the kinetic energy of the out-of-step motion of two groups of generators along both sides of the cutset at which the out-of-step conditions occur, while inter-machine oscillations within these two groups of generators decrease essentially. 44 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems The easiest way to implement an indirect method for calculating the transmission angle is the use of angle dependence of transmission current. The disadvantage of this method is a wide scatter of operating angle values of the OSPS under the assumed current pickup settings due to various possible compositions and structure of ties in the cutset in different schemes and conditions of power system. Besides, this dependence is nonlinear. The lesser error is obtained by the use of the so called phantom scheme, i.e. by modeling of the voltage phasor of a point located at some distance from the site of automatic system placement, for example a receiving end of transmission line. Such an approach is used in the OSPS installed in power systems in Russia. Particularly complicated conditions for selective operation of OSPS occur in the multi-frequency out-of-step conditions along several cutsets (Brinkis, 1975). Further development of selective OSPS has resulted in the creation of a multifunctional device. The device makes it possible not only to eliminate the out-of-step conditions if they have occurred but also to prevent their occurrence. It has two stages of control actions (Brinkis, 1975): the control actions of the first stage are intended to prevent the loss of stability and for this purpose generation is disconnected in the surplus part of the system and fast reserve is used (or secondary load is shed) in the deficient part. If these control actions are insufficient and fail to prevent out-of- step operation the control actions of the second stage are triggered and split power interconnection. The use of synchronized voltage phase mea- surements obtained from PMU offers principally new capabilities of implementing the selective OSPS and selective out-of-step protection system (Phadke, 2008). Some OSPSs have been lately suggested on the basis of PMU. In (Centeno, 1997, Bozchalui, 2006) in order to reveal tran- sient instability the equal-area criterion is used when representing the system by a two-machine equivalent. Its parameters are determined by the complex values of power system state variables. In (Padiyar, 2006) the measurements of voltage phases and differences of their first derivatives are used to forecast power system stability losses ac- cording to the criterion based on energy function. In (Yutian, 2008) an integrated criterion is suggested to reveal the center of oscillations with the use of estimates of the voltage magnitude projection at some point of the tie line between two parts of the system and current along this tie line when using the two-machine equivalent of power system on the basis of the generators motion coherence in these two parts of the system which is estimated on the basis of currently measured angles. The authors of this chapter suggest the prin- ciples of creating a modified selective out-of-step protection and prevention system (SOSPPS) with the use of PMU measurements. Its efficiency is demonstrated on the test power system. Principles of Designing a Modified SOSPPS The Scheme of Interrelation Between States and Control Actions Loss of synchronism in power system operation at a cutset can be caused by two main reasons: • The maximum admissible transfer capabil- ity of the cutset is exceeded and, thus, the a periodic static stability of the system is lost; • The transient stability is lost as a result of disturbance on one of the ties or near the considered cutset. In both cases an indicator for loss of synchro- nism and the beginning of out-of-step conditions is the difference in voltage phases on the ends of the most critical tie line of the considered cutset. In other words there is some maximum value of the voltage phase difference δ lim as , whose excess indicates the beginning of the out-of-step condi- tions. 45 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems In order to avoid this critical situation it is necessary to maintain the cutset load at the level not exceeding some admissible level correspond- ing to δ δ lim lim < as . The difference between δ lim and δ lim as should take into account irregular varia- tions of flows along the tie lines and the need to ensure transient stability of power systems under standard disturbances. In Russia dispatching centers of power systems use the recommended values of transmission loading margins under normal and post emergency states. In the power systems of UCTE there are no similar explicit recommendations. Nevertheless, setting the value δ δ lim lim < as can be expedient. Thus, power systems can have four states (Figure 18): secure, dangerous, emergency (out- of-step conditions) and post-emergency. The se- cure state of power systems is determined by the condition δ δ ij < lim . PMU measurements are used to trace the current value of δ ij t ( ) . The dangerous state of power system occurs at δ δ ij > lim . For the power system to return to a secure state it is necessary to perform control actions to reduce the loading of the cutset by decreasing the gen- eration of power plants on the transmitting side and by using fast reserve (or disconnecting sec- ondary consumers) on the receiving side. If these control actions are sufficient the power system returns to the normal state. However, if the control actions are insufficient the system passes to the emergency state (out-of-step conditions) which is eliminated by disconnecting the cutset (by di- viding the power system). Should the splitting of the power system be unsuccessfully, then an emergency situation can develop and the post- emergency state may turn out to be severe and even turn into a blackout. In the event of a suc- cessful splitting the generation and load in both subsystems are balanced by generation discon- nection in the surplus subsystem and by auto- matic frequency load shedding in the deficient subsystem. Post-emergency state in this case will be less severe as compared to the previous one. Figure 18. A scheme of interrelation between power system states and control actions in SOSPPS 46 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems It should be noted that traditionally in Russia’s power system dispatching practice automatic load shedding and OSPS are considered separately due to the fact that the former is adjusted and operates using the power flow values as an indicator of overload while the latter is intended for the trans- mission angle action, with transmission angles being determined by indirect methods (Sovalov, 1988). The use of one and the same indicator which is the difference between PMU-measured voltage phases on both ends of power transmission allows one to consider both types of automatic systems as a single integrated emergency control system. Criteria for Actions of SOSPPS’s Stages As noted above the conditions for transition from normal (safe) state to the emergency state is for- mulated as δ δ ij > lim . Hence the criterion for action of the cutset unloading stage of SOSPPS will look as C t act ul ij = ( ) > ( ) δ δ lim . (20) In the event that the action of the cutset unload- ing stage is insufficient or inefficient, then the difference in the voltage phases along the critical tie line of the cutset at its overload continues to increase and reaches the value δ lim as . This indicates the loss of aperiodic static stability of the power system along the considered cutsets and the need to split the system. The criterion for action of the SOSPPS’s division stage will have the form C t act as ij as = ( ) > ( ) δ δ lim . (21) To formulate the criterion for action of SOS- PPS’s division stage according to the conditions of transient instability of power system under large disturbances it is necessary to use the second derivative of the difference between the voltage phases of a critical time line in the cutset. Decrease in the second derivative of voltage phase differ- ence indicates conservation of transient stability of EPS. System transition to an emergency state (out-of-step condition) is revealed provided that at least for three cycles of measurements by using PMU, the second derivative value of voltage phase difference for the critical tie line at the cutset does not go down below some small value dδ min . In this case each cycle may account for several scores of milliseconds. Theoretically, dδ min = 0 , how- ever practically this value is not equal to zero because of errors and noise in measurements and also inaccurate determination of the second de- rivative due to discrete measurements. Determina- tion of the acceptable value dδ min is an indepen- dent problem. Hence, for the direct power flow through the cutset from node if to node j the criterion for action of SOSPPS’s division stage subject to transient stability will have the form C t d t dt d ij ij + = ( ) > ( ) ∧ ( ) ≥ ∧ ∆δ δ δ 0 2 2 min ... ∧ − ( ) ≥ d t T dt d ij S 2 2 2 δ δ min , (22) where T S – cycle length between the PMU mea- surements. The corresponding criterion C − for the reverse power flow through the cutset (from node j to node i) is determined in a similar way. The general criterion of transition to an emergency state (out-of-step condition) and the action of SOSPPS’s division stage is written in the following way: C C C C as act as = ∧ ∨ ( ) ( ) + − . (23) 47 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems As a result EPS is split into two isolated subsystems. Related Problems The formulated approach for improving SOSPPS based on PMU measurements includes only its basic principles illustrated by the test example later in Chapter III. Actually consideration should also be given to the related problems to be solved in the course of approach application. Below are the main problems. As indicated above, it is reasonable to measure voltage phases on the basis of PMU on the ends of the critical tie line at the cutset. The problem is that the increase of transmitted power along the cutset results in different loading of individual tie lines at the cutset. Such a situation is caused by the parameters of the tie lines and also the structure and parameters of adjacent electric networks. This un-homogeneity of an electric network is revealed in different disturbance-sensitivity of nodes and tie lines at the loaded cutset (Voitov, 1999). In other words those elements affect operation parameters (voltage, power flows etc.) changing to variable extents. Hence, conditions for transition to the out-of-step operation are formed first of all in the most sensitive tie line. The tie line turns out to be critical at the cutset and it is expedient to place PMUs on its ends. It should be noted that significance of a critical time line at the cutset requires additional studies. It is explained by the fact that with the start of out-of-step condition change in the voltage angles will be observed in all tie lines of the cutset. It is important to establish the extent to which the change in tie line loading at the beginning of out-of-step condition is significant in terms of the efficiency of SOSPPS operation. Another problem is the necessity for verifica- tion of criterion (23). It has two components. The first is associated with available errors and noise in the measurements by using PMU, delays in in- formation transmission, measurement frequency, etc. These technical properties should be studied thoroughly and individually. And the results of studies will determine specific features of the designs of automatic systems. The other component of the problem is the ac- curate determination of the second derivatives of variation of voltage phase differences. It depends on the monotone change of phase differences and the length of intervals between measurements, as well as on measurement errors. The problem is that the second derivatives must be calculated by numerical differentiation of measured parameters. This question also requires thorough additional studies. The results of studies on both components determine efficiency of using criterion (22) and in particular, certainty in setting the value dδ min The issue about selectivity of action of the modified SOSPPS at the multi-frequency out-of- step condition for the case of stability loss at several cutsets remains to some extent open. It seems that selectivity of work of automatic systems should be sufficiently high and acceptable, since the change of voltage phases on the ends of tie lines at the cutset is a quite definite indicator of the beginning out-of-step condition. Here the value δ lim as is close to 90° and the value δ lim is uniquely determined by the state variables of the critical tie line of the cutset and the required margins of its transfer capability. Test Studies Let the test electric power system operates in post-emergency conditions when the tie 8-5 is loaded at 90% of its maximal transmission capa- bility, and voltage mutual angles equal δ 8 5 − = 36,6 and δ 202 100 − = 50,5. Let us consider as a disturbance the unsched- uled disconnecting the one of two lines of the tie 8-5. The behaviors of voltage mutual angles and their time-derivatives without any control actions are shown in Figure 19. 48 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems Suppose the system is equipped with SOSPPS, and a starting value for action of the cutset unload- ing stage (see criterion (20)) is set as δ min( ) 8 5 − = 52,2. At the time of t = 0,4 s the control actions will be realized as partial disconnections (of generation in power surplus part of the system and of load in its deficient part). Suppose the larger disconnections are to be highly undesirable through technical and/or economical limitations. The behaviors of voltage mutual angles and their time-derivatives with above mentioned control actions are shown in Figure 20. Figure 20 demonstrates the inefficiency of undertaken control actions for providing the sys- tem stability. The non-periodic growth of mutual angles in the cutset, which appeared virtually straight after the disturbance, lasts also after these actions (although not so fast as without them). If we suppose (only with a view to exemplify the study) the inadmissibility of further mutual asyn- chronous motion for the power system, then the starting value for action of the cutset division stage (see criterion (21)) in accordance with Fig- ure 20 is to be set as δ lim( ) 8 5 − as = 57,3. At that case the system is being divided at the time of t = 0,5 s (when the first derivative of the angle reaches its maximum d dt δ 8 5 − = 44 grad/s). After splitting the system into two separate subsystems (one of them with the surplus and other with the lack of active power) each subsystem faces the challenge of bringing the frequency to admissible level. The solution is in the further reducing the power (of the generation and load respectively). This reducing may ensue less than that would be required under saving the parallel Figure 19. Time behavior of δ ( ), dδ/dt ( ) and d 2 δ/dt 2 ( ),) in the absence of control actions: a) for the tie 8-5, b) for the tie 202-100 49 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems operation with unified frequency. In general the system splitting involves the more beneficial effect the higher power of the subsystem which separates with the power lack. CONCLUSION In conclusion, we note the following: 1. Essential sophistication of the operat- ing conditions of current EPSs enhances danger of heavy system emergencies and requires improvement and development of the principles and control systems of EPS operating conditions. For this purpose it is necessary to apply new methods and tools for measuring operating parameters, their transfer, processing and application of operating conditions control of EPS. The suggested basic principles of the system of monitoring and forecasting the operating conditions and control of EPS substantially enhance efficiency and adaptability of the coordinated operation and emergency control in EPS. The results described in the paper illustrate efficiency of the approach and applied methods and information technologies. 2. Structural and functional decomposition of state estimation problem is an effective method to solve the problems arising during calculation of large schemes. The proposed two-level algorithm for structural decom- Figure 20. Time behavior of δ ( ), dδ/dt ( ) and d 2 δ/dt 2 ( ) when maximum permissible unload- ing the cutset: a) for the tie 8-5, b) for the tie 202-100 50 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems position of the SE problem allows one to simultaneously process the data for local subsystems of considerably smaller dimen- sionality; decrease the adverse impact of in homogeneity of the calculated scheme and telemetric information when calculating one-voltage-class subsystems; essentially simplify solution of the coordination prob- lem which, in this case, does not require iterative calculations by subsystems; and reduce the time for SE problem solving for the entire scheme. 3. Dynamic state estimation with application of the Kalman filter can be used to forecast all the EPS state variables for a short period of time. The regular filter adjustment im- proves the forecast quality. Measurements from PMU that are also applied as the state vector components and the precise measure- ments improve the forecast results. 4. The need for wider application of monitor- ing systems is growing increasingly urgent in the light of the future possibility to in- terconnect the main power grids of Europe and Russia. The technological progress in the last decades has shown that the use of perspective information technologies, first of all ANN, can provide reliable operation of future interconnected power grids of EU and Russia, optimal use of energy resources on vast territories and mutually beneficial electricity trade between different regions in terms of market requirements. 5. Specific features of using the singular analysis have been studied to determine sensor and weak points in EPS consisting of a great number of subsystems. Separation of sensor and weak points for the intercon- nected power system is shown to be possible for each subsystem independently. 6. The absence of the control devices coordi- nation during the post-disturbance period is one of the main causes of the voltage instability, which permanently occurs in power systems all over the world. The pro- posed multi-agent control system provides reactive power control by coordinating the work of different discrete and continu- ous control devices in a post-disturbance period. The reactive power control in a post-disturbance period prevents generator tripping and maintains load bus voltages within the normal range. The efficiency of this approach has been proved by numerical simulations. 7. After splitting the system into two separate subsystems (one of them with the surplus and other with the lack of active power) each subsystem faces the challenge of bringing the frequency to admissible level. The solution is in the further reducing the power (of the generation and load respec- tively). This reducing may ensue less than that would be required under saving the parallel operation with unified frequency. In general the system splitting involves the more beneficial effect the higher power of the subsystem which separates with the power lack. ACKNOWLEDGMENT The study was supported by the Grants of Lead- ing Scientific School of RF#1857.2008.8 and of Russian Foundation of Basic Researches #09-08- 91330 and by Federal Agency for Science and Innovations within Federal Program “R&D in Pri- ority Areas of Russia’s Science and Technological Complex Development for 2007-2012”. The study was supported by the call FP7-ENERGY-2008- RUSSIA, FP7 Cooperation Work Programme: Theme 5 Energy 51 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems REFERENCES Abdel-Rahman, K., Mill, L., Phadke, A., De La Ree, J., & Liu, Y. (2001). Internet based wide area information sharing and its roles in power system state estimation. In Proc. IEEE Power Eng. Soc. 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IEEE Transactions on Power Systems, 20(2), 611–617. doi:10.1109/TPWRS.2005.846209 56 Coordinated Intelligent Operation and Emergency Control of Electric Power Systems APPENDIX: LIST OF AUTHORS The problem of monitoring, forecasting and control in electric power system: Voropai N.I. Decomposition of power system state estimation problem with the use of PMU data for large di- mension schemes: Kolosok I.N., Korkina E.S., Paltsev A.S. PMU for fast calculation of steady state in electric power systems: Glazunova A.M. Artificial intelligence technologies for monitoring large power interconnections: Kurbatsky V.G., Tomin N.V. Study of the properties of a large electric power system by using singular analysis: Gamm A.Z., Golub I., Bershansky R.G A Multi-Agent Approach to Coordination of Different Emergency Control Devices Against Volt- age Collapse: Panasetsky D. A Advanced Emergency Control System for Prevention and Elimination of Power System out-of-Step Operation Using PMU: Voropai N.I, Rehtanz C., Efimov D.N., Popov D.B., Häger U. 57 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 2 DOI: 10.4018/978-1-61350-138-2.ch002 Vo Ngoc Dieu Asian Institute of Technology, Thailand Weerakorn Ongsakul Asian Institute of Technology, Thailand Hopfeld Lagrange Network for Economic Load Dispatch ABSTRACT In this chapter, a Hopfeld Lagrange network (HLN) is proposed for solving economic load dispatch (ELD) problems. HLN is a combination of Lagrangian function and continuous Hopfeld neural network where the Lagrangian function is directly used as the energy function for the continuous Hopfeld neu- ral network. In the HLN method, its energy function augmented by Hopfeld terms from the continuous Hopfeld network could damp out oscillation of the conventional Hopfeld network during the conver- gence process. Consequently, the proposed HLN can overcome the disadvantages of the conventional Hopfeld network in solving optimization problems for its simpler implementation, better global solution, faster convergence time, and larger scale applications. The proposed method has been tested on differ- ent ELD problems including all thermal units, thermal units with fuel constraint, and both thermal and hydro units. The obtained results from the test cases have shown that the proposed method is effective and effcient for solving the ELD problems. Therefore, the HLN method is the new contribution to the development of new methods for solving optimization problems in power systems. 58 Hopfeld Lagrange Network for Economic Load Dispatch INTRODUCTION Power system engineering has the longest his- tory of development among the various areas within electrical engineering. Since the practical numerical optimization methods applied to power system engineering and operation, they have been playing a very important role in economic opera- tion of power systems. The value contributed by the power system optimization is considerable in economics for large utilities from fuel cost, operational reliability, and security. In power system operation, the problem allocat- ing among the available thermal power generating units to the customers’ load demands in an eco- nomic, secure and reliable way has been identified and received great attention since the beginning of the 20 th century (Happ, 1977; Chowdhury & Rahman, 1990). The problem has been formulated as an optimization problem which is to minimize fuel cost of overall online generating units while satisfying load demand and other constraints over a considered schedule time. This problem has been frequently known as the economic load dispatch (ELD) problem. The simplest form of the ELD problem can be considered as to minimize the total fuel cost through determining the allocation of power generation of each units among a set of committed units in a thermal power plant subject to a constraint that total power generation equals to load demand or among a set of committed units in different thermal power plants subject to a con- straint that total power generation equals to load demand plus transmission power loss. This type of ELD problem is referred to the conventional problem applied in vertically integrated power systems. The more complicated ELD problems can be arranged in ascending order as more con- straints added: • The generator capacity limits are considered. • There are conficts among the consid- erations such as economy, security, and emission. • Fuel, labor and maintenances constraints are added. • The optimal power solution considers both active and reactive control variables. • The problem is considered in deregulated environment. In fact, the ELD problem involves the solu- tion of two different problems. The first one is pre-dispatch problem or unit commitment (UC) problem which requires selecting optimal units among the available ones to meet the expected load demand with a specified reserve of operation over a scheduled time horizon. The last one is the on-line ELD which requires satisfying the load demand among the actually committed units so as to minimize total cost of supplying the require- ment of the system. Due to the great values contributed to the economic operation of power systems, the ELD problems have been attracted the attention many researchers from 1920s with several solution meth- ods proposed to deal with more complicated and larger scale problems. One of the earliest methods to find economic results for power generation schedule was known as equal incremental method, where the optimum solution is obtained when all the marginal cost of the committed generating units are equal (Stahl, 1930, 1931). Since digital computers were used in 1950s the numerical methods have been continuously developed for solving more complicated and larger problems with more efficient and better quality solution. Several solution methods have been proposed for solving the problems including conventional, artificial intelligent, and hybrid methods. Many conventional methods have been widely used for solving the ELD problems such as dynamic pro- gramming (DP) (Liang, Glover & Glover, 1992), linear programming (LP) (Wells, 1968), quadratic 59 Hopfeld Lagrange Network for Economic Load Dispatch programming (QP) (Irving & Sterling, 1985), inte- rior point method (IPM) (Ponnambalam, Quintana & Vanelli, 1992), and Lagrangian relaxation (LR) (Fisher, 1973). Conventional methods require the models of optimal generation scheduling problems to be represented as piecewise linear or polyno- mial approximations of monotonically increasing nature. However, such an approximation may lead to sub-optimal solution, resulting in huge loss of revenue over the time. Hence, the new trend in the recent time is to use more realistic models of hydro and thermal plants. In recent years, meta-heuristic optimization techniques have attracted much attention of re- searchers due to their ability to seek for global optimal solution for problems with complicated constraints. These methods have proved to be very efficient since they do not place any restric- tion on the shape of the cost curves and other non-linearity in model representation. Although these heuristic methods do not always guarantee to find the globally optimal solution, they can provide a reasonable solution (sub-optimal near globally optimal) in a sufficient computational time. Among the many artificial intelligence based methods, some popular ones have been implemented for solving the ELD problems consisting of Hopfield neural network (HNN) (Park, Kim, Eom, & Lee, 1993), simulated annealing (SA) (Wong & Fung, 1993), tabu search (TS) (Ongsakul, Dechanupaprittha, & Ngamroo, 2004), ant colony search algorithm (ACSA) (Song, Chou, & Stonham, 1999), genetic algorithm (GA) (Bakirtzis, Petridis & Kazarlis, 1994), evolutionary programming (EP) (Wong & Yuryevich, 1998), differential evolution (DE) (Nomana & Iba, 2008), and particle swarm optimization (PSO) (Jeyakumar, Jayabarathi & Raghunathan, 2006). Most of the conventional methods can offer good solution in a short com- putational time but they can only deal with simple and small or medium-scale problems meanwhile most of the meta-heuristic methods can deal with more complicated and larger scale problems. However, the meta-heuristic methods may suffer from slow convergence and local optimum for large-scale problems. A clear consensus is pres- ently heading toward the hybrid models, which are the combinations of both conventional and non-conventional methods and can handle the present day complicated problems commonly seen within developed countries. Moreover, parallel techniques are also designed for solution methods to reduce computational time in large- scale problems. However, the development of these techniques is still limited due to hardware dependence. On the other hand, developing new methods which can deal with complicated prob- lems and obtain fast solution is being continued. In the recently new trends, hybrid systems are considered as promising methods and widely used for optimal generation scheduling. Many hybrid systems have been proposed for solving the ELD problems such as fuzzy logic and GA (Song, Wang, Wang & Johns, 1997), hybrid EP and sequential QP (Attaviriyanupap, Kita, Tanaka & Hasegawa, 2002), combined GA and TS (Ruangpayoongsak, Ongsakul & Runggeratigul, 2002), hybrid PSO and sequential QP (Victoire & Jeyakumar, 2004), hybrid EP and LP (Somasundaram, Lakshmiramanan & Kup- pusamy, 2005), combined DE and QP (Coelho & Mariani, 2006), etc. Hybrid systems can be usually the combinations whether among the conventional methods or between the conven- tional methods and the meta-heuristic methods or among the meta-heuristic methods to utilize the advantages of element methods. Therefore, the hybrid systems can deal with more compli- cated problems and obtain better solution with shorter computational time than many single meta-heuristic search methods. In this chapter, a new method based on a com- bination of continuous Hopfield neural network and Lagrangian function is proposed for solving the ELD problems including: Basic ELD problem: This is a very simple form of ELD problem. The problem is to minimize an 60 Hopfeld Lagrange Network for Economic Load Dispatch objective of total cost for thermal generating units subject to power balance constraint and power generation limits and ramp rate constraints for each unit during a schedule time horizon, usually 1 hour. The objective function considered for this problem here is a sum of quadratic fuel cost functions of all online units and the power loss in transmission system is computed via Kron’s loss formula where the power loss is a function of power outputs of units. Fuel constrained ELD problem: This problem is more complex than the basic ELD problem with more objective and constraints added. The objec- tive of the problem is to minimize both total fuel cost and emission level of thermal generating units while satisfying different constraints including power balance, fuel delivery, fuel storage, genera- tor capacity limits, fuel delivery limits, and fuel storage limits for a certain period of time. Both the objectives of fuel cost and emission considered in this problem are modeled as quadratic func- tions which are the function of power outputs of generating units. Hydrothermal ELD problem: This problem includes both thermal and hydro generating units but only fuel cost of thermal units is considered while neglecting the total cost of hydro units since it is very small and negligible. The hydraulic constraints for hydro units are also included in addition to the constraints for the thermal units. The purpose of this problem is to minimize total fuel cost of thermal generating units subject to power balance, continuity of reservoir head, and generator capacity limit constraints. The functions considered in this problem including fuel cost of thermal units and water discharge and reservoir head variation for hydro units are quadratic functions. BACKGROUND Continuous Hopfield neural networks (Hopfield, 1982, 1984) have been widely used for solving optimization problems in different fields. The continuous Hopfield neural networks are a recur- rent network type that operates in an unsupervised manner. The action of a Hopfield network is based on the minimization of its energy function which is mapped from an optimization problem to the network will converge to a solution of the problem. One of the advantages of the Hopfield network is that it can efficiently handle variable limits by its sigmoid function. However, the applications of the Hopfield network to the optimization problems are limited to simple problems with linear con- straints due to the complex process of mapping from the problem to the neural network. Moreover, large number of iterations and oscillation during convergence process are also the major concerns that the Hopfield network can be suffered while solving optimization problems. In the implementation of the conventional continuous Hopfield neural network (HNN) to the ELD problems (Park et al., 1993; Su & Chiou, 1997), an energy function for the problem is pre- defined including objective and constraints associ- ated with weighting factors, and then mapped into the HNN to determine the weighting connections for the neurons. There are many drawbacks for such an application. Firstly, the solution by the HNN for the problem is sensitive to the selected weighting factors associated with the defined energy function which may lead to local optimal solution if these weighting factors are not carefully tuned. Secondly, HNN is very difficult to deal with the complicated problems with nonlinear constraints since the problem constraints have to be linearized before implementing in HNN. Lastly, the computational effort of HNN for solving the ELD problem is high since it needs large number of iterations to obtain optimal solution, thus it is dif- ficult for HNN to deal with large-scale problems. Some improvements for the conventional HNN have been proposed to overcome the mentioned drawbacks. To speed up the computational time for HNN, the sigmoid function of continuous neurons has been linearized (Su & Chiou, 1997, 2000). 61 Hopfeld Lagrange Network for Economic Load Dispatch By doing this way, the solution for the problem is directly found with a very short computational time similar to analytical approach. However, this improvement can be applied to simple problems with non-binding inequality constraints. Another improvement of HNN has been proposed in (Yal- cinoz & Short, 1997) where the energy function of HNN is formulated in quadratic programming form for identifying with quadratic programming problem to determine the weight connections for the neurons. For this improvement, the improved HNN can deal with large-scale problems and its speed of calculation has been also considerably improved. Nevertheless, this formulation can only apply to quadratic programming problems with linear constraints. An adaptive HNN has been proposed in (Lee, Sode-Yome & Park, 1998; Lee, Nuroglu & Sode-Yome, 2000) to speed up the convergence of HNN by adaptively adjusting slope, bias, and learning rates of neurons. With the new adjustment techniques, the adaptive HNN can deal with non-convex problems and its computational speed has been also improved. However, the implementation of this neural net- work is similar to the conventional HNN; that is the weight connections for neurons have to be pre-determined and the problem constraints have to be linearized. Recently, a modification for HNN has been proposed in (da Silva, Nepomuceno & Bastos, 2004) by representing the energy of HNN in two terms, a confinement term that groups the constraints and an optimization term that conducts the network output to the equilibrium points. The minimization for energy function of this modi- fied HNN is conducted in two stages for the two corresponding terms of the energy function. This modified HNN can deal with more complicated problem compared to the conventional HNN and its ability to find global optimal solution has been also improved. However, for implementation this modified neural network, the problem constraints also need to be linearized. In this research, a new improvement of con- tinuous Hopfield neural network, called Hopfield Lagrange network (HLN), is proposed to over- come to the difficulties of the Hopfield network. In the proposed HLN method, the Lagrangian function is directly used as the energy function of the Hopfield network. The advantages of the proposed neural network over to the conventional Hopfield network are as follows: • The proposed neural network is not nec- essary to predefne an energy function as- sociated with penalty factors and map the problem into the Hopfeld network for determining the synaptic interconnections among the neurons. • Since the proposed neural network uses Lagrangian function as the energy function for the Hopfeld network, it can effciently handle constraints of the problems without causing constraint mismatch. Moreover, the proposed neural network is not limited to the simple problems with linearized con- straints as the Hopfeld network, especially for the time-coupling constraints. • The proposed neural network can give a very fast convergence to the optimal solu- tion compared to the conventional Hopfeld network. • The proposed neural network can eas- ily deal with large-scale and complicated optimization problems via Lagrangian relaxation. The proposed HLN model is solved using sub-gradient technique with updating step sizes which will be easily tuned for each problem while the slope of sigmoid function for continuous neurons can be fixed. With the new improve- ments, the proposed HLN method could solve any optimization problems that the Hopfield network can. Moreover, the solution quality obtained by the proposed neural network is also higher than that from the conventional HNN. Therefore, the newly proposed neural network could be one of 62 Hopfeld Lagrange Network for Economic Load Dispatch the new options for solving optimization problems in power systems. HOPFIELD LAGRANGE NETWORK AND APPLICATIONS Hopfield Lagrange Network for Optimization Problem Optimization Problem Formulation The constrained optimization problem is formu- lated as follows: Min f x k ( ) (1) subject to g x i k ( ) = 0i = 1, …, M (2) x x x k k k ,min ,max ≤ ≤ k = 1, …, N (3) where f(x k ) objective function to be minimized; g i (x k ) equality constraint; x k independent variable; x k,min , x k,max lower and upper bounds of variable x k . Hopfield Lagrange Network Algorithm The Lagrangian function for the problem is for- mulated as follows: L f x g x k i i k i M = + = ∑ ( ) ( ) λ 1 (4) where λ i is Lagrangian multiplier associated with constraint i. To apply the Lagrangian function in HLN, the continuous and multiplier neurons corresponding to independent variables and Lagrangian multipli- ers are respectively needed. In HLN, the neurons representing continuous variables are called continuous neurons, and the neurons representing Lagrange multiplier are called multiplier neurons. The energy function for HLN is formulated based on the Lagrangian function as follows: E f V V g V g V dV k x i i k x i M c V k N k x = + + = − = ∑ ∫ ∑ ( ) ( ) ( ) , , , , λ 1 1 0 1 (5) where V k,x output of continuous neuron k corre- sponding to x k ; V i,λ output of multiplier neuron i corresponding to λ i ; g c -1 inversed sigmoid function of continuous neurons. The last term in (5) is the Hopfield term of continuous neurons where its global effect is displacement of solutions toward the interior of the state space (van den Berg & Bioch, 1993). The dynamics of the neural network are defined such that the energy function (5) should be mini- mized with respect to the continuous neurons and maximized with respect to the multiplier neurons. The network dynamics are defined as follows: dU dt E V f V V V g V V U k x k x k x k x i i k x k x k x , , , , , , , , ( ) ( ) = − ∂ ∂ = − ∂ ∂ + ∂ ∂ + λ (6) dU dt E V g V i i i k x , , , ( ) λ λ = ∂ ∂ = (7) where U k,x total inputs of continuous neuron k cor- responding to the output V k,x ; U i,λ total inputs of multiplier neuron i corresponding to the output V iλ . The inputs of neurons at iteration n are updated based on the dynamics from (6) and (7) as follows: 63 Hopfeld Lagrange Network for Economic Load Dispatch U U E V k x n k x n x k x , ( ) , ( ) , = − ∂ ∂ −1 α (8) U U E V i n i n i , ( ) , ( ) , λ λ λ λ α = + ∂ ∂ −1 (9) where α x and α λ are positive updating step sizes for the inputs of continuous and multiplier neurons, respectively. The sigmoid function of continuous neurons for determining the relationship between the inputs and outputs is defined by a monotonically increasing function as follows: V g U x x U x k x c k x k k k x k , , ,max ,min , ,min ( ) tanh = = − + ( ) + 2 1 σ (10) where σ is a positive scaling factor known as slope which determines the shape of the sigmoid function. The shape of the sigmoid function is given in Figure 1. The transfer function to determine the outputs of multiplier neurons from their inputs is defined by a linear function as follows: V g U U i m i i , , , ( ) λ λ λ = = (11) The diagram for the proposed HLN is given in Figure 2. Selection of Parameters The proper parameter selection will guarantee rapid convergence for the neural network. So far, there is no method to find optimal parameters for the neural network. Therefore, the parameters are Figure 1. Sigmoid function of continuous neurons with different slopes where x k,max = 1 and x k,min = 0 64 Hopfeld Lagrange Network for Economic Load Dispatch tuned based on experiments. Based on experiments some observations are draw as follows. If the slope σ < 1, the neural network converges very fast but the obtained solution may be local optimum. In contrast, if the slope σ > 1, the solu- tion from the neural network is global optimum but slightly slower convergence, the larger value of σ used the better solution obtained. Therefore, the preferable values for σ is ranging from 10 to 100, since higher values of σ lead to longer to converge but the improvement in the obtained solution is inconsiderable. The updating step sizes α x and α λ for neurons usually depend on the problem being considered. It is observed that the larger the values of the updating step sizes, the closer the discrete system behavior of the neural network, producing values at the upper and lower limits of each neuron. On the contrary, the smaller the values of updating step sizes, the slower convergence of the neural network. To determine these parameters, a small value will be chosen first and then gradually in- crease until the network behaves like a discrete system. The proper values will be obtained. Note the values of the updating step sizes are usually smaller than 1. Initialization The neural network requires initialization for each neuron. It is observed that a good initialization for multiplier neurons can speed up the convergence process. However, this initialization does not af- fect on the final solution by the neural network. In this research, the initial outputs of continu- ous neurons are initialized based on “medium start”, e.g. the outputs of continuous neurons are initialized at middle point of independent variable limits as follows: V x x k x k k , ( ) ,max ,min 0 1 2 = + ( ) (12) where V k,x (0) is the initialization of V k,x of continu- ous neuron k. The multiplier neurons can be initialized at zero. However, to speed up the convergence pro- cess of the neural network, the multiplier neurons is initiated by the solution of the equation in (6), Figure 2. Discrete-time implementation of Hopfield Lagrange network 65 Hopfeld Lagrange Network for Economic Load Dispatch in which total inputs of neurons are neglected. The obtained solution is the initial value for the multiplier neurons: V f V V g V V i k x k x i k x k x , ( ) , , , , ( ) ( ) λ 0 = − ∂ ∂ ∂ ∂ (13) where V i,λ (0) is the initial value of V i,λ of multiplier neuron i. The initial inputs of neurons are calculated based on their inversed sigmoid and transfer functions in (10) and (11), respectively as follows: U V x x V k x k x k k k x , ( ) , ( ) ,min ,max , ( ) ln 0 0 0 1 2 = − − σ (14) U V i i , ( ) , ( ) λ λ 0 0 = (15) where U k,x (0) and U i,λ (0) are the initial values of continuous and multiplier neurons, respectively. Stopping Criteria The algorithm of the neural network will be termi- nated when ever maximum error from the neural network is lower than a pre-specified threshold or the maximum allowable number of iterations is reached. The maximum error at iteration n from the neural network is defined as follows Err g V V V V V n i k x n k x n k x n i n i n max ( ) , ( ) , ( ) , ( ) , ( ) , ( max ( ) , , = − − − − 1 λ λ 11) { } (16) where Err max (n) maximum error from the neural network; ε pre-specified threshold; N max maximum allowable number of iterations. Overall Procedure The overall procedure of the proposed HLN for solving optimization problem is described as follows: • Step 1: Select parameters for the neural network. • Step 2: Initialize all neurons using (12) - (15). • Step 3: Choose a threshold ε and the maxi- mum number of iterations N max . Set n = 1. • Step 4: Calculate dynamics of neurons us- ing (6) - (7). • Step 5: Update total inputs of neurons us- ing (8) - (9). • Step 6: Calculate outputs of neurons using (10) - (11). • Step 7: Calculate maximum error Err max (n) using (16). • Step 8: If n < N max and Err max (n) > ε, n = n + 1 and return to Step 4. Otherwise, stop. The algorithm is also represented in a flow chart as shown in Figure 3. Proof of Convergence for HLN To illustrate how the dynamics of neural network from (6) and (7) cause the energy function in (5) to be minimized with respect to continuous neurons and maximized with respect to multiplier neurons, the effects on energy function due to the status changes in the continuous neurons and multiplier neurons are investigated. Consider the effect of the status change in the continuous neurons on the energy function: dE dt E V dV dt k x k x = ∂ ∂ , , (17) Substituting V x,k in (10) into (17): 66 Hopfeld Lagrange Network for Economic Load Dispatch dE dt E V dg U dU dU dt k x c k x k x k x = ∂ ∂ , , , , ( ) (18) Substituting (6) into (18): dE dt dg U dU dU dt c k x i k x = − ( ) , , 2 (19) Since g c (U k,x ) is a monotonically increasing function as shown in Figure 1, the value of the derivative dg c (U k,x )/dU k,x is always positive. Con- sequently, the right hand side of Equation (19) is always negative. Therefore, the energy function (5) is always minimized when there is a change in the status of the continuous neurons. On the other hand, the effect of a change in the status of the multiplier neurons associated with equality constraints on the energy function is considered as follows: dE dt E V dV dt i i = ∂ ∂ , , λ λ (20) Substituting V i,λ in (11) into (20): dE dt E V dg U dU dU dt i m i i i = ∂ ∂ , , , , ( ) λ λ λ λ (21) Substituting (7) into (21): dE dt dU dt i = ,λ 2 (22) Figure 3. Algorithm for HLN 67 Hopfeld Lagrange Network for Economic Load Dispatch It is obvious that the right hand side of equa- tion (22) is always positive. Therefore, the energy function always seeks for maximum value when there is a status change on the multiplier neurons associated with equality constraints. HLN for Solving Basic ELD Problem Problem Formulation The objective of the basic ELD (BELD) problem here is to minimize total cost of thermal generating units of a system over some appropriate period (one hour typically) while satisfying various constraints including power balance, generator power limits, and ramp rate constraints. Mathematically, the BELD problem is formu- lated as follows: Min F a b P c P i i i i i i N = + + ( ) = ∑ 2 1 (23) subject to Power balance constraint P P P i i N L D = ∑ − − = 1 0 (24) P PB P B P B L i ij j j N i N i i i N = + + = = = ∑ ∑ ∑ 1 1 0 1 00 (25) Generator operating limits P P P i i i ,min ,max ≤ ≤ ; i = 1, 2, …, N (26) Ramp rate constraints P P UR i i i − ≤ 0 , if generation increases (27) P P DR i i i 0 − ≤ , if generation decreases (28) where a i , b i , c i fuel cost coefficients for unit i; B ij , B 0i , B 00 transmission loss formula coeffi- cients; DR i ramp down rate limit of unit i (MW/h); N total number of online units; P D total load demand of the system (MW); P i output power of unit i (MW); P i 0 initial output power of unit i (MW); P i,min , P i,max lower and upper generation limits of unit i (MW); P L total network loss of the system (MW); UR i ramp up rate limit of unit i (MW/h). HLN Implemented to the BELD Problem The Lagrangian function L of the problem is formulated as follows: L a b P c P P P P i i i i i i N D L i i N = + + ( ) + + − = = ∑ ∑ 2 1 1 λ (29) To represent in HLN, N continuous neurons and one multiplier neurons are required. The energy function E of the problem is formulated based on the Lagrangian function as follows: 68 Hopfeld Lagrange Network for Economic Load Dispatch E a bV cV V P P V g i i pi i pi i N D L pi i N c = + + ( ) + + − + = = − ∑ ∑ 2 1 1 1 λ (( ) V dV V i N pi 0 1 ∫ ∑ = (30) where V λ output of multiplier neuron representing Lagrangian multiplier λ; V pi output of continuous neuron i representing for output power P i . The dynamics of neurons inputs are derived as follows: dU dt E V b cV V P V U pi pi i i pi L pi pi = − ∂ ∂ = − ÷ ( ) ÷ ∂ ∂ − í ( · · · · \ ) ÷ ' ! 2 1 λ 11 11 + 1 1 1 ' ! 1 11 + 1 1 1 (31) dU dt E V P P V D L pi i N λ λ = + ∂ ∂ = + − = ∑ 1 (32) where ∂ ∂ = + = ∑ P V B V B L pi ij pj j N i 2 1 0 (33) U λ input of multiplier neuron corresponding to the output V λ.; U pi input of continuous neurons corresponding to the outputs V pi . The algorithm for updating inputs of neurons is defined: U U E V pi n pi n i pi ( ) ( ) = − ∂ ∂ −1 α (34) U U E V n n λ λ λ λ α ( ) ( ) = + ∂ ∂ −1 (35) The outputs of continuous neurons represent- ing for output power of units are calculated via the sigmoid function: V g U P P U pi c pi i high i low pi = = − í ( · · · · \ ) ÷ ( ) l l l ÷ ( ) tanh , , 2 1 σ PP i low , (36) where the new generator limits are redefined as follows: P P P UR i high i i i , ,max min , = + { } 0 (37) P P P DR i low i i i , ,min max , = − { } 0 (38) P i,high maximal possible power output of unit i; P i,low minimal possible power output of unit i. The outputs of multiplier neurons are defined by a transfer function as follows: V λ λ λ = = g U U m ( ) (39) The outputs of neurons are initialized by: V P P pi i i ( ) ,max ,min 0 2 = + (40) V N b cV P V i i pi L pi i N λ ( ) ( ) 0 0 1 1 2 1 = + −∂ ∂ = ∑ (41) The maximum error for the network at iteration n is calculates as follows: Err P V V P P V V n n pi n n D L pi n i N max ( ) ( ) ( ) ( ) ( ) max , , max , = { } = + − = ∑ ∆ ∆ ∆ λ 1 ppi n pi n n n V V V ( ) ( ) ( ) ( ) , − − − − 1 1 λ λ (42) 69 Hopfeld Lagrange Network for Economic Load Dispatch Numerical Results A test system consists of three online thermal generating units supplying a load demand of 850 MW with unit data given in Table 1. Ramp rate constraints are neglected. The transmission loss coefficients B are given by: B ij = × − 0 3 0 0 0 0 9 0 0 0 1 2 10 4 . . . For implementation of HLN to the problem, the slope of sigmoid function is fixed at σ = 100 and the updating step sizes for neurons are tuned for each case. The maximum number of iterations and the maximum error for the neural network are set to 2,500 and 10 -4 , respectively. The proposed HLN method is coded in Matlab and run on a 2.1 GHz PC. When power loss is neglected, the selected updating step sizes are α i = 0.0225 and α λ = 0.0005, and the initial output values of the neurons are set based on (40) and (41) as follows: V pi (0) = [375 250 125] T , V λ (0) = 9.0283. The corresponding inputs for the neurons are calculated based on the inverse functions of sigmoid function (36) for continuous neuron and transfer function (39) for multiplier neurons as follows: U pi (0) = [0 0 0] T and U λ (0) = 9.0283. The proposed HLN produces a total cost of 8,194.05 ($/h) with the obtained solution as follows: λ = V λ = 9.1502 ($/MWh) P 1 = V p1 = 394.037 (MW) P 2 = V p2 = 333.496 (MW) P 3 = V p3 = 122.467 (MW) In this case, the proposed HLN method finds the optimal solution with 27 iterations in 0.005 seconds. The maximum error of computation Er- r max , energy function of Hopfield neural network E, energy production cost λ, and unit power outputs during the convergence process of HLN are given in Figures 4, 5, 6, and 7, respectively. In Figure 4, the maximum error is high at the beginning and when it is lower than the pre-specified threshold of 10 -4 , the algorithm will stop due to the stop- ping criteria satisfied. The energy function of the HLN as shown in Figure 5 also varies the same way with maximum error with high value at the beginning and getting lower during the iterative process and reaches the minimum point as the stopping criteria satisfied. In contrast, the energy production cost in Figure 6 is lower at the begin- ning this is because the total power generation from the units is less than the load demand which causes the power balance constraint unsatisfied. When the total power generation from the units increases to satisfy the power demand the energy production cost also increases. The power outputs of generating units in Figure 7 oscillate at the beginning and then they reach the stable state as iterations increased. As observed, the optimal solution is obtained when all maximum error, energy function, and energy production reach the stable region; that is the difference between two consecutive iterations is inconsiderable. Table 1. Data for the three-generating unit system Unit a i ($/h) b i ($/MWh) c i ($/MW 2 h) P i,max (MW) P i,min (MW) 1 561 7.92 0.00156 600 150 2 310 7.85 0.00194 400 100 3 78 7.97 0.00482 200 50 70 Hopfeld Lagrange Network for Economic Load Dispatch Figure 5. Energy function of HLN for three-unit system neglecting power loss Figure 4. Maximum error of HLN for three-unit system neglecting power loss 71 Hopfeld Lagrange Network for Economic Load Dispatch Figure 6. Energy production cost for three-unit system neglecting power loss Figure 7. Power generation for three units neglecting power loss 72 Hopfeld Lagrange Network for Economic Load Dispatch When power loss is included, the selected updating step sizes are α i = 0.02 and α λ = 0.001, and the outputs of neurons are initialized at V pi (0) = [375 250 125] T , V λ (0) = 9.3312. Their correspond- ing inputs of neurons determined by inverse functions of sigmoid and transfer functions are U pi (0) = [0 0 0] T and U λ (0) = 9.3312, respectively. The total cost produced by the HLN method is 8,344.21 ($/h) and the solution is found as follows: λ = V λ = 9.5302 ($/MWh) P 1 = V p1 = 435.409 (MW) P 2 = V p2 = 299.666 (MW) P 3 = V p3 = 130.746 (MW) P L = 15.821 (MW) In this case, the HLN method finds the optimal solution with the same number of iterations as in the case neglecting power loss in 0.010 seconds. In the obtained solutions, all constraints are met; that is, generator outputs are within there lower and upper limits and total power generation from the generators totally meets the load demand plus power loss (if included) requirement. Obvi- ously, in the case with power loss neglected, the total operation cost and energy production cost are lower than those for the case with power loss. HLN for Solving Fuel Constrained ELD Problem Problem Formulation Fuel constrained ELD (FELD) problem or fuel scheduling is an important part of utility for opera- tion and planning since it is a complex problem of very large dimensions with a wide range of time periods and a large set of constraints and variables. The fuel used by a generating unit may be obtained from different contracts at different prices. Fuel contracts are generally under a take- or-pay agreement including both maximum and minimum limits on delivery of fuel to generating units over life of the contract. The fuel storage is usually within a specified limit to allow for inac- curate load forecasts and the inability to deliver on time of suppliers (Asgarpoor, 1994). Assuming that the entire schedule time hori- zon is divided into M subintervals each having a constant load demand and that all generating units are available and remain on-line for M subintervals. The objective is to simultaneously minimize generation cost and emission level of generating units over the M subintervals such that the constraints for power balance, fuel delivery and fuel storage for any given subinterval as well as maximum-minimum fuel delivery, fuel storage, and generator operating constraints for each generating unit are satisfied. The problem formulation for a system hav- ing N thermal generating units scheduled in M subintervals is as follows (Basu, 2002). Min {F fc + F em } (43) F t a b P c P fc k fi fi ik fi ik i N k M = + + ( ) = = ∑ ∑ 2 1 1 (44) F t a b P c P em k ei ei ik ei ik i N k M = + + ( ) = = ∑ ∑ 2 1 1 (45) subject to Power balance constraints P P P ik i N Lk Dk = ∑ − − = 1 0 ; k = 1,…, M (46) P P B P B P B Lk ik ij jk j N i N i ik i N = + + = = = ∑ ∑ ∑ 1 1 0 1 00 (47) Fuel delivery constraint 73 Hopfeld Lagrange Network for Economic Load Dispatch F F ik i N Dk = ∑ − = 1 0 ; k = 1, …, M (48) Fuel storage constraint X X F t Q ik ik ik k ik = + − −1 ; i = 1, …, N (49) Q d e P f P ik i i ik i ik = + + 2 ; k = 1, …, M (50) Generator operating limits P P P i ik i ,min ,max ≤ ≤ ; i = 1, …, N ; k = 1, …, M (51) Fuel delivery limits F F F i ik i ,min ,min ≤ ≤ ; i = 1, …, N; k = 1, …, M (52) Fuel storage limits X X X i ik i ,min ,max ≤ ≤ ; i = 1, …, N; k = 1, …, M (53) The fuel storage at subinterval k in (49) can be rewritten in terms of initial fuel storage as follows: X X F t Q ik i il l il l k = + − ( ) = ∑ 0 1 (54) where a ei , b ei , c ei emission coefficients for thermal unit i; a fi , b fi , c fi fuel cost coefficients for thermal unit i; B ij , B 0i , B 00 transmission loss formula coeffi- cients; d i , e i , f i fuel consumption coefficients for ther- mal unit s; F Dk fuel demand of the units during subinterval k, in tons; F em emission function of generating units; F fc fuel cost function of generating units; F ik fuel delivery for thermal unit i during subin- terval k, in tons; F i,min , F i,max lower and upper fuel delivery limits for thermal unit i, in tons; M number of subintervals of scheduled period; N total number of thermal units; P Dk load demand of the system during subinter- val k, in MW; P Lk transmission loss of the system during sub- interval k, in MW; P ik output power of thermal unit i during subin- terval k, in MW; P i,min , P i,max lower and upper generation limits of thermal unit i, in MW; Q ik fuel consumption function of thermal unit i in subinterval k, in tons/h; t k duration of subinterval k, in hours; X ik fuel storage for unit i during subinterval k, in tons; X i,min , X i,max lower and upper fuel storage limits for thermal unit i, in tons. HLN Implemented to the FELD Problem The Lagrange function L of the problem is for- mulated as follows: 74 Hopfeld Lagrange Network for Economic Load Dispatch L t a b P c P a b P c P k fi fi ik fi ik ei ei ik ei ik i N k = ÷ ÷ ( ) ÷ ÷ ÷ ( ) l l l = = ∑ 2 2 1 11 1 1 1 M k Lk Dk ik i N k M k ik i N Dk P P P F F ∑ ∑ ∑ ∑ ÷ ÷ − í ( · · ·· \ ) ÷ − í ( · = = = λ γ ·· ·· \ ) ÷ − − ÷ ( ) í ( · · ·· \ ) = = = ∑ ∑ k M ik ik i il l il l k i X X F t Q 1 0 1 1 η NN k M ∑ ∑ =1 (55) To represent in HLN, 3N×M continuous neurons and (N+2)×M multiplier neurons are required. The energy function E of the problem is formulated based on the Lagrangian function in terms of neurons as follows. E t a b V c V a b V c V k fi fi pik fi pik ei ei pik ei pik i = ÷ ÷ ( ) ÷ ÷ ÷ ( ) l l l = 2 2 1 NN k M k Lk Dk pik i N k M k fik i N V P P V V V ∑ ∑ ∑ ∑ = = = = ÷ ÷ − í ( · · ·· \ ) ÷ 1 1 1 1 λ γ ∑∑ ∑ ∑ − í ( · · ·· \ ) ÷ − − ÷ ( ) í ( · · = = F V V X V t Q Dk k M ik xik i fil l il l k 1 0 1 η ··· \ ) ÷ ÷ ÷ = = − − − ∑ ∑ ∫ ∫ i N k M c V c V c g V dV g V dV g V pik fik 1 1 1 0 1 0 1 ( ) ( ) ( ))dV V i N k M xik 0 1 1 ∫ ∑ ∑ í ( · · · · · \ ) = = (56) where V pik output of continuous neuron represent- ing for output power P ik ; V fik output of continuous neuron representing for fuel delivery F ik ; V xik output of continuous neuron representing for fuel storage X ik ; V λk output of multiplier neuron associated with power balance constraint; V γk output of multiplier neuron associated with fuel delivery constraint; V ηik output of multiplier neuron associated with fuel storage constraint. The dynamics of HLN for updating neuron inputs are defined as follows: dU dt E V t b c V t b c V V P pik pik k fi fi pik k ei ei pik k L = − ∂ ∂ = − ÷ ( ) ÷ ÷ ( ) ÷ ∂ 2 2 λ kk pik ik k ik pik pik V V t dQ dV U ∂ − í ( · · · · \ ) ÷ ÷ ' ! 1 1 1 1 1 + 1 1 1 1 1 ' 1 η !! 1 1 1 1 1 + 1 1 1 1 1 (57) dU dt E V V V U fik fik k ik fik = − ∂ ∂ = − − + { } γ η (58) dU dt E V V U xik xik ik xik = − ∂ ∂ = − + { } η (59) dU dt E V P P V k k Dk Lk pik i N λ λ = + ∂ ∂ = + − = ∑ 1 (60) dU dt E V V F k k fik i N Dk γ γ = + ∂ ∂ = − = ∑ 1 (61) dU dt E V V X V t Q ik ik xik i fil l il l k η η = + ∂ ∂ = − − + ( ) = ∑ 0 1 (62) where ∂ ∂ = + = ∑ P V B V B Lk pik ij pjk j N i 2 1 0 (63) ∂ ∂ = + Q V e fV ik pik i i pik 2 (64) U pik , U fik , U xik inputs of continuous neurons corresponding to the outputs V pik , V fik and V xik , respectively; U λk , U γk , U ηik inputs of multiplier neurons corresponding to the outputs V λk , V γk and V ηik , respectively. 75 Hopfeld Lagrange Network for Economic Load Dispatch The algorithm for updating inputs of neurons at iteration n is as follows: U U E V pik n pik n p pik ( ) ( ) = − ∂ ∂ −1 α (65) U U E V fik n fik n f fik ( ) ( ) = − ∂ ∂ −1 α (66) U U E V xik n xik n x xik ( ) ( ) = − ∂ ∂ −1 α (67) U U E V k n k n k λ λ λ λ α ( ) ( ) = + ∂ ∂ −1 (68) U U E V k n k n k γ γ γ γ α ( ) ( ) = + ∂ ∂ −1 (69) U U E V ik n ik n ik η η η η α ( ) ( ) = + ∂ ∂ −1 (70) where α p , α f , α x continuous neuron updating step sizes; α λ , α γ , α η multiplier neuron updating step sizes. The outputs of neurons representing for output power, fuel delivery and fuel storage of units are determined by: V g U P P U pik c pik i i pik = = − í ( · · · · \ ) ÷ ( ) l l ( ) tanh ,max ,min 2 1 σ ll ÷ P i,min (71) V g U F F U fik c fik i i fik = = − ( ) + ( ) ( ) tanh ,max ,min 1 2 σ ++ F i,min (72) V g U F F U fik c fik i i fik = = − ( ) + ( ) ( ) tanh ,max ,min 1 2 σ ++ F i,min (73) The outputs of multiplier neurons are deter- mined by: V λ λ λ k m k k g U U = = ( ) (74) V γ γ γ k m k k g U U = = ( ) (75) V η η η ik m ik ik g U U = = ( ) (76) The maximum error for the neural network at iteration n is determined as follows: Err P F X V V V k ik ik pik fik xik max max , , , , , = { } ∆ ∆ ∆ ∆ ∆ ∆ (77) where ∆P P P V k Dk Lk pik i N = + − = ∑ 1 (78) ∆F V F ik fik i N Dk = − = ∑ 1 (79) ∆X V X V t Q ik xik i fil l il l k = − − + ( ) = ∑ 0 1 (80) ∆V V V pik pik n pik n = − − ( ) ( ) 1 (81) ∆V V V fik fik n fik n = − − ( ) ( ) 1 (82) ∆V V V xik xik n xik n = − − ( ) ( ) 1 (83) 76 Hopfeld Lagrange Network for Economic Load Dispatch Numerical Results The test system includes five thermal generat- ing units remaining online for a period of three weeks. The system data and demand are given in Tables 2 and 3, respectively. The system power loss is neglected. The parameters of HLN for the problem are selected after tuning as follows: σ = 100, α p = 3.5x10 -5 , α f = α x = α λ = 1.25, α γ = 2x10 -6 and α η = 3.5x10 -7 . The maximum number of iterations and the maximum error for the neural network are set to 2500 and 10 -4 , respectively. In this problem, the optimal solution can be affected by the initial conditions of fuel storage. For considering the effects of the initial storage conditions to the optimal solution, the problem is considered for 3 cases with 3 different initial storages as follows. Case 1: The initial storage for 5 units is X i0 = [2000 5000 5000 8000 8000] T tons. This is also called “full case” since the fuel stored at the begin- ning of the schedule time is enough for generating units to operate in certain duration before fuel delivered. In this case, the optimal solution for the problem is rather easily found since the problem constraints are not so restricted. The total cost and emission obtained by the HLN method for the problem are $1,044,728.25 and 534,488.74 kg, respectively. The solution for this case is given in Table 4. As shown in the table, λ k represents for energy production cost, γ k represents for fuel Table 2. Data for five-unit system Unit 1 2 3 4 5 a fi ($/h) 25 60 100 120 40 b fi ($/MWh) 2.0 1.8 2.1 2.2 1.8 c fi ($/MW 2 h) 0.008 0.003 0.001 0.004 0.002 a ei (kg/h) 80 50 70 45 30 b fi (kg/MWh) -0.805 -0.555 -0.955 -0.600 -0.555 c ei (kg/MW 2 h) 0.018 0.015 0.012 0.008 0.012 d i (ton/h) 0.83612 2.00669 3.34448 4.01338 1.33779 e i (ton/MWh) 0.066890 0.060200 0.070230 0.073580 0.060200 f i (ton/MW 2 h) 0.00026756 0.00010033 0.00004013 0.00013378 0.00005017 P i,max (MW) 75 125 175 250 300 P i,min (MW) 20 20 30 40 50 F i,max (tons) 1000 1000 2000 3000 3000 F i,min (tons) 0 0 0 0 0 X i,max (tons) 10000 10000 20000 30000 30000 X i,min (tons) 0 0 0 0 0 Table 3. Demand of five-unit system Subinterval 1 2 3 Duration t k (h) 168 168 168 Load demand P Dk (MW) 700 800 650 Fuel demand F Dk (tons) 7000 7000 7000 77 Hopfeld Lagrange Network for Economic Load Dispatch delivery cost, and η ik represents for fuel storage cost for each unit for each sub-interval. The computational time for this case is 0.13 seconds. Case 2: The initial storage for 5 units is X i0 = [2000; 5000; 5000; 500; 8000] T tons. This is also called “shortage case” since the initial fuel storage for unit 4 can only guaranty it to operate in a very short term. The solution for this case is more dif- ficult to be found since the constraint condition is more restricted than the full case. In this case, the total cost and emission obtained by the pro- posed method are $1,044,701.09 and 534,515.92 kg, respectively. The solution for this case is given in Table 5. Due to the initial fuel shortage, the fuel delivered to unit 4 in this case is more than that in Case 1 while fuel delivered to other units is less. For this case, the computational time is 0.17 seconds. Case 3: The initial storage for 5 units is X i0 = [2000; 2500; 2500; 8000; 500] T tons. This case is also a shortage case with the initial fuel short- age for unit 5 and lower initial fuel storage than that in Case 1 for units 2 and 3. This case is more restricted than Case 2 since the initial storage is lower. Therefore, the optimal solution is also more difficult to be found. For this case, the proposed method gives a total cost of $ 1,044,738.45 and an emission of 534,478.54 kg with a computa- tional time of 0.27 seconds. The obtained solution for this case is given in Table 6. In this case, the fuel delivered to unit 5 is also increased while fuel delivered to the others is reduced. The results from the three cases show that the final solutions are little affected by the initial conditions of fuel storage. The proposed HLN could find the corresponding optimal solution for each case. In all cases, the obtained total costs and emissions are not much difference from each other. In this multi-objective optimization problem, the single objective optimization is also considered as an option for decision maker. In this case, the single objective problems are also considered for purity of fuel cost dispatch and purity of emission dispatch with the initial storage from Case 1. In these single objective cases, the optimal solution is easier to be found than the cases with multi- objectives since there is no conflict between the objectives. The parameters of HLN for these cases are chosen as follows: α p = 10 -5 , α f = α x = α λ = 0.1, and α γ = α η = 10 -7 . The remaining parameters are Table 4. Solution for Case 1 Sub interval λ k ($/MWh) γ k ($/ton-h) Unit 1 2 3 4 5 1 942.6 0.0012 P ik (MW) 75.00 21.26 175.00 167.07 161.67 F ik (10 3 tons) 0.7816 0.5425 1.5275 2.1183 2.0300 X ik (10 3 tons) 1.7950 3.9770 3.8996 7.3750 8.1688 η ik ($/ton-h) 0.0076 0.0021 0.0071 0.0056 0.0049 2 1,148.1 0.0023 P ik (MW) 75.00 125.00 175.00 218.03 206.97 F ik (10 3 tons) 0.7697 0.5971 1.5804 2.1278 1.9250 X ik (10 3 tons) 1.5781 2.9707 2.8520 6.1286 7.7741 η ik ($/ton-h) 0.0084 0.0043 0.0090 0.0068 0.0053 3 884.1 0.0031 P ik (MW) 75.00 111.58 162.07 152.57 148.78 F ik (10 3 tons) 0.7739 0.6619 1.6544 2.0978 1.8120 X ik (10 3 tons) 1.3653 2.1652 2.0312 5.6629 7.8554 η ik ($/ton-h) 0.0092 0.0064 0.0109 0.0073 0.0052 78 Hopfeld Lagrange Network for Economic Load Dispatch the same as the ones selected for the three cases above. Fuel Cost Objective Only: In this case, there only fuel cost objective is minimized while the emission objective is neglected. The obtained total cost by HLN is $1,002,468.61 and the emis- sion 744,675.06 kg. It is obvious that when the fuel cost objective is priority to be considered, the total cost is much lower than that in the case of bi-objective case meanwhile the emission in this case is much higher and all constraints are satisfied. The obtained solution for the economic dispatch is given in Table 7. Emission objective only: This case is opposite to the case considering only fuel cost objective. The obtained emission level in this case is Table 6. Solution for Case 3 Sub interval λ k ($/MWh) γ k ($/ton-h) Unit 1 2 3 4 5 1 942.6 0.0039 P ik (MW) 75.00 121.25 175.00 167.09 161.66 F ik (10 3 tons) 0.6141 0.6259 1.5930 1.5408 2.6262 X ik (10 3 tons) 1.6275 1.5604 1.4650 6.7974 1.2652 η ik ($/ton-h) 0.0082 0.0084 0.0127 0.0061 0.0156 2 1148.1 0.0057 P ik (MW) 75.00 125.00 175.00 218.04 206.96 F ik (10 3 tons) 0.5890 0.7311 1.7417 1.5148 2.4234 X ik (10 3 tons) 1.2298 0.6881 0.5788 4.9378 1.3690 η ik ($/ton-h) 0.0098 0.0130 0.0176 0.0081 0.0152 3 884.2 0.0067 P ik (MW) 75.00 111.57 162.04 152.60 148.79 F ik (10 3 tons) 0.5990 0.9113 1.9567 1.4531 2.0800 X ik (10 3 tons) 0.8421 0.1320 0.0606 3.8269 1.7181 η ik ($/ton-h) 0.0119 0.0216 0.0290 0.0096 0.0140 Table 5. Solution for Case 2 Sub interval λ k ($/MWh) γ k ($/ton-h) Unit 1 2 3 4 5 1 942.7 0.0039 P ik (MW) 75.00 21.27 175.00 167.34 161.69 F ik (10 3 tons) 0.6894 0.4206 1.3338 2.8664 1.6898 X ik (10 3 tons) 1.7027 3.8549 3.7059 0.6236 7.8284 η ik ($/ton-h) 0.0079 0.0023 0.0074 0.0193 0.0052 2 1148.3 0.0057 P ik (MW) 75.00 125.00 175.00 217.98 207.02 F ik (10 3 tons) 0.6673 0.4636 1.3914 2.9414 1.5363 X ik (10 3 tons) 1.3834 2.7151 2.4694 0.1914 7.0445 η ik ($/ton-h) 0.0091 0.0049 0.0098 0.0252 0.0059 3 884.2 0.0067 P ik (MW) 75.00 111.59 162.08 152.53 148.80 F ik (10 3 tons) 0.6828 0.5441 1.5212 2.8310 1.4209 X ik (10 3 tons) 1.0795 1.7916 1.5152 0.4593 6.7345 η ik ($/ton-h) 0.0106 0.0076 0.0125 0.0208 0.0062 79 Hopfeld Lagrange Network for Economic Load Dispatch 521,793.49 kg and the total cost $1,072,673.58. The obtained total cost in this case is much higher than the case with only fuel cost objective while the emission level is opposite to the previ- ous case. In fact, the performance of emission dispatch is the same manner with the economic dispatch except the different objective coefficients. The solution for this emission dispatch is given in Table 8. It can be observed from the obtained result that the power outputs of generating units in this case are different to those from the eco- nomic dispatch since they are decided by the different objective coefficients. The obtained test results from the proposed HLN above are better than those from the con- ventional Hopfield network in (Basu, 2002) for Table 7. Solution for fuel cost objective only Sub interval λ k ($/MWh) γ k ($/ton-h) Unit 1 2 3 4 5 1 451.7 0.0011 P ik (MW) 43.00 125.00 175.00 61.03 295.97 F ik (10 3 tons) 0.7470 0.5495 1.5324 1.9964 2.1747 X ik (10 3 tons) 2.1214 3.9461 3.9045 8.5664 6.9541 η ik ($/ton-h) 0.0066 0.0021 0.0071 0.0046 0.0060 2 537.7 0.0022 P ik (MW) 74.98 125.00 175.00 125.02 300.00 F ik (10 3 tons) 0.7368 0.6065 1.5881 1.8905 2.1780 X ik (10 3 tons) 1.8718 2.9491 2.8647 8.2345 5.8707 η ik ($/ton-h) 0.0073 0.0044 0.0089 0.0049 0.0071 3 435.6 0.0029 P ik (MW) 37.00 125.00 175.00 49.04 263.96 F ik (10 3 tons) 0.6925 0.6888 1.6836 1.7422 2.1929 X ik (10 3 tons) 2.0064 2.0345 1.9204 8.6951 5.1670 η ik ($/ton-h) 0.0069 0.0068 0.0112 0.0045 0.0078 Table 8. Solution for emission objective only Sub interval λ k ($/MWh) γ k ($/ton-h) Unit 1 2 3 4 5 1 468.3 0.0012 P ik (MW) 75.00 111.41 162.68 211.66 139.25 F ik (10 3 tons) 0.7809 0.5321 1.5110 2.1715 2.0046 X ik (10 3 tons) 0.7679 0.5853 1.5614 2.2237 1.8617 η ik ($/ton-h) 0.0076 0.0019 0.0069 0.0061 0.0047 2 612.4 0.0024 P ik (MW) 75.00 125.00 175.00 250.00 175.00 F ik (10 3 tons) 0.7710 0.6377 1.6159 2.2506 1.7249 X ik (10 3 tons) 1.7943 4.0664 4.0284 6.8761 8.3703 η ik ($/ton-h) 0.0084 0.0041 0.0087 0.0077 0.0049 3 421.9 0.0032 P ik (MW) 75.00 102.19 150.67 194.39 127.75 F ik (10 3 tons) 1.5755 3.0482 2.9619 5.3297 8.2359 X ik (10 3 tons) 1.3599 2.3136 2.2371 4.4988 8.4429 η ik ($/ton-h) 0.0092 0.0060 0.0104 0.0087 0.0047 80 Hopfeld Lagrange Network for Economic Load Dispatch all cases considered. This shows that the proposed method is better than the conventional Hopfield neural network in dealing with complicated prob- lems. HLN for Solving Hydrothermal ELD Problem Problem Formulation The objective of hydrothermal ELD (HELD) problem is to minimize the total fuel cost of thermal generators while satisfying hydraulic, power balance, and generator operating limits con- straints. Mathematically, the HELD problem for a hydrothermal system with N 1 thermal units and N 2 hydro units scheduled in M time sub-intervals with t k hours for each is formulated as follows: Min F t a b P c P k i i ik i ik i N k M = + + ( ) = = ∑ ∑ 2 1 1 1 (84) subject to: Power balance constraints P P P P ik i N hk h N Lk Dk = = ∑ ∑ + − − = 1 1 1 2 0 ; k = 1,…, M (85) P P B P B P B Lk pk pq qk q N N p N N p pk p N N = + + = + = + = + ∑ ∑ ∑ 1 1 0 1 00 1 2 1 2 1 2 (86) Continuity of reservoir head constraints d d t f r q hk hk k h hk hk = + − ( ) −1 ; h = 1, …, N 2 (87) q P d hk hk hk = × Φ Ψ ( ) ( ) (88) Φ( ) P a b P c P hk ph ph hk ph hk = + + 2 (89) Ψ( ) d a b d c d hk dh dh hk dh hk = + + 2 (90) Generator operating limits P P P i ik i ,min ,max ≤ ≤ ; i = 1, …, N 1 ; k = 1, …, M (91) P P P h hk h ,min ,max ≤ ≤ ; h = 1, …, N 2 ; k = 1, …, M (92) In terms of water availability, the Equation (87) can be rewritten as follows: t q r d d f W k hk hk k M h hM h h − ( ) = − ( ) = = ∑ 1 0 (93) where a i , b i , c i cost coefficients for thermal unit i; a ph , b ph , c ph water discharge coefficients for hydro unit h; a dh , b dh , c dh reservoir head variation coefficients for hydro unit h; B pq , B 0p , B 00 coefficients for the system; d h0 , d hM the initial and final height of the reser- voir head of hydro unit h, in ft; d hk the height of the reservoir head of hydro unit h in interval k, in ft; f h the surface of the vertical sided tank of hydro unit h; P ik generation output of thermal unit s during sub-interval k, in MW; P hk generation output of hydro unit h during subinterval k, in MW; 81 Hopfeld Lagrange Network for Economic Load Dispatch P h min , P h max lower and upper generation limits of hydro unit h, in MW; P i min , P i max lower and upper generation limits of thermal unit s, in MW; P Dk load demand of the system during subinter- val k, in MW; P Lk transmission loss of the system during sub- interval k, in MW; q hk rate of water flow from hydro unit h in inter- val k, in acre-ft per hour or MCF per hour; r hk reservoir inflow for hydro unit h in interval k, in acre-ft per hour or MCF per hour; W h volume of water available for generation by hydro unit h during the scheduling period; Φ(P hk ) water discharge function for hydro unit h at subinterval k; Ψ(P hk ) reservoir head variation function for hydro unit h at subinterval k. When effect of the height of the reservoir head is neglected, the problem is called fixed-head HELD with the constraints (87) and (89) neglected. In contrast, the problem is called variable-head HELD when the variation of the reservoir head is included. HLN Implemented to the HELD Problem The Lagrange function L is formulated as follows: L t a b P c P P P P P k i i ik i ik i N k M k Lk Dk ik i N hk h = ÷ ÷ ( ) ÷ ÷ − − = = = = ∑ ∑ ∑ 2 1 1 1 1 1 λ 11 1 1 1 2 2 N k M h k hk hk k M h h N t q r W ∑ ∑ ∑ ∑ í ( · · · · \ ) ÷ − ( ) − l l l l = = = γ '' ! 1 1 1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1 1 1 ' ! 1 1 1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1 1 1 (94) To implementation in Hopfield Lagrange model, (N 1 +N 2 )×M continuous neurons and N 2 +M multiplier neurons are required. The energy func- tion E of the problem is described in terms of neurons as follows: E t a bV cV V P P V V k i i pik i pik i N k M k Lk Dk pik s N = ÷ ÷ ( ) ÷ ÷ − − = = = ∑ ∑ ∑ 2 1 1 1 1 1 λ pphk h N k M h k hk hk k M h V t q r W = = = ∑ ∑ ∑ í ( · · · · \ ) ÷ − ( ) − l l l l 1 1 1 2 γ hh N c V i N c V h N g V dV g V dV pik phk = − = − = ∑ ∫ ∑ ∫ ∑ ÷ ÷ í ( · · · · · 1 1 0 1 1 0 1 2 1 2 ( ) ( ) \\ ) ' ! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ' ! 1 1 1 1 1 1 1 1 1 1 1 = ∑ k M 1 11 1 1 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (95) where V pik output of continuous neuron ik repre- senting P ik ; V phk output of continuous neuron hk represent- ing P hk ; V λk , V γh outputs of the multiplier neurons associ- ated with power balance and water constraint, respectively. The dynamics of Hopfield Lagrange model for updating neuron inputs based on the previous information are follows: 82 Hopfeld Lagrange Network for Economic Load Dispatch dU dt E V t b cV V P V pik pik k i i pik k Lk pik = − ∂ ∂ = − ÷ ( ) ÷ ∂ ∂ − í ( · · · · \ ) 2 1 λ ÷ ' ! 1 11 + 1 1 1 ' ! 1 11 + 1 1 1 U pik (96) dU dt E V V P V V t q V phk phk k Lk phk h k hk p = − ∂ ∂ = − ∂ ∂ − í ( · · · · \ ) ÷ ∂ ∂ λ γ 1 hhk phk U ÷ ' ! 1 11 + 1 1 1 ' ! 1 11 + 1 1 1 (97) dU dt E V P P V V k k Dk Lk pik i N phk h N λ λ = + ∂ ∂ = + − − = = ∑ ∑ 1 1 1 2 (98) dU dt E V t q r W h h k hk hk k M h γ γ = + ∂ ∂ = − ( ) − = ∑ 1 (99) where ∂ ∂ = + + = = ∑ ∑ P V B V B V B Lk pik ip ppk p N ih phk h N i 2 2 1 1 0 1 2 (100) ∂ ∂ = + + = = ∑ ∑ P V B V B V B Lk phk hi pik i N hq pqk q N h 2 2 1 1 0 1 2 (101) ∂ ∂ = = + ( ) q V d d V dV d b c V hk phk hk phk phk hk ph ph phk Ψ Φ Ψ ( ) ( ) ( ) 2 (102) B ip loss coefficients related to thermal plants; B hq loss coefficients related to hydro plants; B ih , B hi loss coefficients between thermal and hydro plants, B ih = B hi T ; U pik , U phk inputs of the neurons ik and hk, re- spectively; U λk , U γh inputs of the multiplier neurons. The algorithm for updating inputs of neurons at step n is as follows: U U E V pik n pik n i pik ( ) ( ) = − ∂ ∂ −1 α (103) U U E V phk n phk n h phk ( ) ( ) = − ∂ ∂ −1 α (104) U U E V k n k n k λ λ λ λ α ( ) ( ) = − ∂ ∂ −1 (105) U U E V h n h n h γ γ γ γ α ( ) ( ) = − ∂ ∂ −1 (106) where α i , α h updating step sizes for continuous neurons; α λ , α γ updating step sizes for multiplier neurons. The outputs of continuous neurons are calcu- lated by a sigmoid function: V g U P P U pik c pik i i pik = = − ( ) + ( ) ( ) tanh ,max ,min 1 2 σ ++ P i,min (107) V g U P P U phk c phk h h phk = = − ( ) + ( ) ( ) tanh ,max ,min 1 2 σ ++P h,min (108) Since multiplier neurons are unconstrained outputs, the outputs are defined as below: V λk = g m (U λk ) = U λk (109) V γh = g m (U γh ) = U γh (110) The maximum error for the neural network is: Err P W V V k h pik phk max max , , , = { } ∆ ∆ ∆ ∆ (111) where 83 Hopfeld Lagrange Network for Economic Load Dispatch ∆P P P V V k Dk Lk pik i N phk h N = + − − = = ∑ ∑ 1 1 1 2 (112) ∆W t q r W h k hk hk k M h = − ( ) − = ∑ 1 (113) ∆V V V pik pik n pik n = − − ( ) ( ) 1 (114) ∆V V V phk phk n phk n = − − ( ) ( ) 1 (115) Numerical Results Fixed-Head HELD Problem In this case, the reservoir head variation of hydro units is neglected; therefore water discharge of each hydro unit in (88) is a function of only its generation output. The test system has two thermal and two hydro plants with their characteristics given as follows: F 1 (P 1 ) = 380 + 6.75P 1 + 0.00225P 1 2 $/h 47.5 MW ≤ P 1 ≤ 450 MW F 2 (P 2 ) = 600 + 5.28P 2 + 0.0055P 2 2 $/h 100 MW ≤ P 2 ≤ 1000 MW q 3 (P 3 ) = 260 + 8.5P 3 + 0.00986P 3 2 acre-ft/h 0 MW ≤ P 3 ≤ 250 MW q 4 (P 4 ) = 250 + 9.8P 4 + 0.0114P 4 2 acre-ft/h 0 MW ≤ P 4 ≤ 500 MW where F 1 and F 2 are fuel cost functions of thermal power plants 1 and 2, respectively and q 3 and q 4 are water discharge functions for hydro power plants 3 and 4, respectively. Water inflow of reservoirs during schedule period is supposed to be zeros. Transmission loss coefficient matrix is given below, per MW: B = 4 0 . 1.0 1.5 1.5 1.0 3.5 1.0 1.2 1.5 1.0 3.99 2.0 1.5 1.2 2.0 4.9 × − 10 5 The schedule time horizon is 48h which is divided in four sub-periods with 12 hours for each supplying to the load demand of [1200 1500 1400 1700] MW. The allowable volumes of water for hydro plants 3 and 4 for the whole period are given by: W 3 = 125,000 acre-ft W 4 = 286,000 acre-ft The parameters of the HLN for the problem are selected after tuning as follows: σ = 100, α i = α h = 3×10 -4 , α λ = 10 -2 and α γ = 7.5×10 -7 . The maximum number of iterations and the maximum error for the neural network are set to 2,500 and 10 -4 , respectively. When the system power loss is neglected, the total power generation from the thermal and hydro units is balanced to only load demand. The proposed method provides a total cost of $ 353,444.60 with a computational time of 0.8 seconds. The water discharge cost for each hydro plant for the whole schedule time is [0.73 0.51] T $/acre-ft. Obviously, this water discharge cost reflects to the practice that the marginal cost for hydro is small and negligible in the operating cost calculation. Therefore, the energy produc- tion cost for the system is mainly based on the energy production cost from thermal units. The solution obtained by the HLN method for this case is given Table 9. As observed from this result, all constraints including power balance and water discharge are satisfied. 84 Hopfeld Lagrange Network for Economic Load Dispatch The obtained result by HLN method for this case is better than that from the conventional Hopfield neural network in (Basu, 2003). This confirms that the proposed HLN is more efficient than the conventional Hopfield neural network in approach to complicated problems. When the system power loss is included, the total power generation from both thermal and hydro units balances to load demand plus power loss in the system. The HLN method obtains a total cost of $ 375,933.65 with the water discharge cost for each hydro plant for the whole period is [0.76 0.52] T $/acre-ft for a computational time of 0.11 seconds. The total cost and energy production cost in this case are obviously higher than those in the case without power loss. This is because the allowable volumes of water for hydro units are fixed, thus the power outputs from thermal units are increased to compensate to power loss in the system leading to more fuel consumption. The final solution for this case is given in Table 10. This result is also satisfies all constraints of power balance and water discharge. Variable-Head HELD Problem This case considers all constraints as in the problem formulation. The test system consists of two thermal and two hydro plants. Their data is given below: Table 10. Solution for fixed-head HELD problem with power loss Subinterval 1 2 3 4 Duration t k (h) 12 12 12 12 Load demand P Dk (MW) 1200 1500 1400 1700 Production cost λ k ($/MWh) 111.09 129.20 122.93 147.42 Power loss P Lk (MW) 31.42 48.92 42.57 63.69 Thermal unit 1 P 1k (MW) 442.16 450.00 450.00 450.00 Thermal unit 2 P 2k (MW) 326.19 445.10 404.21 563.69 Hydro unit 3 P 3k (MW) 160.56 247.12 217.39 250.00 Hydro unit 4 P 4k (MW) 302.52 406.69 370.96 500.00 Water discharge q 3k (acre-ft) 22547.18 35552.36 30885.46 36015.00 Water discharge q 4k (acre-ft) 1095.33 73453.53 65451.15 96000.00 Table 9. Solution for fixed-head HELD problem neglecting power loss Subinterval 1 2 3 4 Duration t k (h) 12 12 12 12 Load demand P Dk (MW) 1200 1500 1400 1700 Production cost λ k ($/MWh) 103.53 116.55 111.66 129.67 Thermal unit 1 P 1k (MW) 417.01 450.00 450.00 450.00 Thermal unit 2 P 2k (MW) 304.37 403.01 366.06 502.38 Hydro unit 3 P 3k (MW) 167.84 243.09 214.92 250.00 Hydro unit 4 P 4k (MW) 310.78 403.91 369.02 497.62 Water discharge q 3k (acre-ft) 23572.79 34907.03 30507.11 36015.00 Water discharge q 4k (acre-ft) 52760.45 72817.82 65025.60 95395.30 85 Hopfeld Lagrange Network for Economic Load Dispatch F 1 (P 1 ) = 25 + 3.2P 1 + 0.0025P 1 2 $/h F 2 (P 2 ) = 30 + 3.4P 2 + 0.0008P 2 2 $/h Φ 3 (P 3 ) = 0.1980 + 0.306P 3 + 0.000216P 3 2 MCF/h Ψ 3 (d 3 ) = 0.90 - 0.0030d 3 + 0.00001d 3 2 ft Φ 4 (P 4 ) = 0.9360 + 0.612P 4 + 0.000360P 4 2 MCF/h Ψ 4 (d 4 ) = 0.95 - 0.0025d 4 + 0.00002d 4 2 ft d 30 = 300 ft; d 40 = 250 ft f 3 = 1000 M square ft; f 4 = 400 M square ft W 3 = 2850 MCF; W 4 = 2450 MCF The transmission loss coefficient matrix is: B = 1 40 . 0.10 0.15 0.15 0.15 0.60 0.10 0.13 0.15 0.10 0.68 0.65 0.15 0.13 0.65 0.70 × − 10 4 The schedule time for this problem is 24 hours with zero water inflow during the scheduled period. The load demand for the whole schedule time is given in Figure 8. The parameters of the HLN are selected for the problem after tuning as follows: σ = 100, α i = α h = 2×10 -2 , α λ = 2.5×10 -4 and α γ = 1.25×10 -4 . The maximum number of iterations and maximum error for the neural network are set to 2,500 and 10 -4 , respectively. Figure 8. Load demand for variable-head HELD problem 86 Hopfeld Lagrange Network for Economic Load Dispatch When power loss is neglected, the total power generation from the thermal and hydro plants is balanced to only load demand at each interval for the whole schedule time horizon. The obtained total cost by HLN is $ 62,839.58 and the water discharge cost of hydro plants [10.23 3.93] T $/ MCF with a computational time of 0.13 seconds. The solution by the HLN for this case is given in Table 11. As observed from the table, based on the obtained schedule, hydro plant 4 is off at hours 2-4 for low load demand and generates high power at the high load demand hours 9-20 so as its total power generation is fitted to the pre-fixed allowable discharge water volume. The power generation from hydro plant 3 during the schedule time is similar to hydro plant 4. However, hydro plant 3 is not off at the hours of low load demand since the allowable water discharge volume for this plant is higher than that for plant 4 which can guarantee it to operate for the whole scheduled time. The water head of the hydro plants changes according to the water discharge for each time- interval of one hour. With the contribution of the hydro power generation in the system, the energy production cost is lower than the case with all thermal unit system. The power generation outputs of plants for this case for the whole schedule time are given in Figure 9. Table 11. Solution for variable-head HELD problem neglecting power loss Hr. P D (MW) λ ($/MWh) P 1 (MW) P 2 (MW) P 3 (MW) P 4 (MW) d 3 (ft) d 4 (ft) 1 800 3.9349 147.44 337.17 281.47 33.92 299.91 249.91 2 700 3.8566 132.03 289.42 262.04 16.50 299.82 249.87 3 600 3.7770 116.42 241.31 242.27 0 299.74 249.87 4 600 3.7768 116.38 241.16 242.46 0 299.66 249.86 5 600 3.7766 116.33 241.02 242.65 0 299.59 249.86 6 650 3.8166 124.18 265.17 252.99 7.65 299.50 249.84 7 800 3.9331 147.08 336.06 282.65 34.21 299.41 249.75 8 1000 4.0878 177.52 430.73 321.99 69.76 299.30 249.57 9 1330 4.3427 227.64 586.94 386.73 128.68 299.17 249.23 10 1350 4.3566 230.37 595.45 390.74 133.44 299.03 248.89 11 1450 4.4326 245.24 641.81 410.44 152.50 298.88 248.48 12 1500 4.4695 252.45 664.28 420.33 162.93 298.73 248.05 13 1300 4.3123 221.68 568.35 381.11 128.86 298.60 247.72 14 1350 4.3494 228.96 591.06 390.99 138.98 298.47 247.36 15 1350 4.3477 228.63 590.01 391.06 140.30 298.33 246.99 16 1370 4.3615 231.32 598.42 395.04 145.22 298.19 246.62 17 1450 4.4216 243.10 635.14 410.79 160.96 298.04 246.20 18 1570 4.5128 260.87 690.49 434.45 184.19 297.89 245.71 19 1430 4.4019 239.24 623.09 406.90 160.78 297.75 245.29 20 1350 4.3381 226.73 584.11 391.23 147.93 297.61 244.91 21 1270 4.2745 214.26 545.22 375.59 134.93 297.48 244.56 22 1150 4.1804 195.75 487.53 352.15 114.58 297.36 244.27 23 1000 4.0635 172.73 415.83 322.85 88.58 297.25 244.05 24 900 3.9853 157.35 367.98 303.36 71.31 297.15 243.88 87 Hopfeld Lagrange Network for Economic Load Dispatch When power loss included in the problem, the total power generation from the thermal and hy- dro plants has to satisfy load demand plus power loss in the system. The total cost is $ 67,952.42 with the water discharge cost of [10.40 3.99] T $/ MCF for each hydro plant. The total computa- tional time of HLN for this case is 0.15 seconds. The final solution is given in Table 12. The sched- ule for this system in this case is also similar to the case neglecting power loss except higher thermal power generation to compensate the power loss leading to higher energy production. The power generation outputs of power plants for this case and the comparison of energy production costs for both cases during the whole schedule time are given in Figures 10 and 11, respectively. For the both cases, the variations of power generation outputs and energy production costs are corresponding to the variation of the load demand in the whole schedule time horizon. Future Research Directions For further research directions based on the HLN method, more developments of HLN and its broader implementations to optimization problems in power systems will be considered as follows: • Adaptive updating mechanism will be con- sidered to replace the current updating step sizes since they need to be tuned in the HLN method for each problem. • Other ELD problems for thermal units such as combined heat and power economic dis- patch, economic dispatch with piecewise fuel const function, economic dispatch with prohibited operating zones etc will be considered and solved by implementation of the proposed HLN method. Figure 9. Power generation of plants for variable-head HELD problem neglecting power loss 88 Hopfeld Lagrange Network for Economic Load Dispatch • The HLN method will be also applied for solving hydrothermal economic dispatch with cascaded hydro plants. • The implementation of the HLN for solv- ing large-scale optimization problems in power systems will be also studied due to its fast convergence to optimal solution. CONCLUSION In this chapter, the proposed HLN method has been efficiently implemented for solving different ELD problems including basic economic load dispatch, fuel constrained economic load dispatch and hy- drothermal economic load dispatch. By directly using Lagrangian function as the energy function of continuous Hopfield network in the HLN, it is not necessary to pre-define an energy function for the problem and map the problem into neural network like the conventional Hopfield network. Moreover, the HLN method can simultaneously process all variables and constraints, so it can quickly converge to optimal solution. The ob- tained results from the test cases have shown that the proposed HLN is reliable for finding optimal solutions of the considered problems. The obvi- ous advantages of the proposed HLN method for Table 12. Solution for variable-head HELD problem with power loss Hr. P D (MW) λ ($/MWh) P L (MW) P 1 (MW) P 2 (MW) P 3 (MW) P 4 (MW) d 1 (ft) d 2 (ft) 1 800 4.2028 22.31 151.45 364.54 276.36 29.97 299.91 249.92 2 700 4.0849 16.97 135.06 314.40 255.75 11.77 299.83 249.89 3 600 3.9627 12.40 117.71 261.49 233.19 0 299.75 249.89 4 600 3.9624 12.40 117.67 261.38 233.35 0 299.68 249.88 5 600 3.9622 12.40 117.63 261.26 233.51 0 299.60 249.88 6 650 4.0262 14.59 126.79 289.16 246.10 2.53 299.52 249.87 7 800 4.2010 22.31 151.17 363.72 277.39 30.04 299.43 249.79 8 1000 4.4428 35.37 184.06 464.41 319.54 67.36 299.32 249.62 9 1330 4.8671 64.19 239.46 633.66 390.54 130.52 299.19 249.28 10 1350 4.8922 66.24 242.61 643.27 394.87 135.49 299.05 248.92 11 1450 5.0270 77.03 259.47 694.60 416.83 156.13 298.90 248.51 12 1500 5.0946 82.77 267.76 719.81 427.84 167.37 298.75 248.07 13 1300 4.8190 61.18 233.17 614.55 383.66 129.80 298.61 247.73 14 1350 4.8841 66.24 241.42 639.73 394.51 140.58 298.47 247.37 15 1350 4.8821 66.24 241.14 638.89 394.43 141.78 298.33 247.00 16 1370 4.9072 68.33 244.27 648.45 398.73 146.89 298.19 246.62 17 1450 5.0145 77.04 257.67 689.27 416.24 163.86 298.05 246.19 18 1570 5.1813 91.20 278.02 750.99 442.93 189.26 297.89 245.69 19 1430 4.9820 74.81 253.53 676.74 411.49 163.06 297.74 245.26 20 1350 4.8712 66.26 239.54 634.14 393.80 148.77 297.60 244.88 21 1270 4.7630 58.27 225.67 591.84 376.32 134.44 297.47 244.54 22 1150 4.6058 47.34 205.20 529.34 350.44 112.36 297.36 244.25 23 1000 4.4164 35.39 180.01 452.28 318.55 84.56 297.25 244.04 24 900 4.2935 28.46 163.36 401.32 297.55 66.24 297.15 243.88 89 Hopfeld Lagrange Network for Economic Load Dispatch Figure 10. Power generation of plants for variable-head HELD problem with power loss Figure 11. Energy production costs for both cases with and without power loss 90 Hopfeld Lagrange Network for Economic Load Dispatch solving the economic dispatch problems in power systems as well as optimization problems are its ability to efficiently deal with nonlinear objectives and constraints, to properly handle time-coupling constraints by Lagrangian function and variable limits by sigmoid function of continuous neurons in Hopfield neural network, to quickly find the optimal solution for the problems, and to deal with very large-scale problems with multiple schedule periods. In addition, unlike the population based methods such as evolutionary programming, dif- ferential evolution or particle swarm optimization, the proposed method needs only one run to obtain the optimal solution that does not depend on the initially assumed solution for the algorithm. 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Electrical and Energy Systems, 23(6), 435–442. doi:10.1016/S0142- 0615(00)00084-3 Yalcinoz, T., & Short, M. J. (1998). Neural net- works approach for solving economic dispatch problem with transmission capacity constraints. IEEE Transactions on Power Systems, 13(2), 307–313. doi:10.1109/59.667341 Yalcinoz, T., Short, M. J., & Cory, B. J. (1999). Security dispatch using the Hopfield neural net- work. IEE Proceedings. Generation, Transmission and Distribution, 146(5), 465–470. doi:10.1049/ ip-gtd:19990506 KEY TERMS AND DEFINITIONS Economic Load Dispatch: One of the optimi- zation problems in power systems. In this problem, it is assumed that the generating units are online during the considered schedule time. The objective of the economic dispatch problem is usually to minimize the total cost of thermal generating units while satisfying the unit and system constraints such as power balance, power generation limits, ramp rate constraints, etc. Energy Function: A function of the outputs of neurons defined for Hopfield neural network. In the Hopfield neural network, any change in the status of continuous neurons always leads to minimization of the energy function. Fuel Constrained Economic Load Dispatch: The economic dispatch problem with more con- straints of fuel delivery and fuel storage for each generating unit. Hopfield Lagrange Network: A continuous Hopfield neural network with its energy func- tion based on Lagrangian function. By using the Lagrangian relaxation for the energy function, the Lagrange Hopfield network is simpler, easier, and more efficient than the conventional Hopfield neural network in solving optimization problems. Hydrothermal Economic Load Dispatch: An economic dispatch problem for both thermal and hydro generating units. In this problem, the hydro constraints are also taken into consideration in addition to the thermal and system constraints. This problem is more complicated than the eco- nomic dispatch problem due to integration of time-coupling constraints. Lagrangian Function: A function used to convert a constrained optimization problem to an unconstrained optimization problem so that the problem could be easier to be solved. Sigmoid Function: A nonlinear function used to calculate the outputs of continuous neurons based on their inputs. In the sigmoid function, its slope can be adjusted leading to the change of the function shape and the outputs will be changed accordingly. Transfer Function: A linear function used to calculate the outputs of multiplier neurons based on their inputs. The slope of this function cannot be usually adjusted and the outputs of neurons are equally set to their inputs. 95 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 3 DOI: 10.4018/978-1-61350-138-2.ch003 INTRODUCTION Globally, buildings are responsible for approxi- mately 40% of the total world annual energy con- sumption. Most of this energy is for the provision of lighting, heating, cooling, and air conditioning. Increasing awareness of the environmental im- pact of CO 2 , NO x and CFCs emissions triggered a renewed interest in environmentally friendly cooling, and heating technologies. Under the 1997 Montreal Protocol, governments agreed to phase out chemicals used as refrigerants that have the potential to destroy stratospheric ozone. It was therefore considered desirable to reduce energy consumption and decrease the rate of depletion of world energy reserves and pollution of the en- vironment. One way of reducing building energy consumption is to design buildings, which are Abdeen Mustafa Omer Energy Research Institute, UK Renewable Energy and Sustainable Development ABSTRACT The increased availability of reliable and effcient energy services stimulates new development alter- natives. This article discusses the potential for such integrated systems in the stationary and portable power market in response to the critical need for a cleaner energy technology. Anticipated patterns of future energy use and consequent environmental impacts (acid precipitation, ozone depletion and the greenhouse effect or global warming) are comprehensively discussed in this chapter. Throughout the theme several issues relating to renewable energies, environment, and sustainable development are ex- amined from both current and future perspectives. It is concluded that green energies like wind, solar, ground-source heat pumps, and biomass must be promoted, implemented, and demonstrated from the economic and/or environmental point view. 96 Renewable Energy and Sustainable Development more economical in their use of energy for heat- ing, lighting, cooling, ventilation and hot water supply. Passive measures, particularly natural or hybrid ventilation rather than air-conditioning, can dramatically reduce primary energy con- sumption (Omer, 2009a). However, exploitation of renewable energy in buildings and agricultural greenhouses can, also, significantly contribute towards reducing dependency on fossil fuels. Therefore, promoting innovative renewable ap- plications and reinforcing the renewable energy market will contribute to preservation of the ecosystem by reducing emissions at local and global levels. This will also contribute to the amelioration of environmental conditions by replacing conventional fuels with renewable ener- gies that produce no air pollution or greenhouse gases (during their use). The provision of good indoor environmental quality while achieving energy and cost efficient operation of the heating, ventilating and air-conditioning (HVAC) plants (devices) in buildings represents a multi variant problem (Omer, 2009b). The comfort of building occupants is dependent on many environmental parameters including air speed, temperature, rela- tive humidity and air quality in addition to lighting and noise. The overall objective is to provide a high level of building performance (BP), which can be defined as indoor environmental quality (IEQ), energy efficiency (EE) cost efficiency (CE), and environmental performance (EP). • Indoor environmental quality is the per- ceived condition of comfort that building occupants experience due to the physical and psychological conditions to which they are exposed by their surroundings. The main physical parameters affecting IEQ are air speed, temperature, relative humidity and air quality. • Energy effciency is related to the provi- sion of the desired environmental condi- tions while consuming the minimal quan- tity of energy. • Cost effciency is the fnancial expenditure on energy relative to the level of environ- mental comfort and productivity that the building occupants attained. The overall cost effciency can be improved by im- proving the indoor environmental quality and the energy effciency of a building. Several definitions of sustainable development have been put forth, including the following com- mon one: development that meets the needs of the present without compromising the ability of future generations to meet their own needs. The World Energy Council (WEC) study found that without any change in our current practice, the world energy demand in 2020 would be 50-80% higher than 1990 levels (WEC, 2009). According to the USA Department of Energy (DoE) report, annual energy demand will increase from a current capacity of 363 million kilowatts to 750 million kilowatts by 2020 (DoE, 2009). The world’s energy consumption today is estimated to 22 billion kWh per year, 53 billion kWh by 2020 (WEC, 2009). Such ever-increasing demand could place signifi- cant strain on the current energy infrastructure and potentially damage world environmental health by CO, CO 2 , SO 2 , NO x effluent gas emissions and global warming (ASHRAE, 2005). Achiev- ing solutions to environmental problems that we face today requires long-term potential actions for sustainable development. In this regards, renew- able energy resources appear to be the one of the most efficient and effective solutions since the intimate relationship between renewable energy and sustainable development. More rational use of energy is an important bridge to help transition from today’s fossil fuel dominated world to a world powered by non-polluting fuels and advanced technologies such as photovoltaics (PVs) and fuel cells (FCs) (Abdeen, 2008a). An approach is needed to integrate renewable energies in a way to meet high building perfor- mance. However, because renewable energy sources are stochastic and geographically diffuse, 97 Renewable Energy and Sustainable Development their ability to match demand is determined by adoption of one of the following two approaches (EUO, 2000): the utilisation of a capture area greater than that occupied by the community to be supplied, or the reduction of the community’s energy demands to a level commensurate with the locally available renewable resources. For a northern European climate, which is characterised by an average annual solar irradi- ance of 150 Wm -2 , the mean power production from a photovoltaic component of 13% conver- sion efficiency is approximately 20 Wm -2 (Duffie and Beckman, 1980). For an average wind speed of 5 ms -1 , the power produced by a micro wind turbine will be of a similar order of magnitude, though with a different profile shape. In the UK, for example, a typical office building will have a demand in the order of 300 kWhm -2 yr -1 (EUO, 2000). This translates into approximately 50 Wm -2 of façade, which is twice as much as the available renewable energies (Lysen, 1983). Thus, the aim is to utilise energy efficiency measures in order to reduce the overall energy consumption and adjust the demand profiles to be met by renewable ener- gies. For instance, this approach can be applied to greenhouses, which use solar energy to provide indoor environmental quality. The greenhouse effect is one result of the differing properties of heat radiation when it is generated at different temperatures. Objects inside the greenhouse, or any other building, such as plants, re-radiate the heat or absorb it. Because the objects inside the greenhouse are at a lower temperature than the sun, the re-radiated heat is of longer wavelengths, and cannot penetrate the glass. This re-radiated heat is trapped and causes the temperature inside the greenhouse to rise. Note that the atmosphere surrounding the earth, also, behaves as a large greenhouse around the world. Changes to the gases in the atmosphere, such as increased carbon dioxide content from the burning of fossil fuels, can act like a layer of glass and reduce the quantity of heat that the planet earth would otherwise radi- ate back into space (Brain, and Mark, 2007). This particular greenhouse effect, therefore, contributes to global warming. The application of greenhouses for plants growth can be considered one of the measures in the success of solving this problem. Maximising the efficiency gained from a green- house can be achieved using various approaches, employing different techniques that could be ap- plied at the design, construction and operational stages. The development of greenhouses could be a solution to farming industry and food security (Abdeen, 2008b). Energy security, economic growth and envi- ronment protection are the national energy policy drivers of any country of the world. As world populations grow, many faster than the growth rate of 2%, the need for more and more energy is exacerbated (Figure 1). Enhanced lifestyle and energy demand rise together and the wealthy in- dustrialised economics, which contain 25% of the world’s population, consume 75% of the world’s energy supply (WEC, 2009). The world’s energy consumption today is estimated to 22 billion kWh per year (WEC, 2009). About 6.6 billion metric tons carbon equivalent of greenhouse gas (GHG) emission are released in the atmosphere to meet this energy demand (WEC, 2009). Approximately 80% is due to carbon emissions from the com- bustion of energy fuels (Abdeen, 2008c). At the current rate of usage, taking into consideration population increases and higher consumption of energy by developing countries, oil resources, natural gas and uranium will be depleted within a few decades. People could depend on new nuclear technologies that will enable much slower uranium depletion in the future. As for coal, it may take two centuries or so. Technological progress has dramatically changed the world in a variety of ways. It has, however, also led to developments e.g., environmental problems, which threaten man and nature. Build-up of carbon dioxide and other GHGs is leading to global warming with unpre- dictable but potentially catastrophic consequences. When fossil fuels burn, they emit toxic pollutants that damage the environment and people’s health 98 Renewable Energy and Sustainable Development with over 700,000 deaths resulting each year, ac- cording to the World Bank review of 2000. At the current rate of usage, taking into consideration population increases and higher consumption of energy by developing countries, oil resources, and natural gas will be depleted within a few decades. A Figure 2 shows the annual and estimated world population and energy demand, and Figure 3 the world oil productions in the next 10-20 years. As for coal, it may take two centuries or so. One must therefore endeavour to take precautions today for a viable world for coming generations. Research into future alternatives has been and still being conducted aiming to solve the complex problems of this recent time e.g., rising energy requirements of a rapidly and constantly growing world population and global environmental pol- lution. Therefore, options for a long-term and environmentally friendly energy supply have to be developed leading to the use of renewable sources (water, sun, wind, biomass, geothermal, hydrogen production by electrolysis of water and fuel cells. Renewables could shield a nation from the negative effect in the energy supply, price and related environment concerns. Hydrogen for fuel cells and the sun for PV have been considered for many years as a likely and eventual substitute for oil, gas, and coal. The sun is the most abundant element in the universe. The use of solar thermal energy or solar photovoltaic (PVs) for the everyday electricity needs has a distinct advantage: avoid consuming resources and degrading the environment through pollut- ing emissions, oil spills and toxic by-products. A one-kilowatt PV system producing 150 kWh each month prevents 75 kg of fossil fuel from being mined (WEC, 2009), and 150 kg of CO 2 from entering the atmosphere and keeps 473 litres of water from being consumed (Abdeen, 2008d). Electricity from fuel cells can be used in the same way as grid power: to run appliances and light bulbs and even to power cars since each gallon of gasoline produced and used in an inter- nal combustion engine releases roughly 12 kg of CO 2 , a GHG that contributes to global warming. People, Power and Pollution Over millions of years ago plants covered the earth, converting the energy of sunlight into living tissue, Figure 1. Annual and estimated world population and energy demand in [Million of barrels per day of oil equivalent (MBDOE)] (Omer, 2008a) 99 Renewable Energy and Sustainable Development some of which was buried in the depths of the earth to produce deposits of coal, oil and natural gas. The past few decades, however, have experienced many valuable uses for these complex chemical substances, manufacturing from them plastics, textiles, fertiliser and the various end products of the petrochemical industry. Indeed, each decade sees increasing uses for these products. Renew- able energy is the term used to describe a wide range of naturally occurring, replenishing energy sources. Coal, oil and gas, which will certainly be of great value to future generations, as they are to ours, are non-renewable natural resources. This is particularly true now as it is, or soon will be, technically and economically feasible to sup- ply all of man’s needs from the most abundant energy source of all, the sun. The sunlight is not only inexhaustible, but, moreover, it is the only energy source, which is completely non-polluting. Figure 2. World oil productions in the next 10-20 years (Omer, 2008a) Figure 3. Volume of oil discovered worldwide (Omer, 2008a) 100 Renewable Energy and Sustainable Development Industry’s use of fossil fuels has been blamed for warming the climate. When coal, gas and oil are burnt, they release harmful gases, which trap heat in the atmosphere and cause global warm- ing (Bos et al, 1994). However, there has been an ongoing debate on this subject, as scientists have struggled to distinguish between changes, which are human induced, and those, which could be put down to natural climate variability. Never- theless, industrialised countries have the highest emission levels, and must shoulder the greatest responsibility for global warming. However, ac- tion must also be taken by developing countries to avoid future increases in emission levels as their economies develop and populations grow, as clearly captured by the Kyoto Protocol (Abdeen, 2008e). Notably, human activities that emit carbon dioxide (CO 2 ), the most significant contributor to potential climate change, occur primarily from fossil fuel production. Consequently, efforts to control CO 2 emissions could have serious, negative consequences for economic growth, employment, investment, trade and the standard of living of individuals everywhere. Scientifically, it is dif- ficult to predict the relationship between global temperature and GHG concentrations. The climate system contains many processes that will change if warming occurs. Critical processes include heat transfer by winds and tides, the hydrological cycle involving evaporation, precipitation, runoff and groundwater and the formation of clouds, snow, and ice, all of which display enormous natural variability (UNECA, 2003b). The equipment and infrastructure for energy supply and use are designed with long lifetimes, and the premature turnover of capital stock in- volves significant costs. Economic benefits occur if capital stock is replaced with more efficient equipment in step with its normal replacement cycle. Likewise, if opportunities to reduce future emissions are taken in a timely manner, they should be less costly. Such a flexible approach would allow society to take account of evolving scientific and technological knowledge, while gaining experience in designing policies to address climate change (Abdeen, 2009a). The World Summit on Sustainable Develop- ment in Johannesburg in 2002 committed itself to ‘‘encourage and promote the development of renewable energy sources to accelerate the shift towards sustainable consumption and produc- tion’’. Accordingly, it aimed at breaking the link between resource use and productivity. This can be achieved by the followings: • Trying to ensure economic growth does not cause environmental pollution. • Improving resource effciency. • Examining the whole life-cycle of a product. • Enabling consumers to receive more infor- mation on products and services. • Examining how taxes, voluntary agree- ments, subsidies, regulation and informa- tion campaigns, can best stimulate inno- vation and investment to provide cleaner technology. The energy conservation scenarios include rational use of energy policies in all economy sectors and the use of combined heat and power systems, which are able to add to energy savings from the autonomous power plants. Electricity from renewable energy sources is by definition the environmental green product. Hence, a renew- able energy certificate system, as recommended by the World Summit, is an essential basis for all policy systems, independent of the renewable energy support scheme. It is, therefore, important that all parties involved support the renewable energy certificate system in place if it is to work as planned. Moreover, existing renewable energy technologies (RETs) could play a significant miti- gating role, but the economic and political climate will have to change first. The change in climate is real. It is happening now, and GHGs produced by human activities are significantly contributing to it. The predicted global temperature increase of 101 Renewable Energy and Sustainable Development between 1.5 and 4.5 o C could lead to potentially catastrophic environmental impacts (DEFRA, 2006). These include sea level rise, increased frequency of extreme weather events, floods, droughts, disease migration from various places and possible stalling of the Gulf Stream. This has led scientists to argue that climate change issues are not ones that politicians can afford to ignore, and policy makers tend to agree (DEFRA, 2006). However, reaching international agreements on climate change policies is no trivial task as the difficulty in ratifying the Kyoto Protocol has proved (UNECA, 2004). Therefore, the use of renewable energy sources and the rational use of energy, in general, are the fundamental inputs for any responsible energy policy. However, the energy sector is encounter- ing difficulties because increased production and consumption levels entail higher levels of pollu- tion and eventually climate change, with possibly disastrous consequences. At the same time, it is important to secure energy at an acceptable cost in order to avoid negative impacts on economic growth. To date, renewable energy contributes as much as 20% of the global energy supplies worldwide (Abdeen, 2009b). Over two thirds of this comes from biomass use, mostly in develop- ing countries, some of it unsustainable. Yet, the potential for energy from sustainable technologies is huge. On the technological side, renewables have an obvious role to play. In general, there is no problem in terms of the technical potential of renewables to deliver energy. Moreover, there are very good opportunities for RETs to play an important role in reducing emissions of GHGs into the atmosphere, certainly far more than have been exploited so far. However, there are still some technical issues to address in order to cope with the intermittency of some renewables, particularly wind and solar. Yet, the biggest problem with rely- ing on renewables to deliver the necessary cuts in GHG emissions is more to do with politics and policy issues than with technical ones (DEFRA, 2006). For example, the single most important step governments could take to promote and increase the use of renewables is to improve access for renewables to the energy market. This access to the market needs to be under favourable conditions and, possibly, under favourable economic rates as well. One move that could help, or at least justify, better market access would be to acknowledge that there are environmental costs associated with other energy supply options and that these costs are not currently internalised within the market price of electricity or fuels. This could make a significant difference, particularly if appropriate subsidies were applied to renewable energy in recognition of the environmental benefits it offers. Similarly, cutting energy consumption through end-use efficiency is absolutely essential. This suggests that issues of end-use consumption of energy will have to come into the discussion in the foreseeable future (Levine et al, 2005). However, RETs have the benefit of being environmentally benign when developed in a sensitive and appropriate way with the full involve- ment of local communities. In addition, they are diverse, secure, locally based and abundant. In spite of the enormous potential and the multiple benefits, the contribution from renewable energy still lags behind the ambitious claims for it due to the initially high development costs, concerns about local impacts, lack of research funding and poor institutional and economic arrangements (IPCC, 2001). Hence, an approach is needed to integrate renewable energies in a way that meets high building performance requirements. However, because renewable energy sources are stochastic and geographically diffuse, their ability to match demand is determined by adoption of one of the following two approaches (Parikn et al, 1999): the utilisation of a capture area greater than that occupied by the community to be supplied, or the reduction of the community’s energy demands to a level commensurate with the locally available renewable resources. 102 Renewable Energy and Sustainable Development Energy and Population Growth Urban areas throughout the world have increased in size during recent decades. About 50% of the world’s population and approximately 7.6% in more developed countries are urban dwellers (UNIDO, 2007). Even though there is evidence to suggest that in many ‘advanced’ industrialised countries there has been a reversal in the rural-to- urban shift of populations, virtually all population growth expected between 2000 and 2030 will be concentrated in urban areas of the world (UN, 2002b). With an expected annual growth of 1.8%, the world’s urban population will double in 38 years (UNIDO, 2007). With increasing urbanisation in the world, cities are growing in number, population and complexity. At present, 2% of the world’s land surface is covered by cities, yet the people living in them consume 75% of the resources consumed by mankind (WRI, 2004). Indeed, the ecological footprint of cities is many times larger than the areas they physically occupy. Economic and social imperatives often dictate that cities must become more concentrated, making it necessary to increase the density to accommodate the people, to reduce the cost of public services, and to achieve required social cohesiveness. The reality of modern urbani- sation inevitably leads to higher densities than in traditional settlements and this trend is particularly notable in developing countries (Omer, 2010a). Generally, the world population is rising rap- idly, notably in the developing countries. Historical trends suggest that increased annual energy use per capita, which promotes a decrease in population growth rate, is a good surrogate for the standard of living factors. If these trends continue, the stabi- lisation of the world’s population will require the increased use of all sources of energy, particularly as cheap oil and gas are depleted. The improved efficiency of energy use and renewable energy sources will, therefore, be essential in stabilising population, while providing a decent standard of living all over the world (UN, 2002a). Moreover, energy is the vital input for economic and social development of any country. With an increase in industrial and agricultural activities the demand for energy is also rising. It is, however, a well- accepted fact that commercial energy use has to be minimised. This is because of the environmental effects and the availability problems. Consequent- ly, the focus has now shifted to non-commercial energy resources, which are renewable in nature. This is bound to have less environmental effects and also the availability is guaranteed. However, even though the ideal situation will be to encour- age people to use renewable energy resources, there are many practical difficulties, which need to be tackled. The people groups who are using the non-commercial energy resources, like urban communities, are now becoming more demanding and wish to have commercial energy resources made available for their use (UNEP, 2000). This is attributed to the increased awareness, improved literacy level and changing culture (Abdeen, 2009c). The quality of life practiced by people is usually represented as being proportional to the per capita energy use of that particular country. It is not surprising that people want to improve their quality of life. Consequently, it is expected that the demand for commercial energy resources will increase at a greater rate in the years to come (WRI, 2004). Because of this emerging situation, the policy makers are left with two options: either to concentrate on renewable energy resources and have them as substitutes for commercial energy resources or to have a dual approach in which renewable energy resources will contribute to meet a significant portion of the demand whereas the conventional commercial energy resources would be used with caution whenever necessary (UNECA, 2002). Even though the first option is the ideal one, the second approach will be more appropriate for a smooth transition (UN, 2001). 103 Renewable Energy and Sustainable Development Energy and Environmental Problems Technological progress has dramatically changed the world in a variety of ways. It has, however, also led to developments of environmental problems, which threaten man and nature (UNECA, 2003a). During the past two decades the risk and reality of environmental degradation have become more apparent. Growing evidence of environmental problems is due to a combination of several fac- tors since the environmental impact of human activities has grown dramatically because of the sheer increase of world population, consumption, industrial activity, etc., throughout the 1970s most environmental analysis and legal control instru- ments concentrated on conventional effluent gas pollutants such as SO 2 , NO x , particulates, and CO (Table 1). Recently, environmental concerns has extended to the control of micro or hazardous air pollutants, which are usually toxic chemical substances and harmful in small doses, as well to that of globally significant pollutants such as CO 2 . Aside from advances in environmental science, developments in industrial processes and struc- tures have led to new environmental problems. For example, in the energy sector, major shifts to the road transport of industrial goods and to individual travel by cars has led to an increase in road traffic and hence a shift in attention paid to the effects and sources of NO x and volatile organic compound (VOC) emissions. Environmental problems span a continuously growing range of pollutants, hazards and ecosys- tem degradation over wider areas. The main areas of environmental problems are: major environ- mental accidents, water pollution, maritime pol- lution, land use and sitting impact, radiation and radioactivity, solid waste disposal, hazardous air pollutants, ambient air quality, acid rain, strato- spheric ozone depletion and global warming (greenhouse effect, global climatic change) (Table 2). The four more important types of harm from man’s activities are global warming gases, ozone destroying gases, gaseous pollutants and micro- biological hazards (Table 3). Notably, human activities that emit carbon dioxide (CO 2 ), the most significant contributor to potential climate change, occur primarily from fossil fuel production. Con- sequently, CO 2 emissions could have serious, negative consequences for economic growth, employment, investment, trade and the standard of living of individuals everywhere. The earth is warmer due to the presence of gases but the global temperature is rising. This could lead to Table 1. EU criteria pollutant standards in the ambient air environment (Omer, 2008a) Pollutant EU limit CO 30 mg/m 2 ; 1h NO 2 200 μg/m 2 ; 1h O 3 235 μg/m 2 ; 1h SO 2 250-350 μg/m 2 ; 24 h 80-120 μg/m 2 ; annual PM 10 250 μg/m 2 ; 24 h 80 μg/m 2 ; annual SO 2 + PM 10 100-150 μg/m 2 ; 24 h 40-60 μg/m 2 ; annual Pb 2 μg/m 2 ; annual Total suspended particulate (TSP 260 μg/m 2 ; 24 h HC 160 μg/m 2 ; 3 h 104 Renewable Energy and Sustainable Development the sea level rising at the rate of 60 mm each decade with the growing risk of flooding in low- lying areas (Figure 4). At the United Nations Earth Summit at Rio in June 1992 some 153 countries agreed to pursue sustainable development (Boulet, 1987). A main aim was to reduce emission of carbon dioxide and other GHGs. Reduction of energy use in buildings is a major role in achieving this. Carbon dioxide targets are proposed to encourage designers to look at low energy designs and energy sources. Problems with energy supply and use are related not only to global warming that is taking place, due to effluent gas emission mainly CO 2 , but also to such environmental concerns as air pollution, acid precipitation, ozone depletion, forest destruction and emission of radioactive substances (Table 4). These issues must be taken into consideration simultaneously if humanity is to achieve a bright energy future with minimal environmental impacts. Much evidence exists, which suggests that the future will be negatively impacted if humans keep degrading the environ- ment. During the past century, global surface tem- peratures have increased at a rate near 0.6 o C/ century and the average temperature of the At- lantic, Pacific and Indian oceans (covering 72% of the earth surface) have risen by 0.06 o C since 1995. Global temperatures in 2001 were 0.52 o C Table 2. Significant EU environmental directives in water, air and land environments (Omer, 2008a) Environment Directive name Water Surface water for drinking Sampling surface water for drinking Drinking water quality Quality of freshwater supporting fish Shellfish waters Bathing waters Dangerous substances in water Groundwater Urban wastewater Nitrates from agricultural sources Air Smokes in air Sulphur dioxide in air Lead in air Large combustion plants Existing municipal incineration plants New municipal incineration plants Asbestos in air Sulphur content of gas oil Lead in petrol Emissions from petrol engines Air quality standards for NO 2 Emissions from diesel engines Land Protection of soil when sludge is applied 105 Renewable Energy and Sustainable Development Table 3. The external environment (Omer, 2009) Damage Manifestation Design NO x , SO x Irritant Low NO x burners Acid rain land damage Low sulphur fuel Acid rain fish damage Sulphur removal Global warming Thermal insulation CO 2 Rising sea level Heat recovery Drought, storms Heat pumps O 3 destruction Increased ultra violet No CFC’s or HCFC’s Skin cancer Minimum air conditioning Crop damage Refrigerant collection Legionnellosis Pontiac fever Careful maintenance Legionnaires Dry cooling towers Figure 4. Change in global sea level (Omer, 2008a) Table 4. Global emissions of the top fourteen nations by total CO 2 volume (billion of tones) (Omer, 2009) Rank Nation CO 2 Rank Nation CO 2 Rank Nation CO 2 1 2 3 4 USA Russia China Japan 1.36 0.98 0.69 0.30 6 7 8 9 India UK Canada Italy 0.19 0.16 0.11 0.11 11 12 13 14 Mexico Poland S. Africa S. Korea 0.09 0.08 0.08 0.07 106 Renewable Energy and Sustainable Development above the long-term 1880-2000 average (the 1880-2000 annually averaged combined land and ocean temperature is 13.9 o C). Also, according to the USA Department of Energy, world emissions of carbon are expected to increase by 54% above 1990 levels by 2015 making the earth likely to warm 1.7-4.9 o C over the period 1990-2100, as shown in Figure 5. Such observation and others demonstrate that interests will likely increase regarding energy related environment concerns and that energy is one of the main factors that must be considered in discussions of sustainable development. New and renewable sources of energy can make an increasing contribution to the energy supply mix of the world in view of favourable renewable energy resource endowments, limita- tions and uncertainties of fossil fuel supplies, adverse balance of payments and the increasing pressure on environment from conventional en- ergy generation. Among the renewable energy technologies, the generation of mechanical and electrical power by wind machines has emerged as a techno-economi- cal viable and cost-effective option (Omer, 2010b). Environmental Transformations In recent years a number of countries have adopted policies aimed at giving a greater role to private ownership in the natural resource sector. For ex- ample, in the UK the regional water companies have been privatised and have been given a con- siderable degree of control over the exploitation of the nation’s regional water resources. Similar policies have been followed in France and other European countries. Typically, a whole range of new regulatory instruments such as technological standards accompanies such privatisation on water treatment plants, minimum standards on drinking water quality, price controls and maximum with- drawal quotas. While some of these instruments address problems of monopolistic behaviour and other forms of imperfect competition, the bulk of regulatory measures is concerned with establishing ‘good practices’ aimed at maintaining the quality of the newly privatised resources as a shorthand. Society has to meet the freshwater demands of its population and its industry by extracting water from the regional water resources that are provided by the natural environment (lakes, rivers, aquifers, Figure 5. Global mean temperature changes over the period of 1990-2100 and 1990-2030 (Omer, 2009) 107 Renewable Energy and Sustainable Development etc.). These water resources are renewable but potentially destructible resources. While moder- ate amounts of human water extractions from a given regional water system can be sustained for indefinite periods. Excessive extractions will change the geographical and climatic conditions supporting the water cycle and will diminish the regenerative capacity of the regional water system, thereby reducing the potential for future withdrawals. Typically, recovery from any such resource degradation will be very slow and dif- ficult, if not impossible; resource degradation is partially irreversible (Erreygers, 1996). To make sustainable water extraction economi- cally viable, the sustainable policy has to break even (all costs are covered by revenues) while unsustainable policy has to be unprofitable (costs exceed revenues): (1+r) vt -1 = 5y t + v t (1) Where: r is the interest rate, t=year, y t is the revenue, v t is initial costs recovered by revenue, and vt -1 is all costs are covered by revenues. (1+r) vt -1 > 105y t (2) (1+r) vt -1 < [105/(105-5)] v t (3) The term [105/(105-5)] is to define the natural productivity factor of the water resource as (1+g) = [105/(105-5)]; g is the natural productivity rate. Rate g will be close to zero if the sustainable extraction level is much smaller than the unsustain- able level. Using g, the equation can be as follows: v t > (1+r)/(1+g) v t-1 (4) Regulatory measures that prevent resource owners from adopting certain unsustainable extraction policies are a necessary pre-condition for the effective operation of a privatised natural resource sector. Unregulated water privatisation would result in an inflationary dynamics whose distributional effects would threaten the long- term viability of the economy. This inflation- ary dynamics is not due to any form of market imperfection but is a natural consequence of the competitive arbitrage behaviour of unregulated private resource owners. Sustainability Concept Absolute sustainability of electricity supply is a simple concept: no depletion of world resources and no ongoing accumulation of residues. Relative sustainability is a useful concept in comparing the sustainability of two or more generation technolo- gies. Therefore, only renewables are absolutely sustainable, and nuclear is more sustainable than fossil. Energy used to produce devices and plants for renewable energy is not sustainable. How- ever, any discussion about sustainability must not neglect the ability or otherwise of the new technologies to support the satisfactory opera- tion of the electricity supply infrastructure. The electricity supply system has been developed to have a high degree of resilience against the loss of transmission circuits and major generators, as well as unusually large and rapid load changes. It is unlikely that consumers would tolerate any reduction in the quality of the service, even if this were the result of the adoption of otherwise benign generation technologies. Renewables are generally weather-dependent and as such their likely output can be predicted but not controlled. The only control possible is to reduce the output below that available from the resource at any given time. Therefore, to safeguard system stability and security, renewables must be used in conjunction with other, controllable, generation and with large- scale energy storage. There is a substantial cost associated with this provision (Abdeen, 2009d). It is useful to codify all aspects of sustain- ability, thus ensuring that all factors are taken into account for each and every development proposal. Therefore, with the intention of promoting debate, the following considerations are proposed: 108 Renewable Energy and Sustainable Development 1. Long-term availability of the energy source or fuel. 2. Price stability of energy source or fuel. 3. Acceptability or otherwise of by-products of the generation process. 4. Grid services, particularly controllability of real and reactive power output. 5. Technological stability, likelihood of rapid technical obsolescence. 6. Knowledge base of applying the technology. 7. Life of the installation – a dam may last more than 100 years, but a gas turbine probably will not. 8. Maintenance requirement of the plant. Environmental Aspects Environmental pollution is a major problem facing all nations of the world. People have caused air pollution since they learned to how to use fire, but man-made air pollution (anthropogenic air pollution) has rapidly increased since industriali- sation began. Many volatile organic compounds and trace metals are emitted into the atmosphere by human activities. The pollutants emitted into the atmosphere do not remain confined to the area near the source of emission or to the local environment, and can be transported over long distances, and create regional and global envi- ronmental problems. The privatisation and price liberalisation in energy fields has been secured to some extent (but not fully). There should be availability and adequate energy supplies to the major productive sectors. The result is that, the present situation of energy supplies is for better than ten years ago. A great challenge facing the global community today is to make the industrial economy more like the biosphere, that is, to make it a more closed system. This would save energy, reduce waste and pollution, and reduce costs. In short, it would enhance sustainability. Often, it is technically feasible to recycle waste in one of several dif- ferent ways. For some wastes there are powerful arguments for incineration with energy recovery, rather than material recycling. Cleaner produc- tion approach and pollution control measures are needed in the recycling sector as much as in another. The industrial sector world widely is responsible for about one third of anthropogenic emissions of carbon dioxide, the most important greenhouse gas. Industry is also an important emitter of several other greenhouse gases. And many of industry’s products emit greenhouse gases as well, either during use or after they become waste. Opportunities exist for substantial reduc- ing industrial emissions through more efficient production and use of energy: fuel substitutions, the use of alternative energy technologies, process modification, and by revising materials strategies to make use of less energy and greenhouse gas intensive materials. Industry has an additional role to play through the design of products that use less energy and materials and produce lower greenhouse gas emissions. Table 5 summarises the classification of data requirements. Development in the environmental sense is a rather recent concern relating to the need to man- age scarce natural resources in a prudent manner- because human welfare ultimately depends on ecological services. The environmental interpre- tation of sustainability focuses on the overall viability and health of ecological systems- defined in terms of a comprehensive, multiscale, dy- namic, hierarchical measure of resilience, vigour and organisation. Natural resource degradation, pollution and loss of biodiversity are detrimental because they increase vulnerability, undermine system health, and reduce resilience. The envi- ronmental issues include: • Global and transnational (climate change, ozone layer depletion). • Natural habitats (forests and other ecosystems). • Land (agricultural zones). • Water resources (river basin, aquifer, water shed). 109 Renewable Energy and Sustainable Development • Urban-industrial (metropolitan area, air-shed). Environmental sustainability depends on sev- eral factors, including: • Climate change (magnitude and frequency of shocks). • Systems vulnerability (extent of impact damage). • System resilience (ability to recover from impacts). Economic importance of environmental issue is increasing, and new technologies are expected to reduce pollution derived both from productive processes and products, with costs that are still unknown. This is due to market uncertainty, weak appropriability regime, lack of a dominant design, and difficulties in reconfiguring organisational routines. The degradation of the global environ- ment is one of the most serious energy issues. Various options are proposed and investigated to mitigate climate change, acid rain or other envi- ronmental problems. Additionally, the following aspects play a fundamental role in developing environmental technologies, pointing out how technological trajectories depend both on exog- enous market conditions and endogenous firm competencies: 1. Formulating regulations concerning intro- duction of zero emission vehicles (ZEV), create market demand and business develop- ment for new technologies. 2. Each stage of technology development requires alternative forms of division and coordination of innovative labour, upstream and downstream industries are involved in new forms of inter-firm relationships, caus- ing a reconfiguration of product architectures and reducing effects of path dependency. 3. Product differentiation increases firm capa- bilities to plan at the same time technology reduction and customer selection, while meeting requirements concerning network externalities. 4. It is necessary to find and/or create alter- native funding sources for each research, development and design stage of the new technologies. Action areas for producers: • Management and measurement tools- adopting environmental management sys- tems appropriate for the business. • Performance assessment tools- making use of benchmarking to identify scope for im- pact reduction and greater eco-effciency in all aspects of the business. Table 5. Classifications of data requirements (Omer, 2008b) Plant data System data Existing data Size Life Cost (fixed and variation Operation and Maintenance) Forced outage Maintenance Efficiency Fuel Emissions Peak load Load shape Capital costs Fuel costs Depreciation Rate of return Taxes Future data All of above, plus Capital costs Construction trajectory Date in service System lead growth Fuel price growth Fuel import limits Inflation 110 Renewable Energy and Sustainable Development • Best practice tools- making use of free help and advice from government best practice programmes (energy effciency, environ- mental technology, resource savings). • Innovation and ecodesign- rethinking the delivery of ‘value added’ by the business, so that impact reduction and resource ef- fciency are frmly built in at the design stage. • Cleaner, leaner production processes- pur- suing improvements and savings in waste minimisation, energy and water consump- tion, transport and distribution, as well as reduced emissions. Tables (6-8) indicate energy conservation, sustainable develop- ment and environment. • Supply chain management- specifying more demanding standards of sustainabil- ity from ‘upstream’ suppliers, while sup- porting smaller frms to meet those higher standards. • Product stewardship- taking the broad- est view of ‘producer responsibility’ and working to reduce all the ‘downstream’ ef- fects of products after they have been sold on to customers. • Openness and transparency- publicly re- porting on environmental performance against meaningful targets; actively us- ing clear labels and declarations so that customers are fully informed; building stakeholder confdence by communicat- ing sustainability aims to the workforce, the shareholders and the local community (Figure 6 and Table 9). With the debate on climate change, the prefer- ence for real measured data has been changed. The analyses of climate scenarios need an hourly weather data series that allows for realistic changes in various weather parameters (REN21, 2007). By adapting parameters in a proper way, Table 6. Classification of key variables defining facility sustainability Criteria Intra-system impacts Extra-system impacts Stakeholder satisfaction Standard expectations met. Relative importance of standard expectations. Covered by attending to extra-system resource base and ecosystem impacts Resource base impacts Change in intra-system resource bases. Significance of change. Resource flow into/out of facility system. Unit impact exerted by flow on source/sink system. Significance of unit impact. Ecosystem impacts Change in intra-system ecosystems. Significance of change. Resource flows into/out of facility system. Unit impact exerted by how on source/sink system. Significance of unit impact. Table 7. Energy and sustainable environment Technological criteria Energy and environment criteria Social and economic criteria Primary energy saving in regional scale Sustainability according to greenhouse gas pollutant emissions Labour impact Technical maturity, reliability Sustainable according to other pollutant emissions Market maturity Consistence of installation and maintenance re- quirements with local technical known-how Land requirement Compatibility with political, legislative and administrative situation Continuity and predictability of performance Sustainability according to other envi- ronmental impacts Cost of saved primary energy 111 Renewable Energy and Sustainable Development Table 8. Positive impact of durability, adaptability and energy conservation on economic, social and environment systems Economic system Social system Environmental system Durability Preservation of cultural values Preservation of resources Meeting changing needs of economic de- velopment Meeting changing needs of individuals and society Reuse, recycling and preservation of resources Energy conservation and saving Savings directed to meet other social needs Preservation of resources, reduction of pol- lution and global warming Figure 6. Link between resources and productivity Table 9. The basket of indicators for sustainable consumption and production Economy-wide decoupling indicators 1. Greenhouse gas emissions. 2. Air pollution. 3. Water pollution (river water quality). 4. Commercial and industrial waste arisings and household waste not cycled. Resource use indicators 5. Material use. 6. Water extraction. 7. Homes built on land not previously developed, and number of households. Decoupling indicators for specific sectors 8. Emissions from electricity generation. 9. Motor vehicle kilometres and related emissions 10. Agricultural output, fertiliser use, methane emissions and farmland bird populations. 11. Manufacturing output, energy consumption and related emissions.. 12. Household consumption, expenditure energy, water consumption and waste generated 112 Renewable Energy and Sustainable Development data series can be generated for the site. Weather generators should be useful for: • Calculation of energy consumption (no ex- treme conditions are required) • Design purposes (extremes are essential), and • Predicting the effect of climate change such as increasing annually average of temperature. This results in the following requirements: • Relevant climate variables should be gen- erated (solar radiation: global, diffuse, di- rect solar direction, temperature, humidity, wind speed and direction) according to the statistics of the real climate. • The average behaviour should be in accor- dance with the real climate. • Extremes should occur in the generated series in the way it will happen in a real warm period. This means that the gener- ated series should be long enough to assure these extremes, and series based on aver- age values from nearby stations. Growing concerns about social and environ- mental sustainability have led to increased interest in planning for the energy utility sector because of its large resource requirements and production of emissions (Roriz, 2001). A number of conflicting trends combine to make the energy sector a major concern, even though a clear definition of how to measure progress toward sustainability is lacking. These trends include imminent competition in the electricity industry, global climate change, expect- ed long-term growth in population and pressure to balance living standards (including per capital en- ergy consumption). Designing and implementing a sustainable energy sector will be a key element of defining and creating a sustainable society. In the electricity industry, the question of strategic planning for sustainability seems to conflict with the shorter time horizons associated with market forces as deregulation replaces vertical integration. Sustainable low-carbon energy scenarios for the new century emphasise the untapped potential of renewable resources. Rural areas can benefit from this transition. The increased availability of reliable and efficient energy services stimulates new development alternatives. It is concluded that renewable environmentally friendly energy must be encouraged, promoted, implemented, and demonstrated by full-scale plant especially for use in remote rural areas (CEC, 2000). This is the step in a long journey to encourage a progressive economy, which continues to provide us with high living standards, but at the same time helps reduce pollution, waste mountains, other environmental degradation, and environmental rationale for future policy-making and interven- tion to improve market mechanisms. This vision will be accomplished by: • ‘Decoupling’ economic growth and envi- ronmental degradation. The basket of indi- cators illustrated shows the progress being made. Decoupling air and water pollution from growth, making good headway with CO 2 emissions from energy, and transport. The environmental impact of our own in- dividual behaviour is more closely linked to consumption expenditure than the econ- omy as a whole. • Focusing policy on the most important en- vironmental impacts associated with the use of particular resources, rather than on the total level of all resource use. • Increasing the productivity of material and energy use that are economically effcient by encouraging patterns of supply and de- mand, which are more effcient in the use of natural resources (the aim is to promote innovation and competitiveness) and in- vesting in areas such as energy effciency, water effciency and waste minimisation. 113 Renewable Energy and Sustainable Development • Encouraging and enabling active and informed individual and corporate consumers. On some climate change issues (such as global warming), there is no disagreement among the scientists. The greenhouse effect is unquestion- ably real; it is essential for life on earth. Water vapour is the most important GHG; next is carbon dioxide (CO 2 ). Without a natural greenhouse ef- fect, scientists estimate that the earth’s average temperature would be –18 o C instead of its present 14 o C. There is also no scientific debate over the fact that human activity has increased the concentration of the GHGs in the atmosphere (especially CO 2 from combustion of coal, oil and gas) (Leszek and Jakub, 2009). The greenhouse effect is also being amplified by increased concentrations of other gases, such as methane, nitrous oxide, and CFCs as a result of human emissions. Most scientists predict that rising global temperatures will raise the sea level and increase the frequency of intense rain or snowstorms. Climate change scenarios sources of uncertainty and factors influencing the future climate are: • The future emission rates of the GHGs. • The effect of this increase in concentration on the energy balance of the atmosphere. • The effect of these emissions on GHGs concentrations in the atmosphere, and • The effect of this change in energy balance on global and regional climate. Wastes Waste is defined as an unwanted material that is being discarded. Waste includes items being taken for further use, recycling or reclamation. Waste produced at household, commercial and industrial premises are control waste and come under the waste regulations. Waste Incineration Directive (WID) emissions limit values will favour efficient, inherently cleaner technologies that do not rely heavily on abatement. For existing plant, the requirements are likely to lead to improved control of: • NO x emissions, by the adoption of infur- nace combustion control and abatement techniques. • Acid gases, by the adoption of abate- ment techniques and optimisation of their control. • Particulate control techniques, and their optimisation, e.g., of bag flters and elec- trostatic precipitators. Lifecycle analysis of several ethanol feedstocks shows the emissions per ton of feedstock are high- est for corn stover and switchgrass (about 0.65 tons of CO 2 per ton of feedstock) and lowest for corn (about 0.5 ton). Emissions due to cultivation and harvesting of corn and wheat are higher than those for lignocellulosics, and although the lat- ter have a far higher process energy requirement (Figure 8). GHG emissions are lower because this energy is produced from biomass residue, which is carbon neutral. The waste and resources action programme has been working hard to reduce demand for virgin aggregates and market uptake of recycled and secondary alternatives (Figure 7). The pro- gramme targets are: • To deliver training and information on the role of recycling and secondary aggregates in sustainable construction for infuences in the supply chain, and • To develop a promotional programme to highlight the new information on websites. Sulphur in Fuels and Its Environmental Consequences Organic sulphur is bonded within the organic structure of the coal in the same way that sulphur 114 Renewable Energy and Sustainable Development is bonded in simple thio-organics, e.g., thiols. Sulphur contents of coals vary widely, and Table 10 gives some examples. Control of SO 2 Emissions Emissions will also, of course, occur from petroleum-based or shale-based fuels, and in heavy consumption, such as in steam raising. There will frequently be a need to control SO 2 emissions. There are, broadly speaking, three ways of achieving such control: • Pre-combustion control: involves carrying out a degree of desulphurisation of the fuel. • Combustion control: incorporating into the combustion system something capable of trapping SO 2 . • Post-combustion control: removing SO 2 from the fue gases before they are dis- charged into the atmosphere. Table 11 gives brief details of an example of each. The Control of NO x Release by Combustion Processes Emission of nitrogen oxides is a major topic in fuel technology. It has to be considered even in the total absence of fuel nitrogen if the temperature is high enough for thermal NO x , as it is in very many industrial applications. The burnt gas from the flame is recirculated in two ways: • Internally, by baffing and restricting fow of the burnt gas away from the burner, re- sulting in fame re-entry of part of it. • Externally, by diverting up to 10% of the fue gas back into the fame. Particles Some of the available control procedures for particles are summarised in Table 12. Figure 9 shows the variation of distribution factor with particle size. Figure 7. Comparison of thermal biomass usage options, CHP displacing natural gas as a heat source (Omer, 2009) Billion tones (Bton) Scenarios are (1) household, (2) commercial, (3) agriculture and (4) industrial Table 10. Representative sulphur contents of coals (Meffe et al, 1996) Source Rank Sulphur content (%) Ayrshire, Scotland Lancs. /Cheshire, UK S. Wales, UK Victoria, Australia Pennsylvania, USA Natal, S. Africa Bulgaria Bituminous Bituminous Anthracite Lignite Anthracite Bituminous Lignite 0.6 Up to 2.4 Up to 1.5 Typically 0.5 0.7 Up to 4.2 2.5 115 Renewable Energy and Sustainable Development Figure 8. The lifecycle energy balance of corn and Switchgrass reveal a paradox: corn, as an ethanol feedstock requires less energy for production, i.e., more of the original energy in starch is retained in the ethanol fuel. Nevertheless, the Switchgrass process yields higher GHG emissions. This is because most of the process energy for Switchgrass process is generated from biomass residue. 116 Renewable Energy and Sustainable Development Figure 9. The variation of distribution factor against particle size for coal undersizes in a classifier. The sizes correspond to mid-point for ranges (Omer, 2008c) Table 11. Examples of SO 2 control procedures (Meffe et al, 1996) Type of control Fuel Details Pre-combustion Fuels from crude oil Alkali treatment of crude oil to convert thiols, RSSR, disulphides; solvent removal of the disulphides Post-combustion Coal or fuel oil Alkali scrubbing of the flue gases with CaCO 3 /CaO Combustion Coal Limestone, MgCO 3 and/or other metallic compounds used to fix the sulphur as sulphates Table 12. Particle control techniques (Meffe et al, 1996) Technique Principle Application Gravity settlement Natural deposition by gravity of particles from a horizontally flowing gas, collection in hoppers Removal of coarse particles (>50 µm) from a gas stream, smaller particles removable in principle but require excessive flow distances Cyclone separator Tangential entry of a particle-laden gas into a cylindrical or conical enclosure, movement of the particles to the enclosure wall and from there to a receiver Numerous applications, wide range of particles sizes removable, from = 5 µm to = 200 µm, poorer efficiencies of collection for the smaller particles Fabric filters Retention of solids by a filter, filter materials in- clude woven cloth, felt and porous membranes Used in dust removal for over a century Electrostatic precipitation Passage of particle-laden gas between elec- trodes, application of an electric field to the gas, resulting in acquisition of charge by the particles and attraction to an electrode where coalescence occurs, electrical resistivity of the dust an important factor in performance Particles down to 0.01 µm removable, ex- tensive application to the removal of flyash from pulverised fuel (pf) combustion 117 Renewable Energy and Sustainable Development Ground Source Heat Pumps The ground is as universal as air and solar radiation (Mortal, 2002). Over the past twenty years, as the hunt for natural low-carbon energy sources has intensified, there has been an increased endeavour to investigate and develop both earth and ground water thermal energy storage and usage (Lund, Freeston, and Boyd, 2005). Geothermal energy solutions, although well known, are another in our armoury of renewable energy sources that are within our immediate grasp to use and integrate with an overall energy policy (Huttrer, 2001). For high temperature heat storage with tem- peratures in excess of 50 o C the particular concerns were: • Clogging of wells and heat exchangers due to fnes and precipitation of minerals. • Water treatment to avoid operational prob- lems resulting from the precipitation of minerals. • Corrosion of components in the groundwa- ter system. • Automatic control of the ground water system. Three main techniques that are used to ex- ploit the heat available are geothermal aquifers, hot dry rocks and GSHPs. Geothermal energy is the natural heat that exists within the earth and that can be absorbed by fluids occurring within, or introduced into the crystal rocks. Heat pump technology can be used for heating only, or for cooling only, or be ‘reversible’ and used for heat- ing and cooling depending on the demand. More generally, there is still potential for improvement in the performance of heat pumps. As consumers in less-developed countries increase their capacity of electricity and green power, developed nations are starting to realise the benefits of using low-grade thermal energy for green heat applications that do not require high-grade electricity. This shift will not only benefit renewable energies that are designed for space conditioning, but also will contribute to the global mix of green power and green heat capacity. Earth energy (also called geothermal or ground source heat pumps or GeoExchange), which transfers absorbed solar heat from the ground into a building for space heating or water heating. The same system can be reversed to reject heat from the interior into the ground in order to provide cooling. A typical configuration buries polyethylene pipe below the frost line to serve as the head source (or sink), or it can use lake water and aquifers as the heat medium (Omer, 2008c). Effects of Urban Density Compact development patterns of buildings can reduce infrastructure demands and the need to travel by car. As population density increases, transportation options multiply and dependence areas, per capita fuel consumption is much lower in densely populated areas because people drive much less. Few roads and commercially viable public transport are the major merits. On the other hand, urban density is a major factor that deter- mines the urban ventilation conditions, as well as the urban temperature. Under given circumstances, an urban area with a high density of buildings can experience poor ventilation and strong heat island effect. In warm-humid regions these fea- tures would lead to a high level of thermal stress of the inhabitants and increased use of energy in air-conditioned buildings (Reddy, Williams, and Johansson, 2007). However, it is also possible that a high-density urban area, obtained by a mixture of high and low buildings, could have better ventilation condi- tions than an area with lower density but with buildings of the same height. Closely spaced or high-rise buildings are also affected by the use of natural lighting, natural ventilation and solar energy. If not properly planned, energy for elec- tric lighting and mechanical cooling/ventilation may be increased and application of solar energy 118 Renewable Energy and Sustainable Development systems will be greatly limited. Table 13 gives a summary of the positive and negative effects of urban density. All in all, denser city models require more careful design in order to maximise energy efficiency and satisfy other social and develop- ment requirements. Low energy design should not be considered in isolation, and in fact, it is a measure, which should work in harmony with other environmental objectives. Hence, building energy study provides opportunities not only for identifying energy and cost savings, but also for examining the indoor and outdoor environment (Aroyeun, et al., 2009). Energy Efficiency and Architectural Expression The focus of the world’s attention on environmen- tal issues in recent years has stimulated response in many countries, which have led to a closer examination of energy conservation strategies for conventional fossil fuels. Buildings are im- portant consumers of energy and thus important contributors to emissions of greenhouse gases into the global atmosphere. The development and adoption of suitable renewable energy technol- ogy in buildings has an important role to play. A review of options indicates benefits and some problems (BS, 1989). There are two key elements to the fulfilling of renewable energy technology potential within the field of building design; first the installation of appropriate skills and attitudes in building design professionals and second the provision of the opportunity for such people to demonstrate their skills. This second element may only be created when the population at large and clients commissioning building design in particu- lar, become more aware of what can be achieved and what resources are required. Terms like passive cooling or passive solar use mean that the cooling of a building or the exploitation of the energy of the sun is achieved not by machines but by the building’s particular morphological organisation ((EFC, 2000). Hence, the passive approach to themes of energy savings is essentially based on the morphological articulations of the construc- tions. Passive solar design, in particular, can realize significant energy and cost savings. For a design to be successful, it is crucial for the designer to have a good understanding of the use of the building. Few of the buildings had performed as expected by their designers. To be more precise, their performance Table 13. Effects of urban density on city’s energy demand Positive effects Negative effects Transport: • Promote public transport and reduce the need for, and length of, trips by private cars. Infrastructure: • Reduce street length needed to accommodate a given number of inhabit- ants. • Shorten the length of infrastructure facilities such as water supply and sewage lines, reducing the energy needed for pumping. Thermal performance: • Multi-story, multiunit buildings could reduce the overall area of the build- ing’s envelope and heat loss from the buildings. • Shading among buildings could reduce solar exposure of buildings during the summer period. Energy systems: District cooling and heating system, which is usually more energy ef- ficiency, is more feasible as density is higher. Ventilation: • A desirable flow pattern around buildings may be obtained by proper ar- rangement of high-rise building blocks. Transport: • Congestion in urban areas reduces fuel efficiency of vehicles. Vertical transportation: • High-rise buildings involve lifts, thus increasing the need for electricity for the vertical transportation. Ventilation: • A concentration of high-rise and large buildings may impede the urban ventilation conditions. Urban heat island: • Heat released and trapped in the urban areas may in- crease the need for air conditioning. • The potential for natural lighting is generally reduced in high-density areas, increasing the need for electric lighting and the load on air conditioning to remove the heat result- ing from the electric lighting. Use of solar energy: • Roof and exposed areas for collection of solar energy are limited. 119 Renewable Energy and Sustainable Development had been compromised by a variety of influences related to their design, construction and opera- tion. However, there is no doubt that the passive energy approach is certainly the one that, being supported by the material shape of the buildings has a direct influence on architectural language and most greatly influences architectural expres- siveness (Lazzarin et al, 2002). Furthermore, form is a main tool in architectural expression. To give form to the material things that one produces is an ineluctable necessity. In architecture, form, in fact, summarises and gives concreteness to its every value in terms of economy, aesthetics, functionality and, consequently, energy efficiency (David, 2003). The target is to enrich the expres- sive message with forms producing an advantage energy-wise. Hence, form, in its geometric and material sense, conditions the energy efficiency of a building in its interaction with the environ- ment. It is, then, very hard to extract and separate the parameters and the elements relative to this efficiency from the expressive unit to which they belong. By analysing energy issues and strategies by means of the designs, of which they are an inte- gral part, one will, more easily, focus the attention on the relationship between these themes, their specific context and their architectural expres- siveness. Many concrete examples and a whole literature have recently grown up around these subjects and the wisdom of forms and expedients that belong to millennia-old traditions has been rediscovered. Such a revisiting, however, is only, or most especially, conceptual, since it must be filtered through today’s technology and needs; both being almost irreconcilable with those of the past. Two among the historical concepts are of special importance. One is rooted in the effort to establish rational and friendly strategic relations with the physical environment, while the other recognises the interactions between the psyche and physical perceptions in the creation of the feeling of comfort. The former, which may be defined as an alliance with the environment deals with the physical parameters involving a mixture of natural and artificial ingredients such as soil and vegetation, urban fabrics and pollution (Zuatori, 2005). The most dominant outside parameter is, of course, the sun’s irradiation, our planet’s primary energy source. All these elements can be measured in physical terms and are therefore the subject of science. Within the second concept, however, one considers the emotional and intellectual en- ergies, which are the prime inexhaustible source of renewable power (Anne et al, 2005). In this case, cultural parameters, which are not exactly measurable, are involved. However, they repre- sent the very essence of the architectural quality. Objective scientific measurement parameters tell us very little about the emotional way of perceiv- ing, which influences the messages of human are physical sensorial organs. The perceptual reality arises from a multitude of sensorial components; visual, thermal, acoustic, olfactory and kinaesthet- ics. It can also arise from the organisational quality of the space in which different parameters come together, like the sense of order or of serenity. Likewise, practical evaluations, such as useful- ness, can be involved too. The evaluation is a wholly subjective matter, but can be shared by a set of experiencing persons (Randal et al, 1998). Therefore, these cultural parameters could be dif- ferent in different contexts in spite of the inexorable levelling on a planet- wide scale. However, the parameters change in the anthropological sense, not only with the cultural environment, but also in relation to function. The scientifically measurable parameters can, thus, have their meanings very profoundly altered by the non-measurable, but describable, cultural parameters. However, the low energy target also means to eliminate any excess in the quantities of material and in the manufacturing process necessary for the construction of our built environment. This claims for a more sober, elegant and essential expression, which is not jeopardising at all, but instead enhanc- ing, the richness and preciousness of architecture, while contributing to a better environment from an aesthetic viewpoint (Yadav et al, 1997). Argu- 120 Renewable Energy and Sustainable Development ably, the most successful designs were in fact the simplest. Paying attention to orientation, plan and form can have far greater impact on energy performance than opting for elaborate solutions (EIBI, 1999). However, a design strategy can fail when those responsible for specifying materials for example, do not implement the passive solar strategy correctly. Similarly, cost-cutting exercises can seriously upset the effectiveness of a design strategy. Therefore, it is imperative that a designer fully informs key personnel, such as the quantity surveyor and client, about their design and be prepared to defend it. Therefore, the designer should have an adequate understanding of how the occupants or processes, such as ventilation, would function within the building (Lam, 2000). Thinking through such processes in isolation without reference to others can lead to conflicting strategies, which can have a detrimental impact upon performance. Likewise, if the design intent of the building is not communicated to its occupants, there is a risk that they will use it inappropriately, thus, compromising its performance. Hence, the designer should communicate in simple terms the actions expected of the occupant to control the building. For example, occupants should be well informed about how to guard against summer overheating. If the designer opted for a simple, seasonally adjusted control; say, insulated sliding doors were to be used between the mass wall and the internal space. The lesson here is that designers must be prepared to defend their design such that others appreciate the importance and interrelation- ship of each component (IEA, 2008). A strategy will only work if each individual component is considered as part of the bigger picture. Failure to implement a component or incorrect installation, for example, can lead to failure of the strategy and consequently, in some instances, the build- ing may not liked by its occupants due to its poor performance. Energy Efficiency Energy efficiency is the most cost-effective way of cutting carbon dioxide emissions and improve- ments to households and businesses. It can also have many other additional social, economic and health benefits, such as warmer and healthier homes, lower fuel bills and company running costs and, indirectly, jobs. Britain wastes 20 per cent of its fossil fuel and electricity use (Witte, et al., 2002). This implies that it would be cost-effective to cut £10 billion a year off the collective fuel bill and reduce CO 2 emissions by some 120 million tones. Yet, due to lack of good information and advice on energy saving, along with the capital to finance energy efficiency improvements, this huge potential for reducing energy demand is not being realised (Paul, 2001). Traditionally, energy utilities have been essentially fuel providers and the industry has pursued profits from increased volume of sales. Institutional and market arrange- ments have favoured energy consumption rather than conservation. However, energy is at the centre of the sustainable development paradigm as few activities affect the environment as much as the continually increasing use of energy. In addition, more than three quarters of the world’s consump- tion of these fuels is used, often inefficiently, by only one quarter of the world’s population. Without even addressing these inequities or the precious, finite nature of these resources, the scale of environmental damage will force the reduction of the usage of these fuels long before they run out (WB, 2003b). Throughout the energy generation process there are impacts on the environment on local, national and international levels, from opencast mining and oil exploration to emissions of the potent greenhouse gas carbon dioxide in ever increasing concentration. Recently, the world’s leading climate scientists reached an agreement that human activities, such as burning fossil fuels for energy and transport, are causing the temperature to rise. The Intergovernmental Panel 121 Renewable Energy and Sustainable Development on Climate Change has concluded that ‘‘the bal- ance of evidence suggests a discernible human influence on global climate’’. It predicts a rate of warming greater than any one seen in the last 10,000 years, in other words, throughout human history. The exact impact of climate change is difficult to predict and will vary regionally. It could, however, include sea level rise, disrupted agriculture and food supplies and the possibility of more freak weather events such as hurricanes and droughts. Indeed, people already are wak- ing up to the financial and social, as well as the environmental, risks of unsustainable energy generation methods that represent the costs of the impacts of climate change, acid rain and oil spills. The insurance industry, for example, concerned about the billion dollar costs of hurricanes and floods, has joined sides with environmentalists to lobby for greenhouse gas emissions reduction. Friends of the earth are campaigning for a more sustainable energy policy, guided by the principle of environmental protection and with the objec- tives of sound natural resource management and long-term energy security. The key priorities of such an energy policy must be to reduce fossil fuel use, move away from nuclear power, improve the efficiency with which energy is used and increase the amount of energy obtainable from sustainable, renewable sources (WB, 2004). Efficient energy use has never been more crucial than it is today, particularly with the prospect of the imminent introduction of the climate change levy (CCL). Establishing an energy use action plan is the es- sential foundation to the elimination of energy waste. A logical starting point is to carry out an energy audit that enables the assessment of the energy use and determine what actions to take. The actions are best categorised by splitting measures into the following three general groups: 1. High priority/low cost: These are normally measures, which require minimal investment and can be implemented quickly. The followings are some examples of such measures: A. Good housekeeping, monitoring energy use and targeting waste-fuel practices. B. Adjusting controls to match requirements. C. Improved greenhouse space utilisation. D. Small capital item time switches, thermo- stats, etc. E. Carrying out minor maintenance and repairs. F. Staff education and training. G. Ensuring that energy is being purchased through the most suitable tariff or contract arrangements. 2. Medium priority/medium cost: Measures, which, although involve little or no design, involve greater expenditure and can take longer to implement. Examples of such measures are listed below: A. New or replacement controls. B. Greenhouse component alteration, e.g., insulation, sealing glass joints, etc. C. Alternative equipment components, e.g., energy efficient lamps in light fittings, etc. 3. Long term/high cost: These measures require detailed study and design. They can be best represented by the followings: A. Replacing or upgrading of plant and equipment. B. Fundamental redesign of systems, e.g., com- bined heat and power (CHP) installations. This process can often be a complex experience and therefore the most cost-effective approach is to employ an energy specialist to help. 122 Renewable Energy and Sustainable Development Policy Recommendations for a Sustainable Energy Future Sustainability is regarded as a major consideration for both urban and rural development. People have been exploiting the natural resources with no consideration to the effects, both short-term (environmental) and long-term (resources crunch). It is also felt that knowledge and technology have not been used effectively in utilising energy re- sources (Mildred, and Trevor, 2009). Energy is the vital input for economic and social development of any country. Its sustainability is an important factor to be considered. The urban areas depend, to a large extent, on commercial energy sources. The rural areas use non-commercial sources like firewood and agricultural wastes (WB, 2003a). Sustainability is regarded as a major con- sideration for both urban and rural develop- ment. People have been exploiting the natural resources with no consideration to the effects, both short-term (environmental) and long-term (resources crunch). It is also felt that knowledge and technology have not been used effectively in utilising energy resources. Energy is the vital input for economic and social development of any country. Its sustainability is an important factor to be considered. The urban areas depend, to a large extent, on commercial energy sources. The rural areas use non-commercial sources like firewood and agricultural wastes. With the present day trends for improving the quality of life and sustenance of mankind, environmental issues are considered highly important (Felice and Alessio, 2010). In this context, the term energy loss has no significant technical meaning. Instead, the exergy loss has to be considered, as destruction of exergy is possible. Hence, exergy loss mini- misation will help in sustainability. In the process of developing, there are two options to manage energy resources: (1) End use matching/demand side management, which focuses on the utilities. The mode of obtaining this is based on economic terms. It is, therefore, a quantitative approach. (2) Supply side management, which focuses on the renewable energy resource and methods of utiliz- ing it. This is decided based on thermodynamic consideration having the resource-user tempera- ture or exergy destruction as the objective criteria. It is, therefore, a qualitative approach. The two options are explained schematically in Figure 10. The exergy-based energy, developed with supply side perspective is shown in Figure 11. The following policy measures had been iden- tified: • Clear environmental and social objectives for energy market liberalisation, includ- ing a commitment to energy effciency and renewables. • Economic, institutional and regulatory frameworks, which encourage the transi- tion to total energy services. • Economic measures to encourage utility investment in energy effciency (e.g., lev- ies on fuel bills). • Incentives for demand side management, including grants for low-income house- holds, expert advice and training, stan- dards for appliances and buildings and tax incentives. • Research and development funding for re- newable energy technologies not yet com- mercially viable. • Continued institutional support for new re- newables (such as standard cost-refective payments and obligation on utilities to buy). • Ecological tax reform to internalise exter- nal environmental and social costs within energy prices. • Planning for sensitive development and public acceptability for renewable energy. Energy resources are needed for societal devel- opment. Their sustainable development requires 123 Renewable Energy and Sustainable Development a supply of energy resources that are sustainably available at a reasonable cost and can cause no negative societal impacts. Energy resources such as fossil fuels are finite and lack sustainability, while renewable energy sources are sustainable over a relatively longer term. Environmental concerns are also a major factor in sustainable development, as activities, which degrade the environment, are not sustainable (Jeremy, 2005). Hence, as much as environmental impact is as- sociated with energy, sustainable development requires the use of energy resources, which cause as little environmental impact as possible. One way to reduce the resource depletion associated with cycling is to reduce the losses that accompany the transfer of exergy to consume resources by in- creasing the efficiency of exergy transfer between resources i.e. increasing the fraction of exergy Figure 11. Exergy based optimal energy model Figure 10. Supply side and demand side management approach for energy 124 Renewable Energy and Sustainable Development removed from one resource that is transferred to another (Erlich, 1991). As explained above, exergy efficiency may be thought of as a more accurate measure of energy efficiency that accounts for quantity and quality aspects of energy flows. Improved exergy efficiency leads to reduced exergy losses (WB, 2006). Most efficiency improvements produce direct environmental benefits in two ways. First, operating energy input requirements are reduced per unit output, and pollutants generated are correspondingly reduced. Second, consideration of the entire life cycle for energy resources and technologies suggests that improved efficiency reduces environmental impact during most stages of the life cycle (Dragana, 2008). Quite often, the main concept of sustainability, which often inspires local and national authorities to incorporate en- vironmental consideration into setting up energy programmes have different meanings in different contexts though it usually embodies a long-term perspective (WB, 2007). Future energy systems will largely be shaped by broad and powerful trends that have their roots in basic human needs. Combined with increasing world population, the need will become more apparent for success- ful implementation of sustainable development (White, and Robinson, 2008). Heat has a lower exergy, or quality of energy, compared with work. Therefore, heat cannot be converted into work by 100% efficiency. Some examples of the difference between energy and exergy are shown in Table 14. The terms used in Table 14 have the following meanings: Carnot Quality Factor (CQF) = (1-T o /T s ) (5) Exergy = Energy (transferred) x CQF (6) Where T o is the environment temperature (K) and T s is the temperature of the stream (K). Various parameters are essential to achieving sustainable development in a society. Some of them are as follows: • Public awareness • Information • Environmental education and training • Innovative energy strategies • Renewable energy sources and cleaner technologies • Financing • Monitoring and evaluation tools The development of a renewable energy in a country depends on many factors. Those important to success are listed below: 1. Motivation of the population The population should be motivated towards awareness of high environmental issues, rational use of energy in order to reduce cost. Subsidy programme should be implemented as incentives to install renewable energy plants. In addition, image campaigns to raise awareness of renew- able technology. 2. Technical product development Table 14. Qualities of various energy sources (Omer, 2008a) Source Energy (J) Exergy (J) CQF Water at 80 o C 100 16 0.16 Steam at 120 o C 100 24 0.24 Natural gas 100 99 0.99 Electricity/work 100 100 1.00 125 Renewable Energy and Sustainable Development To achieve technical development of renewable energy technologies the following should be ad- dressed: • Increasing the longevity and reliability of renewable technology. • Adapting renewable technology to house- hold technology (hot water supply). • Integration of renewable technology in heating technology. • Integration of renewable technology in ar- chitecture, e.g., in the roof or façade. • Development of new applications, e.g., so- lar cooling. • Cost reduction. 3. Distribution and sales Commercialisation of renewable energy technol- ogy requires: • Inclusion of renewable technology in the product range of heating trades at all levels of the distribution process (wholesale, and retail). • Building distribution nets for renewable technology. • Training of personnel in distribution and sales. • Training of feld sales force. 4. Consumer consultation and installation To encourage all sectors of the population to participate in adoption of renewable energy tech- nologies, the following has to be realised: • Acceptance by craftspeople, marketing by them. • Technical training of craftspeople, initial and follow-up training programmes. • Sales training for craftspeople. • Information material to be made available to craftspeople for consumer consultation. 5. Projecting and planning Successful application of renewable technologies also requires: • Acceptance by decision makers in the building sector (architects, house technol- ogy planners, etc.). • Integration of renewable technology in training. • Demonstration projects/architecture competitions. • Renewable energy project developers should prepare to participate in the carbon market by: ◦ Ensuring that renewable energy proj- ects comply with Kyoto Protocol requirements. ◦ Quantifying the expected avoided emissions. ◦ Registering the project with the re- quired offces. ◦ Contractually allocating the right to this revenue stream. • Other ecological measures employed on the development include: ◦ Simplifed building details. ◦ Reduced number of materials. ◦ Materials that can be recycled or reused. ◦ Materials easily maintained and repaired ◦ Materials that do not have a bad in- fuence on the indoor climate (i.e., non-toxic). ◦ Local cleaning of grey water. ◦ Collecting and use of rainwater for outdoor purposes and park elements. ◦ Building volumes designed to give maximum access to neighbouring park areas. ◦ All apartments have visual access to both backyard and park. 126 Renewable Energy and Sustainable Development 6. Energy saving measures The following energy saving measures should also be considered: • Building integrated solar PV system. • Day-lighting. • Ecological insulation materials. • Natural/hybrid ventilation. • Passive cooling. • Passive solar heating. • Solar heating of domestic hot water. • Utilisation of rainwater for fushing. Improving access for rural and urban low- income areas in developing countries through energy efficiency and renewable energies will be needed. Sustainable energy is a prerequisite for development. Energy-based living standards in developing countries, however, are clearly below standards in developed countries. Low levels of access to affordable and environmentally sound energy in both rural and urban low-income areas are therefore a predominant issue in developing countries. In recent years many programmes for development aid or technical assistance have been focusing on improving access to sustainable energy, many of them with impressive results. Apart from success stories, however, experi- ence also shows that positive appraisals of many projects evaporate after completion and vanishing of the implementation expert team. Altogether, the diffusion of sustainable technologies such as energy efficiency and renewable energies for cooking, heating, lighting, electrical appliances and building insulation in developing countries has been slow. Energy efficiency and renewable energy programmes could be more sustainable and pilot studies more effective and pulse releasing if the entire policy and implementation process was considered and redesigned from the outset. New fi- nancing and implementation processes are needed which allow reallocating financial resources and thus enabling countries themselves to achieve a sustainable energy infrastructure. The links be- tween the energy policy framework, financing and implementation of renewable energy and energy efficiency projects have to be strengthened and capacity building efforts are required. FUTURE RESEARCH DIRECTIONS Energy constitutes the motive force of the civiliza- tion and it determines, in a high degree, the level of economy development as a whole. Despite the increase use of different type of energy, particu- larly, renewable energy sources, fossil fuels will continue dominating the energy combinations in the world near future. However, oil reserves are declining and this situation would have a nega- tive impact in the future economic development of many countries all over the world. Climate change issues, the reduced world re- serves of fossils, and higher and higher fuel prices play an important role in the development of clean technologies, such as biohydrogen, biodiesel and bioethanol, for producing renewable energy. This research gathers and presents current research from across the globe in the study of clean energy resources, their production and developments. In Asia, the import energy dependency is ris- ing. Unless Europe can make domestic energy more competitive in the next 20 to 30 years, around 70% of the Asian’s energy requirements, compared to 50% today, will be met by imported products some of them from regions threatened by insecurity. Now, the energy requirements of the different countries are so high that, for the first time in the humanity’s history, there is a need to consider different types of available energy sources and their reserves to plan the economic development of the countries. At the same time, there is also a need to use these sources in the most efficient possible manner in order to sustain that development. 127 Renewable Energy and Sustainable Development Sustainable energy is the provision of energy such that it meets the needs of the present without compromising the ability of future generations to meet their needs. A broader interpretation may al- low inclusion of fossil fuels and nuclear fission as transitional sources while technology develops, as long as new sources are developed for future gen- erations to use. A narrower interpretation includes only energy sources, which are not expected to be depleted in a time frame relevant to the human race. Sustainable energy sources are most often regarded as including all renewable sources, such as biofuels, solar power, wind power, wave power, geothermal power and tidal power. It usually also includes tech- nologies that improve energy efficiency. This new and important handbook gathers the latest research from around the globe in the study of sustainable energy and highlights such topics as: monitoring sustainable energy development; methane; energy and territory; biodiesel production; electrochemi- cal hydrogen storage; environmental policies in an electricity sector and others). The move towards a de-carbonised world, driven partly by climate science and partly by the business opportunities it offers, will need the pro- motion of environmentally friendly alternatives, if an acceptable stabilisation level of atmospheric carbon dioxide is to be achieved. This requires the harnessing and use of natural resources that produce no air pollution or greenhouse gases and provides comfortable coexistence of human, livestock, and plants. This study reviews the energy-using technologies based on natural resources, which are available to and applicable in the farming industry. Integral concept for buildings with both excel- lent indoor environment control and sustainable environmental impact are reported in the present communication. CONCLUSION There is strong scientific evidence that the average temperature of the earth’s surface is rising. This is a result of the increased concentration of carbon dioxide and other GHGs in the atmosphere as re- leased by burning fossil fuels. This global warming will eventually lead to substantial changes in the world’s climate, which will, in turn, have a major impact on human life and the built environment. Therefore, effort has to be made to reduce fossil energy use and to promote green energies, particu- larly in the building sector. Energy use reductions can be achieved by minimising the energy demand, by rational energy use, by recovering heat and the use of more green energies. This article was a step towards achieving that goal. The adoption of green or sustainable approaches to the way in which society is run is seen as an important strategy in finding a solution to the energy problem. The key factors to reducing and controlling CO 2 , which is the major contributor to global warming, are the use of alternative approaches to energy generation and the exploration of how these alternatives are used today and may be used in the future as green energy sources. Even with modest assumptions about the availability of land, comprehensive fuel-wood farming programmes offer significant energy, economic and environmental benefits. These benefits would be dispersed in rural areas where they are greatly needed and can serve as linkages for further rural economic development. The nations as a whole would benefit from savings in foreign exchange, improved energy security, and socio-economic improvements. With a nine-fold increase in forest – plantation cover, a nation’s resource base would be greatly improved. The international community would benefit from pollution reduction, climate mitigation, and the increased trading opportunities that arise from new income sources. The non-technical issues, which have recently gained attention, include: (1) Environmental and ecological factors e.g., carbon sequestration, reforestation and revegetation. (2) Renewables as a CO 2 neutral replacement for fossil fuels. (3) Greater recognition of the importance of renewable energy, particularly modern bio- mass energy carriers, at the policy and planning 128 Renewable Energy and Sustainable Development levels. (4) Greater recognition of the difficulties of gathering good and reliable renewable energy data, and efforts to improve it. (5) Studies on the detrimental health efforts of biomass energy particularly from traditional energy users. ACKNOWLEDGMENT A special thanks to my spouse Kawthar Abdelhai Ali for her support and her unwavering faith in me. 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Sustainable De- velopment in the 21st Century.http://lnweb18. worldbank.org/ESSD/sdvext.nsf/43ByDocName/ SustainableDevelopmentint World Bank. (WB). (2007). World Bank Sus- tainable Development Reference Guide, http:// www. WorldBankSustainableDevelopmentRef- erenceGuide. 135 Renewable Energy and Sustainable Development KEY TERMS AND DEFINITIONS Renewable Energy: Renewable energy is energy generated from natural resources such as sunlight, wind, rain, tides, and geothermal heat, which are renewable (naturally replenished). Energy obtained from sources that are essentially inexhaustible (unlike, for example the fossil fuels, of which there is a finite supply). Energy sources that are, within a short time frame relative to the Earth’s natural cycles, sustainable, and include non-carbon technologies such as solar energy, hydropower, and wind, as well as carbon-neutral technologies. Solar Energy: Energy from the sun that is converted into thermal or electrical energy; “the amount of energy falling on the earth is given by the solar constant, but very little use has been made of solar energy”. Energy derived ultimately from the sun. It can be divided into direct and indirect categories. Most energy sources on Earth are forms of indirect solar energy, although we usually do not think of them in that way. Solar energy uses semiconductor material to convert sunlight into electric currents. Although solar energy only pro- vides 0.15% of the world’s power and less than 1% of US energy, experts believe that sunlight has the potential to supply 5,000 times, as much energy as the world currently consumes. Biomass Energy: The energy embodied in organic matter (“biomass”) that is released when chemical bonds are broken by microbial digestion, combustion, or decomposition. Biofuels are a wide range of fuels, which are in some way derived from biomass. The term covers solid biomass, liquid fuels and various biogases. Biofuels are gaining increased public and scientific attention, driven by factors such as oil price spikes and the need for increased energy security. Wind Energy: Kinetic energy present in wind motion that can be converted to mechanical en- ergy for driving pumps, mills, and electric power generators. Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to make electricity, wind mills for mechanical power, wind pumps for pumping water or drainage, or sails to propel ships. Hydropower: Hydropower, hydraulic power or waterpower is power that is derived from the force or energy of moving water, which may be harnessed for useful purposes. Hydropower is using water to power machinery or make elec- tricity. Water constantly moves through a vast global cycle, evaporating from lakes and oceans, forming clouds, precipitating as rain or snow, and then flowing back down to the ocean. Geothermal Energy: Geothermal power (from the Greek roots geo, meaning earth, and thermos, meaning heat) is power extracted from heat stored in the earth. This geothermal energy originates from the original formation of the planet, from radioactive decay of minerals, and from solar energy absorbed at the surface. Heat transferred from the earth’s molten core to under- ground deposits of dry steam (steam with no water droplets), wet steam (a mixture of steam and water droplets), hot water, or rocks lying fairly close to the earth’s surface. Resource Management: Efficient incident management requires a system for identifying available resources at all jurisdictional levels to enable timely and unimpeded access to resources needed to prepare for, respond to, or recover from an incident. Resource management is the efficient and effective deployment for an organization’s resources when they are needed. Such resources may include financial resources, inventory, hu- man skills, production resources, or information technology (IT). Sustainable Development: Development, which seeks to produce sustainable economic growth while ensuring future generations’ ability to do the same by not exceeding the regenerative capacity of the nature. In other words, it’s trying to protect the environment. A process of change in which the resources consumed (both social and ecological) are not depleted to the extent that they cannot be replicated. Environmentally friendly 136 Renewable Energy and Sustainable Development forms of economic growth activities (agriculture, logging, manufacturing, etc.) that allow the con- tinued production of a commodity without damage to the ecosystem (soil, water supplies, biodiversity or other surrounding resources). Environment: The natural environment, commonly referred to simply as the environment, encompasses all living and non-living things oc- curring naturally on Earth or some region thereof. The biophysical environment is the symbiosis be- tween the physical environment and the biological life forms within the environment, and includes all variables that comprise the Earth’s biosphere. Greenhouse Gases: Greenhouse gases are gases in an atmosphere that absorb and emit radiation within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The main greenhouse gases in the Earth’s atmosphere are water vapour, carbon dioxide, methane, nitrous oxide, and ozone. Changes in the concentration of certain greenhouse gases, due to human activity such as fossil fuel burning, increase the risk of global climate change. 137 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 4 DOI: 10.4018/978-1-61350-138-2.ch004 Fouad Kamel University of Southern Queensland, Australia Marwan Marwan Queensland University of Technology, Australia Demand-Side Response Smart Grid Technique for Optimized Energy Use ABSTRACT The chapter describes a dynamic smart grid concept that enables electricity end-users to be acting on controlling, shifting, or curtailing own demand to avoid peak-demand conditions according to informa- tion received about electricity market conditions over the Internet. Computer-controlled switches are used to give users the ability to control and curtail demand on a user’s premises as necessary, follow- ing a preset user’s preferences. The computerized switching provides the ability to accommodate local renewable energy sources as available. The concept offers further the ability to integrate charging electrical vehicles during off-peak periods, helping thus substantially improving the utilization of the whole electricity system. The approach is pursuing improved use of electrical energy associated with improved energy management, reduced electricity prices and reduced pollution caused by excessive use of combustion engine in transport. The technique is inherently restricted to take effect in frame of energy tariff regimes based on real-time price made to encourage and reward conscious users being proactively participating in holistic energy management strategies. 138 Demand-Side Response Smart Grid Technique for Optimized Energy Use INTRODUCTION The traditional user-supplier rapport in the elec- trical energy market has historically evolved following a strategy implying whenever a load is switched on it is expected to be fulfilled by the supplier at the expected time and quality. Grow- ing electrical demands followed by constantly growing supply led to troubled electrical services manifested mainly by daily and seasonal excessive peak and low demands. Those chronic peaks on electrical networks are usually associated with compromised quality, risk of forced outages and high-priced energy supply; while low-demands on the other side might be driving some power plants to be operating at critical economic vi- ability. Demand-side-response techniques are helping electricity users to become proactively participating in averting detrimental conditions presently prevailing in the electricity sector (Kamel, 2009b). Coordinated strategies shall help achieving improved use of electrical power plants and electricity infrastructure, besides in- tegrated use of different types of energy sources. (Chua-Liang Su & Kirschen, 2009) proposed a day-ahead market-clearing mechanism that allows consumers to submit complex bids. Those bids are expected to give consumers the opportunity to specify constraints on their hourly and daily consumptions in the same way as generators can specify the operating constraints on their generat- ing units. It is a day-ahead market with complex bids and offers whose objective is to maximize the social welfare. The social welfare is described as the difference between the value that consumers attach to the electrical energy that they buy and the cost of producing this energy. Not all consumers have the ability or the motivation to adjust their demand as a function of price. Part of the demand will therefore remain perfectly inelastic. There- fore, consumers were classified into two types, price-taking and price-sensitive. Price-taking is those consumers who have, in theory, an infinite marginal value as otherwise the consumers would have placed price responsive bids with a finite marginal value attached. Plant Capacity Factor The plant capacity factor (PCF) or the so also called utilization factor of a power plant is, by definition, the proportion of the actual electrical energy generated yearly by the plant to the quantity of electrical energy, which would be generated if the plant was operated at rated power for full year’s time (8760 hours) as reported by Brinkmann (1980). The factor has a direct influence on the energy cost as can be deduced from the following equation of the fixed charge method according to De-Meo (1978), Leonard (1977), Chobotov (1978) and Clorefeine (1980): c E = c tr FCR / (T o PCF) + c op (1) where c E is the cost of energy generated, c tr cost of installed power including taxes during the installation period, FCR fixed charge rate of the capital, normally 15…18% a year according to Leonard (1977) and Leonard (1978), T o =8760 (h) the hours per year, PCF plant capacity factor and c op the operation and maintenance cost of the plant. For plants operating 24 hour/day, 7 days a week, i.e. 8760 hour/year PCF is a unity, which produces the least possible energy cost and best economic conditions. For power plants operat- ing any less than 8760 hour/year the PCF will respectively be lower (below unity) what drives the cost of the produced energy to be accordingly higher, equation (1). Figure 1 illustrates the impact of the plant ca- pacity factor on the cost of the produced energy. The calculation is made on the basis of the cost of the installed power c tr = $1000/kW, capital fixed charge rate FCR = 0.17 and the operation and maintenance cost of the plant c op = $0.02/ kWh. It is evident that a power plant operated at low plant capacity factor e.g. PCF = 0.1 (this is 2.4 hour/day) will be producing energy at $150/ 139 Demand-Side Response Smart Grid Technique for Optimized Energy Use MWh, while operated continuously for 24 hour will produce energy at a cost of $25/MWh. Figure 1 depicts the importance of operating power plants and electrical network infrastructure at elevated plant capacity factor, close to the unity, in order to verify best economic perfor- mance. Various efforts on avoiding peak demands on the electrical network are mainly aiming at leveling demand throughout the year in order to achieve as high plant capacity factors as possible for all electrical power components. Additionally, leveling demands is pursued to avert or delay the urgency to expand generation capacity and net- work infrastructure to cope with consistently rising peak demands. Important methods to avert or delay peak demands are represented in demand- side response activities, both on the supplier and on the user’s side. Demand Side Response and Smart Grid Technologies Demand Side Response (DSR) Demand Side Response (DSR), as described by Albadi & El Saadany (2007) can be defined as the changes in electricity usage by end-use cus- tomers from their normal consumption patterns in response to changes in the price of electricity over time. Parvania & Fotuhi-Firuzabad (2010) describe DSR as tariff or program established to motivate change in electric consumption by end-use customers in response to change in the price of electricity over time. Further on, DSR programs provide means for utilities to reduce the power consumption and save energy, maximize utilizing the current capacity of the distribution system infrastructure, reducing or eliminating the need for building new lines and expanding the system as described by Dam, Mohagheghi & Stoupis (2008). Vos (2009) described demand response as an integral part of the smart grid, is a cost effective, rapidly deployed resource that provides benefits to utilities and customers. Some advantages of DSR according to Greening (2010) are: increased economic efficiency of the electricity infrastruc- ture, enhanced reliability of the system, relief of power congestions and transmission constraints, reduced energy prices and mitigated potential market power. Further on, demand response can help reduce peak demands and therefore reduce spot price volatility as illustrated by Nguyen (2010). In addition, Hyung Seon & Thomas (2008) Figure 1. Impact of the plant capacity factor on the cost of the produced energy (Kamel, 2009b) 140 Demand-Side Response Smart Grid Technique for Optimized Energy Use described demand-side-response participation would help electricity power markets operate in a more efficient way. Based on a review of current utility programs, the Electric Power Research Institute (EPRI) estimated that demand response has the potential to reduce peak demand in the U.S. by 45,000 MW as reported by Walawalkar, Blumsack, Apt & Fernands (2008). Therefore, the implementation of DSR programs is expected to improve economic efficiency in the electricity market. In the United Kingdom, various techniques have been used to develop load electricity man- agement. One of the methods is called responsive demand or demand side management program and was developed in the early 1960s (Hamidi, Li & Robinson, 2009). This system served to maintain the security of electricity supply and limited the facilities for electricity generation, transmission and distribution. This program has been partici- pating in improving the economy, security and reliability of the electricity industry as well as eliminating the environmental concerns (Hamidi, Li & Robinson, 2009). However, later in 2007 the British Government initiated the building of the “Energy Demand Research Project” which focused on the actual benefits of demand response for consumers (Torriti, Hassan & Leach, 2009). The British Government is currently con- sidering the economic benefits of the Demand Side Response program, as this system requires a high implementation cost. Besides that, the government must first conduct a reform of the electricity industry to support this program, for instance: by restructuring the electricity price and market, transmission and distribution as well as the retail sector. According to Torriti, Hassan & Leach (2009) much of the debate around the economic potential of Demand Response focuses on the actual benefits of DR for consumers, and it provides some benefits and weaknesses for both the government and the user. Hence, there are five technology specifications that can potentially compromise such as: a minimum meter specifi- cation, smart enables meters that substitute old meters, dumb meters combined with smart boxes, retrofit devices and clip-on costumer display unit (Torriti, Hassan & Leach, 2009). Similar to what has occurred in UK, in Finland, Interruptible Programmes as a part of demand side response model have been used as distur- bance reserve for several years (Torriti, Hassan & Leach, 2009). Utilisation of the demand response program is more effective to overcome peak load, breakdown and manage electricity supply to all customers. This plan is not just applied by small-costumers but also has been used by large- scale industry. Therefore, in 2005 total Demand Response potential in Finnish large-scale industry was estimated at about 1280 MW, which represents 9% of the Finnish power demand peak (Stam, 2005). Following that, in 2008 the Finnish main electricity utility invested in an advance metering reading system to automatically read, control and manage all 60,000 of its customer metering points (Torriti, Hassan & Leach, 2009). In Korea, the Demand Side Management program has been used for several years. In the 1970s, several programs were introduced in Load Management, for instance: night thermal-storage per rates program (1972), inverted block pro- gram (1974), the seasonal tariff (1977) and the time of use tariff (1977) (Jin-Ho, Tae-Kyung & Kwang-Seok, 2009). However, this program has not reached the maximum results to control load demand for peak demand sessions. Therefore, 2006, after the revision of the law, the government announced its 3 rd National Electricity Demand Forecast and Supply Plan which addressed the government’s main concerns about the Demand Side Management (Jin-Ho, Tae-Kyung & Kwang- Seok, 2009). In China, demand side management started from 1990s (Zhong, Kang & Liu 2010). In Australia, implementation of the DSR program has been conducted several years ago. In late 2002, the Energy Users Association of 141 Demand-Side Response Smart Grid Technique for Optimized Energy Use Australia (EUAA) conducted a trial to demonstrate the benefits of a DSR aggregation process which would enable electricity consumers to respond to both the extreme prices and extreme peak demand (Fraser, 2005). This experiment was conducted by end-users to determine the value of an effective DSR for electricity consumers and its impact in terms of supporting an energy saving program. This trial was supported by the Victorian, New South Wales and Commonwealth Government, as well as the CSIRO, to implement a Demand Side Response Facility Trial (Energy User Association of Australia Document, 2010). In the experiment described above, the Aus- tralian Government through the EUAA involved customer to participate in the DSR trial. This experiment was conducted in three regions that fall under the National Electricity Market op- eration, New South Wales, South Australia and Victoria (Jones, 2004). These areas are regarded to represent the electricity load in Australia, and the results obtained show some significant ben- efits of using DSR for consumer and electricity providers. Hence, in December 2003 the Minis- terial Council for Energy advised the Council of Australian Governments (COAG) on the need for further reform of the energy market to enhance active energy user participation (Jones, 2004). The energy users association of Australia tar- geting a demand-side-response action, according to Fraser (2005), summarizes that, for example, South Australian electricity consumers only use the highest 10% of their maximum electrical demand on the network less than 0.5% of the time per year, i.e., for about 40 hours per year. The report is stating further: while the electric- ity consumers are insulated from price volatility by ‘flat’ electricity prices, they are also paying a significant and undisclosed (hard to evaluate) premium in their retail electricity prices to cover the retail supplier’s costs of managing the risks of the extreme price volatility. Demand Side Response Models Many different economic models are used to represent Demand Side Response programs. In the report of the strategic plan of the International Energy Agency (2010) DSR is divided into two basic categories, namely the time based program and the incentives based program. According to Aalami H.A, Moghaddam M.P & Yousefi G.R (2008) the specific types of time based program are: time of use, real time pricing (RTP) and critical peak pricing; Federal Energy Regulatory Commission (2006) reports, while the specific types of incentive based program consist of di- rect load control (DLC), Interruptible/curtailable (I/C), demand bidding (DB), emergency demand response program (EDRP), capacity market (CAP) and ancillary service markets (A/S) programs. An overview of selected DSR models: I/C pro- gram, the EDRP, TOU and the proposed model, as presented in Figure 2. In the following a brief description of three popular market available models: I/C program, the EDRP and TOU. Interruptible and Curtailable Program The interruptible/Curtailable program has traditionally been one of the most common demand-side-management (DSM) tools used by electric-power utilities, which customers sign an interruptible-load contract with a utility to reduce their demand at a fixed time during the system’s peak-load period or at any time requested by the utility (Yu, Zhang, Chung & Wong, 2005). This service provides incentives/rewords to customers participating to curtail electricity demand. The electricity provider sends directives to the user for following this program at certain times. The user must obey those directives to curtail their electricity when being notified from the utility or face penalties. For example: the customer must curtail their electricity consumption starting from 6:00 pm – 7:00 pm; those customers who are fol- lowing will get a financial bonus/reword to their 142 Demand-Side Response Smart Grid Technique for Optimized Energy Use electricity bill from the utility. In California the incentive of I/C program was $700/MWh/month in 2001 as reported in (Aalami H.A, Moghaddam M.P & Yousefi G.R, 2009). Emergency Demand Response Program Emergency demand response program is energy- efficient program that provides incentives to customers who can reduce electricity usage for a certain time; this is usually conducted at the time of limited availability of electricity. According to Covino (2003) emergency demand response pro- gram provide participant with significant intensive to reduce load. To participate on this program, all customers are expected to reduce their energy consumption during the events. Tyagi & Black (2010) described this program will determine which houses must be included in the event to minimize cost and disruption, while alleviating the overload condition. When asked to curtail, and verified to have performed, the resource is paid the higher of $500/MWh (Rahimi & Ipakchi, 2010). In New York, emergency demand response program allows participant to be paid for reducing Figure 2. Models of DSR programs: a) Interruptible/Curtailable, b) Emergency Demand Response, c) Time Of Use and d) the Proposed Model (Marwan & Kamel, 2010b) 143 Demand-Side Response Smart Grid Technique for Optimized Energy Use their energy consumption upon notice from the New York Independent System Operator that an operating reserves deficiency or major emergency exists (Lawrence & Neenan, 2003). Time of Use Program According to Na & Ji-Lai (2006) Time of Use is one of the important demand side management methods, TOU demand side will response to the price and will change the shape of the demand curve. Further on, Time of Use rate is the most obvious strategy developed for the management of the peak demand in the world, which is designed to encourage the consumer to modify the pattern of electricity usage (Wen-Chen, Yi-Ping & Tzu- Hao, 2007). For applying this program, the utility does not provide reward or penalty to customer. To participate, all customers are required to remove their energy consumption during peak session to off-peak session as soon as their receipt informa- tion from the utility. Kirschen suggested (2003) in this type of contract, the rate is fixed for the duration of the contract but depends on the time of the day. As compared to the flat rate contract, some of the risk is shifted from the retailer to the consumer because the consumer has an incentive to consume during periods when the rates are lower. Calculation of Energy Consumption for Maximized Benefit Different models are used in Demand Side Re- sponse program planning as described by the Federal Energy Regulatory Commission (2006). In the report of the strategic plan of the International Energy Agency (2010), DSR is divided into two basic categories, namely, the time based program and the incentives based program. In Aalami H.A, Moghaddam M.P & Yousefi G.R (2008) the fol- lowing approach is used to calculate the savings in electricity expenditure based on price, demand, incentives and costumer benefits associated with the DSR program used. The change in energy consumption ∆d(t) at the time t when the user changes demand from d(t) to do(t) is: ∆d(t)= d(t)- do(t) (2) For participating in the DSR program, the total incentives P∆d(t), when A(t) is paid as incentive to the costumer at the time t for each kWh load reduction, can be calculated as the following: P(∆d(t))=A(t).∆d(t) (3) The total penalty PEN·Δd(t) when the consumer does not commit to the obligations as a member of the DSR program, pen(t) is the penalty per kWh at the time t and D(t) is the DSR program contract level of consumption in kWh, will be accounted as the following: PEN·(Δd(t))=pen(t).{D(t)-[d(t)-do(t)]} (4) The total customer’s benefit S a member of the DSR program can make at a certain time t is made up of income and expenditures. The contract could be mentioning a benefit from joining the program so that e.g.B(d(t)) is the customer income during that period from the use of d(t) kWh, at the same time the customer could be receiving additional incentives P(∆d(t)) as described in Equation(2). The cost of the consumed electricity and any penalty for not following the program, if applicable, will be deducted from the income as the following: S=B(d(t))+P(Δd(t))-d(t).r(t)-PEN(Δd(t)) (5) where,r(t) is the rate the customer pays per kWh electricity at that time. 144 Demand-Side Response Smart Grid Technique for Optimized Energy Use To maximize the customer benefit the slope ∂S/∂d(t) should be equal to zero, accordingly: ∂ ∂ = ∂ ∂ + ∂ ∂ − − ∂ ∂ = S d t B d t d t P d t d t r t PEN d t ( ) ( ( )) ( ) ( ( )) ( ) ( ) ( ) ∆ 0 (6) This leads to: ∂ ∂ = − + B d t d t r t A t pen t ( ( )) ( ) ( ) ( ) ( ) (7) The benefit function most often used according to Schweppe, Caramanis, Tabors & Bohn (1988) is the quadratic benefit function: ∂ = + − + − B d t Bo t ro t d t do t d t do t t do t ( ( )) ( ) ( ).{ ( ) ( )}. ( ) ( ) ( ) ( ) 1 2β (8) Where: Bo(t) Benefit when d(t) =do(t) ($) ro(t) Nominal rate for electricity consumption ($/kWh) β(t) Elasticity parameter β( , ) ( ) ( ) . ( ) ( ) t h ro h do t d t r h = − ∂ ∂ (9) The elasticity parameter β is a unit-less factor indicating how strong the energy demand depends on energy price, i.e. the effect the energy price on demand. The multiplier ro h do t ( ) ( ) helps transforming the parameter into a unit-less factor by referring to initial known conditions. By differentiating Equation (8) and solving for ∂ ∂ B d t d t ( ( )) ( ) and substituting the result in (7) r t A t pen t ro t d t do t t do t ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) − + = + − 1 2β (10) When the customer is participating in a DSR program, the customer consumption d(t) for a maximized benefit can be calculated from Equa- tion (10) as the following: d t do t t t r t ro t A t pen t ro t ( ) ( ) ( , ) [ ( ) ( ) ( ) ( ) ( ) = + − − + 1 β (11) Integration Renewable Energy Sources and Electricity Vehicles to DSR Smart Grid System Integrating renewable energy with power genera- tion is a new way to improve reliability, sustain- ability and cost effectiveness on the electrical network. According to Hammons (2006) the key challenges that need to be considered in the composition of future network include distributed generation and the integration of renewable energy sources, such as biomass, wind and solar. The utilization of renewable energy is expected to be leading to the harmony between humans and nature with low pollution and sustainable accessibility to resources as described in Figure 3. Some countries have applied smart grid tech- nology for renewable energy utilization. In Japan, using solar power generation systems in every ordinary house is the most active project in smart grid researches as described by Li & Yao (2010). The significant amount of installed wind power in the German power system in 2008 produced more than 22 GW producing between 1500 - 7700 GWh/month as reported in Hammons (2006). On the other hand, electricity vehicles (EV) technology brings impacts to the electrical distri- bution grid. According to Clement-Nyns, Haesen & Driesen ((2010) the vehicle can not only charge, but also discharge and thus inject energy to the 145 Demand-Side Response Smart Grid Technique for Optimized Energy Use grid. In addition, there are social, environmental and economic advantages in switching to elec- tricity vehicles as described by Anna Cain, Iain MacGill & Bruce (2010). The User’s DSR Concept This concept helps developing the technical tools to be independently implemented and managed by end-users to enable control energy consumption accustomed to user’s preferences. The proposed DSR Smart-Grid scheme is targeting flattening load profiles by averting periods of peak de- mands helping thus redistributing the load profile throughout the day/year. The scheme helps electri- cal generating plants and electrical infrastructure to be operated 24 hour/day achieving thus higher utilization factor, enhanced efficiency and con- siderably reduced energy price. The presented user’s side DSR concept is providing the needed balance in the electrical system to complement the efforts undertaken by suppliers to mitigate peak demands and improve supply reliability and stability, Figure 4. The concept is presenting a low-cost DSR technique implemented at user’s premises, which assists electricity end-users to be shifting loads around the clock averting peak-demand periods and making use of on-site renewable energy sources as appropriate. This shall help users to be engaged in mitigating peak demands on the elec- tricity network. The proposed concept comprises a technical set-up of a programmable internet relay, a router, solid state switches in addition to the suitable software to control electricity demand, Figure 5. The software’s on appropriate multime- dia tool (CD Rom) offers users optimized control of energy consumption. The concept enables commercial and indus- trial customers on fluctuating energy prices to be achieving immediate financial savings. For resi- dential customers on flat-rate tariffs, in contrast, users are gaining financial benefits from reducing energy consumptions at peak-demand periods. Residential customers on different tariffs, where energy price differs with day time and network conditions (e.g. night tariffs), they are gaining financial benefits also from shifting loads from day- to night-times, when electricity is cheaper. The scheme uses a router and a programmable internet relay and solid-state switches to control electrical demand at the user’s premises. The relay Figure 3. Smart grid network diagram (Energy Efficiency and Conservation Authority, 2009) 146 Demand-Side Response Smart Grid Technique for Optimized Energy Use Figure 4. The proposed user’s smart grid demand-side-response scheme (DSR) balancing conventional supplier’s smart grid DSR programs Figure 5. The user’s DSR concept 147 Demand-Side Response Smart Grid Technique for Optimized Energy Use is programmed to receive and act upon information received from the AEMO on the internet about demand/price conditions. Figure 6 illustrates the control regime, where three appliances are con- trolled by three solid-state switches receiving on/ off signals from the relay. Consumers use local computers to set-up their preferences for appliance profile usage and pri- orities, e.g. Table 1. The profile of appliances identifies when an appliance is run according to electricity price or network conditions (national demand). Pursuant to the order from the relay to a solid-state switch, household appliances con- nected to that switch can be turned on/off. All control systems above are implemented by a shell script under a Linux operation system. Figure 7 shows the pseudo code of the controller that is executed with each interaction. Table 1 illustrates an example of an appliance profile. All control systems above is implement- ed by a shell script under a Linux operation system. ELECTRICITY INDUSTRY DEVELOPMENT IN AUSTRALIA (CASE STUDY) In Eastern and Southern states of Australia the Australian Energy Market Operator is manag- ing the power flow across the Australian Capital Territory, New South Wales, Queensland, South Australia, Victoria and Tasmania. The AEMO is regularly updating energy demand and prices current situations publicly on the internet. The presented concept is using programmable internet relays and controllable electronic switches to be proactively responding to demand/price peaks and congestions conditions. The technique is globally valid in other electricity markets under similar operating conditions. Figure 8 depicts an example of an actual energy demand and prices situation. The price curve is closely following the demand curve. Electricity prices are typically at their lowest level at night during times of low demand (off-peak). Prices are rising daily according to two Figure 6. Control Regime Table 1. Example of appliance profile Appliance Start After Finish Before Session Time Kettle 08.00 AM 04.00 PM Off-peak Session Washing Machine 06.00 AM 10.00 AM Off-peak Session Air Condition 06.00 AM 04.00 PM Off-peak Session 148 Demand-Side Response Smart Grid Technique for Optimized Energy Use major peak demands in the morning and evening. It is to be noted that electricity prices in Figure 8 are wholesale regional references prices (RRP) i.e. prices traded to electricity suppliers. Electrical energy at this stage still needs to be transmitted to the different localities then distributed to end- users. End-users could be industrial, commercial or residential. Usually industrial and commercial end-users are contracting electricity suppliers on special agreements to provide the service satis- fying their requirements. For most residential electricity customers, electricity pricing typically follow one set price “flat-rate”. Residential users are often also offered a night tariff, where elec- tricity prices are substantially reduced. The night tariff corresponds off-peak times. Figure 9 illustrates the frequency of electric- ity demand supplied in Queensland during the year 2008 as extracted from data of the Australian Energy Market Operator (2009). The figure indi- cates mainly the fact that the higher the load above the base load the lesser likely the extent of their duration will be. Base load power stations are those operated twenty four hours/day throughout the year corresponding to 8760 h/year, a utiliza- tion factor of 1. Those power stations are provid- ing the most economic operation at the least possible energy price. Any loads exceeding the base load are usually covered by other power plants operated for shorter periods of time at utilization factor lesser than 1, thus generating energy at high prices. Accordingly, the intermittent operation of the expensive to-run power plants makes their operation even more expensive. Figure 10 illustrates the occurrence of the regional reference wholesale price RRP in Queensland during the year 2008; extracted from the Australia Energy Market Operator (2009). The figure indicates mainly that low-priced supplies are taking place at very high occurrences of more than 80% a year, while high prices happen at lower occurrences. For instance, prices around AUD $20/MWh are occurring at frequencies of about 80%, while prices of over $50/MWh have occurrences of less than 10%. Based on data of 31 December 2008, Queensland total electricity generating capacity was 12487 MW; coal-fired power stations pro- Figure 7. Pseudo code of the control loop 149 Demand-Side Response Smart Grid Technique for Optimized Energy Use Figure 8. Wholesale electricity price in AUD $/MWh and demand in MW for a typical day in Queensland on 5th May 2009(Australia Energy Market Operator, 2009) Figure 9. Occurrence of electrical energy demand Queensland during 2008. Peak demand 8413 MW, base-load 4100 MW and total supplied electrical energy 52.18 TWh (Kamel, 2009b) 150 Demand-Side Response Smart Grid Technique for Optimized Energy Use vided 70% of this total capacity, while gas-fired electricity accounted for 17% and renewable energy accounted for around 5% as stated by the Department of Employment Economic Develop- ment and Innovation (2010). These power gen- erations are used to provide electrical energy for all consumers in the Queensland area: residential, commercial and industrial. However, the amounts of energy produced from various generators de- pend on market demand, price and availability of sources. Figure 11 illustrates electricity generation in Queensland according to the Department of Employment Economic Development and Innova- tion (2010). Most of the power stations are directly con- nected to the transmission system. The Queensland electricity transmission system is provided by Powerlink, licensed to operate more than 12,000 kilometres of Queensland high voltage transmis- sion network, transporting electricity from the generators to the distribution networks as by (Department of Employment Economic Develop- ment and Innovation, 2009). The distribution network is carrying electricity from the transmis- sion system to consumers. In Queensland, EN- ERGEX and ERGON energy are purchasing electrical energy from the Energy Market and distributing it to the customer. ERGON e.g. pro- vides energy at several tariff options to end users. For example, Tariff 11 for all domestic consump- tion 18.84 ¢/kWh, while the night rate Tariff 31 for all consumption 7.7 ¢/kWh and the economy Tariff 33 for all consumption 11.32 ¢/kWh (Ergon Energy, 2010). According to Queensland Competition Au- thority (2000), the total energy consumption in Australian grew at an annual rate of 2.6% for the 25 years to 1997/1998. In the 2007- 2008 period according to Department of Employment Economic Development and Innovation (2009a) the annual electricity consumption in Queensland has grown by over 29% or approximately 10500 GWh, making Queensland the second highest consumer of electricity in Australia. This indicated that Queensland has a significantly greater number Figure 10. Electricity wholesale price RRP in Queensland in 2008 (Kamel, 2009b). 151 Demand-Side Response Smart Grid Technique for Optimized Energy Use of high energy users than any other state, most of these in regional Queensland. Narayan & Smith (2005) describes since the beginning of the 1990s, Australia’s electric power industry has undergone a series of structural reforms. In Queensland, the electricity industry was restructured on 1 July 1998 to prepare the industry for participating in the competitive Na- tional Electricity Market, which is responsible for structure, rules and regulations in the delivery of energy to customers (Department of Employment Economic Development and Innovation, 2009b). The National Electricity Market Management Company (NEMMCO) Limited was the Whole- sale Market and Power System Operator for the Australian NEM. NEMMCO was established in 1996 to administer and manage the NEM, develop the market and continually improve its efficiency and as of 1 July 2009 was replaced by the Aus- tralian Energy Market Operator. To improve governance, and enhance the reli- ability and sustainability of the State’s electricity system, the Australian Government has created a collaborative electricity and gas industry in the form of the Australian Electricity Market Opera- tor (Australian Energy Market Operator, 2010), which commenced operation on 1 July 2009. The AEMO is managing power flows across the Australian Capital Territory, New South Wales, Queensland, South Australia, Victoria and Tasma- nia. Western Australia and the Northern Territory are not currently connected to this market primarily because of their geographic distance from the rest of the market. AEMO’s responsibilities include wholesale and retail energy market operation, infrastructure and long term market planning demand forecasting data and scenario analysis as described in (Australian Energy Market Opera- tor, 2010). The electricity market comprises of a wholesale sector and a competitive retail sector. All electricity dispatched in the market must be traded through the central spot market. The Market structure of NEMMCO / AEMO can be presented as in Figure 12. Figure 11. Electricity generation in Queensland (Department of Employment Economic Development and Innovation, 2010) 152 Demand-Side Response Smart Grid Technique for Optimized Energy Use Figure 12. The Market structure of NEMMCO/AEMO (Department of Resources Energy and Tourism, 2009) Figure 13. Fluctuation of electricity price in Queensland (Marwan & Kamel, 2010a) 153 Demand-Side Response Smart Grid Technique for Optimized Energy Use Marwan & Kamel (2010a) summarized in Figure 13 an example of classic fluctuations in electricity price in Queensland, from 22 May 2008 to 22 May 2009. This graph illustrates that the average price during that time was in the range of $50/MWh (¢5/kWh) Regional Reference Wholesale Price (RRP), however, extreme prices occurred exceeding $500/MWh (¢50/kWh). The graph indicates also that excessive demands are occurring regularly in all states on the intercon- nected power network. Fraser (2005) stated that customers, even those bound by flat-rate contracts, must bear the additional cost for managing the corresponding extreme prices. Controlled Scenario Using the User’s DSR Scheme In order to evaluate the effect of the proposed scheme on electricity energy saving the electricity price/demand in Queensland for the period 10 th - 12 nd May 2010 has been used. In the following, ten scenarios have been formulated to demonstrate the results as presented in Figure 14 and sum- marized in Table 2. Scenario 1, In this scenario users are shifting 375 MWh peak electricity usage occurring be- tween 17:00 pm-19:00 pm towards the time pe- riod 19:00 pm-21:30 pm when energy demand and prices are low. All participants are suggested to set-up the electricity profile to stop chosen appliance from running during that time. For example, kettle, washing machine and air condi- tion could be effectively operated at optional times of the day. No savings in energy cost due to ap- plicable day-time tariffs. However, the scheme was still able to remove congestions out of peak demand areas. Scenarios 2, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 pm to the period between 21:30 pm to 23:30 pm. Achievable savings $21149 per day. Scenario 3, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 Figure 14. Controlled Scenarios 154 Demand-Side Response Smart Grid Technique for Optimized Energy Use pm to the period between 23:30 pm to 01:00 am. Achievable savings $28200 per day. Scenario 4, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 pm to the period between 01:00 am to 03:00 am. Achievable savings $28200 per day Scenario 5, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 pm to the period between 03:00 am to 05:30 am. Achievable savings $28200 per day Scenario 6, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 pm to the period between 05:30 am to 07:00 am. Achievable savings $28200 per day Scenario 7, Users are shifting peak demand of 375 MWh occurring between 17:00 pm-19:00 pm to the period between 06:30 am to 10:30 am. Achievable savings $3525 per day Scenario 8, Users are shifting peak demand of 1730 MWh occurring between 10:30 am-19:30 pm. All participants are suggested to set-up the electricity profile to stop some appliance to run during this time. User can run chosen appliances between 19:30 pm to 23:30 pm. Achievable sav- ings in energy cost $48785. Scenario 9, Users are shifting peak demand of 1730 MWh occurring between 10:30 am-19:30 pm to the period between 23:30 pm to 01:30 am. Achievable savings $130096 per day. Scenario 10, Users are shifting peak demand of 1730 MWh occurring between 10:30 am-19:30 pm to the period between 01:30 am to 04:00 am. Achievable savings $130096 per day. Economic Model While the concept is designed to be targeting flat- tening the national electrical demand throughout the year the concept involves an economic model based on the maximization of financial benefits to electricity users. The scheme is applicable in regions managed by the Australian Energy Man- agement Operator (AEMO) and other regions under similar conditions. Usually the electricity price is high during peak demands and low at off-peak periods. The concept allows customers controlling consumption to avoid peak demands periods. In case the user is on other DSR program with the supplier, the scheme is still allowing ad- ditional savings besides the benefits and saving already achievable through the DSR agreement. For commercial and industrial customers on fluctuating energy prices implementing the scheme will enable achieving immediate financial savings. For residential customers on flat-rate tariffs, in Table 2. Results of some scenarios Scenario NR Time to Curtail Load Time to Reconnect Load Load to Curtail Day Tarrif 18.84 ¢kWh Night Tarrif 11.32 ¢kWh Saving ($) 1 17.00 pm to 19.00 pm 19:00 pm to 21:30 pm 375 70650 NA NA 2 21:30 pm to 23:30 pm 375 70650 49501 21149 3 23:30 pm to 1:00 am 375 70650 42450 28200 4 1:00 am to 3:00 am 375 70650 42450 28200 5 3:00 am to 5:30 am 375 70650 42450 28200 6 5:30 am to7:00 am 375 70650 42450 28200 7 6:30 am to 10:30 am 375 70650 67125 3525 8 10.30 am to 19.30 pm 19:30 am to 23:30 am 1730 325923 277147 48785 9 23:30 pm to 01:30 am 1730 325923 195836 130096 10 1.30 am to 4:00 am 1730 325923 195836 130096 155 Demand-Side Response Smart Grid Technique for Optimized Energy Use contrast, users are gaining financial benefits from reducing energy consumptions at certain times a day; mainly averting peak-load periods or using off-peak night tariffs. Multimedia Tool The concept includes a multimedia tool (CD- Rom) run on local computers at user’s premises to allow implementing and operating the DSR model continuously. The CD-Rom is containing an introductory part to address the electricity peak demand issue to the user, a programming part, where the user will be recording operation profiles for the different appliances and an execu- tive part, where the information is transferred to the programmable relay, which on turn sending signals to electronic switches to operate the dif- ferent appliances. Significance Figure 15 shows customers fully curtailing energy withdrawals at any energy price above $55/MWh as example. Figure 16 shows achievable energy savings in Queensland by curtailing energy de- mand over a certain energy prices. Referring to Figure 16, the technique is able to remove 6.1 TWh/year from a total of 52.18 TWh/year if users are setting switches to curtail own loads at any regional reference prices above $50/MWh; this is a percentage of 11.7% of the total demand. In case users chose to curtail loads at $40/MWh, the savings will be 11.1 TWh/year; a percentage of 21.2%, and 24.8 TWh/year at a $30/MWh curtailment; a 47.5%. Figure 17 depicts the case where coordinated strategies are able to lead customers to defer loads from times of peak-demand to times of low- demands. Such a procedure shall help flatten the total energy demand to meet a constant average of 5941 MW for Queensland, achieving considerable improvement in the system utilization and thus in the whole system economics. In such a procedure the technique enables deferring 3.26 TWh/year from peak to off-peak times. Queensland Government (2009) is describing: transport is the fourth largest source of Queensland’s greenhouse gas emissions, contrib- uting 10.4 per cent to Queensland’s total emission profile and the Queensland Government will invest Figure 15. Day electricity demand curtailed for wholesale regional reference price not to exceed AUD $55/MWh in Queensland in 2008 (Kamel 2009a) 156 Demand-Side Response Smart Grid Technique for Optimized Energy Use $1.4 million to undertake a trial of low-emission diesel-electric buses in the public transport fleet. The Department of Resources Energy and Tourism (2009) is indicating 1359 PJ (377.5 TWh) were used for transport in Australia in 2006-07 while 1695 PJ (460.83 TWh) for electricity generation (1TWh = 3.6 PJ) as illustrated in Figure 18. The technique offers further the present elec- trical supply system to be supplying the transport sector for the use of charging electric vehicles at low-demand times (at night). Figure 19 depicts the possibility to utilize 21.52 TWh/year of elec- trical capacity, mainly of peak-load power stations, otherwise not used. The procedure helps enhanc- Figure 16. Achievable energy savings by curtailing energy demand over a certain energy prices in Queensland (Kamel, 2009a) Figure 17. Occurrence and average electrical energy demand Queensland (Kamel, 2009a) 157 Demand-Side Response Smart Grid Technique for Optimized Energy Use ing the utilization of present electrical power stations to approach a plant capacity factor close to the unity, achieving thus an optimal use of power plants. FUTURE RESEARCH DIRECTION For future research direction on DSR method, more development of modeling both on-site renewable energy sources and electricity vehicles connected to the distribution grid on the Australian national electricity market, will be considered as follows: Figure 18. Energy consumption in Australia (Department of Resources Energy and Tourism, 2009) Figure 19. Electrical energy demand Queensland Vs maximum utilization of generating capacity (Ka- mel, 2009a) 158 Demand-Side Response Smart Grid Technique for Optimized Energy Use • Optimization of on-site renewable energy sources to distribution grid under DSR method in Australian national electricity market. • Deployment of plug-in electricity vehicles and their impacts to the Australian national electricity market. CONCLUSION The concept is aiming to achieve moderated energy demand, reduced energy prices and curbed price volatility, improved grid usability and reliability, and reduced energy consumption. The concept is making use of the internet and modern com- munication technologies to maximize benefit for users and suppliers. Additionally, the concept is providing additional capacity more quickly and more efficiently than new supplies. The flexibility provided lowers the likelihood and consequences of forced outages as well. 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KEY TERMS AND DEFINITIONS Smart Grid: is a form of electricity network utilizing digital and computer technology. A smart grid delivers electricity from suppliers to consumers using two-way digital communications to control appliances at consumers’ homes; this saves energy, reduces costs and increases reli- ability and transparency. Market Conditions: are characteristics of electricity market, such as electricity price and de- mand, which could be introduced to all customers. Switch: is an electrical component that can break an electrical circuit, interrupting the cur- rent or diverting it from one conductor to another. On-Site Renewable Energy: is an energy sources generated from natural resources, such as biodiesel, photovoltaic and wind. These energies are provided by customers. Electrical Vehicle: is as an electric driven vehicle, uses one or more electric motors for propulsion. Electric vehicles include electric cars, electric trains, electric lorries, electric airplanes, electric boats, electric motorcycles and scooters and electric spacecrafts. Electrical Generation: is the process of creat- ing electricity from other forms of energy. Energy Management: is a system of com- puter-aided tools used by operators of electric utility grids to monitor, control, and optimize the performance of the generation and/or transmis- sion system. 164 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 5 INTRODUCTION Energy is a vital issue for human society and also an important topic for economical development. Energy consumption has physically started with the industrial revolution. In the initial phase of the industrial revolution, steam machine has been utilized to obtain power by using coal. Because of the hard structure of steam machine and environ- mentally negative effects of coal, new fossil fuels emerged such as gas and crude oil. Comparing with the coal, gas has provided cleaner burning power Selcuk Cebi Karadeniz Technical University, Turkey Cengiz Kahraman Istanbul Technical University, Turkey İhsan Kaya Yıldız Technical University, Turkey Soft Computing and Computational Intelligent Techniques in the Evaluation of Emerging Energy Technologies ABSTRACT The global warming and energy need requires developing emerging energy technologies for the electric- ity, heat, and transport markets. The emerging energy technologies aim at increasing effciency of energy utilization processes from energy sources and diminish CO 2 exhalation. The main aim of the chapter is to exhaustively present soft computing and computational intelligent techniques in the evaluation of emerging energy technologies. In the scope of the chapter, classifcation of emerging energy technolo- gies, their application trends in the literature, a brief explanation for soft computing and computational intelligent techniques, and literature survey of related techniques on both emerging energy technologies and energy planning are included. Moreover, technique for order performance by similarity to ideal solution, analytic hierarchy processes, and their fuzzy structures are introduced. DOI: 10.4018/978-1-61350-138-2.ch005 165 Soft Computing and Computational Intelligent Techniques plants and cleaner heating of homes. In addition, crude oil made possible new transportation options such as road vehicle and aircraft by invention of the internal combustion engine (Vanek and Albright, 2008). Nowadays, fossil fuels play an important role in the transport and stationary. However, it is thought that current energy systems are not sustain- able since most of the world primary energy use is from fossil fuels (Kajikawa et al., 2007). There are two serious hazards with fossil fuels; the first one is that the production of fossil fuel has been predicted to diminish at the middle of this century (Kajikawa et al., 2007; Jefferson, 2006) and the other is that fossil fuels have caused emission of greenhouse gases into the atmosphere and also global warming. Global warming and fossil fuel depletion are two of the most important issues of this century. The considerations of energy security and climate change force increased societal interest in technologies that enable a reduction in the use of fossil fuels. It has been well-recognized that an effective solution to these issues is to develop non-carbon-dioxide-emitting and inexhaustible energy resources and energy technologies (Chen et al., 2009). Recently, discovering of nuclear power have provide both to diminish our dependence on fossil fuel resources, and also to provide electricity without any emissions of harmful air pollutants. Although nuclear power is cleaner than many other forms of energy production and although nuclear energy can be produced in large quanti- ties over short periods of time, nuclear power generates harmful radiation and throwing out of nuclear waste which is produced by nuclear power plants is difficult and expensive. Negative effects of both fossil and nuclear technology, renewable energy technologies became more advanced and the range of their applications became broader (Vanek and Albright, 2008). Therefore, sustainable and renewable energy sources such as sun, wind, geothermal, biomass, wave etc. and emerging energy technologies have been attracted greater interest as an important concept while energy planning of a country. In addition, it is thought that it is an urgent need to develop highly ef- ficient energy utilization processes from energy sources effectively and substitute energy sources since the emerging energy technologies are still in an early phase of development (Jacobsson and Bergek, 2004; Kajikawa et al., 2007). Therefore, recent budgets for governmental research and development (R&D) for energy technologies have increased to support emerging energy re- searches (Hultman and Koomey, 2007). Moreover, European Union is committed in supporting the development of emerging energy technologies, in improving the use of renewable energy, and in increasing the energy efficiency, to reach global objectives of sustainability, competitiveness, and security of energy supply (Segurado et al., 2009). When any investment or design decision about energy systems is required, a number of goals or criteria that are local, regional, or global must be taken into account. It is possible to classify these into three categories; (1) Physical goals which meet physical requirements that make it possible for the system to operate. (2) Financial goals which are monetary objectives related to the energy system. (3) Environmental goals which are the objectives related to the way in which the energy system im- pacts the natural environment. Regional or global impacts include the emissions of greenhouse gases that contribute to climate change, air pollutants that degrade air quality and physical effects from extracting resources used either for materials or energy (Vanek and Albright, 2008). Therefore, the emerging technologies have high degree of uncertainty and it represents the large variety of opportunities that a new technology has to offer. This uncertainty creates opportunities for inves- tors to engage in emerging technologies. Thus, the relation between uncertainty and the decision of investors to engage in emerging technologies is very complex (Mejer et al., 2007). Furthermore, traditional techniques or conventional (hard) computing models may not present an effective solution dealing with the problems in which the dependencies between variables are complex or 166 Soft Computing and Computational Intelligent Techniques ill-defined. And, these solutions may not satisfy the decision-makers’ expectations. The selection of the most suitable sustainable energy technol- ogy for implementation is a complex problem that includes multiple conflicting goals or criteria. In particular, the difficulties dealing with information about qualitative criteria such as social, cultural etc. during the evaluation of many conflicting cri- teria makes the problem complex. For example, a new energy technology may need to provide good value for money, low maintenance costs, while at the same time having a large and stable energy output and positive social and environmental effects. Multicriteria decision making methods (MCDM) among the soft computing methods are useful and effective tools in order to take into ac- count simultaneously all the basic aspects of the decision making problems while other decision- support tools, such as cost–benefit analysis are not well effective (Burton and Hubacek, 2007; Karakosta et al., 2010). Therefore, soft computing (SC) and computational intelligent (CI) techniques have been widely used in the literature to solve complex problems. SC and CI techniques which are based on copying ability of human mind under uncer- tainty and imprecision are emerging approaches (Konar, 2007). The main characteristics of SC are representation and processing of human mind and knowledge, qualitative and approximate reasoning, computing with words, and biologi- cal models of problem solving and optimization, and are directly related to intelligent systems and applications (Karray and Silva, 2004). In this re- spect, these techniques differ from the respective conventional computing techniques in that they are tolerant of imprecision, uncertainty, partialtruth, and approximation. The soft computing techniques comprises of fuzzy logic, artificial neural net- works, probabilistic reasoning and meta-heuristic techniques such as genetic algorithm, tabu search, etc. (Altun and Yalcinoz, 2008). The main aim of this section is to introduce the most known and the most used SC and CI techniques for complex problems in emerging energy technologies and energy science that cannot be satisfactorily solved using conventional crisp computing techniques. In particular, multicriteria decision making methods dealing with decision making problems in emerg- ing energy technologies and energy science have been emphasized. The organization of the chapter is as follows: Section 2 presents the classification of emerging energy technologies. Section 3 introduces the most known MCDM techniques in the literature. Section 4 includes the most used MCDM methods (AHP and TOPSIS) and information axiom, newly presented to literature. Section 5 presents the lit- erature survey for emerging energy technologies. The trends for the emerging energy technologies and SC and CI techniques are given. Finally, concluding remarks are given in Section 5. EMERGING ENERGY TECHNOLOGIES The emerging energy technologies (EETs) are classified into six main groups in terms of usage area. These are building technology, industry technology, transportation technology, coal technology, non-conventional fuel technology, and biomass technology. The classification is presented in Figure 1(Lee et al., 2009). Emerg- ing energy technologies for building includes lighting, air conditioning, building envelop, and building system technologies. Industrial emerg- ing energy technologies are classified into waste heat technologies, common technologies, and petroleum refinery and fine chemical technolo- gies. Transportation technologies involve fuel efficiency improvement technologies, hybrid electronic technologies, electric, hydrogen fuel cell, and biodiesel technologies. Coal emerging energy technologies are classified into direct uti- lization technology and conversion technologies. Non-conventional fuel technologies are oil shale/ oil sand technologies and gasification technolo- 167 Soft Computing and Computational Intelligent Techniques gies of waste. Biomass technologies are direct utilization and conversion technologies. Figure 2 and Figure 3 presents the trends for emerging energy technologies based on years and application areas of EETs, respectively. The years between 1990 and 2010 are divided into four periods as 1990-1995, 1996-2000, 2001-2005, and 2006-2010 and numbers of publications in SCI index are analyzed. Figure 2 presents the attractiveness of emerging energy technologies in the literature while Figure 3 presents the most attractive years for each technology. According to Figure 2, biomass technology is the most attractive topic for researchers between the years 1990-1995. In the same period, building technology is the second attractive topic. Although the attractiveness of biomass technology is the first at the second period, its popularity decreas- es and the popularity of building and coal tech- nologies have increased according to previous period. At the third period, while the popularity of biomass has continues, the popularity of non- conventional fuel, transportation, and industry technologies have increased. Finally, the popular- ity of coal and transportation technologies have dramatically increases at the last period. According to the Figure 3, popularity of the each emerging energy technology has been clearly increasing year by year except for non- conventional fuel technology. SOFT COMPUTING AND COMPUTATIONAL INTELLIGENT TECHNIQUES Soft computing (SC) and computational intelligent (CI) techniques are used to obtain the closest solu- tions to computationally-hard problems. The basis of the SC and CI techniques are founded on bio- logical or behavioral phenomena related to humans or animals, and analogues of these technologies Figure 1. Classification of EETs 168 Soft Computing and Computational Intelligent Techniques exist in many human and animal systems (Uhrig and Tsoukalas, 1999). SC and CI techniques are vitally practical tools for many complex problems since they can tolerant of imprecision, uncertainty, partial truth, and approximation. However, tra- ditional hard computing methods are often too cumbersome for complex problems. They need a precisely stated analytical model and often a lot of computational time (Zadeh, 1965). Following the hardware technology advances, SC and CI techniques have been intensely studied and im- proved in the last years, and nowadays practical applications become a reality. Such techniques present several advantages when compared to traditional ones, such as: (i) acquisition of better results in the optimization processes when no prior knowledge is available, (ii) possibility of application to problems to which the conventional Figure 2. The popularity of EETs with respect to years Figure 3. Trends for EETs 169 Soft Computing and Computational Intelligent Techniques methods are not suitable, (iii) simulation of hu- man cognition processes, instead of trying to solve deterministically what is not deterministic (Schirru et al, 1999). The term “soft computing and computational intelligence” in its broadest sense, encompasses a number of technologies that includes, but is not limited to, artificial neural networks (ANN), genetic algorithms (GA), fuzzy logic models, ant colony techniques (AC), tabu search (TS), expert systems (ExS), multicriteria decision making methods etc. These are the well known soft computing and computational intelligence techniques in the literature. Beside of these techniques, genetic programming (GP), artificial immune system (AIS), harmony search (HS), scatter search (SC), variable neighborhood search (VNS), pattern search (PS), differential evolution (DE), evolutionary programming (EP), evolutionary strategies (ES), simulated anneal- ing (SA), particle swarm optimization (PSO), swarm intelligence (SI) etc. are the relatively new developed tools. However, these techniques are currently not as popular especially with regard to the emerging energy technology. Thus, only the main tools are briefly highlighted in this section. The artificial neural networks (ANN) were first introduced by McCulloch et al. (1943), who suggested that the biological function of the human brain could be emulated by a simplified computational model (Saridakis and Dentsoras, 2008). The technique is a computational model and it is inspired of biological neural networks. The ANNs are structured with a set of inter con- nected layers, each of them composed of nodes; the typology of connections and nodes (called neurons) characterizes the different typologies of neural networks (Bertini et al. 2010). Outputs of neurons in a given layer are the inputs of neurons in the next layer. First and last layers are called input and output layers, respectively, while those in between are hidden layers. Neurons are character- ized by a transfer function, which is applied to an appropriate function of inputs. The main advantage of ANN is that it does not need any mathemati- cal model, since it learns from historical data to recognize non-evident relations and patterns in a set of input–output variables, without any prior assumption about their nature (Pena et al., 2010). The structure of ANN is given in Figure 4. Genetic algorithms (GAs) are global search and optimization techniques motivated by the process of natural selection in biological system (Gen and Cheng, 2000; Kaya, 2009). GA as a field of study was initiated and developed in the early 1970’s by John Holland (Holland, 1975, 1992) and his students, but its applications to real-world practical problems was almost three decades in developing. GA approaches are good at solving the ill-posed problems such as non- convex functions, non-differentiable functions, domains not connected, badly behaved functions, multiple local optima, and multiple objectives Figure 4. The structure of ANN 170 Soft Computing and Computational Intelligent Techniques (Miranda et al., 1998). The main advantages of GA is that it present an approximate solution in relatively short time compared with other random searching methods, such as simulated annealing or dynamic programming (Won and Park, 2003). The first population of GA is a randomly selected initial solution set. To obtain an optimum solution, a search is conducted by moving from the initial population of individuals to a new population using genetics-like operators such as selection, crossover and mutation, which are inspired from the mechanics of natural selection and genetics encountered in natural life. Each individual rep- resents a candidate to the optimization solution and is modeled by a value called chromosome. The GA operators perform task on the chromo- some, in the reproduction process, in order to produce new generations so that solution at the global optimum may be obtained. The operation is based on a selective nature, i.e. the best candi- dates in terms of fitness are chosen as parent so that the new generation holds best genetic heritage. For this purpose, a fitness function assigns a fit- ness value to each individual within the population. This fitness value is the measure for the quality of an individual. The basic optimization procedure involves nothing more than processing highly fit individuals in order to produce better individuals as the search progresses. A typical genetic algo- rithm cycle involves four major processes of fitness evaluation, selection, recombination and creation of a new population. Based on fitness criterion, poorer performing individuals are gradually taken out, and better individuals have a greater possibility of conveying genetic informa- tion to the next generation (Altun and Yalcinoz, 2008). The cycle of GA is illustrated in Figure 5. Ant colony (ACO) which is used for solving combinatorial optimization problems is a coop- erative search algorithm inspired by the behavior of ants in finding paths from the nest to food (Yang and Zhuang, 2010). In the early 1992, ACO was proposed to literature as a metaheuristic optimiza- tion tool as by Dorigo (1992). High concentrations of pheromones indicate more favorable paths that other members should follow in order to reach the optimal solution (Al-Rashidi and El-Hawary, 2009). ACO is based on the indirect communica- tion of a colony of simple agents, called ants, mediated by (artificial) pheromone trails. The pheromone trails in ACO serve as distributed, numerical information which the ants use to Figure 5. The cycle of genetic algorithms (Konar, 2000) 171 Soft Computing and Computational Intelligent Techniques probabilistically construct solutions to the problem being solved and which the ants adapt during the algorithm’s execution to reflect their search ex- perience (Dorigo and T. Stützle, 2003). Tabu search (TS) is another algorithm which is used for the solution of combinatorial optimization problems like the traveling salesman problem. TS method originally proposed by Fred Glover (Glover, 1986) is based on neighborhood search procedure such that the algorithm iteratively moves from a solution to another solution in the related neighborhood, until it reaches any stopping criterion. The basic principle of TS is to pursue lo- cal search whenever it encounters a local optimum by allowing non-improving moves; cycling back to previously visited solutions is prevented by the use of memories, called tabu lists, which record the recent history of the search (Grandeu, 2003). TS is a powerful algorithmic approach that has been applied with great success to many difficult combinatorial problems. The best feature of TS is that it easily handle complicating constraints. Thus, TS heuristics generally find good solutions very early in the search. Both depth and breadth need to be achieved in the searching process. Although depth is usually not a problem for TS, breadth can be a critical issue (Gendreau and Potvin, 2010). MCDM techniques are also known as SC and CI techniques. MCDM techniques are classified into two groups as Multiple Objective Decision Making (MODM) and Multiple Attribute Deci- sion Making (MADM). The difference between MADM and MODM is that MADM is associated with problems of which numbers of alternatives have been predetermined. The Decision Maker (DM) is to select/rank a finite number of courses of action. On the other hand, MODM is not associated with the problems in which alternatives have been predetermined (Lai and Hwang, 1994). In other words, MODM techniques present optimization of an alternative or alternatives on the bases of prioritized objectives while MADM techniques present selection of an alternative from a set of alternatives based on prioritized attributes of the alternatives. MCDM Techniques The well-known and the most used MADM tech- niques in the literature are Analytic Hierarchical Process (AHP) (Saaty, 1980), Technique for Order Performance by Similarity to Ideal Solu- tion (TOPSIS) (Hwang and Yoon, 1981), Simple Additive Weighting method (SAW) (Hwang and Yoon, 1981), Elimination By Aspects (EBA) (Tversky, 1972), ELimination and Choice Ex- pressing REality (ELECTRE) (Bernard, 1968), Preference Ranking Organisation METHod for Enrichment Evaluations (PROMETHEE) (Brans and Vincke, 1985). Besides these methodologies, relatively new decision making methodologies such as information axiom method (Suh, 1990), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) (Opricovic and Tzeng, 2004) etc. or integrated methods like Hierarchical TOP- SIS (Kahraman et al, 2007), have been proposed to solve complex decision making problems (Cebi and Kahraman, 2010a). In the literature, there are also fuzzy MCDM techniques such as fuzzy TOPSIS (Chen, 2000), fuzzy AHP (Buckley, 1985, Chang, 1996; Laarhoven and Pedrycz, 1983), fuzzy VIKOR (Opricovic and Tzeng, 2004), fuzzy information axiom (Kulak and Kahraman, 2005a; 2005b; Kulak et al., 2005; Kahraman and Cebi, 2009) etc. in order to make decision makers cope with incomplete and vague information. In this chapter AHP, TOPSIS, Fuzzy AHP, Fuzzy TOPSIS and information axiom among the MCDM techniques are presented. Analytic Hierarchy Process The analytic hierarchy process (AHP) is based on pairwise comparisons. This provides an advantage when there is no any quantitative information about the problem. The mains steps of the AHP is as follows (Önüt and Soner, 2008); 172 Soft Computing and Computational Intelligent Techniques Step 1. The pairwise comparison matrix is constructed. Let C 1 ,C 2 ,…,C n symbolize a set of elements, while a ij represents a quantified judg- ment on a pair of elements C i and C j . The relative importance of two elements is rated using a scale with the values 1, 3, 5, 7 and 9, where refers to “equally important”, “slightly more important”, “strongly more important”, “demosrably more important”, and “absolutely more important”, respectively (Saaty, 1980). This produces a n×n square matrix A as follows: A a C C C a a a a a a ij n n n n n = 1 2 12 1 12 2 1 2 1 1 1 1 1 1 . (1) where a ij =1 when i=j, and a ij =1 / a ij for i,j=1,2,…,n. Step 2. The comparison matrix is normalized and weights are obtained. A a t a t a t a t a t a t n n n n n n = 1 1 1 12 2 1 21 1 2 1 1 2 2 (2) t a j ij i n = = ∑ 1 (3) where i and j represents row and column number, respectively. Then, a set of numerical weights, w 1 , w 2 , …, w n are obtained by averaging of rows. Step 3. The consistency analysis is done; A w w i i * * max = λ (4) and the consistency index is obtained as follows: CI n n = − − ( ) max λ 1 (5) CR CI RI = (6) where RI represents the average consistency index over numerous entries of same order reciprocal matrices (Saaty, 1980). If CR≤0.1the matrix is accepted as consistent, otherwise the evaluation procedure is repeated until consistency is satisfied. TOPSIS Method In TOPSIS method, the distance to both positive and negative ideal solution is calculated and an alternative is the best if the alternative has the shortest distance from the positive ideal-solution and the longest distance from the negative-ideal solution (Yoon and Hwang, 1981). The TOPSIS method can be summarized as follows (Önüt and Soner, 2008): Let A 1 ,A 2 ,…,A j be the j different alternatives. For alternative A j the rating of the ith aspect is denoted by f ij which is the value of the ith criterion function for the alternative A j , and n is the number of the criteria. Then Step 1. The normalized decision matrix is obtained by; r f f ij ij ij j n = = ∑ 2 1 , j=1,2,…,J and i=1,2,…,n (7) Step 2. The weighted normalized value v ij is calculated as: v w r ij i ij = ∗ j=1,2,…,J and i=1,2,…,n (8) where w i is the weight of the ith attribute or cri- terion, and 173 Soft Computing and Computational Intelligent Techniques w i i n = ∑ = 1 1. (9) Step 3. The positive ideal solution A*and the negative ideal solution A - are determined as: A v v v i I v i I i j ij j ij ∗ ∗ ∗ = = { ∈ ∈ } { , ..., } (max ), (min ) ' '' 1 (10) A v v v i I v i I i j ij j ij − − − = = { ∈ ∈ } { , ..., } (min ), (max ) ' '' 1 (11) where I’ is a set of benefit criteria and I’ is a set of cost criteria. Step 4. The distance to positive ideal solution is calculated by; D v v j ij i i n ∗ ∗ = = − ∑ ( ) 2 1 , j=1,2,…,J (12) Similarly, the distance to the negative-ideal solution is obtained by; D v v j ij i i n − − = = − ∑ ( ) 2 1 , j=1,2,…,J (13) Step 5. The relative closeness coefficient of the alternative A j is defined by; C D D D j j j j ∗ − ∗ − = + , j=1,2,…,J (14) Step 6. The alternatives are ranked with respect to closeness coefficients. Fuzzy Analytic Hierarchy Process In the literature, there are at least three different fuzzy AHP algorithms. The first algorithm in fuzzy AHP was proposed by van Laarhoven and Pedrycz (1983), which compared fuzzy ratios described by triangular membership functions. Then, Buckley (1985) presented fuzzy priorities of comparison ratios whose membership functions trapezoidal. And the last one is proposed by Chang (1996) with the use of triangular fuzzy numbers for pairwise comparison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic ex- tent values of the pairwise comparisons. In this chapter, Buckley’s (1985) fuzzy AHP approach is presented in detail. Step 1. Pairwise comparison matrices are constructed. Each element( c ij ) of the pairwise comparison matrix (C) is a linguistic terms pre- senting which is the more important of two cri- teria. The pairwise comparison matrix is given by; … … … C c c c c c c k n n n n = 1 1 1 12 1 21 2 1 2 , k=1,2,3,…,K (15) where C k is a pairwise comparison matrix belongs to k th expert for FR m . For the evaluation procedure, the linguistic terms given in Table 1a are used. Arithmetic mean is used to aggregate expert opinions. Step 2. Weights are calculated. At first, the fuzzy weight matrix is calculated by Buckley’s Method as follows (Hsieh et al., 2004); r c c c i i i in n = ⊗ ⊗ ⊗ ( ... ) / 1 2 1 (16) w r r r r i i n = ⊗ + + + − ( ... ) 1 2 1 (17) where r i is the geometric mean of fuzzy com- parison value and w i indicated by triangular fuzzy numbers w L M U i i i i ( , , ) is fuzzy weight of i th criterion. 174 Soft Computing and Computational Intelligent Techniques Step 3. After the fuzzy relative weight matrix is obtained, defuzzification process which converts a fuzzy number into a crisp value is utilized. At first, fuzzy numbers will be defuzzified into crisp values and then normalization procedure will be applied. For the defuzzification process, centroid method, which provides a crisp value based on the center of the gravity, is selected since it is the most commonly used method (Opricovic and Tzeng, 2004). w w w L M U w i i j j n i i i j j n = = + + = = ∑ ∑ 1 1 (18) Fuzzy TOPSIS Fuzzy TOPSIS methodology consists of four main steps which are listed below (Chen, 2000): Step 1. Evaluation values are normalized be- cause of two different scales. To avoid the com- plicated normalization formula used in classical TOPSIS, the linear scale transformation is used to obtain normalized fuzzy decision matrix de- noted by R . R r r a c b c c c ij mxn ij ij j ij j ij j = ⇒ = [ ] , , * * * (19) where c c j i ij * max = if criterion is benefit. Other- wise, if criterion is cost, following equation is used. r a c a b a a ij j ij j ij j ij = − − − , , where a a j i ij − = min (20) Step 2. The weighted normalized fuzzy deci- sion matrix is constructed as follows: V v i m j n v r w ij mxn ij ij j = = = = [ ] , , , , , , . 1 2 1 2 (21) Step 3. Then, the distances (d i * , d i − ) of each alternative from fuzzy positive-ideal solution (FPIS, A*) and fuzzy negative-ideal solution (FNIS, A - ) are calculated, respectively. A v v v where v A v v v n j n * * * * * ( , , ...., ) ( , , ) ( , , ...., ) = = = − − − − 1 2 1 2 1 1 1 wwhere v j − =( , , ) 0 0 0 (22) d d v v i m d d v v i m i ij j j n i ij j j * * ( , ) , , , ( , ) , , , = = = = = − − ∑ 1 1 2 1 2 == ∑ 1 n (23) Table 1a. Linguistic scale for weight matrix (Hsieh et al., 2004) Linguistic scales Scale of fuzzy number (1,1,3) Equally important (Eq) (1,3,5) Weakly important (Wk) (3,5,7) Essentially important (Es) (5,7,9) Very strongly important (Vs) (7,9,9) Absolutely important (Ab) 175 Soft Computing and Computational Intelligent Techniques Step 4. A closeness coefficient (CC i ) is calcu- lated by using d i * and d i − in Equation (10). CC d d d i m i i i i = + = − − * , , , 1 2 (24) The alternatives are ranked via CC i . An alter- native which is closest to the FPIS (A*) and the farthest from FNIS (A - ) among all alternatives is the best alternative. CC i value of the best alterna- tive is the biggest and it approaches to 1. Information Axiom Information axiom is the second axiom of the axiomatic design methodology and it is used for decision making tool. The second axiom is used to select the best alternative when two or more alternatives satisfy the first axiom. The informa- tion axiom states that the alternative having the highest probability of success is the best design. In another word, the alternative having the least information content is the best (Suh, 2001). In- formation content (I j ) is defined in terms of prob- ability of satisfying FR j (p j ), where j th functional requirement. The information content is given by Equation(25). I p j j = log 2 1 (25) The logarithmic function is chosen so that the information content can be additive when there are many FRs that must be satisfied simultane- ously (Suh, 1990). If there is more than one FR, the information content of a system (I system ) is calculated by Equation 26. I p p system j j m j j m = − = = = ∑ ∑ log log ( / ) 2 1 2 1 1 (26) The probability of success (p j ) is calculated by Equation 27 (Figure 6). p common range system range = (27) where system range and common range are defined by the area of system range and by the intersection area of the system range and design range which is determined by a functional requirement of the design, respectively. Kulak and Kahraman (2005a, 2005b) devel- oped the information axiom to be used under fuzzy environment for the solution of the complex decision making problems. The main difference Figure 6. System, design and common ranges 176 Soft Computing and Computational Intelligent Techniques between the conventional information axiom and the fuzzy information axiom is that the fuzzy in- formation axiom uses fuzzy numbers. Kulak et al. (2005) developed unweighted and weighted multi attribute axiomatic design approaches includ- ing both crisp and fuzzy criteria and applied the methodology to an equipment selection problem. Kulak (2005) developed a decision support system for the selection of a material handling system. Then, Kahraman and Cebi (2009) extended the usability of the fuzzy information axiom for vari- ous decision making problems. LITERATURE SURVEY FOR EMERGING ENERGY TECHNOLOGIES In this section, a literature survey has been pre- sented. At first, the general applications of SC and CI techniques and trends on energy problems in last five years are presented. Then, the applications on EETs have been given. The literature survey is divided into two categories since the applica- tions of SC and CI techniques on the evaluation of emerging energy technologies do not yield a huge material in the literature; one of them is the studies related to MCDM and the other is related to rest of SC and CI techniques. Some studies for the last five years deal with the applications of SC and CI techniques on energy planning have been given in Table 1. Table 2 presents the applications of SC and CI techniques on EETs. The number of presented publications on energy problems does not include all in the literature. Since we aimed to demonstrate the usefulness and possible ap- plications of SC and CI techniques, the papers published in last five years are presented. Except MCDM methods, the other SC and CI techniques are widely used in the literature to forecast energy demand or energy supply. In particular, ANN is the most widely used technique in all to predict energy demand or supply (Table 1b). In addition, there are a few studies in the literature to take into account EETs based on SC and CI techniques. For instance, ANN and GA techniques are generally used for sizing photo- voltaic (PV) technology, since these methods present a good solution (Table 2). The performance of the PV systems depends upon several factors such as solar radiation, ambient temperature and wind speed. In order to size a PV system so that it can work properly, efficiently and economi- cally to meet the desired load requirements under the local meteorological conditions, the charac- teristic performance of each component in the PV system is required (Mellit et al. 2008). According to Table 2, the most used technique is ANN too for sizing problem of PV system. Table 2 indicates that SC and CI techniques have an increasing popularity on the sizing of PV-systems. In par- ticular, the numbers of the applications using SC and CI technologies are In the literature, MCDM methods have become increasingly popular in decision-making for en- ergy planning. Table 3 illustrates applications of MCDM methods on the solution of energy plan- ning in last five years. Furthermore, the applications of MCDM methods on emerging energy technology are more than other SC and CI techniques. These studies are summarized as follows; Beccali et al. (2003) used ELECTRE III method for the selection of suitable energy technologies in renewable energy technology diffusion plan. In the study, technological alternatives given in Table 4 are evaluated under the criteria which are classified into four main groups such as technological criteria, energy and environmental criteria, social and economic criteria (Table 5). The evaluations are implemented in three differ- ent scenarios; environmental–oriented scenario, economy-oriented scenario, and energy saving and rational use scenario. Pohekar and Ramachandran (2006a, 2006b) assessed the utility of parabolic solar cooker (PSC) under the criteria techno-economic, social, be- havioral and commercial comparing with other 177 Soft Computing and Computational Intelligent Techniques contemporary cooking energy devices. In the paper, the alternatives; chulha, improved chulha, kerosene stove, biogas stove, lpg stove, micro wave oven, electric oven, solar box cooker, para- bolic solar cooker are evaluated under thirty criteria. The criteria are categorized under five main criteria such as technical, economical, social, behavioral, and commercial (Table 6). Burton and Hubacek (2007) investigated a local case study of different scales of renewable energy provision for local government in the UK. In the study, the perceived social, economic, and environmental cost of the small-scale energy were compared with the large-scale alternatives. In order to investigate whether the energy could have been generated at a lower social, economic, and environmental cost if large-scale projects had been available, a multi-criteria decision making (MCDM) methodology, MACBETH, was used to compare the advantages and disadvantages of a number of different renewable energy tech- nologies. MACBETH method proposed by (Bana Table 1b. The applications of SC and CI techniques related to energy planning for last five years Author ANN ACO GA TS Other Eynard et al. (2010) √ Paolli et al. (2010) √ Li and Shi (2010) √ Li and Su (2010) √ Cinar et al. (2010) √ Azadeh et al (2010) Network based fuzzy inference system Pao (2009) √ Ünler (2008) SI Neto and Fiorelli (2008) √ Abdel-Aal (2008) √ Azadeh et al (2008a) √ González-Romera et al. (2008) √ Azadeh et al (2008b) Fuzzy System Sozen and Arcaklioglu (2007) √ Toksari (2007) √ Pao (2007) √ Hamzaçebi (2007) √ Azadeh and Tarvendian (2007) √ Ediger and Akar (2007) ARIMA Gareta et al. (2006) √ Murat and Ceylan (2006) Ozturk et al. (2005) √ Ceylan et al. (2005), √ Haldenbilen and Ceylan (2005) √ Sozen et al. (2005a, 2005b) √ González and Zamarreño (2005) √ Dong et al (2005) Vector machine 178 Soft Computing and Computational Intelligent Techniques e Costa and Vansnick, 1997). In the basis of the MACBETH, a series of pairwise comparisons, where a decision-maker is asked to specify the difference in attractiveness between all of the alternatives is included. In the study eight renew- able energy technologies of differing scales are considered such as solar photovoltaic, micro-wind, micro-hydro, large-scale wind, large-scale hydro, energy from waste, landfill gas and biomass (wood chippings) based on the definition of renewable energy used by the UK government under eight criteria such as; capital cost, operation and main- tenance cost, generation capacity, lifespan, carbon emissions, noise, impact upon the natural environ- ment and social effects. These criteria were se- lected in order to consider the viability of renew- able energy developments and the need to have a breadth of criteria covering social, economic and environmental issues (Burton & Hubacek, 2007). Doukas et al. (2007) presented a direct and transparent MCDM approach, using linguistic variables, to assist policy makers in formulating technological energy priorities towards a sustain- able energy system. In the paper, technologies given in Table 7 are handled under following criteria; economic (including investment cost criterion and economic visibility using payback period criterion), environmental (including con- tribution to confrontation of the climate change phenomenon criterion and effects on natural environment criterion), technological (includ- ing efficiency rate criterion and knowledge of the innovative technology criterion), and social (including contribution to employment oppor- tunities’ creation criterion and contribution to Table 2. SC and CI techniques for sizing problem of PV technology ANN GA Fuzzy Logic Other Ben Salah and Ouali (2011) √ Fuzzy Systems Mellit et al. (2010) √ √ Mellit (2010) √ √ Liao(2010) Genetic K means algorithm Venayagamoorthy and Welch (2010) √ Chaouachi et al. (2010) √ Thiaux et al. (2010) √ Chang(2009) √ Ashhap (2008) √ Mellit and Benghanem (2007) √ Dufo-Lopez et al. (2007) √ Senjyua et al.(2007) √ Mellit et al. (2007) √ Karatepe (2006) √ Hontaria et al. (2005) √ Mellit et al.(2005) √ Zang and Bai (2005) √ √ Dufo-Lopez, Bernal-Agustin. (2005) √ Bahgat et al. (2004) √ Hussein et al. (2004) Learning networks Benlarbi et al. (2004) √ 179 Soft Computing and Computational Intelligent Techniques Table 3. The applications of MCDM methods on energy planning AHP TOPSIS OTHER APPLICATION Ma et al. (2005) √ Determining the land-suitability assessment of potential energy systems Madlener and Stagl (2005) PROMETHEE Designing the renewable energy policy instruments Lee et al. (2007) √ Determining the priorities in technology development for the energy efficiency and greenhouse gas control plans Madlener et al. (2007) PROMETHEE Determining the best energy planning Georgiou et al. (2008) ELECTRE III Evaluation of projects on clean technologies Lee et al. (2008) √ Evaluation of hydrogen energy technologies Mróz (2008) ELECTRE III Determining the most compromise scenarios of the commu- nity heating system modernization and development Papadopoulos and Karagi- annidis (2008) ELECTE III Determining the achievable penetration of renewable energy sources Thakker et al. (2008) √ Selection of wave energy extraction turbine blade material Buchholz et al. (2009) Multi-criteria analysis Design and implementation of sustainable bioenergy projects Cavallaro (2009) Multi-criteria analysis Assessment of concentrated solar thermal technologies Kahraman et al. (2009) √ Axiomatic Design Selection of the best renewable alternative Kowalski et al. (2009) Multi-criteria analysis Evaluation of renewable energy scenarios Lee et al. (2009) √ Determining the priority the weights of energy Technologies Madlener et al. (2009) ELECTRE III Comparison of the renewable energy conversion plants Rivière and Marlair (2009) A new method Ranking the risks pertaining for biofuel chains Cavallaro (2010a) ELECTRE III Selection of production processes of thin-film solar technol- ogy Cavallaro (2010b) √ Comparing different heat transfer fluids Ghafghazi et al. (2010) PROMETHEE To evaluate and rank energy sources Heo et al. (2010) √ Evaluation of factors for renewable energy Kahraman and Kaya (2010) √ Determining the best energy policy Kaya and Kahraman (2010) √ VIKOR Determining the best renewable energy alternative and energy production site for Istanbul Lee et al. (2010) √ Data envelopment analysis Evaluation of relative efficiency of the research and develop- ment performance in the national hydrogen energy technol- ogy development Rovere et al. (2010) Multi-criteria analysis Selection of the best renewable energy source Lee et al. (2010) √ Prioritizing the weights of hydrogen energy technologies Nixon et al. (2010) √ Determining the best solar thermal collection technology for electricity generation Sadeghzadeh and Salehi (2010) √ Determining the strategic technologies of fuel cells as con- verters in the automotive industry 180 Soft Computing and Computational Intelligent Techniques Table 4. Energy technologies (Beccali et al., 2003) Energy source Technology/Action Solar energy 1 Domestic solar water heaters 2 Solar water heating for large demands at low levels of temperature 3 PV roofs: Grid connected system generating electric energy (without storage) Wind energy 4 Wind turbines (grid connected) Hydraulic energy 5 Hydro plants in derivation schemes 6 Hydro plants in existing water distribution networks Biomass 7 High efficiency wood boilers 8 CHP plants fed by agricultural wastes or energy crops Animal manure 9 CHP plants fed by biogas Energy saving in residential and industry sectors 10 Building insulation Combined Heat and Power (CHP) 11 High efficiency lighting 12 High efficiency electric householders appliances 13 High efficiency boilers 14 Plants coupled with refrigerating adsorption machines Table 5. Main and sub criteria used for evaluation of energy technologies (Beccali et al., 2003) Main Criteria Sub-criteria Technological criteria Targets of primary energy saving in regional scale Technical maturity, reliability Consistence of installation and maintenance requirements with local technical know-how Continuity and predictability of performances Cost of saved primary energy Energy and environmental criteria Sustainability according to greenhouse pollutant emissions Sustainability according to other pollutant emissions Land requirement Sustainability according to other environmental impacts Social and economic criteria Labor impact Market maturity Compatibility with political legislative and administrative situation 181 Soft Computing and Computational Intelligent Techniques regional development criterion). In the paper a two-staged method was developed using linguistic ordered weighted averaging (LOWA) and ordered weighted maximum (OWMAX) operators for the technologies assessment. The energy technologies are firstly identified and the most promising is chosen based on the country’s specific priorities and objectives. Lee et al. (2007) determined the priorities for energy technology development in the sectors of energy efficiency improvement and greenhouse gas (GHG) control plans (EGCP) for a new na- tional energy and resource technology R&D plan (NERP)by using the analytic hierarchy process (AHP). They focused on the areas of energy ef- ficiency improvement and GHG control. In the paper, in order to determine priorities of energy technologies, 9 energy technologies from 3 sectors given in Table 8 in terms of GHG control and 34 energy technologies from six sectors given in Table 9 in terms of energy efficiency improvement are evaluated under a set of criteria. The hierarchy of the criteria consists of five main criteria and five sub criteria. The main criteria are United Nations framework convention on climate change, economic spin-off, technical spin-off, urgency of technology development, and quantity of energy use. The sub-criteria are possibility of developing technologies (domestic technical level and pos- sibility of commercialization), potential quantity of energy saving (quantity of energy saving and quantity CO2 saving), market size (domestic market size, potential export market size, and effect of generating hiring), investment cost, and ease of energy use (ease of product, applicable area of other technologies). In another study, Lee et al. (2009) prioritized the energy technologies against high oil prices in the energy technology roadmap (ETRM) in order to allocate R&D budget strategically. The fuzzy analytic hierarchy process, which integrates the fuzzy theory into the classical AHP approach, is utilized to generate the weights of energy technol- ogy against high oil prices of the ETRM. In the paper, four criteria which are economical spin-off, possibility of commercialization, inner capacity, and technical spinoff are handled. Energy tech- nologies against high oil prices such as building Table 6. Classification of criteria (Pohekar & Ramachandran, 2006a, 2006b) Main Criteria Sub-criteria Main Criteria Sub-criteria Technical Fuel consumption Social Pollution hazards Cooking time Human drudgery Durability Overall safety Quality, reliability Behavioral Aesthetics Sophistication level Motivation to buy Size/weight Taste of food Ruggedness Cleanliness of utensils Continuity of use Ease of operation Need for tracking Type of dishes cooked Nutrition value of food Need for additional cooking system Economic Initial cost Commercial Improvement in models Fuel cost per month Spares and after sales service Maintenance cost per year Distribution network Available subsidy Market research Rate of interest on loan Need for user training 182 Soft Computing and Computational Intelligent Techniques technology, industry technology, transportation technology, coal technology, non-conventional fuel technology, and biomass technology are as- sessed. Lee et al. (2008; 2010a) developed an algorithm by integrating fuzzy analytic hierarchy process (Fuzzy AHP) and the data envelopment analysis (DEA) in order to measure the relative efficiency of the R&D performance in the national hydrogen energy technology development. On the first stage, the fuzzy AHP was used to reflect the vagueness of human thought. On the second stage, the DEA ap- proach was used to measure the relative efficiency of the national R&D performance in the sector of hydrogen energy technology development with economic viewpoints. In the paper, the following criteria was used for the assessment; technological status, hydrogen technology infrastructure, R&D human resources, R&D budgets Lee et al. (2010b) determined the priorities for hydrogen energy technologies by using fuzzy AHP. In the study, four criteria which are economic impact, commercial potential, inner capacity, and technical spin-off are handled to evaluate and determine the weights of five hydrogen energy technologies which are hydrogen production, hydrogen separation and storage, polymer elec- trolyte membrane fuel cell, direct ethanol fuel cell, and solid oxide fuel cell. Table 7. Energy technologies (Doukas et al., 2007) Main Group Sub Group The natural fossil fuels technologies Pressurized Fluidized Bed Combustion Pressurized pulverized coal combustion Natural Gas Combined Cycle The hydrogen technologies Molten Carbonate Fuel Cell; Fuel Cell/Turbine Hybrids Renewable energy technologies Biomass Co-firing; Biomass Gasification; Off-shore Wind farms; Large scale Wind farms; Building Integrated Photovoltaics Table 8. Technologies for GHG (Lee et al., 2007) Sectors Technologies GHG tech CO2 capture storage and conversion tech Non-CO2 gas tech Clean fossil tech Advanced combustion tech Next-generation clean coal tech Clean petroleum and conversion tech DME tech GTL tech Gas hydrate GHG policy GHG mitigation policy 183 Soft Computing and Computational Intelligent Techniques Table 9. Technologies for energy efficiency improvement (Lee et al., 2007) Sectors Technologies Industry High-efficiency drying tech Fine chemical processing Energy conversion tech Unutilized energy tech Energy material tech High-efficiency dying tech Cold storage and freezing tech Process automation and intelligence tech Supercritical fluid process tech Evaporation and distillation tech Adsorption separation tech Membrane separation tech Crystallization tech Building Green building tech Building renovation tech High-efficiency HVAC tech CHP tech Efficiency policy Energy efficiency improvement policy Transportation High efficiency low emission vehicles tech Electricity Superconductor tech Electric power conversion tech High-efficiency electric heating tech Energy storage tech Standby power saving tech Common utilities Heat exchange tech Boiler tech High-efficiency furnace tech Burner tech Motor tech Lighting tech Fluid machine tech 6 major appliances DSM tech 184 Soft Computing and Computational Intelligent Techniques Klemes et al. (2009) developed software named Early Market Introduction of New En- ergy Technologies (EMINENT). The software was developed to analyze the potential impact of new and underdeveloped energy technolo- gies in different sectors emerging from different countries. The software involved two databases; new technologies (which contains renewable electricity generation, renewable heating and cooling technologies, production and distribution of liquid and gaseous bio-fuels, eco-buildings, poly-generation, energy demand management and renewable energy supply in high performance communities, and alternative motor fuels) and sectoral energy supplies and demands (which contains information of the number of consum- ers per sector, type of demand, typical quality of the energy required and the consumption and installed capacity per end-user). The main aim of the program is to evaluate the market potential of energy-related early stage energy technolo- gies in various energy supply chains, and their performance in terms of CO 2 emissions, costs of energy supply, use of primary fossil energy, and in different subsectors of society. Segurado et al. (2009) compared EMINENT with other tools which are carbon dioxide tech- nology database (CO2DB), MARket Allocation (MARKAL), IKARUS, and energy emission economy database (E3database) already on the market for energy technology assessment. The main conclusion of the comparison is that EMI- NENT is the only energy technology assessment tool that targets early stage energy technology. Karakosta et al. (2010) presented the priorities of sustainable electricity generation technologies for five developing countries, namely Chile, China, Israel, Kenya and Thailand by using ELECTRE III. In the paper, energy technologies given in Table 10 were analyzed under accordance with strate- gic/developmental planning, local and regional economic development, co 2 emissions reduction, minimization of the negative effects on the natural environment at national–regional level, contribu- tion to the employment, and contribution to energy independence developing country criteria. Sadegzadeh and Salehi (2010) used TOPSIS methodology to rank the attractiveness and im- portance of the stack of fuel cells as a sub-system. The technologies which are taken into consider- ation as follows; the situation of professional manpower on the industrial and semi-industrial scales, the situation of professional manpower on the laboratory scale, the situation of know-how on the industrial and semi-industrial scales, the situation of know-how on the laboratory scales, the situation of hardware on the industrial and semi-industrial scales, the situation of hardware on the laboratory scale. The criteria used in the evaluation are as follow; production of platinum catalyst powder-carbon, placing catalyst on the carbon base, production of gas penetration layer, production of polymer membrane of ion exchange, construction of membrane collection-electrode Table 10. Examined technologies (Karakosta et al., 2010) Clean coal Wind Steal boiler upgrading Solar (PV) Coal to gas Mini/micro hydro (rivers) Oil steam improvement Biomass (forest/agriculture) boiler Coal steam improvement Biogas for generator Methane combustion Mini/micro decentralized Geothermal Solar towers Hydro (dams) Coal Mine Methane (CMM) for generator 185 Soft Computing and Computational Intelligent Techniques with low heat, plates of current field, technology of waterproofing stack of fuel cell with low heat, and technology of engineering designing of the collection (stack) of fuel cell. Finally, the priorities of allocating power and capital for the develop- ment of technology of fuel cells in automotive industry are as follows; hardware on the labora- tory scale, know-how on the laboratory scale, know-how on the industrial scale, professional manpower on the laboratory scale of laboratory, and professional manpower on the industrial scale. FUTURE RESEARCH DIRECTIONS According to literature survey, the interest on EET has been monotonically increasing day by day. In Figure 7, interest on all EETs has a pick point in the last period except for non-conventional fuel technologies. In particular, in the last period, the researchers’ interest on transportation technologies has the biggest increase. And the coal and industry technologies are also the second and the third at- tractive technologies, respectively. These indicate that the developments on EETs for transportation, coal, and industry keep going on and these topics will be highlighted in near future. In addition, the utilization of SC and CI tech- niques on development of EET technologies has been grown up. And application of SC and CI techniques on energy problems has been also increasing fast. In particular, the application of MCDM on EETs and Energy problems are the most attractive topics in all and it is clearly un- derstood that their popularity will be increase in near future. The percentiles of publications with respect to last five years have been presented in Figure 8. CONCLUSION The main aim of the study is to present SC and CI techniques utilized in the evaluation of emerging energy technologies exhaustively. Therefore, this chapter has presented an extensive review of the literature on SC and CI techniques and their ap- plications of emerging energy technologies. In this purpose, emerging energy technologies have been classified and applications of emerging energy technologies in the literature have been illustrated. Figure 7. Distrubiton of publication percentiles with respect to the determined periods 186 Soft Computing and Computational Intelligent Techniques Then, SC and CI techniques have been briefly explained and various numbers of publications related to their applications on energy planning and emerging energy technologies in the literature have been reviewed. From the literature, following conclusions are obtained; • The interest of researchers in emerging en- ergy technologies has increased in recent years. In particular, the biggest increase has been in transportation and coal tech- nologies. Although, the interest in biomass technology is the top until the last period, the interest in transportation and coal tech- nologies has left behind the interest in bio- mass technology. • For energy planning studies, ANN and AHP are the most used techniques in the literature. Except for MCDM methods, the other SC and CI techniques are usually used to forecast energy demand/supply. • Although applications of SC and CI tech- niques on EETs are narrow, the numbers of publications have been increasing in recent years. Hence, SC and CI techniques have become increasingly popular in application of emerging energy technologies. In par- ticular, MCDM methods have been widely used in decision making of both emerging energy technology and energy planning because of the complexity of the problem. • Although, there are a few studies deal with applications of SC and CI techniques on emerging energy technologies, ANN, GA and AHP techniques are widely used meth- odologies among the published articles in the literature. • ANN and GA is the most used techniques for sizing problem of PV systems while AHP is used to obtain a decision related to EET. • In MCDM applications, social, technical, economical, and commercial criteria are the most used criteria during evaluation of emerging energy technologies. Although the published literature on the EETs based on SC and CI techniques indicates that the popularity of SC and CI techniques has been increasing day by day, there are two gabs in the literature; the first one, there are not any application of other SC and CI techniques such as TS, ACO, SI. 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Expert Systems with Applications, 36(3), 2, 6227–6235. doi:10.1016/j. eswa.2008.07.031 Celik, M., Kahraman, C., Cebi, S., & Er, I. D. (2009c). Fuzzy axiomatic design-based perfor- mance evaluation model for docking facilities in shipbuilding industry: the case of Turkish ship- yards. Expert Systems with Applications, 36(1), 599–615. doi:10.1016/j.eswa.2007.09.055 Engin, O., Çelik, A., & Kaya, I. (2008). A fuzzy approach to define sample size for attributes con- trol chart in multistage processes: An application in engine valve manufacturing process. Applied Soft Computing, 8(4), 1654–1663. doi:10.1016/j. asoc.2008.01.005 Kahraman, C. (2008). Fuzzy Multi-Criteria Deci- sion Making: Theory and Applications with Recent Developments. Berlin: Springer. Kahraman, C., Ruan, D., & Dogan, I. (2003). Fuzzy group decision-making for facility location selection. Information Sciences, 157, 135–153. doi:10.1016/S0020-0255(03)00183-X Kaliszewski, I. (2006). Soft Computing for Com- plex Multiple Criteria Decision Making. USA: Springer. Kaya, I. (2009). A genetic algorithm approach to determine the sample size for attribute control charts. Information Sciences, 179(10), 1552–1566. doi:10.1016/j.ins.2008.09.024 Kaya, I., & Engin, O. (2007). A new approach to define sample size at attributes control chart in multistage processes: An application in engine piston manufacturing process. Journal of Ma- terials Processing Technology, 183(1), 38–48. doi:10.1016/j.jmatprotec.2006.09.022 Konar, A. (1999). Artificial Intelligence and Soft Computing: Behavioral and Cognitive Model- ing of the Human Brain. Boca Raton/ London/ New York/ Washington, D.C.: CRC Press. doi:10.1201/9781420049138 197 Soft Computing and Computational Intelligent Techniques Rayward-Smith, V. J., Osman, I. H., Reeves, C. R., & Smith, G. D. (1996). Modern Heuristic Search Methods. New York, Toronto: Wiley. Schniederjans M. J., Hamaker J.L., Schnieder- jans A. M., Information Technology Investment: Decision-Making Methodology, Tettamanzi, A., & Tomassini, M. (2001). Soft Computing: Integrating Evolutionary, Neural, and Fuzzy Systems. Berlin: Springer. Triantaphyllou, E. (2000) Multi-Criteria Decision Making Methods: A comparative Study, Kluwer Academic Publishers, Baton Rogue/Louisiana. KEY TERMS AND DEFINITIONS Emerging Energy Technology (EET): EET is the technology that improves the utilization performance of energy sources. Multi Criteria Decision Making (MCDM): MCDM is to give the best decision under the multi objective or multi attribute. Multi Attribute Decision Making (MADM): MADM is to select the best alternative under multiple criteria. Multi Objective Decision Making (MODM): MODM is to present the best opportunity by satisfying multiple objectives. Analytic Hierarchy Process (AHP): AHP is a MCDM tool which is based on pairwise comparison when there is not any quantitative information. Technique for Order Performance by similarity to Ideal Solution (TOPSIS): TOPSIS is another MCDM method which is based on measuring the distance to positive and negative ideal solutions. Information Axiom: Information axiom which is based on satisfying level of functional requirements is used to determine the best alterna- tive under multiple criteria. Fuzzy Sets: Fuzzy is based on the membership function definition of an element. In classical sets, either an element is a member of the defined set or not while each member is defined by a member- ship value in a fuzzy sets. 198 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 6 INTRODUCTION Conventional energy sources such as fossil fuels and uranium reserves are limited and adversely impacts on environment, therefore greet interest for utilization of renewable energy has been es- tablished. For recent expansion of renewable en- ergy applications, wind energy generation among other renewable energies has been experiencing a rapid growth. As the use of wind power units increases worldwide, there is a rising interest on their impacts on power system dynamic/control and finding appropriate solutions. Mohammad Saleh University of Kurdistan, Iran Hassan Bevrani University of Kurdistan, Iran Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms: Kurdistan Electric Network Case Study ABSTRACT This chapter presents an overview of key issues and technical challenges in a regional electric net- work, following the integration of a considerable amount of wind power. A brief survey on wind power system, the present status of wind energy worldwide, common dynamic models, and control loops for wind turbines are given. In this chapter, the Kurdistan electric network in the Northwest part of Iran is introduced as a case study system, and an analytical approach is conducted to evaluate the potential of wind power installation, overall capacity estimation, and economic issues, based on the practical data. Then, the impact of high penetration wind power on the system dynamic and performance for various wind turbine technologies is presented. The stability of integrated system is analyzed, and the need for revising of conventional controls and performance standards is emphasized. Finally, a STATCOM-based control approach is addressed to improve the system stability. DOI: 10.4018/978-1-61350-138-2.ch006 199 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms The recent investigation studies indicate that relatively large scale wind generation affects the power system frequency and voltage regulation, as well as other control and operation issues. This impact may increase at the penetration rates that are expected to be high in the next several years. On the other hand, most of existing wind turbine technologies cannot provide necessary control capabilities for the regulation issue. The power system control of the future will require a high degree of flexibility and intelligence to ensure that it can continuously balance fluctuating power and regulate frequency/voltage deviation caused by renewable energy sources such as wind (Bevrani, et al., 2011). This chapter presents an overview of new dy- namical challenges in regional electric networks, following a high penetration of wind power. The Kurdistan electric network in Iran is considered as a case study. Mountainous environment, costly process for electricity production from conven- tional sources, and numerous windy areas make Kurdistan as an appropriate region for installa- tion of wind farms. In this work, an analytical approach is conducted to evaluate the potential of wind power installation and overall capacity estimation, and to study economic issues based on the practical data. The impact of high penetration wind power on the system dynamic and performance for different wind turbine technologies including fixed-speed induction generator (FSIG), doubly-fed induction generator (DFIG) and permanent magnet syn- chronous generator (PMSG) is presented. Using DIgSILENT simulation software, the stability of the integrated system is re-analyzed, and the need for revising of conventional controls and perfor- mance standards is emphasized. Finally, a control approach to improve the system stability using static synchronous compensator (STATCOM) and energy storage devices is addressed. This work is supplemented by some nonlinear simulations on the Kurdistan power system case study using real data and parameters. In the next section, a background with a brief literature review is presented. In section 3, an over- view of wind energy status around the world and Iran is provided. Section 4 presents a discussion about wind power systems and the main control schemes. Section 5 determines the potential of Kurdistan province for wind power generation. In section 6, a preliminary study on wind energy costs in Kurdistan is performed. Section 7 pres- ents a dynamic analysis on the impact of a high wind power penetration on the Kurdistan electric network and introduces an appropriate control solution for its stability improvement. Finally, conclusion and future research directions are presented in sections 8 and 9, respectively. BACKGROUND In order to clarify the interaction behavior between wind farm(s) and the power system, building of an effective dynamic model for wind power systems (WPSs) is needed. Model simplifications and some comparisons between different types of WPSs and wind farm equivalent models are presented in recent performed research works (Mansouri, et al., 2004; Ekanayake, et al., 2003; Slootweg, et al., 2003; Akhmatov, et al., 2006; Fernandeza, et al., 2006; Ledesma & Usaola, 2005). The role of WPS control strategy to qualify system output and stability augmentation is stud- ied in many papers. Optimization control, power smoothing and voltage control of WPSs are most important topics of related new research areas (Senjyu, et al., 2006; Wang & Chang, 2004). Increasing the penetration of wind turbine gen- erators in a power system may affect the system security/stability limits, frequency, voltage and dynamic behavior (Muyeen, et al., 2009; Bev- rani, 2009; Slootweg, 2003; Bevrani, Tikdari, & Hiyama, 2010). This effect can be mostly caused by fluctuation of wind power. The impacts of wind turbines on the power system frequency and voltage have been studied in many research 200 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms works (Jowder, 2009; Radics & Bartholy, 2008; Bevrani & Tikdari, 2010). Power system frequency response model in the presence of high wind power penetration, frequency control issue, and a com- prehensive survey with some new perspectives are already well addressed (Bevrani & Hiyama, 2011; Bevrani, Ghosh, & Ledwich, 2010; Bevrani, Daneshfar, & Daneshmand, 2010). The effects of DFIG and induction generator type of WPSs on the voltage transient behaviors are explained and the disadvantages of the induc- tion generator type are shown in (Nunes, et al., 2004). The loadability of various types of WPSs is studied and it is shown that the DFIG has larger loadability than induction generators (Bevrani & Tikdari, 2010). Frequency nadir in the presence of different types of the WPSs has been also compared in (Erlich, et al., 2006; Gillian, et al., 2005). As argued in the mentioned references, wind turbines affect frequency behavior because they add amount of inertia to the power system. Both stator and rotor windings of induction generator type of WPSs are directly connected to the power grid, but in DFIG type, only stator is directly con- nected and the rotor is linked through a power electronic type converter. The induction generator WPS in turn adds much inertia than DFIG in the power system; and in conclusion, the induction generator WPS frequency response is better than systems with DFIG type in the same conditions. Continuous increase of installed wind power during recent years has forced the system opera- tors and responsible organizations to tighten the performance standards and connection rules – known as grid code - in order to limit the effects of wind power penetration on the power system performance and stability. Interconnection procedures and standards need to be reviewed to ensure that the new op- erating control schemes and their responses are in a consistent manner to all power generation technologies, including wind generating units as variable generation technologies. The revised operating performance standards require that most type of power plants support the electricity network throughout their opera- tion. Important key issues can be considered as steady state and dynamic active/reactive power capability, continuously acting frequency/voltage control and fault ride through behavior. Some commonly used turbine designs have some limits in terms of achieving grid code compliance in several countries. For the wind farms containing these turbines, additional equipments are needed (Maibach, et al., 2007). Variable generation technologies generally refer to generating technologies whose primary energy source varies over time and cannot reasonably be stored to address such variation. Uncertainty and variability are two major factors of a variable generator that distinguish it in con- ventional forms of generation and may impact the overall system planning and operations (Bevrani & Hiyama, 2011). In order to specify wind power potential in a particular site, a long-term record of wind speed has to be statistically analyzed. There are several studies related to the determination of wind characteristics and wind power potential in many countries over the whole world (Radics & Bartholy, 2008; Elamouri, Ben, & Amar, 2008; Al-Abbadi, 2005; Jowder, 2009; Ucar & Balo, 2009; Weigt, 2009) State of Wind Power Generation At present, wind power has effective impact on energy markets. In 2009, more than 38.3 GW of new wind power capacity was installed around the world that bringing the total installed capacity up to 158.5 GW. The main markets driving this growth rate are Asia, North America and Europe. The top five countries in wind energy installed capacity in 2009 were US with 35064 MW (22.1%), PR China with 25805 MW (16.3%), Germany with 25777 MW (16.3%), Spain with 19149 MW (12.1%), and India with 10926 MW (6.9%); while 201 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms the total installed wind power in the rest of world was 41784 MW (26.4%) (GWEC, 2010). Similar to the most countries in the Middle East and Africa, contribution of the wind energy for production of electricity in Iran is relatively low. The total installed capacity of wind turbine in Iran by 2010 is less than 200 MW. There are many suitable areas for installing wind turbines in Iran; however as depicted in Table 1, the major installed wind power is centralized in Manjil and Binalud areas. Because of existing high sources of oil and gas in a relatively low price in Iran, most of elec- tricity has been produced by fossil fuel in the past. However, nowadays for many reasons, as well as other countries there is a great concern towards renewable energies like wind and solar. The gov- ernment and other responsible organizations have put some efforts to expand wind and solar farms in different parts of country. Currently, the poten- tial for wind power generation is estimated to be more than 6500MW. Wind Power Controls A WPS transforms the energy presented in the belonging wind into electrical energy. A general scheme of this system is shown in Figure 1a. Wind energy is transformed into mechanical energy by wind turbine units. Based on rotational speed, the wind turbines can be split into two types: 1. Fixed speed wind turbine (FSWT) 2. Variable speed wind turbine (VSWT) Major characteristics of the FSWT are brush- less and rugged construction, low cost and simplic- ity. The main advantage of the VSWT is that more energy can be extracted for a specific wind speed regime. In addition, the mechanical stress is less; because the rotor acts as a flywheel (Slootweg, 2003). Common VSWT structures are known as DFIG and the PMSG. A FSWT is usually directly equipped with a grid coupled squirrel cage induc- tion generator whose speed variations are limited. The power extracted from the wind energy by a wind turbine can be expressed as follows (Heier, 1998; Bansal, et al., 2002): P AV C m w p = 1 2 3 ρ λ β ( , ) (1) where, P m is the power extracted from the wind, p is the air density (Kg/m 3 ), A is the rotor disc area (m 2 ), V w is the wind speed (m/s), and C p is a power coefficient which is a function of the tip speed ratio λ and the pitch angle of rotor blades β. The tip speed ratio λ is defined by λ ω = r w R V . (2) Table 1. Wind power in Binalud and Manjil areas Area No. of turbines Power (KW) 27 300 2 500 Binalud 18 550 1 600 64 660 Total 112 61840 Manjil 43 660 Total 43 28300 202 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms where, ω r is mechanical angular velocity of the turbine rotor and R is the blade radius of the wind turbine. As shown in Fig. 1b, the drive train model of wind turbines is usually represented by two mass models (Slootweg, Haan, Polinder, & Kling, 2003; Slootweg, Polinder, & Kling, 2003): T T J d dt w m r r − = ω (3) T D K dt m mc r g mc r g = − + − ( ) ∫ ( ) ω ω ω ω (4) T T J d dt m g g g − = ω (5) where, J r , and J g are inertia of wind turbine and generator, ω g is the rotor speed, T m is the me- chanical torque from the generator shaft, T g is the generator electrical torque. Finally, K mc and D mc are the stiffness and damping of mechanichal coupling, repectively. Power extracted from a wind turbine can be controlled in two states, in above and below rated wind speed of wind turbine. In the above rated wind speed, a blade pitch angle controller reduces the power coefficient and thus the power extracted from the wind. The pitch controller limits the generator’s speed to a rated value (ω gen, rated ) by adjusting the pitch angle (β). Second control state (below rated wind speed) exists only for the VSWT generator type. The aim is to control the rotational speed to follow the maxi- mum power point trajectory (MPPT), when wind speed is in change. Since, precise measurement of wind speed is difficult, for maximum power point tracking operation, it is better to use the rotor speed as a control input instead of wind speed. Figure 1. Wind energy conversion system; a) General scheme of WPS, and b) Drive train model 203 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms Modeling and Control of DFIG The control strategy that generally applied to control of VSWT is based on vector control tech- niques. An overview of dynamic model for DFIG wind turbine and the associated control system is shown in Figure 2a (Hansen, et al., 2003; Hansen, et al., 2004). The rotor-side converter operates in a stator flux reference frame that decomposes the rotor current into active power (q-axis) and reactive power (d-axis) components. A fast inner current control loop controls rotor current in d- and q- axis and a slower outer control loop regulates active and reactive powers. The MPPT unit pro- vides the reference signal P Grid,ref for the active power, while the reactive power Q Grid,ref is typi- cally fixed at zero. The grid-side converter controller operates in a grid side converter voltage oriented reference frame (DIgSILENT GmbH, 2003). Active and reactive components of the grid-side converter currents are controlled by the fast inner control loop. The slower outer control loop determines the q-current set point, which regulates the DC-voltage to a pre-defined value. For achieving unity power factor operation of converter, it is sufficient that q-current to be regulated to zero. Figure 2. Overall structure and main control loops of VSWT systems a) DFIG, and b) PMSG 204 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms Modeling and Control of PMSG An overview for dynamic model of the PMSG wind turbine and its control system is shown in Figure 2b. The control structures and related concepts are well discussed in the recent published works (Conroy & Watson, 2008). At the generator-side converter, AC-voltage and active power are regulated (reactive power regulation is optional). The grid-side converter operates in a stator voltage oriented reference frame. A fast inner control loop regulates the d- and q-axis current components of the grid-side PWM-converter. Current references are defined by a slower outer control-loop regulating DC-voltage of the intermediate DC-circuit and reactive power. Wind Energy Potential Assessment in Kurdistan In this section, to determine the potential of wind power generation the hourly measured wind speed data over a period of almost 5 years between 2004 and 2008 from 6 stations in Kurdistan, at 10 m height that obtained from Kurdistan Meteorologi- cal Organization are statically analyzed. Extrapo- lation of the 10 m data, using the power law, is used to determine the wind data at upper heights. The power law used in this study is as follow: V V Ln H Z Ln H Z H ref ref = 0 0 (6) where, V H is the wind speed at height H, V ref is the wind speed at height H ref , and Z 0 is surface roughness length. Gilbert (2004) explains the roughness clas- sifications and roughness lengths. The roughness length for water surface (Class 0), open areas with a few windbreaks (Class 1), farm land with some windbreaks more than 1 km apart (Class 2), urban districts and farm land with many windbreaks (Class 3), and dense urban or forest (Class 4) are determined as 0.0002 m, 0.03 m, 0.1 m, 0.4 m, and 1.6 m, respectively. In this work, since the studied stations are located in near cities or even inside cities and due to mountainous environment of Kurdistan, the roughness lengths for most sta- tions are fixed at 1 (Class 1). Site Selection Gillbert (2004) presented a standard for using in site selection in a wind farm installation pro- cedure. Based on this standard and according to the annual mean wind speed from 2004 to 2008, among considered six cities of Kurdistan (Bijar, Qorveh, Marivan, Saqez, Sanandaj, and Divandarreh), regions of Bijar and Divandarreh are determined as more fair places for wind farm installation (Table 2). Monthly Variation of Mean Wind Speed Figure 3 shows monthly variation of mean wind speed for selected two sites (Divandarreh and Bijar). In both stations, the highest monthly wind speed occurs in March. In Bijar, the lowest wind speed happens in January; while for Divandarreh it happens in December. Wind Rose Diagram The direction of the wind is taken into consider- ation for the sake of installing the wind turbines in a wind farm. The wind rose diagram illustrates the wind direction. Figure 4 shows the wind rose diagram for Bijar and Divandarreh, using the WRPLOT software. Based on these diagrams, the wind mainly blows to the north side of city in Bijar, however for region of Divandarreh, the wind blows mainly in direction of east. 205 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms Wind Power Installation and Economic Issues In this section, the economic evaluation for installing four wind turbines in capacity of 0.8, 1.5, 2 and 3 MW, for Bijar and Divandarreh are estimated using the levelised cost of electricity (LCOE) method. For this purpose, the weibul distribution is obtained for these sites. Wind fre- quency distributions for Bijar and Divandarreh at 60 m height are shown in Figure 5. Table 2. Annual mean speed at 50 m height from the ground for different locations Wind power class Annual mean wind speed ( m /s) Height from sea level (m) Longitude Latitude Location Min Deg Min Deg Class 3 6.73 1883.4 37 47 53 35 Bijar Class 1 5.58 1906.0 48 47 10 35 Qorveh Class 1 3.06 1286.8 12 46 31 35 Marivan Class 1 4.25 1522.8 16 46 15 36 Saqez Class 1 3.40 1373.4 0 47 20 35 Sanandaj Class 3 6.72 2142.6 55 46 4 36 Divandarreh Figure 3. Average wind speeds for different months based on the recorded data from 2004 to 2008, for a) Divandarreh, and b) Bijar 206 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms Wind Power Calculation Calculation of annual energy production from a WPS in a given site requires the considered turbine power curve with weibul distributions of wind speed for the site. In this study, Enercon E-53 (800 KW), Nordex 77 (1.3 MW), Gamesa G90 (2 MW), and Vestas V112 (3 MW) wind turbine technologies are considered. The information related to these wind turbines can be obtained from their manufactures web sites (www.vestas. com, www.nordex-online.com, www.enercon.de, and www.gamesa.es). Capacity factor (CF) is one of important in- dicators for assessing the performance of a wind turbine. The capacity factor of a WPS at a given site can be defined as CF E E p rated = (7) where, E p is the produced energy by the system in the specific period, and E rated is the energy that Figure 4. Wind rose diagrams based on the recorded data from 1992 to 2006, for a) Bijar, and b) Di- vandarreh 207 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms could be produced by the system, while the ma- chine operates at its rated power in the same period. The CF can be written as (Jangamshetti & Rau, 1999): CF V V f V dV f V dV R V V V V R F C R = + ∫ ∫ 1 3 3 ( ) ( ) (8) where, the v c is the cut-in wind speed of wind turbine generator in m/s, the v R is the rated wind speed of wind turbine generator in m/s, and v F is the cut-out wind speed of wind turbine generator in m/s. The above equation can be calculated as CF V V e K K V C C R V C K R C = + − 3 3 3 Γ( ) − − − 3 3 3 [ ( , ) ( , )] γ γ V C K V C K e R K C K V C F K (9) where, γ is the incomplete gamma function (Jan- gamshetti & Rau, 1999; Suresh, et al., 2001). Energy Cost Analysis The LCOE for WPSs can be described as the ratio of the total annualized cost to the annual electricity produced by the system. The following expression can be used to estimate the LCOE delivered by a WPS (Gokcek & Genc, 2009; Nouni, et al., 2006), Figure 5. Frequency distributions of wind speed at 60 m height for a) Bijar, and b) Divandarreh 208 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms LCOE C R C R C R C R C R C E wt wt bb bb ci ci in in misc misc om P = + + + + + $/KWh (10) Here, the E p is annual energy production by delivered WPS, C wt is cost of wind turbine, C bb is cost of battery bank, C ci is the civil work and installation cost, C in is cost of the inverter, C misc is miscellaneous costs such as connecting cables, control panel and other components; and C om is annual operation and maintenance cost. The R wt , R bb , R ci , R in and R misc present the capital recovery factors (R) for wind turbine, battery bank, civil work and installation, inverter and other miscel- laneous components, respectively. For a given discount rate (r) and useful system lifetime (n), the capital recovery factor can be defined as follows: R r r r n n = + + − ( ) ( ) 1 1 1 (11) A break-up of relative costs for different com- ponents of a typical WPS can be easily obtained (Nouni, et al., 2006). The cost evaluation is made by means of this cost break-up for all WPSs. A typical cost table for different wind power tech- nologies is presented (Sathyajith, 2006). A specific cost of WPS can be calculated as follows, C WPS =I WPS P R [$] (12) Where, the I WPS is the specified cost of the WPS. The estimation of the KWh cost of energy delivered by the WPS operating at the given sites has been done under the following assumptions: 1. The lifetime of the WPS (n) is assumed to be 25 years. 2. The discount rate (r) is taken as 12%. 3. Operation and maintenance cost (C om ) is considered to be 2% of initial capital cost of the WPS project (Nouni, et al., 2006) 4. Useful lifetime for the battery bank and inverter are assumed to be 7 and 10 years, respectively (Nouni, et al., 2006). 5. It is assumed that the WPS production is equal to the amount of energy output in each year during its useful lifetime (Türksoy, 1995). The results of cost analysis performed in this study for the WPS with different size ranges are presented in Table 3. From this table, it is seen that the predicted maximum and minimum values regarding electricity cost per kWh for each WPS are calculated by taking into account the limit val- ues of the band interval of WPS specific cost. The minimum levelised cost of electricity is calculated that WPS- Vestas V112 (3 MW) is 0.074 $/kWh, while its maximum value is 0.118 $/kWh. These values are the predicted lowest values for WPS in both cases of Divandarreh and Bijar. According to the all band intervals, the highest electricity costs are calculated in the case of WPS- Gamesa G90 (2 MW) in Bijar, as 0.116 $/kWh for lower-limit and as 0.186 $/kWh for upper- Table 3. Cost analysis per kwh for WPS in Bijar and Divandarreh WPS Divandarreh Bijar CF Cost ($/kwh) CF Cost ($/kwh) Min Max Min Max Enercon E-53 (0.8 MW) 0.2746 0.088075 0.140919 0.2677 0.090345 0.144552 Nordex 77 (1.5 MW) 0.2614 0.092522 0.148035 0.2544 0.095068 0.152109 Gamesa G90 (2 MW) 0.2151 0.112437 0.1799 0.2079 0.116331 0.18613 Vestas V112 (3 MW) 0.3286 0.073601 0.117762 0.3286 0.073601 0.117762 209 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms limit. As seen from the calculation of annual energy production, the WPS of 3 MW rated power among the WPS considered in the study is most attractive in terms of the levelised unit cost. Dynamic Impacts Analysis and Stability Improvement Case Study In this section, transient stability of Kurdistan electric network in the presence of two wind farms in Bijar and Divandarreh are analyzed. A combination of FSIG and DFIG turbines are used in the mentioned wind farms. Single line diagram of Kurdistan network with wind farms is shown in Figure 6. Two 50-MW wind power plants are added to 63 KV bus, near to the cities of Divandarreh and Bijar. It is noteworthy that in Kurdistan, only there is one conventional power plant (Sanandaj Power Plant) with above 200 MW. Detailed system information and power system parameters are given in (Saleh, 2010). Simulation Results In this study, the power system simulation pro- gram, Power Factory (DIgSILENT), is used as a suitable tool for power system modeling and simulation. In the simulation environment, the conventional power plant exciter is represented using the standard model EXST1; the power system stabilizer is represented using a dual-input power system stabilizer model (PSS2A), and governor-turbine is represented by the standard model GAST. Load model is represented using a static model. The voltage dependencies on active and reactive powers are considered as 1 and 2, respectively. For transient stability investigation, a three phase short circuit with duration of 0.34 sec is considered in an important location. The fault location is shown in Figure 6. Figure 7 depicts Figure 6. Single-line diagram of the Kurdistan electric network with two wind farms 210 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms system response including voltages at Divandarreh and Bijar buses (connected to the wind farms), rotor angle of Sanandaj power plant, WPS’s speed, and active and reactive powers. As discussed, the WPSs commonly use the induction generators to convert the wind energy into electrical energy. The induction generators act as reactive power consumers. Therefore, the system voltage would be affected in the presence of wind turbines, especially in the case of fixed- speed type of WPSs. This issue can be also seen from simulation results shown in Figure 7. A decrease in related bus voltages with a permanent oscillation in active power and speed of aggre- gated generators are indicated. It is shown that in view point of reactive power compensation, the Kurdistan grid is much weaker in Bijar than Di- vandarreh area. Stability Improvement For the sake of system frequency and real power compensation in the presence of WPSs, several control approaches are already presented (Bev- Figure 7. System response following a three phase short circuit 211 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms rani & Hiyama, 2011; Bevrani, Daneshfar, & Daneshmand, 2010). In order to reactive power compensation, which is the main control issue in the present work, traditionally the capacitor banks are suggested to use. However, it is noteworthy that capacitor banks cannot provide dynamic compensation for events such as the sudden drop of voltage. In response to above challenge, to improve stability after grid disturbances such as short circuit faults, the STATCOM technology as a powerful control tool is examined. The STATCOM is extensively being used in power systems because of their ability to provide flexible power flow control (Muyeen, et al., 2005). The main motivation for choosing STATCOM in wind farms is their ability to provide bus bar system voltage support either by supplying and/ or absorbing reactive power into the system. The applicability of a STATCOM in wind farms has been investigated and the results from early studies indicate that it is able to supply reactive power requirements of the wind farm under various oper- ating conditions, for improving transient stability (Chun, et al., 2000), as well as enhancement of the steady-state stability margin (Saad-Saoud, et al., 1998). Regarding the grid codes mentioned in Section 2, it is also investigated that the me- dium voltage STATCOM technology which adds the missing functionality to wind farms in order to become grid code compliant. Especially, the voltage control and the fast dynamic behavior during balanced as well as unbalanced grid faults (fault ride-through) are highlighted (Maibach, et al., 2007). An appropriately sized STATCOM can provide the necessary reactive power compensation when connected to a weak grid. Also, a higher rating STATCOM can be used for efficient voltage con- trol and improved reliability in the interconnected grid with wind farms. However, it is noteworthy that the STATCOM rating is limited by economic issues. The location of STATCOM is generally chosen to be a point in the system which needs reactive power. Simulation results show that STATCOM provides effective voltage support at the bus which is connected to the Bijar wind farm. That is why, for stability improvement of the example at hand, a 30-Mvar STATCOM is con- nected to 63 KV bus, near to the Bijar wind farm. Another reason for choosing the mentioned place is that the location of the reactive power support should be as close as possible to a point at which the support is more needed. Furthermore, in the present case study, in addition to the losses reduction and increase of power transfer capabil- ity, the location of the STATCOM to the center of averaged load is more appropriate because the impact of voltage change is more significant at this point. But it is notable that the shipping of reactive power at low voltages in the system running close to its stability margin is not very efficient. Also, the total amount of reactive power transfer avail- able will be influenced by the transmission line power factor. Hence, the compensation devices are always kept as close as possible to the center of equivalent load as the ratio ΔV/Vnominal will be higher for the load bus under fault conditions (Prabhakar, 2008). The system response in the presence of STAT- COM for the accrued fault is shown in the Figure 8. Results show a considerable improvement in transient stability. The transient behavior of wind farms are also improved by injecting large amounts of reactive power during the fault recovery. Flexibility in voltage control for power quality improvement, fast response, and applicability for use with high power/load fluctuation are the main advantages of the proposed STATCOM-based control strategy. FUTURE RESEARCH DIRECTIONS Some important research needs in future can be summarized as follows: 212 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms • Coordination between STATCOM, energy storage devices, power system stabilizers, and excitation controls of conventional power plants can be considered as an im- portant topic for further research in the feld of power systems stability improve- ment. Determine the proper location and size optimizing of STATCOM is another research topic that should be considered. • A more complete dynamic model is need- ed in order to stability analysis and control synthesis in interconnected power systems with a high degree of wind power pen- etration. Further study is needed to defne new grid codes for contribution of large WPSs into the power system stability/per- formance improvement. Future grid codes should clearly impose the requirements on Figure 8. System response with STATCOM support 213 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms the regulation capabilities of the active/re- active power of WPSs. • Control performance standards compliance verifcation remains a major open issue for wind power units. This concerns specifc WPS capabilities and will require the de- velopment of additional standards for test- ing, from the level of the component up to the entire WPS. • Advanced computing algorithm and fast hardware measurement devices are also needed to realize more effective optimal/ adaptive control schemes for the power systems with a high penetration of WPSs. • Since, naturally the wind power is stochas- tic, still it is diffcult to straightly use wind turbine kinetic energy storage in the regu- lation tasks such as frequency control. The contribution of WPSs in active power and frequency regulation refers to the ability of these units to regulate their power out- put (Bevrani, et al., 2010). More effective practical algorithms and control method- ologies are needed to perform these issues. Further studies are needed to coordinate the timing and the size of the kinetic en- ergy discharge with the characteristics of conventional plants. • To allow the increase of wind power pen- etration, a change in regulation reserve policy may be required. In this direction, in addition to the deregulation policies, the amount and location of wind turbines, gen- eration technology, and the size and char- acteristics of the electricity system must be considered as important technical aspects. • Continuous development of communica- tions and information technology, as well as market and regulatory frameworks for generation and consumption is necessary for a power system with intelligent elec- tricity meters and intelligent communica- tions (Bevrani, et al., 2011). • The wind turbine units must meet technical requirements with respect to the voltage, frequency, ability to rapidly isolate faulty parts from the rest to the network, and have a reasonable ability to withstand abnormal system operating conditions. They could be able to function effectively as part of the existing electricity industry particular- ly during abnormal power system operat- ing conditions when power system security may be at risk. High wind power penetration, particularly in the locations far away from major load centers and existing conventional generation units increases the risk of tie-line overloading, and may require network augmentation, and possibly additional interconnections to avoid flow constraints. With increasing wind power penetration, the grid codes for the connection high wind turbines capacity should be also updated (Bevrani, et al., 2011). • Furthermore, the updating of existing emergency frequency control schemes for N-1 contingency, economic assessment/ analysis of the frequency regulation prices, further study on frequency and voltage sta- bility using dynamic demand control and ratios of wind turbine technologies, and quantifcation of reserve margin due to in- creasing wind power penetration (Bevrani, et al., 2010) can be considered as other im- portant research needs in future. CONCLUSION In this chapter an intensive overview of wind en- ergy status around the world and Iran is presented. The dynamic model and the main control loops of wind turbine technologies are explained. As a practical case study, the wind power potential, economic issues, and technical challenges for a high penetration of wind power in Kurdistan 214 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms electric network are discussed. The possibility of connecting a STATCOM to the wind power system in order to provide an efficient control method is explored. The STATCOM as a pure static device with no switched passive components, which provides outstanding performance for both steady state and dynamic operation is used as a suitable control solution to decrease the undesir- able impact of wind power plants on the transient stability and to improve the system performance. It is shown that the proposed STATCOM based design strategy provides dynamic voltage control and power oscillation damping, and improves the Kurdistan network transient stability. 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Voltage and frequency control of parallel operated synchronous generator and induction generator with STATCOM in micro hydro scheme. IET Gener. Transm. Distrib., 1(5), 743–750. doi:10.1049/iet-gtd:20060385 Yang, Z., Shen, C., Zhang, L., Crow, M. L., & Atcit- ty, S. (2001). Integration of a StatCom and Battery Energy Storage. IEEE Transactions on Power Systems, 16(2), 254–260. doi:10.1109/59.918295 KEY TERMS AND DEFINITIONS Power System Stability: The ability of a power system to regain a state of operating equilibrium after being subjected to a physical disturbance, with most systems indices (voltage, angle, and frequency) bounded. Power system stability can take three different forms of rotor angle, voltage, and frequency stabilities. Power System Control: This term is used to define the application of control theory and tech- 219 Dynamic Analysis and Stability Improvement Concerning the Integration of Wind Farms nology, optimization methodologies, and expert/ intelligent systems to improve the performance and functions of power systems during normal and abnormal operations. Capacity Factor: Capacity factor is defined as the ratio of the average power output to the rated output power of the wind energy converter system. Wind Rose Diagram: The wind rose diagram illustrates the wind direction in a given site. Fixed Speed Wind Turbine: Wind turbine that is directly connected to the grid with a small speed variation of its rotor. Variable Speed Wind Turbine (VSWT): This type of wind turbine is decoupled from the grid through a power electronic converter and the rotor acts as a flywheel. Static Synchronous Compensator (STAT- COM): A technology being extensively used as dynamic shunt compensator for reactive power control in transmission and distribution system. Levelised Cost of Electricity (LCOE): The LCOE for WPSs can be described as the ratio of the total annualized cost to the annual electricity produced by the system. Weibull Distribution: The probability dis- tribution, which is widely used to describe the long-term records of wind speeds. 220 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 7 INTRODUCTION We examine in this chapter some new Lagrangian heuristics for an important combinatorial optimi- zation problem, a generalized assignment problem. The classical assignment problem involves profit- maximizing assignment of each task to exactly one agent with each agent being assigned to at most one task (a one-to-one assignment). In the generalized assignment problems capacity limits for agents and/or tasks are recognized allowing one-to-many or many-to-many assignment. To our knowledge, the first generalized assign- ment problem was studied by De Maio and Roveda (1971). They consider a transportation problem where each demand point must be supplied by exactly one supply point. Here the agents are the supply points and the tasks are the demand points. The requirements of the demand points do not de- pend on the particular supply point that supplies it, i.e., the requirements are agent-independent. This model was further developed by Srinivasan and Thompson (1972). They made the requirements agent-dependent and are the first ones to propose the model that is known today as the generalized assignment problem. The term generalized assign- Igor Litvinchev Nuevo Leon State University, Mexico Socorro Rangel São Paulo State University, Brazil Many-to-Many Assignment Problems: Lagrangian Bounds and Heuristic ABSTRACT Modifed Lagrangian bounds and a greedy heuristic are proposed for many-to-many assignment problems taking into account capacity limits for tasks and agents. A feasible solution recovered by the heuristic is used to speed up the subgradient technique to solve the modifed Lagrangian dual. A numerical study is presented to compare the quality of the bounds and to demonstrate the effciency of the overall approach. DOI: 10.4018/978-1-61350-138-2.ch007 221 Many-to-Many Assignment Problems ment problem for this type of problem was first introduced by Ross and Soland (1975). Cattrysse and Van Wassenhove (1992), Mo- rales and Romeijn (2004) and Pentico (2007) in their survey papers identify a variety of applica- tions in which GAP has been used either directly or as a sub-problem within a broader model type. When the tasks are jobs to be performed, and the agents are computer networks, we obtain the problem described by Balachandran (1976). Another example is the fixed-charge plant loca- tion problem, where the agents are capacitated plants and the tasks are customers, where each of the customer demands must be supplied from a single plant (Geoffrion and Graves (1974)). Other applications that have been studied are the location problem (Ross and Soland (1977)), the maximal covering location problem (Klastorin (1979)), various routing problems (Fisher and Jaikumar (1981), Bookbinder and Reece (1988)), assignment in parallel and distributed computing (Pirkul (1986), Bokhari (1987)), R & D planning problems (Zimokha and Rubinshtein (1988)), loading problem in flexible manufacturing systems (Kuhn (1995)), production planning (LeBlanc, Shtub, Anandalingam (1999)). The real life applications of the assignment models frequently involve large number of tasks and/or agents thus resulting in large-scale opti- mization problems. However, most large-scale optimization problems exhibit a structure that can be exploited to construct efficient solution tech- niques. In one of the most general and common forms of a structure the constraints of the problem can be divided into “easy” and “complicated”. In other words, the problem would be an “easy” problem if the complicating constraints could be removed. For example, removing agent constraints in the assignment problems results in independent subproblems corresponding to tasks. A well-known way to exploit this structure is to form a Lagrangian relaxation with respect to complicating constraints. That is, the complicating constraints are relaxed and a penalty term is added to the objective function to discourage their viola- tion. The optimal value of the Lagrangian problem, considered for fixed multipliers, provides an upper bound (for maximization problem) for the original optimal objective. The problem of finding the best, i.e. bound minimizing Lagrange multipliers, is called the Lagrangian dual. Lagrangian bounds are widely used as a core of many numerical tech- niques for integer and combinatorial problems, as well as to measure the progress of the main algorithm and derive stopping criteria. In many approximate and heuristic approaches Lagrang- ian solution is used as a starting or a reference point to construct the algorithm. The literature on Lagrangian relaxation is quite extensive, see, e.g.Lemarechal (2007), Frangioni (2005) and the references therein. Frequently a complex system can be rep- resented as a number of coupled subsystems. Accordingly, all constraints can be divided into binding and block ones, such that dualizing binding constraints results in a decomposable Lagrangian problem. In many cases there are different ways to specify subsystems thus resulting in different decomposable Lagrangian problems for the same original problem. For example, in different varia- tions on the assignment problem we may consider either tasks or agent’s constraints as binding ones. Similar properties have routing problems, produc- tion scheduling, location problems, to mention a few (Lasdon, 2002). An approach to improve classical Lagrangian bound was proposed in Litvinchev (2007) and fur- ther developed in Litvinchev, Rangel & Saucedo (2010). The main idea of this approach is to get a tighter estimation of the penalty (complementar- ity) term arising in the classical Lagrangian func- tion. It is well known that under certain convexity and regularity conditions the penalty turns to zero for the optimal primal-dual pair (complementar- ity condition). However, for nonconvex (integer) problems the complementarity condition is not necessarily fulfilled. An auxiliary optimization problem is used to estimate the penalty term and to 222 Many-to-Many Assignment Problems construct the modified Lagrangian bound and the corresponding modified dual problem. Suppose the original problem has two interesting subset of constraints, i.e. both subsets considered sepa- rately have attractive, while different structures. Then we may relax one subset of constraints in the standard Lagrangian fashion, while using the other subset in the auxiliary problem to estimate the penalty term. In this chapter we specify this approach for the many-to-many assignment problem recog- nizing capacity limits for tasks and agents. From Lagrangian point of view it is important to note that relaxing task constraints gives independent subproblems corresponding to agents, while relax- ing agent constraints results in tasks subproblems. Thus both subproblems arising in the modified bound can be solved in a decomposable fashion. The modified Lagrangian bounds are numeri- cally compared with classical ones and a greedy heuristic is applied to the (unfeasible) Lagrangian solution to get an approximate solution to the original problem. Combining the modified La- grangian bound with a greedy heuristic provides high quality feasible solutions typically within 0.5% of relative difference between primal and dual bounds. If the subgradient scheme is used to solve the dual problem, we may restore feasibility by the (computationally cheap) greedy algorithm in each iteration of the subgradient technique and then use this feasible solution to update parameters of the iterative scheme. Incorporating a feasible greedy solution into the subgradient scheme results in a significant decrease in the number of itera- tions without dropping the quality of the bounds. The reminder of the chapter is organized as follows. In Section 2 we present the basic construc- tions to derive the modified Lagrangian bounds and give an illustrative example. The modified bounds for many-to-many assignment problem are specified in Section 3. Benders and the subgradient techniques to solve the dual problem are presented in Section 4, together with a greedy algorithm to restore feasibility of the Lagrangian solution. Numerical results are given in Section 5, future research directions are presented in Section 6 and Section 7 concludes. BASIC CONSTRUCTIONS TO DERIVE THE MODIFIED LAGRANGIAN BOUNDS Consider the problem: z cx Dx d Ax b x U * max | , , , = ≤ ≤ ∈ { } (1) where x∈R n and the set U can be of general structure and may contain, for example, sign con- straints on x and integrality constraints on some or all components of x. The constraints Dx≤d are m “complicating constraints”, while constraints Ax≤b are considered “nice” in the sense that the optimization problem formed with only these constraints, together with x∈U, is easier than the original problem. Denote by x* an optimal solu- tion of (1) and let X={ x∈U | Ax≤b}. Relaxing the “complicating constraints” and using u, an m-vector of Lagrange multipliers, we can define the standard Lagrangian problem as: z u cx u d Dx x X u ( ) max ( ), , = + − ∈ ≥ { } 0 . (2) We assume for simplicity that it has an optimal solution for all u≥0and therefore we get the well known Lagrangian bound: z z u u * ( ), ≤ ≥ for any 0 . (3) The best Lagrangian bound and the associated Lagrange multipliers u* are obtained by solving the Lagrangian dual problem: z u z u w u D ( ) min ( ) * = ≡ ≥0 . (4) 223 Many-to-Many Assignment Problems Suppose now that the original problem (1) has two interesting subproblems, i.e., both constraints Dx≤d and Ax≤b considered separately, have attrac- tive, while different structures. In this case it may be useful to reformulate the original problem prior to relaxation. Introducing copy constraints,x=y, in the original problem it is possible to build a Lagrangian decomposition (Guignard and Kim, 1987) by dualizing them with n multipliers λ∈R n thus obtaining an x-problem and an y-problem: z c x x X y Dy d y U x y ( ) max ( ) | max | , λ λ λ = − ∈ { } + ≤ ∈ { } (5) The Lagrangian decomposition bound is then stated as: z z z w LD * * ( ) min ( ) ≤ = ≡ λ λ λ (6) and can strictly dominate the standard Lagrang- ian bound obtained by dualizing either set of constraints, Dx≤d or Ax≤b. Instead of creating a copy y of the variable x and imposing the constraint x=y, it is possible to transform the original problem by introducing an aggregated copy constraint Dx=Cy, where Cis a matrix of suitable dimension. The aggregate copy constraint is then dualized providing an aggregated Lagrangian decomposition bound (Maculan & Reinoso, 1992), which, in general, is weaker than w LD . In what follows we consider constructions to improve the standard Lagrangian bound and provide two interpretations of the approach: one using a reformulation of the original problem, and another one in terms of a subproblem to estimate the complementarity term. We assume certain information about an op- timal solution to (P), x*: Assumption. A set W⊆R n is known, such that x*∈W. We will refer to W as the localization of x*, or simply the localization. The set W can be defined by manipulating the constraints of the original problem, by querying a decision maker, etc. We will distinguish the case of a priori localization, when the set W is defined before the Lagrangian problem has been solved for some u≥0 and the associated bound z(u) has been calculated, and a posteriori localization, when W is defined or corrected after the Lagrangian problem has been solved. Consider a further modification of the original problem (1): z cx x X Dx Dy y W M = ∈ ≤ ∈ { } max | , , . (7) Since a pair (x,y)=(x*,x*) is feasible to (7), it is a relaxation of the original problem (1) and hence z*=z M . Note also that if the localization W is such that y∈W implies Dy≤d (this is the case, for example, when constraints Dy≤d are included explicitly in the definition of W) then an optimal x-solution to (7) is feasible to (1) and hence z*≥z M . Thus for such a localization we have z*=z M . Dualizing constraints Dx≤Dy with multipliers u≥0 we get the modified Lagrangian bound: z z z u cx uDx uDy M M x X y W * ( ) max max ≤ ≤ = − { } + { } ∈ ∈ (8) The modified bound z M (u) obtained for the localization W={y|Dy≤d,y∈U} coincides with the aggregated Lagrangian decomposition bound calculated for C=D. To simplify further notations, we use η(u)for the optimal objective value of the first maximization problem in (8), and ξ(u) for the optimal objective of the second. The modified dual problem cor- responding to the bound (MLB) is then stated as: w u u MD u = + { } ≥ min ( ) ( ) 0 η ξ . (9) 224 Many-to-Many Assignment Problems It is possible to derive (8) using other ar- guments. The feasibility of x* to the standard Lagrangian problem implies that cx*+u(d- Dx*)≤z(u). Since x* is feasible to (1) and u≥0, then u(d-Dx*)≥0 yields immediately z*≤z(u) as in (3). The complementarity condition u*(d-Dx*)=0 is fulfilled for convex problems (1) which fulfill certain regularity assumptions. But even for the convex case the term u(d-Dx*) can be strictly positive for u≠u*. For the nonconvex case the complementarity term u(d-Dx*) can be strictly positive for u=u*. Thus we may try to strengthen the standard Lagrangian bound z(u) using more tight estimations of the complementarity term instead of u(d-Dx*)≥0. Since x*∈W, then we have for any localiza- tion W z u cx u d Dx cx u d Dy y W ( ) ( ) min{ ( )} * * * ≥ + − ≥ + − ∈ (10) such that: z cx u d Dx u d Dy x X y W * max{ ( )} min{ ( )} ≤ + − − − ∈ ∈ (11) This bound, after elementary algebraic trans- formations, coincides with z M (u) defined in (8). We may expect that for those integer programs, where the constraints Dx≤d are not active for all feasible solutions, a reasonable choice of W may result in θ( ) min ( ) u u d Dy y W = − { } > ∈ 0 , thus improving the standard Lagrangian bound z(u). Calculating θ(u) so far was solely intended to estimate the complementarity term associated with Dx≤d without taking into account the original objective function. We may “balance” z(u) and θ(u) by introducing some information of the original objective in the modified problem. Let LB and UB be (unknown) lower and upper bounds for the optimal objective of (1). Then we may add to (1) the constraint LB≤cx≤UB and dualize it with multipliers π LB− π UB ≥0. Estimating the extended complementarity term u d Dx UB cx LB cx UB LB ( ) ( ) ( ) * * * − + − + − π π (12) and using the localization W as before, gives the bound z z z u cx uDx cy uDy M M x X y W * ( , ) max ( ) max ) . ≤ ≤ = − − { } + + { } ∈ ∈ π π π 1 (13) The unrestricted dual variable π stands for π LB− π UB . The bound z M (u,π) in (13) uses m+1multipliers, an m-vector u and a scalar π, while the Lagrangian decomposition bound, z(λ), uses an n-vector of multipliers, λ. The modified dual problem corresponding to the bound (LMBπ) is stated as: w u u MD u π π η π ξ π = + { } ≥ min ( , ) ( , ) , 0 , (14) where η(u,π)is used to denote the optimal objective value of the first maximization problem in z M (u,π), while ξ(u,π) stands for the optimal objective of the second. It is not hard to verify that aggregating to the problem (7) the valid constraint cx=cyand dual- izing it together with constraints Dx≤Dy we get exactly the same expression for the bound as in (13). Defining Localizations and Estimating ξ(u,π) The critical issue in using the modified Lagrangian bound (13) is constructing a suitable localization W. From the definition of z M (u,π) in (13) it follows that, in general, the tighter the localization W is, the smaller is ξ(u,π) and the better is the modified upper bound z M (u,π). From this point of view, it is worth to retain in the definition of W as many original constraints as possible. However, the localization should be simple enough to guarantee 225 Many-to-Many Assignment Problems that calculating ξ(u,π) in (13) is “easy” (by our assumption on the original problem, the calcula- tion of η(u,π) is “easy”). In particular, defining W all by all original con- straints, we obviously get w W z MD all π ( ) * = with u*=0, π*=1. Since it can be difficult to calculate ξ(u,π) under the localization defined by all (many) constraints, we may try to use estimations of the corresponding value of ξ(u,π). In particular, this can be done either by simply relaxing some com- plicating constraints, or dualizing them to get the Lagrangian bound, standard or modified. If La- grangian relaxation is used to estimate ξ(u,π), we will refer to this case as the nested Lagrangian relaxation. If a localization W y Dy d y U 0 = ≤ ∈ { } | , is used to define θ( ) min ( ) u u d Dy y W = − { } ≥ ∈ 0 0 for any u≥0, then: w z u z u u z u z u D u u u M u M = ≥ − { } = ≥ ≥ ≥ ≥ ≥ min ( ) min ( ) ( ) min ( , ) min ( , 0 0 0 0 0 θ π ,, ) ( ) π π ≡w W MD 0 (15) and we may possibly strengthen the standard dual bound w D by considering the modified Lagrang- ian dual (14). The bound w W MDπ ( ) 0 calculated fixing π=0 coincides with the aggregated Lagrang- ian decomposition bound (Maculan and Reinoso, 1992). If the localization W 0 is decomposable, that is W 0 =W 01 ×W 02 ×…W 0L , the calculation of ξ(u,π) in (14) reduces to L independent subproblems of smaller dimensions. There are many classes of problems with both X and W having such structure and resulting in decomposable calculations of η(u,π) and ξ(u,π). This is often the case for prob- lems with x ij variables: generalized assignment, facility location, multiple knapsack, cutting and packing problems, among others. Another suitable localization resulting in θ( ) u ≥ 0 i s a sur r ogat e l ocal i zat i on W y U uDy ud s = ∈ ≤ { } | , yi el di ng al so w w W D MD s ≥ π ( ). We may interpret the use of localizations W 0 and W s as follows. Instead of calculating the “exact” ξ(u,π). using the localization W all defined by all original constraints, we simply drop constraints Ax≤b and use the associated estimation of the “exact” ξ(u,π). (possibly combining Dx≤d in a unique constraint as in W s . Another way to estimate ξ π ( , ) u is to use La- grangian relaxation, standard or modified, instead of simply dropping constraints. Suppose that the localization has the form: W y Py p y Y U 1 = ≤ ∈ { } | , , where Y R n ⊆ , p R q ∈ and the matrix Pis di- mensioned accordingly. We assume that the set Y has a favorable structure (for example, decompos- able) and we will handle the constraints y∈Y explicitly, and will dualize the constraints Py≤p using a q-vector of multipliers v ≥ 0. Estimating ξ π ( , ) u by the standard Lagrangian bound yields: ξ π π π ξ π ( , ) max max ( ) ( , , u cy uDy cy uDy v p Py u v y W y Y U L ≡ + { } ≤ + + − { } ≡ ∈ ∈ 1 )), ∀ ≥ v 0 (16) while the modified Lagrangian bound (considered for simplicity without dualizing the “objective copy” constraint) results in the estimation ξ π π π ( , ) max max ) max , u cy uDy cy uDy vPy y W y Y U w U Pw p ≡ + { } ≤ + − { } + ∈ ∈ ∈ ≤ 1 vvPw u v v ML ) ( , , ), { } ≡ ∀ ≥ ξ π 0 (17) and ξ π ξ π ML L u v u v ( , , ) ( , , ) ≤ . 226 Many-to-Many Assignment Problems Based on these estimations of ξ π ( , ) u we get two modified dual problems associated with the nested Lagrangian relaxation for localization W 1 that use m+q+1 multipliers: w W u u MD L u v L π π η π ξ π ( ) min ( , ) ( , ) , , 1 0 = + { } ≥ (18) and w W u u MD ML u v ML π π η π ξ π ( ) min ( , ) ( , ) , , 1 0 = + { } ≥ . (19) If both original constraints, Ax≤b and Dx≤d, considered separately are “easy”, then defining Y={y| Dx≤d } and {Px≤p}={ Ax≤b } results in an “easy” calculation of ξ π L u v ( , , ) . For this case we have w W u u v v MD L u v L L π π η π ξ π η ξ ( ) min ( , ) ( , , ) ( , ) ( , , ) ma , , 1 0 0 1 0 1 = + { } ≤ + = ≥ xx ( ) | , cy v b Ay Dy d y U w D + − ≤ ∈ { } ≡ 2 (20) and w W u u cx uDx uDy Dy d y U MD L L x X π η ξ ( ) ( , ) ( , , ) max max | , 1 0 0 0 ≤ + = − { } + ≤ ∈ { ∈ }} ≤ + − { } ≡ ∈ max ( ) . x X D cx u d Dx w 1 (21) Hence w W MD L π ( ) 1 is at least as good as any of the two standard Lagrangian relaxations. Illustrative Example To give an idea on the behavior of the Lagrangian bounds (standard and modified) using the localiza- tions discussed in Section 2.1 consider the follow- ing binary problem (Freville and Hanafi, 2005): z x x x x x * { , } max = + + + ∈ 0 1 1 2 3 4 2 2 (22) 8 16 3 6 18 1 2 3 4 x x x x + + + ≤ , (23) 5 10 8 16 19 1 2 3 4 x x x x + + + ≤ . (24) The optimal solution to this problem is z*=2 with three alternative optimal points x*∈{(0, 1, 0, 0), (0, 0, 0, 1), (1, 0, 1, 0)}. Freville and Hanafi (2005) present several Lagrangian bounds for this problem instance; a summary of their results is as follows. The linear programming relaxation gives z LP =3.04. The optimal multipliers associ- ated to the copy constraints in the Lagrangian decomposition bound are λ * , , , = ( ) 2 3 1 1 1 2 giving w LD = ≈ 2 2 667 2 3 . . The classical Lagrangian bound obtained by dualizing constraint (23) yields w D 1 2 2 923 12 13 = ≈ . with the corresponding mul- tiplier u 1 1 13 * = . Dualizing constraint (24) gives w D 2 2 2 947 18 19 = ≈ . for u 2 2 19 * = . The surrogate relaxation, obtained by combining the two origi- nal constraints into a single one using two multi- pliers µ =( , . ) 1 0 5 gives the bound w s = 3 . To calculate the modified bounds, let Ax≤b be defined by constraint (24) while constraint (23) stands for Dx≤d and is dualized with the multi- plier u≥0. Let U x = ∈ { } { } 1 0 4 , and suppose that the localization W 1 is defined by the two original constraints, such that constraint (23) is used to define the condition y∈Y and is handled explicitly, while constraint (24) stands for Py≤p and is dualized with multiplier v≥0 in the estima- tion of ξ π L u v ( , , ) . Using a standard technique, we present equivalently the dual problem w W MD L π ( ) 1 as a linear programming problem (master problem) having constraints associated with all feasible points of x Ax b U | ≤ { } (for η π ( , ) u ) and of Y U (for ξ π L u v ( , , ) ). Eliminat- ing the redundant constraints we get the complete master problem: 227 Many-to-Many Assignment Problems w W s t u u MD L u v ( ) min . . , , 1 0 2 2 6 3 3 19 0 = + ≥ − − − − ≥ π η ξ η π π ≥ + + + + + − + − , ξ π π π π 8 14 2 16 9 4 17 10 3 14 2 19 u v u v u v u v v (25) where the constraints for η and ξ correspond to the all-nonzero feasible solutions. The optimal solution to the master problem (25) is π = − 1 25 u = 2 25 , v = 0 , η =1 6 . , ξ =1 2 . giving w W w w MD L D D π ( ) , 1 2.8 min 1 2 = < { } =2.923. If we do not use the copy constraint cx cy = that is setting π = 0 in the above master problem, the corresponding solution is, u = ≈ 1 13 0 0769 . v = ≈ 1 247 0 004 . , η = ≈ 20 13 1 538 . , ξ = ≈ 313 247 1 267 . giving w W MD L ( ) 1 693 247 2.8057 = + = ≈ η ξ . Instead of using the Lagrangian relaxation ξ π L u v ( , , ) to estimate ξ π ( , ) u we may use a sur- rogate relaxation. Let W x x x x x s = ∈ { } + + + ≤ { } 1 0 10 5 21 7 14 27 5 4 1 2 3 4 , | . . be the surrogate localization obtained by mul- tiplying constraint (23) by µ 1 1 = , constraint (24) by µ 2 0 5 = . and summing them up. These mul- tipliers are optimal to the surrogate relaxation of the original problem and result in the surrogate bound w s = 3 . For W=W s the modified dual bound w W MD s π ( )is calculated using the linear master problem. Note that the constraints corre- sponding to the variable η in the master problem remain the same as before. The optimal solution to the new master problem is π = 2 15 , u = 1 15 , η ξ = = 4 3 giving w W MD s π ( ) . = ≈ 2 2 667 2 3 , which coincides with the bound w LD obtained by Lagrangian decomposition. If we use a localiza- tion W=W 0 , defined in this case by the constraint (23), and do not use the copy constraint (cx=cy), the associated bound coincides with the aggre- gated Lagrangian decomposition bound. To cal- culate this bound we need to set π=v=0 in the master problem. The associated solution is u = ≈ 1 13 0 0769 . , η = ≈ 20 13 1 538 . , ξ = ≈ 17 13 1 308 . giving the bound η ξ + = ≈ 37 13 2.846 . Let now constraint (23) stands for Ax≤b and constraint (24) be dualized. Moreover, the latter constraint is handled explicitly in the definition of y∈Y, while the constraint (23) is dualized in the estimation of ξ π L u v ( , , ) . After eliminating the redundant constraints, the complete master problem becomes: w W s t u u u MD L u v ( ) min . . , , 1 0 2 2 10 4 4 29 3 3 24 0 = + ≥ − − − − − − ≥ π η ξ η π π π ≥ + + + + + − , ξ π π π 8 15 2 16 12 3 18 18 u v u v u v v (26) Its optimal solution is π = − 4 15 , u = 2 15 , v = 0, η =1 2 . , ξ =1 6 . giving w W MD L π ( ) 1 2.8 = Fixing π =0 in the master problem (and thus computing the bound without the copy constraint (cx=cy), we get the bound η ξ + = 2.826 . Setting π=v=0 (i.e. calculating the aggregated Lagrangian decomposition bound) yields η ξ + = 2.842 . MODIFIED LAGRANGIAN BOUND FOR MANY-TO-MANY ASSIGNMENT PROBLEM The assignment problems (AP) involve optimally matching the elements of two or more sets. When there are only two sets, they may be referred as 228 Many-to-Many Assignment Problems “tasks” and “agents”. For example, “tasks” may be jobs to be done and “agents” may be the people or machines that can do them. In its original ver- sion, the AP involves assigning each task to a different agent, with each agent being assigned to at most one task (a one-to-one assignment). In the generalized assignment problem (GAP) each task is assigned to one agent, as in the classic AP, but it allows for the possibility that an agent may be assigned to more than one task, while recognizing that a task may use only part of an agent’s capacity rather than all of it. Thus GAP is a one-to-many assignment problem that recognizes capacity limits for agents (see Martello and Toth (1990), Pentico (2007) and the references therein). A further generalization of AP is a many-to- many assignment recognizing capacity limits of both tasks and agents. Such a situation arises, for example, in a medical center, where doctors (agents) have to attend their patients (tasks) in a limited time period, while patients cannot also spend a lot time in the center. This leads to the following optimization model: z c x MMAP x ij ij j n i m = ∈ = = ∑ ∑ max { , } 0 1 1 1 (27) a x b i m ij ij j n i = ∑ ≤ = 1 1 , ... , (28) d x d j n ij ij i m j = ∑ ≤ = 1 1 , ... . (29) In what follows we will refer to the problem (27)-(29) as (MMAP). Here x ij =1 if agent i is assigned to task j, and 0 otherwise, c ij is the profit (utility) of assigning agent i to task j, a ij is the amount of agent i’s capacity used to execute task j, and b i is the available capacity of agent i. It is assumed that each task has its own capacity (time) limit, such that d ij is the amount of task j’s capacity used when executed by agent i, and d j is the available capacity of task j. Note that (MMAP) has a double-decomposable structure: if we dual- ize the first m restrictions (28), then the relaxed problem decomposes into n independent subprob- lems, each having a single knapsack-type restric- tion d x d ij ij i m j = ∑ ≤ 1 , while relaxing the second group of restrictions (29) we get m single knapsack constrained subproblems. To derive the modified bounds for the MMAP problem let us define the sets: X x a x b i m X ij ij ij j n i i m i = ∈ { } ≤ = = = = ∑ 1 0 1 1 1 , | , ... Π X x a x b i ij ij ij j n i = ∈ { } ≤ = ∑ 1 0 1 , | (30) Y x d x d j n Y ij ij ij i m j j n j = ∈ { } ≤ = = = = ∑ 1 0 1 1 1 , | , ... Π Y x d x d i ij ij ij i m j = ∈ { } ≤ = ∑ 1 0 1 , | (31) Py p y a y b i m ij ij ij j n i ≤ { } ≡ ∈ { } ≤ = = ∑ 1 0 1 1 , | , ... (32) and the localization: W y y Y Py p ij 1 1 0 = ∈ { } ∈ ≤ { } , | , . (33) The original constraints included in the set X will be considered as “easy”, while those in Y will be treated as “complicating”. Localization W 1 will be used in the modified Lagrangian dual to cal- culate the value w W MD L ( ) 1 . We will handle con- straints y∈Y explicitly, while restrictions Py≤p will be dualized in the estimation of ξ π ( , , ) u v . L e t u u j n j = = { } ≥ , 1 0 a n d v v i m i = = { } ≥ , 1 0 be the Lagrangian mul- tipliers. Then the modified Lagrangian dual for (MMAP) is: 229 Many-to-Many Assignment Problems w W u v MD L u v π π ϕ π ( ) min ( , , ) , , 1 0 = ≥ (34) where: ϕ π η π ξ π ( , , ) ( , ) ( , , ) u v u u v L = + , (35) η π π ( , ) max ( ) u c u d x x X ij j ij ij j n i i = − − l l l ' ! 1 1 + 1 1 ' ! 1 1 + 1 1 ∈ = = ∑ 1 1 11 m ∑ , (36) ξ π π L y Y ij j ij i ij ij i m u v c u d v a x i ( , , ) max ( = ÷ − l l l ' ! 1 1 + 1 1 ' ! 1 ∈ = ∑ 1 11 + 1 1 ÷ = = ∑ ∑ j n i i i m v b 1 1 (37) SOLVING THE DUAL PROBLEMS In this section we describe two main procedures to solve the dual problems defined in Section 3 for the MMAP. First we apply a constraint gen- eration scheme (Benders method) transforming the modified dual problem (18) into a large-scale linear programming problem (Section 4.1). The main advantage of using Benders technique is that it generates upper and lower bounds for w MD L π in each iteration thus producing near-optimal solutions with guaranteed quality. The objective is to compare the quality of the modified and classical Lagrangian bounds. A simple greedy heuristic to obtain feasible solutions to (MMAP) is presented in Section 4.2. The feasible greedy solution is then used in a subgradient algorithm to obtain the modified bounds (Section 4.3). Solving the Dual Problem by Benders Technique In this section we apply a constraint generation scheme (Benders method) to solve the modified Lagrangian dual (18) without considering the copy constraints, cx=cy, that is setting π=0. The main focus of this approach is to compare the quality of the bounds. Benders technique provides upper and lower bounds for w W MD L ( ) 1 in each iteration thus producing near-optimal values of the dual bounds with guaranteed quality. Let x t T ij t , = { } 1 and y t L ij l , = { } 1 be all feasible points of X and Y. Then the dual prob- lem (MD L ) used to compute w W MD L ( ) 1 can be stated as follows: w W MD L u v R ( ) min ( ) , ; , 1 0 = − ≥ ∈ η ξ η ξ (38) subject to η ≥ + − = = = = ∑ ∑ ∑ u d c u d x t T j j j n ij j ij ij t j n i m 1 1 1 1 ( ) , ... , (39) ξ ≤ − + − = = = = = ∑ ∑ ∑ ∑ u d v b v a u d y l L j j j n i i i m i ij j ij ij l j n i m 1 1 1 1 1 ( ) , ... . (40) In what follows we will refer to the (master) problem (38)-(40) as (MP). The latter is an LP problem having 2+m+n variables and a large number of constraints - one for each feasible point of X and Y. To solve master problem (MP) we use constraint generation scheme in the form of Benders algorithm. We omit here the complete de- scription of this well known iterative method (see Lasdon (2002), and Martin (1999) for details) and focus only on the constraint generation scheme. Consider that on the k-th iteration we have a restricted master problem (RMP k ), having fewer constraints (39) and (40) compared to (MP). Denote its optimal solution by u v k , , , η ξ ( ) . To check the feasibility of this solution to all con- straints (39) we need to verify if: η k j k j j n ij j k ij ij t j n i m u d c u d x t T − ≥ − = = = = ∑ ∑ ∑ 1 1 1 1 ( ) , , ..., , (41) 230 Many-to-Many Assignment Problems or equivalently: η k j k j j n x X ij j k ij ij j n i m x X ij u d c u d x c i − ≥ − ≡ − = ∈ = = ∈ ∑ ∑ ∑ 1 1 1 max ( ) max ( uu d x j k ij ij j n i m ) , = = ∑ ∑ 1 1 (42) where the maximization over X is reduced to independent maximizations over X i due to decom- posable structure of X. That is to verify the fea- sibility with respect to constraints (39) we need to solve m independent subproblems each one having a single knapsack constraint and n binary variables. Denote by x ij k { } their optimal solution. Similarly, to check the feasibility with respect to constraints (40) we need to verify: ξ k j k j j n i k i i m y Y i k ij j k ij ij y Y u d v b v a u d y j − + ≤ − ≡ = = ∈ ∈ ∑ ∑ 1 1 min ( ) min (vv a u d y i k ij j k ij ij i m j n j n i m − = = = = ∑ ∑ ∑ ∑ ) , 1 1 1 1 (43) which results in solving n independent subprob- lems with a single knapsack constraint and m binary variables. Let y ij k { } be their optimal solu- tion. If (42) and (43) are fulfilled, stop with u v k , , , η ξ ( ) optimal to (MP). If (42) fails, add: η ≥ + − = = = ∑ ∑ ∑ u d c u d x j j j n ij j ij ij k j n i m 1 1 1 ( ) (44) to the restricted master problem. If (43) fails, add: ξ ≤ − + − = = = = ∑ ∑ ∑ ∑ u d v b v a u d y j j j n i i i m i ij j ij ij k j n i m 1 1 1 1 ( ) (45) to the restricted master problem. So in each itera- tion we add at most two constraints to (RMP k ) to get the next restricted master problem (RMP k+1 ). On the k-th iteration of Benders technique we have a lower and an upper bound for the optimal value w W MD L ( ) 1 of (MP): LB w W z u u v UB k k k MD L s k s s s k = − ≤ ≤ − { } = = ( ) ( ) min ( ) ( , ) , ... η ξ θ 1 1 (46) where the minimum is taken over all previous iterations and for the iteration s we have: z u u d c u d x s j s j j n ij j s ij ij s j n i m ( ) ( ) = + − = = = ∑ ∑ ∑ 1 1 1 (47) and θ( , ) ( ) u v u d v b v a u d y s s j s j j n i s i i m i s ij j s ij ij s j n i = − + − = = = = ∑ ∑ ∑ 1 1 1 1 mm ∑ (48) The iterative process terminates if, for ex- ample,( ) / , UB LB LB k k k − ≤ ε where ε>0 is a given threshold. Assuming the objective coefficients in (MMAP) are nonnegative we have z MMAP ≥ 0 . The optimal solution u v , , , * η ξ ( ) to the problem (MP) then satisfies: 0 1 ≤ ≤ = − z w W MMAP MD L ( ) * * η ξ , 0 ≤ ≤ = z z u MMAP ( ) * * η . (49) Thus we can add to the master problem (MP) the trivial restrictions η ξ − ≥ 0 and η ≥ 0 at beginning of the constraint generation process in order to prevent the objective function from de- creasing unboundly at early iterations. Restoring Primal Feasibility by a Greedy Heuristic The modified Lagrangian dual (18) provided high- quality bounds for the (MMAP) for the instances tested in (Litvinchev & Rangel, 2008; Litvinchev, Rangel & Saucedo, 2010). It turned out that the corresponding integer Lagrangian solutions (x,y) had a higher degree of primal feasibility and sub- 231 Many-to-Many Assignment Problems optimality than the standard Lagrangian solution. In this section we consider a greedy algorithm to recover primal feasibility. The feasible solution is also used in a subgradient algorithm to obtain the modified bounds (Section 4.3). To get a feasible Lagrangian based solution we use a simple greedy approach. First we try to decrease to zero some components currently equal to 1 to obtain a feasible solution. The choice of the candidate component is based on the smallest decrease of a rounding indicator (e.g. minimal cost component). After a feasible solution is obtained we try to increase to 1 some zero components based on the largest increase of another rounding indicator (e.g., maximal cost component) while maintaining feasibility. Let x 0 be a current binary point not necessary feasible to (MMAP). Let Ω 1 be a set of all pairs (i,j) with x ij 0 0 = and Ω 1 be a set of all pairs (i,j) wi t h x ij 0 1 = . Denot e δ i i ij j ij b a x = − ∑ 0 , σ j j ij i ij d d x = − ∑ 0 . If min , ij i j δ σ { } ≥ 0 then x 0 is feasible to (MMAP). Otherwise, we first decrease, in a greedy manner, some positive x ij 0 to 0 to get a feasible solution (x gr ). Then we try to improve this feasible solution by increasing, in a greedy fashion, some zero components to 1. Algorithm 1 1. Let x 0 be a Lagrangian solution (x y or ). Set x gr = x 0 . 2. Set t r ij ij , as the rounding indicators (e.g.t c r c ij ij ij ij = = , see Comment 1). 3. Feasibility test. 3.1. For x 0 compute δ σ i j , . 3.2. While min , ij i j δ σ { } ≥ 0do (rounding down) 3.2.1. Compute: min ij ij t ∈ { } Ω 1 . Let this minimum be attained for (i,j)’. 3.2.2. Set: 3.2.3. x ij gr = 0 for (i,j)=(i,j)’, 3.2.4. Ω Ω 1 1 = { } \ ( , )' i j , Ω Ω 0 0 = { } ( , )' i j 3.2.5. δ δ σ σ i i i j j j i j a d = + = + ( , )' ( , )' , , 3.3. end_while 4. Let x gr be a feasible solution obtained in the rounding down step, and S 0 0 ⊆ Ω be a set of ( , ) i j ∈ Ω 0 with both a ij i ≤δ and d ij j ≤ σ 5. while S 0 0 ≠ do (rounding up) 5.1. Compute max ij S ij r ∈ { } 0 . Let this maximum be attained for (i,j)’. 5.2. Set 5.2.1. x ij gr =1 for (i,j)=(i,j)’, 5.2.2. Ω Ω 1 1 = { } ( , )' i j , Ω Ω 0 0 = { } \ ( , )' i j 5.2.3. δ δ σ σ i i i j j j i j a d = − = − ( , )' ( , )' , , 5.2.4. update S 0 5.3. end_while 6. Return greedy solution x gr . 7. End Algorithm 1. 232 Many-to-Many Assignment Problems Algorithm 1 gives a summary of the Greedy Heuristic, its flowchart can be seen in Figure 1. Comment 1. The rounding down part of the Algorithm 1 may be based on pure cost criterion t ij =c ij . It is also possible to use another indicator, setting for example, t ij =c ij /max{a ij ,d ij }. In this way we can take into account the impact of the component (i,j) in violating the constraints (the larger the values of a ij ,d ij the faster we get feasibil- ity). Similarly, we can try t ij =c ij /max{a ij /b i ,d ij /d j } since the relative values a ij /b i ,d ij /d j also give a measure of feasibility. In the rounding up part of the Algorithm 1 we may use r ij = t ij . Alternatively, we can use r ij = c ij /min{ a ij , d ij }. Small values of a ij ,d ij help to obtain a small degradation in the solution feasibility. Another possibility is to set r ij =c ij /min{a ij /b i ,d ij /d j }. Figure 1. Flowchart of Algorithm 1 233 Many-to-Many Assignment Problems The Lagrangian solution is always feasible either to the first or to the second group of con- straints of the problem (MMAP). So we can simplify Algorithm 1 by considering only δ σ i j ( ) when rounding down, depending on whether x or y is used for rounding the modified Lagrangian solution. Solving the Dual Problem by the Subgradient Technique A popular approach to solve the dual problem is by subgradient optimization. Here we present the basic steps of the subgradient technique used in Litvinchev et al. (2010a) to calculate w W MD L ( ) 1 and modified to use the greedy solution obtained by the Algorithm 1 (Litvinchev et al., 2010). A more detailed discussion of subgradient optimiza- tion can be found in Martin (1999) and Wolsey (1998). Let u v k , , π ( ) be the values of the Lagrangian multipliers for the iteration k, φ φ π k k k k u v = ( , , ) and x ij k , y ij k be the associated subproblems solu- tions: x c u d x ij k x X k ij j k ij ij j n i = − − l l l ' ! 1 1 + 1 1 ' ! 1 1 + 1 ∈ = ∑ arg max ( ) 1 1 π 11 , (50) y c u d v a x ij k y Y k ij ij k ij i k ij ij i m i = ÷ − l l l ' ! 1 1 + 1 1 ' ∈ = ∑ arg max (π 1 !! 1 1 + 1 1 . (51) After solving the subproblems, a subgradient is directly identified as: γ φ π k k ij ij k j n i m ij ij k j n i m c x c y = ∂ ∂ [ ] = − + = = = = ∑ ∑ ∑ ∑ / 1 1 1 1 (52) α φ i k i k i ij ij k j n i m v b a y = ∂ ∂ [ ] = + = = ∑ ∑ / 1 1 , (53) β φ j k j k ij ij k j n i m ij ij k j n i m u d x d y = ∂ ∂ = − + = = = = ∑ ∑ ∑ ∑ / 1 1 1 1 (54) Denote by s k a vector composed of all γ α β k k k , , { } , let λ π k k k k u v = { } , , and set: λ λ ε φ φ k k k k LB k k s s + = − − 1 2 ( ) , (55) whereε k ∈(0,2], φ LB is a lower bound on φ π * ( ) = w W MD L 1 . Sincez w W MMAP MD L ≤ π ( ) 1 , we may set φ LB equal to the objective function value of (MMAP) associated to a given feasible solu- tion. In what follows we will apply the greedy algorithm in each iteration to get a feasible solu- tion and update φ LB accordingly. Since u,v≥0, the multipliers for the next it- eration are defined as the projection of u k and v k onto the nonnegative orthant, while π has no sign restrictions: u u v v k k k k k k + + + = { } = { } = 1 1 1 0 0 max , , max , , . π π (56) A summary of the subgradient algorithm to compute the modified bound for the (MMAP) is given by Algorithm 2 and its flowchart can be seen in Figure 2. The subgradient method is not monotone, that is, it is not necessary that φ φ k k ≥ +1 . In practice, the parameter ε k is varying in (0,2], beginning with ε k =2. If after K consecutive iterations with a fixed value for ε k the function φ does not improve “sufficiently’”, then a smaller value of ε k is used, say, a half of ε k . The stopping criteria used in Algorithm 2 are: a) maximum iteration number is reached; b) ε k is already small enough; or c) the relative difference between the best integer fea- 234 Many-to-Many Assignment Problems sible solution found so far and the Lagrangian bound is within a given threshold. COMPUTATIONAL TESTS The objective of the following numerical study is to compare the relative quality of the bounds as well as their proximity to the optimal objective. We numerically compare the Lagrangian bounds for two sets of instances of (MMAP): Set1 instances with sizes m×n for m=5,8,10 and n=50 and Set2 instances with m=5,10,20 and n=100. The data were random integers generated as follows: c U a U d U b ij ij ij i ∈ ∈ ∈ [ , ], [ , ], [ , ], 10 5 0 5 25 3 20 = − = − ≤ ≤ ∑ ∑ α α α ( ), ( ), a d d ij i j ij j 1 1 0 1 (57) Figure 2. Flowchart of Algorithm 2 235 Many-to-Many Assignment Problems and divided in three classes (a, b, and c) with respect to the values of α: α(α=1), b(α =0.9) and c(α=0.8). More details of the data generation can be found in Litvinchev et al. (2010a). We divided the computational study for prob- lem (MMAP) in two parts. In Part 1, the standard and modified bound without the copy constraints (π=0) were calculated using the Benders technique described in Section 4.1. These results are pre- sented in Section 5.1. In Part 2 the Lagrangian-type bounds, standard and modified, were calculated by the subgradient method. We used two versions of Algorithm 2 presented in Section 4.3. First we compute the Lagrangian bounds without using the greedy solution given by Algorithm 1. That is, the steps 2 and 3.2 of Algorithm 2 were not executed and we modified step 3.3. Since all the objectives coefficients of problem MMAP are positive, we set φ LB =0 (this parameter is necessary in step 3.5). This version of the subgradient algorithm will be named as Algorithm 2a. Then Algorithm 2 was applied as it is stated in section 4.3. Algorithm 2a (Subgradient algorithm without using a greedy solution) Algorithm 2 with the following modifications: Replace step 2 by: Set φ φ UB LB 0 0 0 = ∞ = , Replace step 3.3 by: Let φ φ LB k LB k + = 1 and φ φ φ UB k UB k k + = { } 1 max , End Algorithm 2a. The Benders and the subgradient algorithm were coded using the modeling language AMPL (Fourer, Gay & Kernighan, 1993) and all the associated optimization subproblems solved by the system CPLEX 10.0 (ILOG, 2006). The runs with the Benders algorithm was executed on a machine Pentium 4, 3.2GHz, 2GB RAM and the runs with the subgradient algorithm were executed on a machine AMD Athlon 64X2 Dual Core, 2.8 GHz and 2048MB RAM. For all problem instances we have calculated: z IP - optimal objective of the problem (MMAP), z LP - optimal objective of the LP relaxation of the problem (MMAP), Algorithm 2 1. Given initial values for u v 0 0 0 , , π . 2. Set φ φ UB LB 0 0 = ∞ = −∞ , . 3. While (not stop) do 3.1. Compute x y ij k ij k , by (50), (51) and let φ φ π k k k k u v = ( , , ) . 3.2. Use Algorithm 1 to obtain feasible solutions x gr and y gr with objec- tive values cx gr and cy gr respectively. 3.3. Letφ φ LB k LB k gr gr cx cy + = { } 1 max , , , φ φ φ UB k UB k k + = { } 1 max , 3.4. Compute s k k k k = { } γ α β , , by (52)-(54). 3.5. Update λ k+1 by (55) with φ φ LB LB k = . 3.6. Project u k and v k onto the nonnegative orthant u u v v k k k k + + = { } = { } 1 1 0 0 max , , max , . 3.7. Make stop tests. 4. end_while 5. end Algorithm 2 236 Many-to-Many Assignment Problems zlag - classical Lagrangian bound w D (comput- ed by Benders and Algorithm 2a), z lag gr - classical Lagrangian bound w D (computed by Algorithm 2), Z MD - modified Lagrangian bound w MD L (com- puted by Benders and Algorithm 2a), z MDπ - modified Lagrangian bound w MD L π (computed by Algorithm 2a), z MD gr π - modified Lagrangian bound w MD L π (computed by Algorithm 2). The relative quality of the bounds was mea- sured by: rel z z z z md ip md ip 0 100 = − − π %, rel z z z z md ip lag ip 1 100 = − − %, rel z z z z md ip lp ip 2 100 = − − %, rel z z z z lag ip lp ip 3 100 = − − %, where each indicator compares two subsequent bounds. Here rel0 indicates improvement obtained by introducing the “objective copy constraint” (cx=cy) in the modified bound, rel1 represents improvement of the modified bound with π = 0 over classical, rel2 shows the strength of the modified bound over LP relaxation, and rel3 compares the quality of classical bound with LP-bound. The proximity to the optimal integer solution was represented by: gap z z z md ip ip 0 100 = − π %, gap z z z gr md gr ip ip 0 100 = − π %, gap z z z md ip ip 1 100 = − %, gap z z z lag ip ip 2 100 = − %, gap z z z gr lag gr ip ip 2 100 = − % gap z z z lp ip ip 3 100 = − %. For the problem instance 20 × 100c we were not able to find the optimal solution, CPLEX aborted due to insufficient memory. The best integer solution found after examining 316,560 nodes in the branch and cut tree was used then to calculate the indicators. Results for MMAP Using Benders Technique In this section we describe the computational results obtained when computing the standard (w D ) and the modified bound w MD L using the Benders technique described in Section 4.1, the objective was to compute the bounds with a con- trolled precision. The constraint generation stops when( ) / . UB LB LB k k k − ≤ 0 0001 or the time limit of two hours was reached. The numerical results obtained for the small and moderate prob- lems in Set1 and Set2 are given in Tables 1 and 2, respectively. For each problem, the tables give the instance dimension (m,n), its class (a,b,c), the relative quality of the bounds (rel1,rel2,rel3), the proximity to the original optimal value (gap1,gap2,gap3), and the respective numbers of iterations, iter(z MD ) and iter(z lag ), required for computing the standard and modified Lagrangian bounds by the constraint generation method. An inspection of the Tables 1 and 2 shows that the modified bound is better than the classical one (rel1<rel3) for all the generated problems and is considerably better for problems of class a. The improvement in the bound for problems of class 237 Many-to-Many Assignment Problems c is insignificant. When z LP is close to z IP (small values of gap3) for both Lagrangian bounds, few possibilities are available for improvements. That is the case for the instance 20×100b which has gap3=0.78 and gap1=0.72 (See Table 2). Overall, the results suggest that the difference between the modified and classical bounds is larger for larger values of gap3. In other words, the worse is the continuous relaxation, the more possibilities we have for improving the classical Lagrangian bound. For all the problems except for the last two in Table 1, we have rel1<rel3; i.e., assuming that z lag sufficiently improves z LP for these prob- lems, the same can be concluded about the relation between z MD and z lag . The number of iterations depends weakly on the type of the Lagrangian bound and tends to increase with dimension. Results for MMAP Using a Subgradient Algorithm All Lagrangian-type bounds were calculated by the subgradient method. First we applied Algo- rithm 2a to compute the modified bound, with and without the copy constraints (z MD, zM D) . Then we applied Algorithm 2 to study how the greedy solution given by Algorithm 1 can improve the bound quality. The latter is also used to speed up the subgradient scheme to solve the modified Lagrangian dual problem. For both Algorithms 2 and 2a we used K=5, and if Table 1. Relative quality of the bounds; results by benders; set1 n=50 class rel1 gap1 iter(z MD ) rel2 gap2 iter(z lag ) rel3 gap3 a 61.28 6.63 426 60.22 10.82 545 98.73 11.01 b 77.82 5.58 577 77.71 7.17 516 99.87 7.18 c 67.28 2.20 860 66.67 3.27 755 99.07 3.3 a 77.99 4.36 609 72.66 5.59 576 93.16 6.00 b 88.07 1.92 751 86.88 2.18 748 97.82 2.21 c 97.77 3.08 925 95.65 3.15 915 97.83 3.22 a 82.48 3.25 639 74.03 3.94 543 89.75 4.39 b 95.74 1.35 844 90.6 1.41 854 94.63 1.49 c 99.38 1.61 851 93.06 1.62 811 93.64 1.73 Table 2. Relative quality of the bounds; results by benders; set2 n=100 m class rel1 gap1 iter(z MD ) rel2 gap2 iter(z lag ) rel3 gap3 a a 66.66 7.40 1195 66.66 11.10 1938 100 11.1 5 b b 77.81 5.05 1548 77.81 6.49 1258 100 6.49 c c 76.85 3.42 2717 76.85 4.45 2452 100 4.45 a a 79.62 3.40 1941 77.62 4.27 2253 97.49 4.38 10 b b 95.00 1.14 2508 93.44 1.20 2843 98.36 1.22 c c 98.93 1.96 2822 98.50 1.98 3548 99.5 1.99 a a 86.95 1.40 2474 76.50 1.61 2414 87.98 1.83 20 b b 96.00 0.72 3988 92.31 0.75 3898 96.15 0.78 c c 93.22 0.55 3117 90.16 0.59 3931 93.44 0.61 238 Many-to-Many Assignment Problems (( ) / ) . φ φ φ k k UB k − ≤ + + 1 1 0 005 for 5 consecutive iterations with fixed ε k , this parameter was updated to ε k+1= ε k /2. The stopping criteria were specified as follows: a) at most 250 iterations were permitted; b) the runs stop if ε k+1 ≤0.005; or c) (( ) / ) . φ φ φ UB k LB k LB k + + + − ≤ 1 1 1 0 0001. The numerical results obtained for the problems in Set1 and Set 2 using Algorithm 2a are given in Tables 3 and 4, respectively. For each problem, the tables give the instance dimension (m,n), its class (a,b,c), the relative quality of the bounds (rel0,rel1,rel2,rel3), the proximity to the original optimal value (gap0,gap1,gap2,gap3). The results in Table 3 (Set 1) and Table 4 (Set 2) were obtained within a time limit of 240 s and 360 s respectively. The values of the indicators were calculated based on the best values of the bounds obtained up to the final iteration. As can be seen from Tables 3 and 4, for all problem in- stances we have rel0 < 100%, that is, the use of the objective copy constraint (cx = cy) has a beneficial effect in the computation of the modi- fied bound. Moreover, gap0 is significantly smaller than min{gap1,gap2,gap3} for all instances (except for 20 × 100c), which means that z MD is superior to all other bounds within the computational time limit. In most cases gap0 < 0.5% and for all problems of the class a the exact bound was ob- tained, gap0 = 0. Note that for problem instances with gap0 = 0 the proposed bound zM D c annot Table 3. Relative quality of the bounds; results by Algorithm 2a (the subgradient method); set1 n=50 m class rel0 gap0 rel1 gap1 rel2 gap2 rel3 gap3 a a 0 0 59.93 6.65 60.37 11.09 100.73 11.01 5 b b 0 0 78.39 5.88 81.79 7.5 104.33 7.18 c c 15.12 0.36 66.47 2.4 72.78 3.61 109.5 3.3 a a 0 0 76.06 4.38 72.96 5.76 95.92 6 8 b b 5.89 0.12 78.72 1.96 88.61 2.49 112.56 2.21 c c 9.67 0.32 98.02 3.35 104.06 3.42 106.16 3.22 a a 0 0 80.88 3.3 75.19 4.08 92.96 4.39 10 b b 20.09 0.28 85.89 1.39 93.56 1.62 108.93 1.49 c 24.83 0.51 109.24 2.04 117.48 1.86 107.55 1.73 Table 4. Relative quality of the bounds; results by Algortihm 2a (the subgradient method); set2 n=100 m class rel0 gap0 rel1 gap1 rel2 gap2 rel3 gap3 a a 0 0 66.68 7.44 67.04 11.16 100.54 11.1 5 b b 0 0 73.43 5.02 77.34 6.84 105.32 6.49 c c 0.93 0.03 70.79 3.37 75.8 4.76 107.07 4.45 a a 0 0 77.61 3.42 78.05 4.41 100.57 4.38 10 b b 5.75 0.07 76.97 1.18 96.52 1.53 125.4 1.22 c c 7.26 0.17 107.98 2.37 118.92 2.19 110.14 1.99 a a 0 0 91.22 1.5 82.13 1.65 90.03 1.83 20 b b 8.4 0.08 107.71 0.98 125.48 0.91 116.5 0.78 c 77.41 0.79 139.73 1.02 165.02 0.73 118.1 0.62 239 Many-to-Many Assignment Problems be outperformed by any other bound. For most instances of class c we have gap3=min{gap1,gap2}, so the LP bound is better than zlo g, zmd o btained within the time limit. In Section 5.1 the results of t he Be nde r s me t hod s howe d t ha t gap1<gap2<gap3for all classes. However, for the class c the difference in these indicators was very modest: for small values of gap3 there is a little scope for bound improvements. As a byproduct of the bound computation ( w MD L π ) an integer Lagrangian solution y was obtained having a much higher degree of primal feasibility and subopti- mality than the standard Lagrangian solution. (see Litvinchev, Rangel & Saucedo, 2010) for more details on the constraint violation and suboptimal- ity of the Lagrangian solutions (x,y)). To study the effect of introducing a heuristic solution on the calculation and quality of the dual bounds we applied Algorithm 2 to compute the standard ( z lag gr ) and the modified ( z MD gr π ) Lagrang- ian bounds. The numerical results obtained for the problems in Set1 and Set 2 are given in Tables 5 and 6, respectively. For each problem, the tables give the instance dimension (m,n), its class (a,b,c), the proximity to the original optimal value (gap0 gr ,gap0,gap2 gr ,gap2) and the number of it- erations (iter). For all instances with gap0 gr =gap0=0.00 the stopping criterion (c) was fulfilled. For all other instances the runs were terminated by the stopping criterion (b). As can be seen from Tables 5 and 6, incorporating a greedy solution in the subgradient algorithm slightly improves the quality (of the approximate values) of the bounds obtained by the subgradient method, but the effect is rather modest. For all problem instances the modified bound (gap0 gr ) is significantly tighter than the classical Lagrangian bounds (gap2 g gap2). More- over, the number of iterations of the subgradient method reduces significantly by using a greedy solution. This takes place for all problem in- stances. Note that the computational cost for one iteration of the subgradient technique (solving integer Lagrangian problems) is much higher than the one for obtaining a greedy solution (simply reordering data). Thus combining the subgradient method with a “cheap feasibility recovering” technique is favorable for this class of problem. The greedy solutions derived by the modified bound are better than the ones resulting from the standard Lagrangian bound (see Litvinchev et al., 2010b for the details). Table 5. Relative quality of the bounds; results by the subgradient method (Algorithm 2 and 2a); set1 n=50 m class gap0 gr gap0 gap2 gr gap2 iter( z MD gr π ) iter( z MDπ ) iter( z lag gr ) iter(Z lag ) a 0 0 10.91 11.09 5 165 55 100 5 b 0 0 7.22 7.5 5 80 74 125 c 0.12 0.36 3.29 3.61 55 110 80 85 a 0 0 5.62 5.76 5 80 55 110 8 b 0.09 0.12 2.19 2.49 75 125 95 200 c 0.11 0.32 3.17 3.42 55 75 80 145 a 0 0 3.96 4.08 5 130 55 65 10 b 0.07 0.28 1.42 1.62 65 70 74 115 c 0.2 0.51 1.63 1.86 55 170 67 115 240 Many-to-Many Assignment Problems Discussion The results obtained by the Benders technique and presented in Tables 1, 2 demonstrate that the modified bounds are tighter than the classical Lagrangian bounds (rel1<100%). For problem instances where the continuous relaxation is weak (gap3 is large enough) the modified bounds are significantly tighter. It is important to note that the values of the bounds obtained by the Bend- ers technique were computed with a high accu- racy, the guaranteed relative error of the bound computation was less than 0.0001. That is, the Benders technique provides “real” values of the bounds and in this sense the indicators presented in Tables 1, 2 are independent on the method used to get the bounds. So we may conclude that the superiority of the modified bounds is an inherent property of the bounds and not the result of the loose computations for the classical bounds. The precise computations by the Benders technique provide the bounds with guaranteed accuracy but result in a high computational cost. Typically the number of the main iterations to solve the master problem (MP) increases significantly with the size of the problem instance: for most instances with m=10,20 presented in the Table 2 it was necessary nearly 2 hours of the CPU-time to get the desired accuracy in the bounds computations. Thus, the use of the Benders technique was important to prove numerically the superiority of the modi- fied bounds, but this method in its current form cannot be recommended for practical calculations of the bounds. To speed up the bounds calculation the sub- gradient technique was used to solve the classical and modified dual problems. In contrast to the Benders method, the subgradient technique does not provide the value of the bounds with the prescribed accuracy. That is, terminating iterations of the subgradient method using the stopping criteria a)-c), we can expect only approximate values of the bounds. As we can see from the Tables 3 and 4, for some instances the value of the indicator rel1 is higher than 100%. This does not mean that the classical bound is tighter, this only means that at the moment that the subgradi- ent algorithm stopped, a better approximation was obtained for the classical bound (see the exact values of rel1 in Tables 1, 2). Tables 3, 4 also Table 6. Relative quality of the bounds; results by the subgradient method (Algorithm 2 and 2a); set2 n=100 m class gap0 gr gap0 gap2 gr gap2 iter( z MD gr π ) iter( z MDπ ) iter( z lag gr ) iter(Z lag ) a 0 0 11.28 11.16 5 190 75 95 5 b 0 0 6.53 6.84 5 100 49 110 c 0.02 0.03 4.48 4.76 70 60 75 110 a 0 0 4.31 4.41 5 175 60 105 10 b 0.04 0.07 1.21 1.53 65 55 70 175 c 0.11 0.17 1.99 2.19 70 85 79 65 a 0 0 1.61 1.65 5 85 49 90 20 b 0.07 0.08 0.76 0.91 70 105 65 135 c 0.11 0.79 0.59 0.73 80 180 49 130 241 Many-to-Many Assignment Problems present the proximity indicator gap0 for the bound w MD L π , obtained by using the objective copy con- straint (cx=cy), and the proximity indicator gap2 for the classical Lagrangian bound. As can be seen from the Tables, gap0 is significantly smaller than gap2. That is the approximation of the boundw MD L π obtained by the subgradient tech- nique is much closer to the optimal objective comparing to the approximation of the classical bound. Moreover, gap0 is almost 10 times smaller than gap1 obtained by the Benders tech- nique and presented in Tables 1, 2. Thus, we may conclude that introducing the objective copy constraint has a beneficial effect in the computa- tion of the modified bound (see the end of the Section 2.1 for theoretical discussion of this sub- ject). Computing the classical Lagrangian bound results in a solution of Lagrangian problem which is frequently used as a starting or reference point in heuristic techniques. In the case of the modified bound we have two Lagrangian solutions, x and y, both different from the classical Lagrangian solution. To recover a feasible solution from an infeasible Lagrangian one we used a simple greedy heuristic (Algorithm 1). The results presented in the Tables 5 and 6 show that: a) combining the subgradient scheme with the best feasible greedy solution (Algorithm 2) improves significantly the convergence of the subgradient method and b) this improvement was obtained without dropping the quality of the bounds and feasible solutions. We note that to get the modified bound the Algorithm 2 either stops after 5-8 iterations or achieves the main improvement (in terms of the quality of the modified bound and the corresponding feasible solution) within the same range of iterations. From practical point of view, it is sufficient to execute at most 10 iterations of the Algorithm 2, extra iterations will only slightly change the overall picture. Thus we may conclude that the proposed ap- proach (Algorithm 2) can be useful for practical solution of the MMAP. It takes a few iterations to get an approximate feasible solution within 0.1% of the relative suboptimality. The main compu- tational cost is associated to solution of the n+m independent one-dimensional knapsack problems ((50), (51)) in each iteration. Recovering feasibility of the modified Lagrangian solution by the greedy algorithm is significantly cheaper. The core of the Algorithm 2 is the modified Lagrangian bound. It provides tight approximation of the optimal objective and results in an integer Lagrangian solution having a high degree of primal feasibil- ity and suboptimality. The use of this Lagrangian solution in a simple greedy algorithm results in a high quality approximate feasible solution to the original problem. FUTURE RESEARCH DIRECTIONS A procedure for tightening Lagrangian bounds was proposed. The main idea of the approach is to estimate the complementarity term in the Lagrangian function. For convex problems under certain regularity conditions the complementarity term turns to zero for the optimal primal-dual pair. However for integer problems the complemen- tarity term can be different from zero even for optimal Lagrange multipliers since we typically have positive optimal multipliers for non-active constraints. We may expect that this approach can be especially useful for discrete problems having a large number of nonactive constraints for feasible solutions. Here we used the approach for assign- ment problems with knapsack-type inequality constraints, which frequently are non-active for feasible solutions. An interesting area for future research is an application of the proposed ap- proach to packing and cutting problems where, by the physical nature of the problem, available resources can not be utilized completely, e.g., packing circles into rectangular or circular areas. Another direction for future research is the use of a posteriori localization, possibly adjusted in 242 Many-to-Many Assignment Problems the course of solving the dual problem. It can be constructed in a surrogate way, similar to local- ization W s mentioned in Section 2.1 or using valid inequalities as in Litvinchev and Rangel (1999) (see also Litvinchev and Tsurkov (2003)). The proposed method results in two subprob- lems - one is similar to the classical Lagrangian problem and the other is used to estimate the complementarity term. Thus we have two La- grangian solutions both different from the clas- sical one. In our computational experiment with many-to-many assignment problems we notice that although solutions to modified Lagrangian dual are unfeasible, constraints are typically much less violated comparing with the classical Lagrang- ian solution. This is the reason why our simple greedy algorithm aimed to restore feasibility of the modified Lagrangian solution provides very high quality approximated solutions to the original problem. It is interesting to see if the same behavior of the modified Lagrangian solutions takes place for other classes of combinatorial problems. It was demonstrated by the computational experiment, that incorporating the greedy feasible solution in the subgradient scheme improves the convergence of the subgradient method. An interesting area for a future research is to use the modified bounds in combination with other greedy approaches, e.g., using different choices for rounding up/down components, as well as with more sophisticated heuristic techniques (see, e.g., Jeet and Kutanoglu (2007)). Another direction for future research is to im- prove the behavior of the subgradient technique by a more suitable choice of the initial values for the Lagrangian multipliers, for example, using optimal duals for the copy constraints Dx ≤ Dy in the LP-relaxation of the problem (7). An alterna- tive to the subgradient method used in this paper would be using more stable approaches such as center-based or bundle algorithms (e.g. Bahience et al. (2002)). FINAL REMARKS AND CONCLUSION In this chapter we presented a Lagrangian heuristic and applied it to a class of the generalized assign- ment problems. Our contribution is threefold. First, we proposed the modified Lagrangian bound based on a more tight estimation of the complementarity term in the Lagrangian function. For the original problem having two interesting sets of constraints we proved that the new bound is at lest as good as the best of the corresponding classical Lagrang- ian bounds. Second, we studied numerically the properties of the two Lagrangian-like solutions arising in the modified bound computations and showed that for the modified Lagrangian solution the original constraints are much less violated than for the classical Lagrangian solution. Third, we merged a greedy technique used to recover the feasibility of the modified Lagrangian solution with the subgradient algorithm thus obtaining an approximate iterative scheme producing high quality feasible solutions. The usefulness of the approach was demon- strated for a class of the generalized assignment problems, though the basic scheme can be applied for a much broader class of problems. In this chapter we focused on the general algorithmic aspects of the proposed Lagrangian based heu- ristic. We sincerely hope that this new approach will be useful for the researches and practitioners working with specific (and not only assignment) problems in power optimization. ACKNOWLEDGMENT This work was partially supported by RFBR, Russia (09-01-00592), Mexican foundations CONACyT (61343), PAICYT (CE008-09), and PROMEP (103.5/09/3905), and Brazilian agencies CNPq and FAPESP. 243 Many-to-Many Assignment Problems REFERENCES Balachandran, V. (1976). 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ADDITIONAL READING Bahiense, L., Maculan, N., & Sagastizabal, C. (2002). The volume algorithm revisited: relation with bundle methods. Mathematical Program- ming, 94, 41–69. doi:10.1007/s10107-002-0357-3 Barahona, F., & Anbil, R. (2000). The volume algorithm: producing primal solutions with a subgradient method. Mathematical Programming, 87, 385–399. doi:10.1007/s101070050002 Beasley, J. E. (1993). Lagrangean relaxation. In Reeves, C. R. (Ed.), Modern heuristic techniques for combinatorial problems (pp. 243–303). Black- well Scientific Publications. 245 Many-to-Many Assignment Problems Boschetti, M., & Maniezzo, V. (2009). Benders decomposition, Lagrangian relaxation and me- taheuristic design. Journal of Heuristics, 15(3), 283–312. doi:10.1007/s10732-007-9064-9 Burkard, R., Dell’Amico, M., & Martello, S. (2009). Assignment problems. Philadelphia: SIAM. doi:10.1137/1.9780898717754 Everett, H. III. (1963). Generalized Lagrange mul- tiplier method for solving problems of optimum allocation of resources. Operations Research, 11, 399–417. doi:10.1287/opre.11.3.399 Fisher, M. L. (1985). An application oriented guide to Lagrangian relaxation. Interfaces, 15, 10–21. doi:10.1287/inte.15.2.10 Geoffrion, A. M. (1974). Lagrangian relaxation and its uses in integer programming. Mathematical Programming Study, 2, 82–114. Guignard, M. (2003). Lagrangian relaxation. Top (Madrid), 11(2), 151–228. doi:10.1007/ BF02579036 Haidar, M., Al-Rizzo, H., Chan, Y., & Akl, R. (2009). User-based channel assignment algo- rithm in a load-balanced IEEE 802.11 WLAN. International Journal of Interdisciplinary Tele- communications and Networking, 1(2), 66–81. doi:10.4018/jitn.2009040105 Held, M., & Karp, R. (1970). The traveling sales- man problem and minimum spanning trees. Op- erations Research, 18, 1138–1162. doi:10.1287/ opre.18.6.1138 Jeet, V., & Kutanoglu, E. (2007). Lagrangian re- laxation guided problem space search heuristics for generalized assignment problems. European Journal of Operational Research, 182, 1039– 1056. doi:10.1016/j.ejor.2006.09.060 Jornsten, K., & Nasberg, M. (1986). A new La- grangian relaxation approach to the generalized assignment problem. European Journal of Opera- tional Research, 27, 313–323. doi:10.1016/0377- 2217(86)90328-0 Kleeman, M., & Lamont, G. (2008). Evolution- ary multi-objective optimization for assignment problems. In Bui, L. T., & Alam, S. (Eds.), Multi- Objective Optimization in Computational Intel- ligence: Theory and Practice (pp. 364–387). IGI Global. doi:10.4018/978-1-59904-498-9.ch013 Lemarechal, C. (2001). Lagrangian relaxation. In Junger, M., & Naddef, D. (Eds.), Computa- tional combinatorial optimization (pp. 115–160). Springer Verlag. doi:10.1007/3-540-45586-8_4 Li, D., & Sun, X. (2006). Nonlinear integer pro- gramming. Springer. Lorena, L. A. N., & Narciso, M. J. (1996). Relax- ation heuristics for generalized assignment prob- lem. European Journal of Operational Research, 91, 600–610. doi:10.1016/0377-2217(95)00041-0 Narciso, M. J., & Lorena, L. A. N. (1999). La- grangean/surrogate relaxation for generalized assignment problems. European Journal of Op- erational Research, 114(1), 165–177. doi:10.1016/ S0377-2217(98)00038-1 Pentico, D. W. (2007). Assignment problems: A golden anniversary survey. European Jour- nal of Operational Research, 176, 774–793. doi:10.1016/j.ejor.2005.09.014 Shapiro, J. F. (1974). A survey of Lagrangean techniques for discrete optimization. Annals of Discrete Mathematics, 5, 113–138. doi:10.1016/ S0167-5060(08)70346-7 246 Many-to-Many Assignment Problems KEY TERMS AND DEFINITIONS Generalized Assignment Problem: Involves profit maximizing assignment of tasks to agents recognizing capacity limits for agents and/or tasks. Many-to-Many Assignment Problem: In- volves profit maximizing assignment of tasks to agents recognizing capacity limits for both agents and tasks. Lagrangian Relaxation: Relaxation of a number of constraints together with aggregating a penalty term to the objective function to discour- age their violation. Lagrangian Multipliers: Coefficients of the linear combination of the constraints used to form a penalty term in the Lagrangian function. Lagrangian Relaxation Bounds: Bounds to the original optimal objective value provided by the Lagrangian problem. Lagrangian Dual Problem: Aims to find Lagrangian multipliers corresponding to the best Lagrangian bound. Lagrangian Heuristic: uses a solution to the Lagrangian (Lagrangian dual) problem as a starting or reference point in a heuristic approach. 247 Many-to-Many Assignment Problems APPENDIX The literature on Lagrangian relaxation is quite extensive. Here we refer the reader to a few pioneer and/or review papers providing a clear exposition of the subject: Everett (1963), Held & Karp (1970), Geoffrion (1974), Shapiro (1974), Fisher (1985), Beasley (1993), Lemarechal (2001), Guignard (2003). To our knowledge, the latter paper presents the most comprehensive and complete revision of the basic ideas used in Lagrangian relaxation and its applications. Numerical techniques of non-differentiable optimization used to solve Lagrangian dual problem can be found in the references cited above. More recent approaches are presented, e.g., in Barahona & Anbil (2000), Bahiense, Maculan & Sagastizabal (2002). Various relaxations in nonlinear integer programming are considered in Li & Sun (2006). The ideas to combine Lagrangian and Benders decomposition techniques with heuristic approaches are presented in Boschetti & Maniezzo (2009). A very complete source on modeling and solution techniques for assignment problems are provided in the recent book of Burkard, Dell’Amico & Martello (2009) and in the survey paper Pentico (2007). More specific Lagrangian-based solution approaches can be found in Jornsten & Nasberg (1986), Lorena & Narciso (1996), Narciso & Lorena (1999), Jeet & Kutanoglu (2007) and the references therein. Multi- objective assignment models and solution techniques are presented in Kleeman & Lamont (2008), while models and algorithms for channel assignment are considered in Haidar et al. (2009) and the references therein. See also the additional reading section. 248 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 8 João Zambujal-Oliveira Instituto Superior Técnico & Technical University of Lisbon, Portugal Power Systems Investments: A Real Options Analysis ABSTRACT Energy projects with extended life cycles and initial investments can be non-proftable under discount cash fow methods. Therefore, real options analysis has become relevant as a pricing technique for these types of projects, with private risks and high investment levels. Following this question, this study analyses different real options approaches to select the most acceptable for investing decisions in the energy sector. Combined cycle natural gas-fred plants constitute relevant generation assets that build- ing decisions can mostly be studied by real options tools. Because traditional pricing approaches fail to consider the worth of fexibility, conditions for creating a signifcantly large options-based value can be found. Being unable to capture the value associated with the decision maker’s ability to react dynamically to changing market conditions, these assets constitute a fne example of fexibility, which contributes to increasing its intrinsic value. The study employs a real options approach that doesn’t need to capture all the uncertainty and proposes a process that directly determines the uncertainty associated with the frst period. The results support that its use can be considered fair. However, it shows that long periods of operation and poor adhesion to the geometric Brownian motion by the project returns might call into question its use in the energy market. The values for option pricing have remained inside acceptable ranges, but some shortfalls could be found. First, the study employs Monte Carlo simulations, which can be viewed as forward-looking processes, and option pricing problems need backward recursive solutions. Second, the study shows that its simplicity produces results as accurate as those gathered from approaches with added complexity and computational needs. DOI: 10.4018/978-1-61350-138-2.ch008 249 Power Systems Investments INTRODUCTION Risks and uncertainties such as electricity, fuel prices, and construction costs characterize the energy market (Thompson et al., 2004). In that sense, case studies for the energy sector are as relevant as they are for pharmaceutical research or hi-tech start-ups. Therefore, the energy market needs a flexible way to approach plant investments and decision-making processes. Investment timing is relevant for energy sector because of the need to trade off the supply and demand for electricity. Adjustments in investment timing place pressure on power prices. This study will evaluate a model’s ability to define the optimal investment rule by considering uncertainties in the costs and revenues, assuming decision flexibility. Combined cycle natural gas- fired plants are relevant generation assets that building decisions can mostly be studied by Real Options Analysis (ROA), (Blyth, 2008). Because traditional pricing approaches fail to take into account the worth of flexibility, the conditions to create a significant large options-based value can be found in these plants. Being unable to capture the value associated with the plant manager’s ability to react dynamically to changing market conditions, these types of uncertainty origins of- fer a large options-based value. Because peaking power plants (as gas-fired) can react quickly to market prices, they constitute fine examples of asset flexibility, which contributes to increasing their intrinsic asset value. Although decision tree analysis improves discount cash flow (DCF), the manager still needs to assign different probabilities to potential results and find out a suitable discount rate. By contrast, ROA simplifies these assumptions and makes the process of choosing discount rates no longer arbitrary. Possible results are assessed and underlying risk profile is recognised under an options-based framework. Given the nature of the energy market, the problem in question arises from the need of an energy production company to know if its power generating plant project has financial viability. The company also wants to know if the present moment is the best time for beginning its invest- ment, given the potential opportunities. Within the real options paradigm, this issue sets up as an evaluation of the deferment or delay option for a power generating plant investment. The real op- tions approach applies derivative pricing theory to the analysis of options opportunities in real assets (Dixit and Pindyck 1994). It can be used to calculate plant values and optimal operating policies while considering plant characteristics. A power plant produces electricity at variable costs and if the (uncertain) electricity price exceeds its costs, it creates a positive contribution margin. Power plants can be seen as a strip of European call option or as path-dependent American Op- tion. Since the expansion of the power plant’s variable costs is also uncertain, power plants can also be appraised as swap options (fuel against electricity). In another perspective, accounting for different plant construction lead times in the face of demand uncertainty can originate differ- ent optimal capacity planning strategies (Gardner and Rogers 1999). Increased uncertainty enlarges the option value of a project by capturing the benefits from managerial/operational flexibility. However, option pricing models still need to bypass some practical shortfalls. Because the source of uncer- tainty should be traded, energy markets should be observed to calculate the volatility in electric- ity prices and assess their impact on revenues. Besides, as market data is scarce, it is usual to estimate expected input parameters with Monte Carlo simulations (Rode et al., 2001). Considering all arguments, this chapter intends to explore the applicability of the approach taken by Brandão et al. (2005) for investments made in the electricity market. This assessment can be made through a feasibility study of an investment in a combined cycle natural gas-fired plant using an ROA. This chapter begins by introducing the 250 Power Systems Investments approach framing of ROA in the energy market. After a suitable framework definition, the study describes the underlying methodology behind the research question. It aims to assess the relevance of calculating the project’s volatility using two different approaches. Then, it describes technol- ogy used in the investment project. The choice of this investment project results from supported reasons of environmental efficiency improvement. At this point, the chapter provides in detail the uncertainty modelling. PROJECT APPRAISAL AND VOLATILITY FUNDAMENTALS The dynamics of investment in the power genera- tion industry is characterized by the existence of different decisions about assets used in the energy generation. These decisions can be undertaken based on the formalization of the investment events in accordance with the real options approach. The following paragraphs illustrate the diverse types of real options and its connection with power generation industry. Traditional capital budgeting analysis as- sumes that projects perform every year of their lifetime. Power plants should have an option to cease the projects during their lives. This can be seen as an abandonment real option. This option gives the owner the right to sell the cash flows over the remainder of the project’s life. When the present value of the remaining cash flows (sal- vage value) falls below the liquidation value, the power facility should be sold. During the project’s evaluation phase, it is necessary to recognize the value represented by the opportunity, to recoup part of the investment, in case the project should be abandoned for scrap value. When electricity price falls below the cost of production, it may be most advantageous to temporarily shutdown until the electricity price recovers. Deng et al. (1998) valuate thermal power plants that operate only when the spark spread is positive. This temporarily shutdown option highlights the importance of developing a dynamic management attitude. A peaking unit power plant can also be used to illustrate a type of growth real option (intensity and scale). This kind of option formerly quantifies the flexibility to expand or contract the scale of a project. Such units have high variable costs and can produce additional power if demand and prices are high. The plant may have option to change the output rate per unit of time or to change the total length of production run time. This option lets the plant to increase the capacity of an existing generation line. If the market conditions are weaker than origi- nally expected, the plant should have a contract option to operate below capacity or even lessen the scale, saving part of the planned investment outlays. This flexibility allows mitigating losses. Using Monte Carlo simulation, Tseng and Barz (2002) assess a power plant capable of switching between two modes. When a power generation facility can restart operations for a previous shut down project in a dormancy state, there are present switching options that permit the facility to expand or contract. The option to switch refers to the feasibility of choosing among alternative operating modes. Basically, this happens when demand is changing, the manage- ment can change the output mix or inputs. The deferment option is valuable when market demand is uncertain and interest rate is volatile. The option to choose when to start a project is a deferment option. It is an extended concept of opportunity cost, which emphasizes that the deci- sion to invest immediately entails renouncing the undertaking a similar investment and postponing the implementation of this particular investment. Fleten and Nasakkala (2010) analyzed a license to build a power plant, evaluating the optimal timing in function of stochastic carbon emission costs. The option to expand allows increase in the scale of a project by investing more follow-on capital. When the market conditions turn out to 251 Power Systems Investments be more favourable than expected, the project can be accelerated or expand the scale of production. Some energy projects can be engineered in a way where the output is contracted in future, forgoing future expenditures as with projects modularized. An electric utility may have the option to switch between various fuel sources to produce electricity (choice of building a coal-fired plant or a plant that burns either coal or gas). The option to use different inputs to produce the same output is known as an input mix option or process flex- ibility (Trigeorgis, 1993). Brekke and Schieldrop (2000) analyzed the fuel switch option and the optimal timing of investing in a plant that can burn natural gas or oil. Traditional decision analysis tools to solve real option valuation problems have derived from Co- peland and Antikarov (2001) and are illustrated in Copeland and Tufano (2004). In Black and Scholes (1973), all risks are market risks and have market equivalents. In Copeland and Antikarov (2001), the opposite is shown; the authors consider that there is no need for a market equivalent because it might even not exist in a portfolio equivalent. It is assumed that the market equivalent is the project value itself. Additionally, this methodology also does not make any distinction between market uncertainties and market equivalents, and private uncertainties and specific risks (Borison, 2005). As a consequence of these aspects, the methodol- ogy of Copeland and Antikarov (2001) is hardly acceptable from the conceptual perspective. Brandão et al. (2005) used basic principles put forward by Nau and McCardle (1991), later improved by Smith and Nau (1995), and employ it to estimate the volatility of returns overtime. The following expression summarizes the revenues and costs in the project function: V R C CF R p q g C z e o c c t t t t t v f t i T , , , , , , , , , µ µ ( ) = ( ) ( ) ( ) + ( ) = ∑ 1 0 (1) and CF R C C R C C t t t t t d T , ( ) = − + − [ ] − ( ) + + 0 1 τ τ ψ (2) where V(R t ,C t ,) represents the net present value (or project value) and CFt ( Rt , Ct ) stands for cash- flows of each period. C0 is the initial investment and Rt(,p,q,g)corresponds to the revenue function with p for electricity price, q for net energy produc- tion and gfor guaranteed production. Ct ( z,e,p,cv , cf ) represents the cost function with z for natural gas price, e for efficiency, o for price for carbon dioxide emissions, cv for variable operation and maintenance costs (O&M costs) and Cf for fixed O&M costs. Cd indicates the depreciation costs and ψT contains the residual value. Lastly, indi- cates the risk-adjusted discount rate, t symbolizes the discrete periods of time and T specifies the project maturity. In order to estimate the forward returns of each year, the study calculate the project value at the end each period with following expression. V CF CF i i i i i T , µ µ ( ) = + ( ) = ∑ 1 1 (3) with V i representing the project value, CF i designat- ing the cash flows of each period and representing the risk-adjusted discount rate. After simulating cash flows to estimate the project value in each period, the method estimates the project returns. Considering a realistic approximation between the geometric Brownian motion (GBM) and the project value progression, its volatility should be similar. With a tree or lattice, there are condi- tions to estimate the option value and take the optimal decision. In the sequence of Copeland and Antikarov (2001), the model assumes a ran- dom variable φ c that represents the return between period 0 and 1. 252 Power Systems Investments ϕ C i n V V CF PV CF CF V = = + ( ) + ln , .., 1 0 1 1 1 0 ∈ − [ ] i n 1 1 , (4) Smith (2005) suggested that CF 1 should be stochastic and the other cash flows (CF 2 ,...,CF n ) should be expected values conditional on the re- sults of the first cash flow. The problem in decision making is finding out the best moment to invest (now or the next period). So, there is no need to capture the uncertainty of all the cash flows (Brandão et al., 2005). This improvement permits to detain directly the uncertainty associated with the first period, rationalising the estimate and providing a fair estimate of the project’s volatility. ϕ B i V V CF V E CF CF V = = + ( ) ( ) + ln 1 0 1 1 1 1 1 0 (5) Brandão et al. (2005) compared this GBM ap- proximation with Smith and Nau (1995) binomial approximations with two individual uncertain- ties in a risk-neutral environment, concluding the results are not deeply different. Considering that a binomial tree increases its complexity with the number of periods and uncertainties, the motivation to make use of a single variable approximation of the stochastic process becomes clear. However, the matching with GBM should be verified, particularly the lognormal distribution and the standard deviation homogeneity of the returns. About the adequacy of Brandão et al.’s (2005) approach to our study, Smith (2005) stated that it should only be applicable for scale options and that deferment options cannot be considered scale options. Brandão et al.’s (2005) allowed this vision but called for some flexibility. Following the framework of Yang and Blyth (2007), the study first calculates the present value of the project without considering any option. Using traditional methods, the assessment of the costs and revenues of the project would involve a DCF analysis, which discounts future cash flows to estimate the net present value and thereby its financial viability. The present value assumes a full knowledge of each variable’s evolution (in- cluding future energy prices and carbon trading prices) and discounts the future cash flows using a risk-adjusted discount rate. Using expression (3), the process begins with the definition of a project value at moment 0 (V 0 ) and moment 1 (V 1 ). Afterwards, using Equation (5) and the market data, it is possible to obtain an initial value for the random variable φ B To perform the Monte Carlo simulation, V 0 is fixed for all it- erations and V 1 is incorporated into the expression (4). This expression represents the project returns and follows a GBM with a drift rate α that repre- sents the mean of the project returns distribution and volatility s obtained from the standard de- viation of the returns variation. Therefore, the project volatility at a time interval Δt corresponds to s t / ∆ and represents the annualised per- centage of the standard deviation. Because the period of cash flow generation is annual, the process directly obtains the annual volatility from the standard deviation because σ equals s. Implic- itly, there is a postulation that project values are log-normally distributed and follow a GBM with a constant volatility. The process to estimate volatilities employs ordinary econometric ap- proaches, using similar regression analyses to isolate price trends. It runs the regressions with the logarithm of values and with its residuals and observes the first-order auto-regressions. The volatility estimates result from the standard error of these auto-regressions. Baltazar (2009) considered revenues as a function of the electricity price (see expression (1)). So, revenues follow a GBM formalised by the expression R(c ) =Ke c w ith a constant K. The variable c t a kes values between 0 and 1 and only varies from the initial period to the next, holding the same value for the following periods. After generating project revenues, expression (5) per- 253 Power Systems Investments mits to obtain the random variable. After running the simulation, it’s available the standard deviation that corresponds to the volatility of project returns. COMBINED CYCLE NATURAL GAS-FIRED PLANT Technology Description The company’s problem evaluates the project’s financial viability. Also suggests the best time to start the project, taking into account the maximiza- tion of present value of the project. The action of the electric market is characterized by its uncer- tainty nature regarding the price of electricity and the fuel cost associated with energy production. This section begins with the case study analysis of a nuclear combined cycle power plant describ- ing technological advances that have enabled a new generation of power plants with high income levels and low costs. In particular, the natural gas combined cycle plants can combine a gas cycle with a steam cycle, which offers a higher efficiency than other power plants. As gas-fired facilities, these plants contribute to the diversification of primary energy sources and take advantage of issuing low emissions compared with other fuels. This relevant characteristic constitutes a key factor to meet the allowed levels of pollution. Making use of an ROA, this study models a problem of a power-generating plant investment problem as a deferment option associated with the spread between electricity prices and variable costs (e.g., fuel costs). The option value rises when interest rates and the time to maturity increase. Ceteris paribus, if the strike price increases, the option price declines. In our real options model, the plant manager has the right to defer the plant building. The power plant’s investment decision process can be defined by call options. The consumption of electricity in Portugal between 2003 and 2007 grew on average 2.6% per year, which represented an increase above economic growth. In 2007, the electricity produc- tion was 47,253 GWh, with 28% generated from natural gas resources. The use of natural gas to produce electricity grew 11% between 2003 and 2007 (Eurostat, 2009). A combined cycle natural gas facility is characterised by advanced technol- ogy with a low environmental impact and high performance compared with coal or fuel oil or natural gas coupled to an alternator. A high volt- age transformer connects the plant to the national distribution network. This combined cycle power plant has efficiency between 55% and 56%, much higher than other power plants. Such efficiency permits consumed energy to be considered a clean source. Its high efficiency also leads to a lower fuel consumption and has contributed to further improvements in environmental impact. The combined cycle natural gas-fired plant has an installed capacity of a 400 MW-type gas turbine combined with a steam cycle. The exhaust gases expelled from the gas turbine are used to generate steam that drives a steam condensation turbine. The two turbines are linked by a single shaft and the quantity of natural gas must be 1.8 times the energy generated. The low emissions of SO 2 , NOx, CO 2 and particulates in combined cycle plants have a positive effect on environ- mental performance shows the carbon emissions for different power plants. Considering the technological superiority of a combined cycle natural gas-fired plant with regard to CO 2 emissions, the following section describes the uncertainties in market production and how the evaluation model considers them. The definition of parameters associated with uncertainties comes from market studies, namely the electricity and fuel markets. Uncertainty Modelling Some uncertain variables, such as electricity price, natural gas price, the price for carbon emissions and project value, should be modelled (Reedman et al., 2006). The modulation process implies 254 Power Systems Investments studying the electricity market and retrieving some historical price data. In this context, Frayer and Uludere (2001) considered that it is appropriate to use contracts with maturities similar to the plant’s estimated life cycle. The Iberian Electricity Market (MIBEL) re- sulted from a partnership between Portugal and Spain. Its aim is to integrate the two electricity systems. The formation of a regional market in the Iberian Peninsula constitutes a step further for the construction of an internal market in the European Union. As a consequence of the daily transactions of electricity contracts, the price var- ies every day. This procedure helps corroborate that futures markets, for electricity and natural gas, have inadequate liquidity to provide reliable market-based forecasts. Because the futures mar- kets represent a small portion of the MIBEL and the contracts are not traded very far in advance. Therefore, projections are made to simulate how prices will change stochastically over time using Monte Carlo techniques. Brandão et al. (2005) only considered the uncertainties with a market equivalent. Although the project contains three market uncertainties (electricity price, natu- ral gas price and the price for carbon emissions), only the first two are modulated as stochastic variables. Because electricity demand has no market equivalent, it is analysed in the sensitivity analysis section. In the current context, the study chooses to model electricity prices using a GBM, for which it is necessary to estimate volatility. Using historical market data since January 2000, which is available from the market opera- tors (OMEL, 2009; OMIP, 2009), it is possible to extract a historical volatility of electricity price of 54%. Assuming this level of annual volatility can provide a mid-to-long-term standard deviation in electricity prices, 10,000 iterations of Monte Carlo simulations (are carried out for a time framework of 25 years (Baltazar, 2009). Algeria provides a large percentage of the natural gas consumed by the Iberian Peninsula. Several port terminals for natural gas in Spain and one in Portugal receive it through the Maghreb– Europe pipeline. The price of Brent constitutes the pattern for the price of natural gas (Monaghan, 2009). Thus, the natural gas price is considered a market uncertainty in this plant project. The estimation of gas price volatility results primar- ily from historical market data between 1987 and 2009 (EIA, 2009). From the analysis of daily spot prices, Baltazar (2009) obtained a Brent histori- cal price volatility of 26%, which serves as the initial value of the simulation process. Following a similar process to the one of the electricity prices, the study uses Monte Carlo simulations (Spinney and Watkins, 1996). Today, carbon emission licenses are daily traded in the carbon exchange market (European Climate Exchange). The launch of new licenses is carried out in stages and depends on an administra- tive grant. After 2012, the changes in the carbon exchange market will invalidate using current prices as references for the future. Uncertainty in the price of carbon emissions results from a biased market and depends on the release of new regulations. Thus, the allowances of carbon don’t Table 1. Pollutant emissions for different types of power plants (g/kWh), Source: Baltazar (2009). Technology Fuel CO2 Nox SO2 Particles Combined Cycle N. Gas 360 0.3 0 0 Conventional N. Gas 560 2 0 0 Conventional Fuel Oil (3%) 750 2 14 0.1 Conventional Fuel Oil (1%) 750 2 5 0.1 Conventional Coal 900 3 7 0.15 255 Power Systems Investments assume a nature of market uncertainty (EUETS, 2009). According to the study of other combined cycle natural gas-fired plants with similar profiles, the study considers an average annual decrease of carbon emissions of 1.1%. Project Value Modelling The project is yet to start and because of economic conditions and adverse financial conjuncture, the company is considering postponing the in- vestment. The combined cycle natural gas-fired plant has two stages: investment and production. These stages are later used to price outlooks and forward cost simulations. The investment stage involves the construction and reliability testing phases. Table 2 describes the base parameters of the investment project. The production phase starts four years after the beginning of the project. This means that building phase takes four years and the reliabil- ity tests are performed during the first two years of production. The present cost of the building phase is €205 million (Table 3). The production phase lasts for 25 years with a 10-year guaranteed power purchase agreement (Baltazar, 2009). Us- ing historical market data since January 2000, it is possible to extract trends from the electricity and natural gas prices. A DCF analysis showed the discounted 29-year net present value is a negative value of €57 million (Baltazar, 2009), considering a risk-adjusted discount rate of 8% and a tax rate of 26.5% (Table 5). Under these conditions, the project should be rejected. This level of project value seems to confirm Frayer and Uludere (2001), who considered that DCF models, based on production cost-based simula- tions (like this one), attribute short cumulative values to typical gas-fired peaking facilities. The DCF analysis includes a deterministic risk appraisal and applies a risk premium over the risk-free interest rate. Therefore, the stochastic nature of price variations is not taken into account. That assumption cannot be accepted in a market with fast technological development, characterised by uncertainties about energy prices, prices for carbon dioxide emissions, raw materials and O & M costs. Although the simplicity of integrating the risk analysis into a unique risk-adjusted dis- count rate is tempting, the disadvantages resulting from a poor understanding of new risks outweigh the benefits. From here, the analysis evolves from a de- terministic DCF model into two directions. One considers the electricity and natural gas prices per se. The other reflects cash flows composed by the difference between the functions of the electricity price and the fuel price. The project income depends primarily on electricity demand and its growth over the years, as well as the elec- tricity price charged in the Iberian market. The electricity cost of production essentially depends on fuel prices such as the natural gas bought in producer countries and distributed through the national natural gas network. Because no reliable long-term market-based predictions for forward fuel prices are available, the method uses the company production cost-based technique. This method retrieves the cost according to the market prices, adding up the other costs associated with Table 2. Base parameters of the project Description Value Initial Investment (M€) 205 Useful Life (years) 29 Risk-adjusted discount rate (annual) 8% Corporate tax rate (annual) 26.50% Table 3. Historical volatility Variable Volatility Electricity Price (EP) 54% Natural Gas (NG) 26% Aggregate (EP,NG) 120% 256 Power Systems Investments carbon dioxide emissions and operations and maintenance. The next phase combines two uncertainties (electricity price and natural gas price) in the cash flow statement and obtains the initial project volatility. This initial value for volatility is dis- similar to individual uncertainties and depends on the structure of the cash flows. Brandão et al. (2005) attributed much of this difference to effects related to operational leverage. In our case, as the difference between costs and revenues is small, a tiny change in revenues or costs has a relevant impact on cash flows. Volatility changes its value according these changes. Considering this framework, the ROA can show the project creates value under different economic and technological conditions. A DCF analysis of deterministic net present value ignores the flexibility to start the project at the right time. When the project value varies stochastically over time, the possibility of waiting and seeing is clearly an asset for managers (Trigeorgis, 1996). Assuming the existing technical conditions, a power plant operation with carbon capture and storage would not be cost effective. However, because technology is improving at a fast pace, the investment might turn out to be cost effective in the near future. The study integrates two uncertainties (elec- tricity price and natural gas price) to evaluate the model value over time. It assumes that the two variables follow a GBM with a volatility of 54%, for the electricity price process and a volatility of 26% for the natural gas price process. The procedure excludes any variable correlation val- ues. When compared with Frayer and Uludere’s (2001) peak (15%) and off-peak values (22%), the volatility estimates seem to be overvalued, which confirms Smith (2005). After considering a two-variable approach, the process of Brandão et al. (2005) implies a combination of the volatility forecasts associated with the two random variables. Although there are alternative ways of achieving it (Smith, 2005; Amendola and Storti, 2008), the process produces a volatility level of 120%. When the uncertainties Table 5. Parameters sensitivity analysis Δ(σ2) (1) Δ(πΔp) (2) (2)/(1) Δ(δ) (1) Δ(πΔp) (2) (2)/(1) -50.00% -51.67% 0.033 10.00% -23.24% -1.324 -58.33% -62.79% 0.076 20.00% -46.89% -1.344 -66.67% -74.60% 0.119 30.00% -71.72% -1.391 -75.00% -85.56% 0.141 Δ(ψ) (1) Δ(πΔp) (2) (2)/(1) Δ(ρ) (1) Δ(πΔp) (2) (2)/(1) 0.00% 0.00% NA 10.00% -10.87% -0.087 -33.33% -23.58% -0.293 20.00% -21.62% -0.081 -66.67% -34.34% -0.485 30.00% -32.50% -0.083 Table 4. Option values for separate and aggregate volatilities Option Value NPV V(ep) V(ng) V(ep,ng) rf Model(1) 159 102 113% 84% 2.16% Model(2) 154 97 172% 2.16% Model(1):volatility of each uncertainty; Model(2):aggregate volatility V(ep): volatility of electricity price; V(ng): volatility of natural gas; V(ep,ng): aggregate volatility; rf: risk-free rate; NPV: net present value 257 Power Systems Investments are somewhat correlated, the project volatility should be higher than the sum of the individual volatilities. In the absence of additional elements, Lima and Suslick (2006) confirmed empirically these considerations in similar projects. In sum- mary, Table 3 shows the historical volatility of uncertainty variables of the model. Using the DCF method, the plant investment shows not to be cost effective (negative project value). Although this method does not take into ac- count price uncertainties and can produce incorrect information to support decisions, modelling these uncertainties allows us to catch the investment opportunity when it becomes cost effective. The following section discusses the pricing of the de- ferment option using the approaches suggested by Copeland and Antikarov (2001), Smith (2005) and Brandão et al. (2005). This section also contains a sensitivity analysis of uncertainties parameters and other variables not modelled stochastically. Deferment Option Analysis Given the project deferment option, the goal is to determine when the investment becomes eco- nomically viable. The present value is negative but the flexibility to defer the investment offers management the possibility to benefit from ran- dom movements in the project value. However, if market conditions change, it will affect the asym- metry in the obligation to invest (Trigeorgis, 1996). The firm has a three-year investment license for starting the plant construction. If the option expires before the end of the license, the invest- ment opportunity is lost. Although there are three market uncertainties (electricity price, natural gas price and the price for carbon dioxide emissions) only the first two are considered. Sensitivity analysis will lead to the uncertainties which have no market-equivalent. This study uses a binomial tree that models the stochastic process (GBM) over the time of the project (Wang and Dyer, 2010). Because Panko (1998) evidenced errors of between 20% and 40% of the appliances, the study avoids the use of binomial lattices to make it safer to examine the results. The approximation of project uncer- tainty applies a risk-neutral valuation and includes options in the decision nodes of the tree. As in Copeland and Antikarov (2001), real option value results from the binomial tree filled with project volatility replicated from forward simulations. The model approach integrates two uncertain- ties (electricity and natural gas price) and one option (to invest or abandon the project during the time of license). The payoff of each period reflects the cash flows that result from the ran- dom variables. Baltazar (2009) studied an initial investment value of €205 million and a risk-free rate of 2.16% (MTSP, 2009). Using simulated volatilities of 113% (electric- ity price) and 84% (natural gas price) obtains, through a binomial tree, a project value of €102 million and three years to maturity deferment option of €159 million (Model(1)). The model considers a binomial tree that matches the returns and assumes an equal initial investment value and risk-free rate. The changed project value differs by only about 5% (€97 million) from the previous approach with an option value of €154 million (Model(2)). The difference can be considered irrelevant, taking into account the initial invest- ment value of €205 million. The next section examines the robustness of the critical parameters such as project volatility, op- tion maturity, electricity demand and the price for carbon dioxide emissions. Assuming all the other variables remain constant, sensitivity analyses show how each parameter individually moves and compares them with the strategic net present value that corresponds to baseline parameterisation. Process Evaluation and Sensitivity Analysis Several tests can be performed to assess the quality of the process simulations. First, it is necessary to corroborate if simulated project values follow 258 Power Systems Investments a normal distribution. Second, it should be seen whether the volatility over the expected project returns remains constant from period to period. The results of the x 2 test with a p value of 5% indicate that the null hypothesis of project returns following a lognormal distribution cannot be rejected. To examine volatility changes over the several periods of the project, the paper calculates the value of φ B by applying expression (5) to all the periods. Because the difference between the values of each period remain in the interval of –0.2% and +0.8%, it can be considered that there are no significant variations in volatility from period to period. For the sensitivity analysis, the study em- ploys the expected threshold values of the cash flow variation (π Δp ) to capture the impact of the variation in the uncertainties parameters. The expression Δπ=((π Δp / π bp )-1)*100 translates the described method where π Δp is the strategic net present value after revised parameterisation and π bp corresponds to a baseline parameterisation. Table 2 considers deviations in the critical parameters in a range between +10% and –75%. Each parameter change has a corresponding varia- tion in the strategic present value (π Δp ). About the direction of variation it is possible to detect differ- ent behaviours between the various parameters. The values tested for the project volatility are the absolute values between 30% and 60%, with intervals of 10% that correspond to variations between –50% and –75%. A negative change in the project value’s vari- ance (σ 2 ) reflects a change in the same direction in the project’s value. Because the test values of volatility deviate from the benchmark, this increases the magnitude of their effects on the project value. The change in the option maturity (time deferral of the project) has the same effects on the project value as the volatility. However, the same percentage change in the project volatility causes an update in the project value twice as great as the change in the deferment period of the project (). The relationship between electricity demand (δ) and price for carbon dioxide emissions (ρ) with the project value is reversed from those shown by the two previous parameters (volatility and maturity). An increase in the value of these variables causes a reduction in the project value. The variation in electricity demand leads to twice the adjustment in the project value of the same percentage change in the price for carbon dioxide emissions. Although there are significant changes in the project value, none of the sensitivity analy- sis procedures call into question the project with regard to its viability. The following section describes some of the latent gaps in an ROA, which could be used as indicators of future research lines. These perspec- tives result from the connection between the DCF and real options paradigms on risk assessment in the decision-making process. FUTURE RESEARCH DIRECTIONS In a certain sense, electricity market is different from other commodities because it’s expensive to store electricity on a large scale. Consequently, electricity prices depend on the customers’ needs, resulting in large fluctuations in demand during the day and in balance problems between demand and production. For that reason, minimizing the production costs and building a flexible adjustment between demand and supply are relevant factors to mitigate market risks and get a significant return on investments. Combined-cycle power plants have low investment costs and short construction times when compared to coal-fired and nuclear plants (Fraser et al., 2000). This chapter analyze investments in gas-fired power plants based on stochastic electricity and natural gas prices. Fleten and Nasakkala (2010) analyze the same variables and find that when the decision to build is considered, the abandonment option does not have significant value. This study can also consider an abandonment option and ad- 259 Power Systems Investments ditionally examine the effects of emission costs on the value of installing CO2 capture technology. Traditional DCF analysis in the energy sector can produce mistaken assessments by ignoring the adaptability and possibility of cash flow change overtime. Some authors consider ROA imprecise and that might even complicate the procedure of identifying the best strategy. This article shows that an ROA can supply added information on the economic viability of energy projects, by valuat- ing the deferment option. The energy market is uncertain and thereby an ROA is an essential tool in strategic decision making. However, to use consistently an ROA, there are some questions to discuss. For projects with equal returns, assuming risk, neutrality and aversion, an ROA chooses the projects with a higher volatility. It contradicts some rules from the traditional literature, which encourage minimising the risk from an equal profitability. Also, an ROA creates some bias in project selection. Increasing the approval rate of unprofitable projects in the short-term and decreas- ing the acceptance rate of projects that with new information might offer new opportunities in the long-term. Future research should try to overcome these problems in order to spread the use of ROA. In terms of technology, the ROA can be extended to choose between electricity generat- ing technologies. The firm can decide when to invest either in a Natural Gas Combined Cycle (NGCC) power plant or in an Integrated Gas- ification Combined Cycle (IGCC) power plant. Furthermore, instead of assuming that fuel prices follow standard geometric Brownian motions can be assumed mean reversions, as in Abadie and Chamorro (2008). CONCLUSION The article shows there is an investment project to be carried out (profitability index of 1.50) with a deferment option that contributes 51.62% (for the index). The proper timing for its implemen- tation is not now. Therefore, the decision maker should take the deferment option and delay its implementation. Compared with other project analyses (Frayer and Uludere, 2001), it seems that project volatility is slightly overvalued. This feature seems to come from the high volatility of electricity price (Alvarado and Rajaraman, 2000) and from a specific pattern of cash flows with high first investments and long periods of opera- tion. Furthermore, sensitivity analysis examines changes in project volatility, period of production, disruptions in electricity demand and changes in prices for carbon dioxide emissions and shows some robustness of the results. Therefore, even with some conceptual con- traindications, ROA approach of Brandão et al. (2005) can be considered fair. This study shows that energy markets with long periods of opera- tion and a reasonable adhesion to the GBM, by the project returns, might call into question its use in these markets. Although the values of op- tion evaluation have remained inside acceptable ranges, some shortfalls could be found. First, the study employs Monte Carlo simula- tions, which can be viewed as forward-looking processes, and option pricing problems need backward recursive solutions. So, these simula- tions can be considered less appropriate to deal with these kinds of option problems. Second, Smith (2005) suggested some alter- native approaches to estimate volatility, such as Longstaff and Schwartz (2001), Farias and Van Roy (2003) and Ibanez and Zapatero (2004). Since our study produces similar results, it is not obvious the extra complexity and computational needs needed by these approaches can produce significantly superior results. Finally, it is broadly accepted that simulation models have a limited ability to model complex options problems and large possibilities of containing spreadsheet errors. It is also consensual that lattices have relevant drawbacks on transparency and intuition. 260 Power Systems Investments REFERENCES Abadie, L., & Chamorro, J. (2008). Valuing flex- ibility: The case of an integrated gasification com- bined cycle power plant. Energy Economics, 30(4), 1850–1881. doi:10.1016/j.eneco.2006.10.004 Alvarado, F., & Rajaraman, R. (2000). Under- standing price volatility in electricity markets. 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European Journal of Operational Research. doi:.doi:10.1016/j.ejor.2010.09.011 KEY TERMS AND DEFINITIONS Binomial options pricing model: Numerical method for the valuation of options proposed by Cox, Ross and Rubinstein (1979). The model uses a lattice based model of the varying price over time of the underlying asset. Combined Cycle: An electrical generating technology in which electricity is produced from otherwise lost waste heat, exiting from one or more gas (combustion) turbines. The exiting heat is routed to a conventional boiler or to a heat re- covery steam generator for use by a steam turbine to generate electricity. Historical Volatility: The annualized Stan- dard Deviation of percent changes in prices over a specific period. It is a hint of past volatility in market prices. Monte Carlo Simulation: Risk analysis techniques in which probable future events are simulated on a computer generating estimated rates of return and risk indexes. Option: The right, but not the obligation, to purchase, sale or contract an underlying asset at a specified price during a defined time period. Real Options Analysis: Applies option valu- ation methods to investment decisions. Risk-Adjusted Discount Rate: The discount rate that applies to a particular risky stream of income; the riskier the project’s income stream, the higher the discount rate. Spark Spread: The relationship between the price of electricity and the price of natural gas or other fuel used to produce electricity. The spark spread reflects the costs, or expected costs, of producing power. 265 Power Systems Investments APPENDIX Table 6. Net and guaranteed energy production (Baltazar, 2009) Year 5 6 7 8 9 10 11 12 13 14 15 16 17 Net energy production (GWh) 1515 1510 1633 1544 1498 1478 1475 1539 1507 1477 1405 1335 Guaranteed production (k€) 7798 7798 7798 7798 7798 7798 7798 7798 7798 0 0 0 Electricity Price (€/MWh) 83.6 85.3 87 88.8 90.5 92.3 94.2 96.1 98 100 102 104 Year 18 19 20 21 22 23 24 25 26 27 28 29 Net energy production (GWh) 1194 1125 1210 1305 1392 1477 1567 1534 1501 1468 1468 Guaranteed production (k€) 0 0 0 0 0 0 0 0 0 0 0 Electricity Price (€/MWh) 108 110 113 115 117 119 122 124 127 129 132 266 Power Systems Investments T a b l e 7 . R e v e n u e s a n d c o s t s o f a c o m b i n e d - c y c l e p l a n t i n v e s t m e n t ( B a l t a z a r , 2 0 0 9 ) . Y e a r 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 N a t u r a l G a s P r i c e s ( € / M W h t ) 3 0 3 0 2 9 3 1 3 2 3 2 3 3 3 3 3 4 3 5 3 5 3 6 3 6 P C I ( % ) 0 . 5 6 0 . 5 6 0 . 5 6 0 . 5 6 0 . 5 6 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 C O 2 C o s t ( € / t ) 2 8 2 8 2 9 2 9 2 9 3 1 3 2 3 4 3 5 3 7 3 9 4 0 4 2 C O 2 E m i s - s i o n ( t ) 5 6 4 , 8 6 1 5 4 9 , 1 4 5 5 4 8 , 2 9 9 5 9 3 , 1 2 8 5 6 1 , 0 4 5 5 4 4 , 6 4 6 5 3 7 , 8 9 9 5 3 7 , 0 3 1 5 6 0 , 3 2 2 5 4 8 , 6 6 7 5 3 7 , 8 6 2 5 1 1 , 7 7 2 4 8 6 , 2 3 8 O & M F i x e d C o s t ( € ) 2 , 3 9 6 2 , 4 4 4 2 , 4 9 3 5 , 3 9 2 5 , 4 4 3 5 , 4 9 4 5 , 5 4 7 5 , 6 0 1 4 , 4 5 6 4 , 5 1 2 4 , 5 7 0 4 , 6 2 8 4 , 6 8 8 O & M V a r i - a b l e C o s t ( € ) 1 , 6 6 2 1 , 6 5 2 1 , 6 8 3 1 , 8 5 6 1 , 7 9 4 1 , 7 7 7 1 , 7 9 2 1 , 8 2 6 1 , 9 4 1 1 , 9 4 0 1 , 9 4 1 1 , 8 8 5 1 , 8 2 9 Y e a r 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 N a t u r a l G a s P r i c e s ( € / M W h t ) 3 7 3 8 3 8 3 9 3 9 4 0 4 1 4 2 4 2 4 3 4 4 4 4 P C I ( % ) 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 0 . 5 5 C O 2 C o s t ( € / t ) 4 4 4 6 4 9 5 1 5 3 5 6 5 8 6 1 6 4 6 7 7 0 7 3 C O 2 E m i s - s i o n ( t ) 4 6 0 , 0 6 4 4 3 5 , 6 8 2 4 1 0 , 2 8 9 4 4 1 , 5 4 1 4 7 6 , 6 1 2 5 0 8 , 9 2 8 5 4 0 , 0 5 0 5 7 3 , 1 7 0 5 6 1 , 5 5 4 5 4 9 , 9 0 9 5 3 8 , 3 9 1 5 3 8 , 3 9 1 O & M F i x e d C o s t ( € ) 4 , 7 4 8 5 , 6 0 2 5 , 6 6 5 5 , 7 2 9 5 , 7 9 5 5 , 8 6 2 5 , 9 3 1 1 4 , 1 7 2 7 , 6 2 1 7 , 6 9 3 7 , 7 6 8 6 , 8 8 0 O & M V a r i - a b l e C o s t ( € ) 1 , 7 6 8 1 , 7 0 8 1 , 6 4 2 1 , 8 0 0 1 , 9 8 3 2 , 1 6 0 2 , 3 3 6 2 , 5 2 9 2 , 5 2 9 2 , 5 2 8 2 , 5 2 6 1 , 8 8 8 267 Power Systems Investments T a b l e 8 . C a s h f l o w s o f t h e c o m b i n e d c y c l e p l a n t i n v e s t m e n t ( B a l t a z a r , 2 0 0 9 ) Y e a r 1 - 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 R e v e n u e s 1 3 6 , 1 9 9 1 2 9 , 1 5 2 1 2 6 , 5 3 3 1 4 5 , 4 2 8 1 4 0 , 8 6 0 1 4 0 , 2 0 9 1 3 9 , 9 4 7 1 4 2 , 6 7 2 1 4 8 , 4 5 6 1 4 9 , 1 4 0 1 4 1 , 7 3 6 1 3 7 , 6 7 0 C o s t s 1 0 4 , 8 8 6 1 0 0 , 0 4 5 9 9 , 7 1 9 1 1 6 , 6 6 8 1 1 2 , 3 5 3 1 1 1 , 5 4 2 1 1 2 , 6 0 8 1 1 4 , 7 3 1 1 2 0 , 6 9 1 1 2 0 , 7 5 2 1 2 1 , 0 0 0 1 1 7 , 8 4 8 E B I T D A 3 1 , 3 1 3 2 9 , 1 0 7 2 6 , 8 1 4 2 8 , 7 6 0 2 8 , 5 0 7 2 8 , 6 6 7 2 7 , 3 3 9 2 7 , 9 4 1 2 7 , 7 6 5 2 8 , 3 8 8 2 0 , 7 3 6 1 9 , 8 2 2 D e p r e c i a - t i o n 9 , 7 8 5 9 , 7 9 2 9 , 7 9 2 9 , 7 9 2 9 , 7 2 2 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 E B I T 2 1 , 5 2 8 1 9 , 3 1 5 1 7 , 0 2 2 1 8 , 9 6 8 1 8 , 7 8 5 1 9 , 1 5 6 1 7 , 8 2 8 1 8 , 4 3 0 1 8 , 2 5 4 1 8 , 8 7 7 1 1 , 2 2 5 1 0 , 3 1 1 T a x e s 5 , 7 0 5 5 , 1 1 9 4 , 5 1 1 5 , 0 2 7 4 , 9 7 8 5 , 0 7 6 4 , 7 2 4 4 , 8 8 4 4 , 8 3 7 5 , 0 0 2 2 , 9 7 4 2 , 7 3 2 I n v e s t m e n t 2 0 5 , 4 2 7 C a s h - f l o w s 2 5 , 6 0 8 2 3 , 9 8 8 2 2 , 3 0 3 2 3 , 7 3 3 2 3 , 5 2 9 2 3 , 5 9 1 2 2 , 6 1 5 2 3 , 0 5 7 2 2 , 9 2 8 2 3 , 3 8 6 1 7 , 7 6 2 1 7 , 0 9 0 D i s c o u n t C a s h - f l o w s 1 7 4 2 9 1 5 1 1 7 1 3 0 1 4 1 2 8 2 3 1 1 7 7 0 1 0 9 2 7 9 6 9 9 9 1 5 6 8 4 3 0 7 9 6 2 5 5 9 9 4 9 8 8 Y e a r 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 R e v e n u e s 1 3 3 , 4 6 3 1 2 8 , 7 7 2 1 2 4 , 9 1 6 1 2 0 , 2 1 5 1 2 9 , 3 2 4 1 3 9 , 3 9 5 1 4 8 , 4 1 9 1 5 8 , 0 3 2 1 6 8 , 0 7 2 1 6 5 , 9 2 0 1 6 3 , 8 4 7 1 6 1 , 4 7 6 1 6 0 0 5 8 C o s t s 1 1 4 , 7 1 7 1 1 1 , 2 0 7 1 0 8 , 6 4 5 1 0 4 , 9 5 6 1 1 5 , 0 0 0 1 2 6 , 4 4 1 1 3 7 , 6 3 9 1 4 9 , 0 2 9 1 6 9 , 6 2 8 1 6 3 , 4 9 5 1 6 3 , 9 3 8 1 6 4 , 3 9 5 1 6 6 7 3 2 E B I T D A 1 8 , 7 4 6 1 7 , 5 6 5 1 6 , 2 7 1 1 5 , 2 5 9 1 4 , 3 2 4 1 2 , 9 5 4 1 0 , 7 8 0 9 , 0 0 3 - 1 , 5 5 6 2 , 4 2 5 - 9 1 - 2 , 9 1 9 - 6 , 6 7 4 D e p r e c i a - t i o n 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 9 , 5 1 1 7 , 2 6 2 3 5 4 E B I T 9 , 2 3 4 8 , 0 5 4 6 , 7 6 0 5 , 7 4 8 4 , 8 1 3 3 , 4 4 3 1 , 2 6 9 - 5 0 8 - 1 1 , 0 6 7 - 7 , 0 8 6 - 9 , 6 0 2 - 1 0 , 1 8 1 - 7 , 0 2 8 T a x e s 2 , 4 4 7 2 , 1 3 4 1 , 7 9 1 1 , 5 2 3 1 , 2 7 5 9 1 2 3 3 6 0 0 0 0 0 0 I n v e s t m e n t C a s h - f l o w s 1 6 , 2 9 8 1 5 , 4 3 1 1 4 , 4 8 0 1 3 , 7 3 6 1 3 , 0 4 9 1 2 , 0 4 2 1 0 , 4 4 4 9 , 0 0 3 - 1 , 5 5 6 2 , 4 2 5 - 9 1 - 2 , 9 1 9 - 6 , 6 7 4 D i s c o u n t C a s h - f l o w s 4 4 0 5 3 8 6 4 3 3 5 5 2 9 4 7 2 5 9 2 2 2 1 5 1 7 7 9 1 4 2 0 - 2 2 7 3 2 8 - 1 1 - 3 3 8 - 7 1 6 N e t P r e s e n t V a l u e - 5 6 9 0 4 268 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 9 INTRODUCTION Distribution network reconfiguration has a history about 35 years 1 and literatures indicate initial ef- forts by Merlin and Back (1975). Their heuristic work focused on power loss reduction where it started with closing all network switches to perform a mesh configuration. Switches are then opened successively to restore radial configuration with less power loss. Thereafter, this method got some improvements by Shirmohammadi and Hong (1989) where introduced as “Sequence Switch Op- eration Method” 2 . Here also, the reconfiguration Armin Ebrahimi Milani Islamic Azad University, Iran Mahmood Reza Haghifam Tarbiat Modares University, Iran Optimal Confguration and Reconfguration of Electric Distribution Networks ABSTRACT Power loss reduction can be considered as one of the main purposes for a distribution system’s design- ers and operators, especially for recent non-governmental networks. Moreover, the nature of power loss challenges different methods to solve this problem, while various studies indicate effectiveness of reconfguration and its high portion for this case. Thus, “reconfguration” can be introduced as an optimization procedure to obtain economical high quality operation by changing the status of sectional- izing switches in these networks. Some major points such as using different switch types, considering number of switching and time varying loads, which are almost neglected or not applied simultaneously in most pervious essays, are the main motivation to propose this chapter. A heuristic practical scheme is proposed to perform optimal reconfguration, and all previous neglected topics are fully discussed. Proposed method will apply to sample distribution networks, and the effectiveness of this method will be discussed through several case studies and comparisons. DOI: 10.4018/978-1-61350-138-2.ch009 269 Optimal Confguration and Reconfguration of Electric Distribution Networks procedure starts by closing all network switches which are then opened one after another so as to establish the optimum power flow in the network. This is while, many approximations of pervious method have been overcome in this algorithm and the computation takes less time. Civanlar et al. (1988) made use of method which is known as a “Branch Exchange” opera- tion. This method suggested the opening of any switch was required to correspond to the closure of another switch, ensuring that the radial con- figuration of the distribution network would be preserved. A year after, Baran and Wu (1989) succeeded to improve the method of Branch Ex- change by offering two approximated power flow Equations in 1989. Their power flow Equations introduced by recursive approximation of P, Q and V for each branch. Liu (1989) in the same year, Taylor, Chiang and Jeon (1990) in next years presented various heuristic method for distribution feeder recon- figuration. Wagner (1993), compares different major reconfiguration methods. This comparison depicts considerable economic advantages by us- ing presented heuristic methods especially for real time operations. He indicated that an important loss reduction was obtained through simulations in Canadian networks during a one year period. Genetic Algorithm applied in distribution sys- tem reconfiguration for reduction of real power loss by Nara et al. (1992) for the first time. They compared obtained results with the results of Simu- lated Annealing (SA) method and concluded that although the genetic algorithm has less assurance but it can be faster that SA. After introducing GA method and due to its effectiveness, many works done by refine or suggest heuristic techniques to this algorithm to compensate long solution time. Sarfi et al. (1996) presented an algorithm based on “Network Partitioning Method” after their efforts to use refined genetic algorithm for reconfiguration of distribution networks. Before that, Chen and Cho (1993) have performed an analysis of hourly reconfiguration scheme. They have studied the hourly load patterns over an interval of a year in order to define the hourly load conditions for each season. They have used Branch and Bound technique for obtaining mini- mum loss configuration considering hourly load patterns over annual intervals. It was the year that Kashem et al. (1999) investigated the load rear- rangement and proposed their famous method for load balancing in distribution systems. Huang and Chin (2002) proposed an algorithm based on fuzzy operation in order to deal with feeder reconfiguration problem. They suggested this method to reduce power loss as well as to acquire the load balance. More Artificial intel- ligence based methods, such as (Ahuja, 2007; Mendoza, 2009; Milani 2010) are other useful procedures proposed for reconfiguration of dis- tribution networks, recently. By review the full history of distribution network reconfiguration, can perceive a vast bibliography on this optimization problem. As it mentioned before, it includes general attempts to find a global optimal solution, new approximate methods (Civanlar, 1988), (Baran, 1989) and al- ternative paradigms of approaching the problem, such as evolutionary computation (Nara, 1992) and other bio-inspired techniques (Ahuja, 2007). What is more considerable here is that most of these approaches consider fixed demands at each load point (usually the maximum demands forecast for the planning period). However, loads vary during any given planning period, with a dif- ferent pattern for each bus, and these variations must be considered in the search for a minimum loss configuration. Also it seems considering different switch types will affect on optimal configuration and reconfiguration of electric distribution networks. MAIN FOCUS OF THE CHAPTER After a brief introduction to electric distribution networks, their configuration and reconfiguration, 270 Optimal Confguration and Reconfguration of Electric Distribution Networks this chapter will focus on some issues involved with reconfiguration of electric distribution net- works and provides practical answers to these major points. Through this investigation readers learn complete concepts of an optimal reconfigura- tion procedure to reduce power loss and total costs, while they will get some basic information and knowledge about electric distribution networks’ configuration. Fully discussion about this subject in following sections supplies a perfect insight to this problem and its issues. INTRODUCTION TO DISTRIBUTION NETWORKS AND THEIR CONFIGURATION Electricity distribution is the final stage in the delivery before retail of electricity to end users. A distribution system’s network carries electric- ity from the transmission system and delivers it to the consumers. In the other words, distribu- tion network provides the final links between the transmission system and demands. Figure 1 gives a basic insight from distribution position in power systems and depicts the main configuration of the network. Typically, a distribution network would include medium-voltage power lines, electrical substations and transformers, low-voltage distribution wiring and sometimes electricity meters. These networks are generally divided into subsystems of radial or loop feeders fitted with number of switches that are normally closed or opened. Customers could be supplied from different substations or by dis- tributed power generations through different routes. These paths are characterized by different mixtures of commercial, industrial and residential customers who might impose time-varying load demands and different service reliability require- ments (Yin & Lu, 2009). Radial distribution networks are the most con- ventional configurations of distribution systems. In such networks, feeders are extended from distribution substations to lateral feeders while all service areas are supplied through feeders. By this definition radial network leaves the station and passes through the network area with no normal connection to any other supply while an intercon- nected conFigure, such as mesh structure, will have multiple connections to other points of supply. In general, the main advantages of radial con- figuration are its simplicity and its low cost (Ahuja, Das & Pahwa, 2007). In radial configuration, the number of disconnecting devices reduces and design of a protection system is not complicated. Moreover, this configuration is widely used for effective coordination of its protective devices (Kashem, Ganapathy & Jasmon, 1999). Figure 2 illustrates single-line diagram of a typical men- tioned distribution network. The loop (or ring) system of distribution starts at the substation and is connected to or encircles an area serving one or more distribution transform- ers or load centers. Unlike the radial network, the conductor of the ring system returns to the same substation. The loop system is more expensive to build than the radial type, but it is more reliable and may be justified in an area where continuity of service is of considerable importance. Figure Figure 1. Distribution position in power system and its main configuration 271 Optimal Confguration and Reconfguration of Electric Distribution Networks 3 illustrates single-line diagram of a typical men- tioned distribution network. INTRODUCTION TO DISTRIBUTION NETWORK’S RECONFIGURATION In original configuration of a distribution network there are some sectionalizing switches (normally closed 3 ) as well as some tie switches (normally opened 4 ) for both protection and configuration management. By changing the status of these switches, the configuration of distribution sys- tem is varied and loads are transferred among the feeders. This could be done while the radial configuration format of electrical supply is still maintained at the end of this process and all load points are not interrupted (Rugthaicharoencheep & Sirisumrannukul, 2009). The whole mentioned operation for reaching a new optimized configura- tion is defined as “Reconfiguration” of distribution networks. Figure 4 illustrates a typical radial distribution network before and after reconfiguration. For this sample network, the operator has followed loss reduction purpose. In this case switches S14 & S15 are closed after reconfiguration. This is while; S8 & S9 are opened to preserve the initial radial structure of network under study. Generally, reconfiguration methods can be divided in to two groups: “General” and “Spe- cific”. In the specific methods, one initial answer is obtained and is used in a specific algorithm to reach further answers up to an improvement point Figure 2. Single-line diagram of a typical radial distribution network Figure 3. Single-line diagram of a typical loop distribution network 272 Optimal Confguration and Reconfguration of Electric Distribution Networks considering the constraints of the problem. In general methods, an algorithm is used for solving the problem and a large range of answer are ob- tained, among which by performing an operation the most improved answer is selected as a final one. The advantages obtained from feeder recon- figuration using any proposed methods are, for example, real power loss reduction, balancing system load, bus voltage profile improvement, increasing system security and reliability, and power quality improvement. Different Switch Types and Number of Switching Consideration To conFigure a distribution network can consider two different switch types; manual and automatic ones. Considering the combination of these two different types of switches simultaneously will result an optimal flexible planning and operating of these networks with the most minimization in costs. Therefore, these benefits can achieve trough two different cases as follow: Configuration Mode Cost minimization can achieve by using differ- ent switch types to conFigure a new distribution system. This procedure will follow by different switch type placement in a statistic manner i.e. an automatic switch will be the best optimal chose for a place with high switching probability where manual ones can be selected for places with less switch operating. Note that in this case there are two different costs which together determine the total cost; first the cost should spend for change the state of switches and second the cost of automation. Considering this differentiations in costs, com- panies can achieve most benefits through their investigations by establish an optimal balance between above maintained costs. Figure 4. Typical radial distribution network before (above) and after (below) reconfiguration 273 Optimal Confguration and Reconfguration of Electric Distribution Networks Reconfiguration Mode Except a huge benefit derives from configura- tion mode by considering mentioned different switch types and their costs, operators can get more benefits through an optimal reconfigura- tion on their networks by applying this scheme. In this case one of the simplest proceedings is to involve the objective function with different costs for different switch types. The result of applying this procedure in optimization problem under study will be a massive reduction in number of switching which consequently reduces not only operation but also maintenance costs. Following simple objective function describes how to generally consider different switch types’ conditions in reconfiguration problems: F Min C w SSA SSA C w SSM fitness A a a a NAS M = − í ( · · ·· \ ) ÷ − = ∑ . . . . 2 1 1 3 mm m m NMS SSM − í ( · · ·· \ ) l l l l − = ∑ 1 1 (1) Where C C A M ≠ and, NAS: Number of Automatic Switching after each reconfiguration NMS: Number of Manual Switching after each reconfiguration C A: Cost of operating for Automatic type switches C M: Cost of operating for Manual type switches SSA x : State of automatic switch in the xth con- figuration SSM x : State of manual switch in the xth con- figuration In this definition, SSA x and SSM x get only two values in each configuration; one or zero, where represent state of close or open respectively. Moreover, in above objective function w 1 and w 2 represent weighing factors refer to automatic and manual switches respectively. By this definition the operator can create an optimal balance between different costs of switches’ operation regarding to the existing conditions and the costs. Note that by omit these factors from proposed objective function, two switch types will get same share in reducing the operating costs. Mentioned objective function can be used simultaneously with other purposes such as power loss reduction to form a multi-objective function. Distribution Feeder Reconfiguration Considering Time Varying Loads Access to load data is one of the most important steps in planning and operating of electrical dis- tribution systems (Hadian & Haghifam, 2009). Different type of loads in this system consisting industrial, commercial and residential can vary with time over a wide rang. This stochastic nature of loads will require a proper procedure to con- sider load variations during different intervals for both the long and medium term system planning, and the day-ahead operation. Thus, considering a probabilistic load flow will help the planer and operator to execute a flexible configuration and reconfiguration corresponding to achieve more benefits in future. BASIC DETERMINISTIC LOAD FLOW The Load Flow (LF) analysis has always been one of the most important analyses in power systems (Papaefthymiou, 2003). The exact formulation of LF problem concerns the determination of real and reactive power flows in each line (branch) of the power system. The data used to solve this problem are the active and reactive loads at load buses as well as the real power generation and voltage magnitudes at the generator buses. Since, in this formulation, single values are used as inputs for the solution of the problem, the name “Deterministic Load Flow (DLF)” has been used 274 Optimal Confguration and Reconfguration of Electric Distribution Networks in order to distinguish this methodology from “Probabilistic Load Flow (PLF)” introduces and discussed in future sections. Back to DLF problem, the general DLF for- mulation can be divided into two aspects: 1. Determination of the State Vector of the system: the magnitude and phase angle of the unknown bus voltages in the system are computed. 2. Determination of the power flows on each line of the system: the state vector is used in this step for the determination of the active and reactive power flows in every branch. In this analysis, the system is modeled by a set of N buses (nodes), which are interconnected by transmission lines (branches). The transmission links are represented by their nominal π-equivalent circuits. From these equivalent circuits numerical values for the series impedances “Z” and conse- quently the line-charging admittance “Y” will calculate to form an n×n bus admittance matrix which includes typical element as: Y Yi Y j Y G jB ij j ij ij ij ij ij ij ij = < = + = + | | | | cos | | sin θ θ θ (2) This symmetrical matrix has two other important characteristics: 1. Y ii the ii-th self admittance (diagonal ele- ment) is equal to the sum of all admittances connected to the i-th node. 2. Y ik the ik-th element of Y (non-diagonal element) is equal to the negative of the admittance in between nodes i and k. The voltage at a typical bus i is given by: V i =|V i |<i = |Vi | (cosi + json i ) (3) Thus, the net current injected into the network at bus i will be given by: I Y V Y V Y V Y V i i i iN N in n n N = + + + = = ∑ 1 1 2 2 1 ... (4) Let Pi and Qi denote the net real and reactive power entering the network at bus i. Then, P jQ V Y V Y VV or V V i i i in n in i n in n i n N i n n − = = < + − = ∑ * | ( | | . | | [cos( θ δ δ δ 1 −− + − + = = ∑ ∑ δ δ δ i n i in in n N n N J G jB ) sin( )[ } 1 1 (5) Consequently, P V V G B i i n in in in in n N = + = ∑ | | . | | [ cos sin ] δ δ 1 (6) Q V V G B i i n in in in in n N = + = ∑ | | . | | [ cos sin ] δ δ 1 (7) where; N: Number of Buses, i n: i − n and θi n: θi − θn The above Equations constitute the polar form of the ac Power-Flow Equations. It can be seen that there are four potentially unknown quantities associated with each bus i; Pi, Qi, δi and |Vi|. For the solution of this problem, the general formula- tion followed in power-flow studies is to identify three types of buses in the system. At each bus i two of the above quantities are specified and the remaining two are calculated. These 3 bus types are introduced as follow: 275 Optimal Confguration and Reconfguration of Electric Distribution Networks Load Buses (P-Q Nodes) In these buses loads are connected, so P i , and Q i are known from historical record, load forecast or measurements; δ i and |V i | are the unknown quantities. Voltage Controlled Buses (Generator Buses, P-V Nodes) At each bus where a generator is connected, the active power generation can be controlled by adjusting the prime mover, and the voltage mag- nitude can be controlled by adjusting the generator excitation. Therefore, P i and |V i | are known and δ i and Q i are the unknown quantities. Slack Bus The power injection at this bus is determined by the power balance Equation of the system. In the formulation of the power flow problem, the power injection in this bus is not pre-specified or scheduled. After the power flow problem has been solved, the difference between the total power which is injected into the system at all other buses and the total output plus the losses, are assigned to the slack bus. The voltage angle of this bus serves as a reference for the angles of all other bus voltages. The other known quantity for this bus is the voltage magnitude |V i |. Obviously, there is no requirement to include the power flow Equations for the slack bus in the power flow problem. With these definitions, the problem is trans- formed to a system of (2N-N g -2) non-linear Equations with (2N-N g -2) state variables to be calculated, where N g is the number of voltage- controlled buses in the system. Due to the non-linearity of these Equations, power-flow calculations usually employ iterative techniques such as “Gauss-Seidel” and “Newton-Raphson” procedures (Papaefthymiou, 2003). PROBABILITY DENSITY FUNCTION A typical daily load profile and concept of its variations is shown in Figure 5. Considering such these patterns for different loads of network, a probabilistic density function (PDF) in each load node can be obtained. It is obvious that by increasing the numbers of segments, results are more accurate while more time consuming and vice versa. Bell shaped curve shown in Figure 6 illustrates a sample PDF plotted by Monte Carlo Method 5 (Rubinstein & Kroese, 2008). MCM is a statisti- cal simulation uses a random sequence of numbers to describe the statistical behavior of a variable. In the other words, for this purpose, MCM uti- lizes repeated trials of the deterministic load flow technique to determine the probability distribu- tions of the nodal powers, line flows and losses. The hypothesis of the Monte Carlo Method, as a mathematical technique, infers the search of an efficient solution instead of an accurate solu- tion (Opazo Mora, Garcia-Santander & Lopez Parra, 2008). Having “expected demand” and its “standard deviation”, desired PDF can be explains as an exponential Equation as follow: f x e x ( ) . . . / ( ) = − − 1 2 1 2 2 2 σ π µ σ (8) where, x: Variable σ: Standard deviation of x μ: Expected value of x In this Equation, to form a standard distribu- tion, expected value of “x” can be consider as load value of the node with maximum occurrence probability through studied time interval. 276 Optimal Confguration and Reconfguration of Electric Distribution Networks PROBABILISTIC LOAD FLOW This section introduces a probabilistic load flow using Point Estimate Method (Usaola, 2008). Let z be a random variable that is function of several independent variables with specific PDFs and x = (x 1 ,..., x n ), z = h(x).where, n: number of independent variables Hence, The probability density functions of each variable xk will be f k (x k ), the joint resultant probability density function will be f x (x 1 ..., x n ) and ∂ ∂ ×∂ × ×∂ = ∃ ≠ ( ) ... , kn x k k kn f x x x if ki kj 1 2 0 (9) With these definitions, μ k,n will be the central moment of order n of the variable x k , where mean and variance are η k and σ 2 k= μ k,2 respectively. for i = 1,..., m points and k = 1,..., n variables, consider the points x k,i = η k + ξ k,i σ k . So that, each points will be associated to a weight p k,i such that p k i i m k n , = = = ∑ ∑ 1 1 1 . Then, z=h(x) can be expanded in multivariate Taylor series around the point η x = (η 1,…, η n ). Us- Figure 5. A typical daily load profile Figure 6. Sample probability density function 277 Optimal Confguration and Reconfguration of Electric Distribution Networks ing this series expansion, the mean of z may be approximated as: η η z x x x i E z E h x h x f x f x h j = = = = + −∞ ∞ −∞ ∞ = ∫ ∫ ∫ [ ] [ ( )] ... ( ) ( ) ... ( ) ( ) ! 1 1 nn j j i j i i j x h x x d ∑ ∑ ∫ = ∞ ∂ ∂ − 1 . ( ) . η (10) Since, ... ( ) ...( ) ( ) x x f x dx k k j k k q x 1 1 1 1 0 − − = −∞ ∞ ∫ ∫ η η (11) for every q, ,j if … ∃ ≠ ∈ { } k k m n l m n , , ..., 1 . Then, η η µ z x j i j i n j j i h j h x = + ∂ ∂ = = ∞ ∑ ∑ ( ) ! , 1 1 2 (12) Since ( ). ( ). . x f x dx k k k k k − = ∀ −∞ ∞ ∫ η 0 If approximate the mean η z by η η η z k i k i n k m i n p h x ≅ = = ∑ ∑ , , ( , ..., , ..., ) 1 1 1 , (13) from the series expansion of the terms of (13) and its approximation to the series (12) in a similar way to the uni-variant case, equaling terms, will arrive at the following system of Equations: p k i i m k i j k j , , , = ∑ = 1 ξ λ , for j=1, …, 2m-1 and k=1,…, n (14) To this system of Equations, it can be added p n k i i m , , = ∑ = 1 1 for each variable k (15) Therefore, there are 2m Equations with 2m unknowns for each variable k, forming a nonlin- ear system. Solving these Equations, the moment of order j for the variable z, m z,j , can be then approximated by: m E[z ] z,j j k 1 = ≅ = = ∑ ∑ p h x k i j k i n i m n , , ( , ..., , ..., ) η η 1 1 (16) PROPOSED PROBABILISTIC PROCEDURE As discussed in previous section, the Point Esti- mate Method can be applied to Probabilistic load flow. Proposed method can be used for following procedure in order to find the uncertainty of the branch power flows and consequently total power losses in distribution network under study: 1. Evaluate the moments of the power injec- tions of each node. 2. Solve the system Equations (14) and (15). 3. From these values, run deterministic power flows for the different values of (η 1 ,..,x k,i ,.., η n ) to obtain power flow results for whole distribution network under study. Note that in this step the solution provides an ensemble of values for the branch power flows and also node voltages. 4. From this ensemble of values, the moments of these variables are found using the Equation (16). 5. In the last step, in order to follow proposed method it is still necessary to obtain the val- ues of the PDF, for the variables of interest 278 Optimal Confguration and Reconfguration of Electric Distribution Networks which is power losses. This can be made, for instance, through “Gram Charlier A” series expansion introducing in following section (Usaola, 2008). “Gram-Charlier A” Series Expansion The Gram-Charlier type A series is a standard measure frequency function, denoted as f(x), with the mean µ GC = 0 and variance σ 2 GC = 1 expanded in a series of derivatives of the standard measure normal (Gaussian) function: G x e x ( ) . = − 1 2 2 2 π (17) so that the mean, variance, and other raw mo- ments can be used to obtain an approximation of the probability density function while the Gram- Charlier type A series for this purpose yields an approximate probability density function of power flow. The derivatives of (17) result in a Taylor series representation called “Gram-Charlier type A” series: f x c H x G x j j j ( ) ( ) ( ) = = ∞ ∑ 0 (18) Where c j are constants based on a function of standardized moments, H j (x) are Hermite poly- nomials, and G(x) is the characteristic Gaussian function. The first two Hermite polynomials are H 0 (x) = 1 and H 1 (x) = x. Further more, the Hermite polynomials obtain from following Equation for i greater than 1: H x x x i k a i i k i k a k ( ) ( ) . . ( ) . ( ) , , = + − − − − − = − 1 2 1 1 2 1 1 3 5 2 33 ∏ (19) where, n m n m n m and t i for t odd i for t even í ( · · · · \ ) = − = ÷ ÷ ' ! !( )! , : , : 1 2 2 2 !! 1 1 1 1 1 + 1 1 1 1 1 The constant c j in the Gram-Charlier type A series is found using standard measure as follow while first two constants will be c 0 =1 and c 1 =0, c j m m m m j j pdf pdf j k j k pdf pdf j = ÷ − − − − 1 1 2 2 1 2 1 2 ! ( ) ( ) . ( ) ( ) ( ) / ( ( )) ( ) −− − = = − ∑ ∏ − í ( · · · · \ ) l l l l 2 1 2 2 1 3 5 2 3 2 1 ( ) , , . ( ) k k t b k i k b ll l l (20) Using the Hermite polynomials, H j (x), and Gram-Charlier constants, c j , a formal expression of f(x) is: f x G x m H m H m pdf pdf pdf ( ) ( ).[ ( ) ( ) ( ( ) ( ) ( ) = + − + + 1 1 2 1 1 6 1 24 2 2 2 3 3 3 4 σ σ σσ σ 4 2 2 4 6 3 − + + m H pdf ( ) ) ...] (21) Since f(x) is found using a standard measure random variable µ GC = 0 and σ 2 GC = 1, f(x) needs to be transformed into a function f(y) so that the probability density function has mean µ pdf = µ GC and variance σ 2 pdf = σ 2 GC . The standard measure transformation used for the Gram-Charlier type A series is: x y pdf pdf = −µ σ (22) 279 Optimal Confguration and Reconfguration of Electric Distribution Networks Where x are the standard measure variables and y are the real variables. The new Gaussian function now becomes, G y e y pdf pdf ( ) . .( ) = − 1 2 1 2 2 π µ σ (23) The resulting probability density function, f(y), is the actual distribution of power flow as: f y c H y G y pdf j j j ( ) . ( ). ( ) = = ∞ ∑ 1 0 σ (24) GENETIC ALGORITHM Genetic algorithm is one of the optimization methods based on heredity and evolution. GA has become an efficient tool for search and opti- mization problems after its first introduction in 1960’s by J. Holland. In This statistic searching algorithm a population of strings (chromosomes or the genotype of the genome), which encode candidate solutions (called individuals or pheno- types) to an optimization problem, evolves toward better solutions. Comparison of GA with Other Conventional Optimization Methods Some differences between GA and other conven- tional optimization methods are as bellow: • GA works with coded parameters rather than parameters themselves. • GA always operates on a whole population of points rather than search from a single point. This useful characteristic improves the chance of reaching to global optimum instead of local one. • GA uses ftness function for evaluation rather than derivatives. So that, it can be easily applied to any kind of continuous or discrete problems. • GA use probabilistic transition operates rather than deterministic rules. • GA does not have any limitation relate to continuity, differentiability and…, gener- ally exist in conventional methods. GA’s Advantages and its Limitations Following list gives some advantages of genetic algorithm generally find in available researches: • Wide solution space. • Complex ftness landscape. • Multi solutions and multi objective function. • Easy to discover global optimum and resis- tant to becoming trapped in local optimum. • Easy modifcation to use in different problems. • Handles poorly understood search spaces easily. • Well performance in large scale optimizations. • Very robust to diffculties in the evaluation of objective function. • Can be employed for a wide variety of op- timization problems. Solves multi-dimen- sional, non-differential, non-continuous, and even non-parametrical problems. • Very easy to understand and practically no need advance knowledge of mathematics. • Can be easily transferred to existing simu- lations and models. Beside all its advantages, there are some limita- tions which can be sense using this algorithm in different optimization problems: • Fitness function identifcation • Premature convergence occurrence • Choosing its various parameters such as size of population, mutation and cross 280 Optimal Confguration and Reconfguration of Electric Distribution Networks over rates, selection method and…which strongly affect on optimal solution. • Not good to identify the local optimum. • Not effective terminator • Have some troubles to fnd the exact global optimum. It is very often when the popula- tions have a lot of subjects. • Requires large number of ftness evalu- ations which increases the computation time. • Like other artifcial intelligence tech- niques, the genetic algorithm cannot assure constant computation times. Even more, the difference between the shortest and the longest optimization computation time is much larger than with conventional gradi- ent methods. Basic GA Concepts To start GA, many individual solutions are ran- domly generated to form an initial population. The population size depends on the nature of the problem, but typically contains several hundreds or even thousands of possible solutions. This initial population and also future reprodused individuals form crospanding chromosomes in the shape of diffrent strings. Chromosome A chromosome or genotype of the genome as a concept of GA consists a string of information which represent characteristic of each individual. By this definition, each gene in a chromosome introduces only one specific individual (or status) where each chromosome represents specific popu- lation (or solution). Before can use these strings there should be a way to encode and decode the initial information and final resulted solutions respectively. Binary coding is one of these methods widely used to encode and decode each gene in a chro- mosome. While there are many other techniques such as using real and decimal numbers, binary coding is the most expanded presentation of a chromosome, because it is simple and traceable. Note that in all these methods searching process will apply on coded strings. Figure 7 represents a simple binary string including coded information. In this string each gene defines the color of each point in Figure 8 where 0 and 1 represent white and black colors respectively. Moreover, first gene in each section of this string determines quarter number for each individual. Selection Selection is a stage in genetic algorithm in which individuals are chosen from a population for later reproduction. This process uses a fitness func- tion to evaluate each individual corresponding to desired objective. Providing fitness values for each indivitual and sort these individuals by their coresponding fitness valuse in next step, selection process ends by selecting induvituals with most fitness and forms a new population for reproduc- tion process. While there are many different types of selec- tion, “Roulette Wheel” is the most commen and simplest method to fulfil the selection process. Figure 9 depics a sample roulette wheel. In this wheel, each individul get its own portion by related fitness persentage. Selection point will show the Figure 7. Sample binary string 281 Optimal Confguration and Reconfguration of Electric Distribution Networks selected individul after each rotation. Following this process, the individual with the most fitness will have the most probability to select and trans- fer to the next generation. This type of selection method can get the form of rout instead of rotation as shown in Figure 9. Again, in this form selection can be assign by choosing a random number (for instance: a value between 0.0 and 1.0 for each iteration in above example) Reproduction Reproduction is a process to generate latter gen- eration of solutions from those picked previously by selection process (crossover) or by changing some genes in a string (mutation). Although there are some other GA operators apply to generate new populations but “crossover” and “mutation” are most commen sulotions as well as almost insepraTable part of a genetic algorith. Type and implementation of these operators depends on encoding and also differs from one problem to another. Crossover For each new solution to be produced by crossover operation, a pair or even a group of parents are selected for breeding. While there are many dif- ferent kinds of crossover, the most common type is single point crossover.In single point crossover one crossover position k is selected randomly from [1, 2, …, N-1], where N is number of variables in each individul. In this step, variables exchange between individuals about this point to produce new offsprings. This process ultimately results in the next generation population of chromosomes that is different from privious generation. Figure 10 illustrates this process, where k is asumed to be 5. Note that for this kind of crossover one can also use more points. See Figure 11 for multi point cross over at points k=5, 8 and 15. Mutation Mutation is another genetic operator that alters one ore more gene values in a chromosome from its initial state. The purpose of mutation is to maintain diversity in the genetic algorith. This operator allows the algorithm to avoid local optimum by preventing the indivituals to be all exactly the same. While Figure 12 illastrate a sample “Flip- Bit” mutation, Uniform, Non-Uniform, Boundary and Gaussian are some other known methods for mutation process. Figure 8. Input information to form desired binary string for Figure 7 Figure 9. Sample rout selection method 282 Optimal Confguration and Reconfguration of Electric Distribution Networks Termination Genetic process repeats until a termination con- dition reaches. Some of common terminating conditions are listed as follow: • Maximum number of generations; Genetic algorithm stops after the specifed numbers of genarations have reached. • Time limit; Genetic algorithm stops after the specifed time has elapsed. • Fitness limit; Genetic algorithm stops if there is no change in ftness for specifed number of genarations. Figure 10. Example of single point cross over Figure 11. example of multi point cross over 283 Optimal Confguration and Reconfguration of Electric Distribution Networks This is while, there are many other condicutions suported by common softwares such as MATLAB including “Function tolerance”, “Nonlinear con- straint tolerance”, “Stall time limit” and “Stall generations”. Basic GA’s Flowchart A flowchart describing main steps in basic genetic algorithm is illustrated in Figure 13 as follow: PROPOSED FITNESS FUNCTION FOR GA Choosing Genetic Algorithm solver, proceed to existing optimization problem, a proper fitness functions most suiTable for proposed method is needed. Let take a look to two typical PDFs for power loss resulted from proposed load flow with different configuration of network (Figure 14): As it is clear from Figure 14, the curve (a) illustrates less overall power loss with more total probability for loss values than the curve (b) due to the network’s configuration diversity. Ap- proximate these curves to the closest triangles, can calculate desired fitness function with less computations. These approximated triangles for above mentioned PDF curves are depicted in Figures 15-(a) and 15-(b) respectively. Considering these different triangle shapes for various configurations under study, basic proposed fitness function can be form as follow: F S w a fitness trg i i i = ÷ ÷ − í ( · · · · \ ) l l l l = ∑ 1 1 1 1 1 2 . ( ) . ll l l l l (25) Figure 12. Individual before and after Flip-Bit mutation Figure 13. Sample of a basic Genetic Algorithm 284 Optimal Confguration and Reconfguration of Electric Distribution Networks Figure 14. Comparison between power loss PDFs for two different configurations of network Figure 15. Approximated sample PDF with triangle shapes 285 Optimal Confguration and Reconfguration of Electric Distribution Networks In this Equation, S trg represents the space of approximated triangles (equal to a a 1 2 2 . ). Mean- while, W 1 is considered as penalty factor for a 1 and a 2 where for the configuration with high prob- ability and low power loss this factor makes a high fitness and vise versa. Several experiments and studies chose the value of “10” for this factor which gives a normal- ized fitness function with more accurate results. By this fitness function, genetic algorithm will search for optimum triangles which just represent the least power lose values with the most total probability of occurrence simultaneously. This is while, in some cases regarding to the condition of the network and decision of the operator, in order to consider the cost of switching, the Equation (1) can be combined easily with above mentioned Equation to form a single fitness function. COMPUTATION RESULTS AND DISCUSSION To examine the efficiency and improvement, the suggested method is developed in MATLAB, on a Pentium-4 PC (1.86GHz & 2GB RAM), and is performed on a sample three-feeder network. Original configuration of this network is illustrated in Figure 4, while the system parameters are acces- sible by Civanlar et al. (1988). Since it was pro- posed for a study with fixed demands, to perform suggested method new different load profiles are added to each load sections which are remained with no change all over the examination process. These profiles are created randomly, with loads ranging from 90% to 110% of the original loads. As the first scenario, only the lose reduction is considered in the objective function. Table 1 designates the numerical results of this experi- ment. With specified load pattern, resulted power loss probability density function is depicted in Figure 16. In the second scenario, two objectives of switching reduction and reduction in loss are ap- plied to optimization problem simultaneously. Table 2 designates the numerical results of this experiment. With specified load pattern, resulted power loss probability density function is de- picted in Figure 17. Although the Table 2 ex- presses less reduction in loss for this scenario than previous one, but implementing the second sce- nario gives more benefits by reduce the number of switching. This benefit is calculated as 405 $ includes income from total loss reduction and cost of switching. To calculate these values following assump- tions are used in this study: • The cost of electricity is $6.5625 per kWh • To simplify the presentation, the network under study includes only one switch type • Each switching cost is set to $203 which is one-twentieth of a new switch installation cost (Yin & Lu, 2009) In order to compare the results of suggested method with other references, the proposed method is applied to two other test systems. The first one is a small system (Baran & Wu, 1989) widely used as a first reference in case studies. Table 1. Numerical results for first scenario Minimum Power Loss (p.u) Maximum Power Loss (p.u) Mean Power Loss (p.u) Total Number of Switching Total Loss Reduction Original 0.07 0.95 0.58 _ 0% After Reconfiguration 0.01 0.73 0.35 6 35.7% 286 Optimal Confguration and Reconfguration of Electric Distribution Networks Table 2. Numerical results for second scenario Minimum Power Loss (p.u) Maximum Power Loss (p.u) Mean Power Loss (p.u) Total Number of Switching Total Loss Reduction Original 0.07 0.95 0.58 - 0% After Reconfiguration 0.03 0.81 0.41 2 25.3% Figure 16. Power loss probability density function for first scenario (before & after reconfiguration) Figure 17. Power loss probability density function for second scenario (before & after reconfiguration) 287 Optimal Confguration and Reconfguration of Electric Distribution Networks Table 3 represents the loss reductions by proposed method in comparison to other available method with several cases for this test network. This is while, total number of switching and total income are other results available in this Table to carry out a better comparison. In this examination the income values are evaluated based on the energy cost of $0.50 per kWh and the switching cost of $8.00 for each pair switching operation as are considered by Fang, Cai & Guo (2005). These results depict the relation between loss reduction and number of switching. It is clear that by increase the number of switching total power loss decrease and vise versa. Unlike the compared method, proposed process found optimal values for number of switching and the power loss by apply a balance between them. Again these con- siderations result in a huge amount of benefit approximately 260,000 $ annually for the network under study. Final comparisons relate to a real large sys- tem. For this network, Table 4 represents the loss reductions and total number of switching resulted by proposed procedure in comparison to Lopez (2004) famous method with three different cases. CONCLUSION In this chapter after review the background of “reconfiguration” thorough major presented meth- ods, electric distribution network, basic concepts and its configuration are introduced. Furthermore one becomes familiar with reconfiguration pro- cedure and its main concepts. Two important points proposed which are original and main concerns in recent years. The proposed chapter fully discussed about these points and proposed new heuristic solutions to overcome mentioned issues in optimal reconfiguration process. This is while, a precise tutorial followed to introduce basic Genetic Algorithm its parameters and main concepts including advantages and limitations. Finally, In order to examine the suggested solution several experiments have been done. Table 3. Comparison between the result of proposed method and other method Other Methods Proposed Method Network Ref. & Case Number Loss Reduction (%) Nu mb e r o f Switching (for 24 hours) Tot al I n- come ($) Loss Reduction (%) Numbe r of Switching (for 24 hours) Tot al In- come ($) Baran (1989) Fang (2005) Case #1 18.33 4 489.50 27.43 6 732.24 Case #2 23.21 4 624.00 Case #3 24.41 12 625.00 Case #4 27.78 16 702.00 Table 4. Comparison between the result of proposed method and other method (Real network) Network/Method Compared Method Proposed Method Real System With 917 Nodes Case Loss Reduction (%) Number of Switching (for 24 hours) Loss Reduction (%) Number of Switching #1 12.52 159 12.26 10 #2 10.86 9 #3 10.28 9 288 Optimal Confguration and Reconfguration of Electric Distribution Networks Moreover, some proposed scenarios are compared with other methods applied in reliable articles. Results depict the relation between loss re- duction and number of switching. This is while; the proposed method found optimal values for number of switching and the power loss by apply a balance between them. FUTURE RESEARCH DIRECTIONS The obtained results in this essay generally des- ignates its efficiency, while further improvements such as solutions to reduce the computation time will result in more optimal reconfiguration of electric distribution networks. One can consider more improved GA or other evolutionary methods to over come such this problem in future works. Considering different energy prices for different time intervals in power markets is another sug- gestion in order to improve proposed method. More over, presents of Distributed Generations (DGs) which are almost new concepts in electric distribution networks, can affect on proposed optimization problem. To follow an optimal configuration or recon- figuration process of these networks it is necessary to provide some models which are flexible with presence of DGs and their conditions. This can also be achieved by adding proper constraints to proposed objective function. Another direction to future researches relates to implementing reconfiguration process for active power loss reduction simultaneously by capaci- tor placement in electrical distribution networks. Further more; one can follow suggested procedure with more objectives such as network’s reliability or voltage profile improvement. REFERENCES Ahuja, A., Das, S., & Pahwa, A. (2007). An AIS- ACO hybrid approach for multi-objective distribu- tion system reconfiguration. IEEE Transactions on Power Systems, 22, 1101–1111. doi:10.1109/ TPWRS.2007.901286 Baran, M. E., & Wu, F. F. (1989). Network recon- figuration in distribution systems for loss reduction and load balancing. IEEE Transactions on Power Delivery, 4, 1401–1407. doi:10.1109/61.25627 Chen, C. S., & Cho, M. Y. (1993). Energy loss reduction by critical switches. 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Optimal reconfiguration of electri- cal distribution network using the refined genetic algorithm. In M.E. El-Hawary, Optimization of Power System Operation. Hoboken, New Jersey: Wiley Publishing. 292 Optimal Confguration and Reconfguration of Electric Distribution Networks KEY TERMS AND DEFINITIONS Electric Distribution Network: An electric distribution network is a system of cables and equipments which deliver electric power to the end users. Configuration: The process of design and implement of an electric distribution system. Reconfiguration: Switching and changing the status of network for better operation. Optimization Problem: An optimization problem is the problem of finding the best solu- tion from all feasible solutions. Switch Types: Maneuver switches in an elec- tric distribution network which can be manual type or operated automatically. Load Flow: An important tool involving numerical analysis applied to power systems to calculate its parameters such as voltage angles and magnitudes. Probability Density Function (PDF): A function that describes the relative chance for a random variable to occur at a given point in the observation space. ENDNOTES 1 1975 to present 2 SSOM 3 N. C. switches 4 N. O. switches 5 Monte Carlo Method (MCM), 1940s. Gen- erally MCMs are a class of computational algorithms that rely on repeated random sampling - wikipedia.org. 293 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 10 DOI: 10.4018/978-1-61350-138-2.ch010 A. G. Tikdari University of Kurdistan, Iran H. Bevrani University of Kurdistan, Iran G. Ledwich Queensland University of Technology, Australia A Descriptive Approach for Power System Stability and Security Assessment ABSTRACT Power system dynamic analysis and security assessment are becoming more signifcant today due to increases in size and complexity from restructuring, emerging new uncertainties, integration of renewable energy sources, distributed generation, and micro grids. Precise modeling of all contributed elements/ devices, understanding interactions in detail, and observing hidden dynamics using existing analysis tools/theorems are diffcult, and even impossible. In this chapter, the power system is considered as a continuum and the propagated electromechanical waves initiated by faults and other random events are studied to provide a new scheme for stability investigation of a large dimensional system. For this purpose, the measured electrical indices (such as rotor angle and bus voltage) following a fault in different points among the network are used, and the behavior of the propagated waves through the lines, nodes, and buses is analyzed. The impact of weak transmission links on a progressive electromechanical wave using energy function concept is addressed. It is also emphasized that determining severity of a disturbance/contingency accurately, without consid- ering the related electromechanical waves, hidden dynamics, and their properties is not secure enough. Considering these phenomena takes heavy and time consuming calculation, which is not suitable for online stability assessment problems. However, using a continuum model for a power system reduces the burden of complex calculations. 294 A Descriptive Approach for Power System Stability and Security Assessment INTRODUCTION Power system angle instability following loss of synchronism of the generators can be considered as a fast instability phenomena (Kundur, 1994, and Bevrani 2009). Detecting of this phenomena and performing adequate emergency actions are important issues to maintain the power system stability. When a disturbance takes place in a power system, the rotor angle of the generators near the occurred fault deviates from their base frames. This deviation propagates through the power system. So, for large disturbances, this may lead to the catastrophic outages, and finally blackout. Because of deregulation and economical issues in power system management and fast growing of electrical power consumers, the transmission lines are usually working close to their stability limits. In other words, nowadays power systems are working under stress. One of problems that a stressed power system is encountered with, is the prediction of instability location. Occurring of a disturbance in a point of large scale power system may initiate instabil- ity in another point of the grid. In this chapter, it is shown that the reason of this problem can be found out from electrical wave propagation phenomenon and identifying the weak links of the system. There are many research reports about wave traveling and propagation phenomenon (Thorp, 1998, Parashar, 2004, Phadke, 2008, Wagner, 1950, Sluis, 2001, Tsai, 2005 and Bank, 2007). Electromechanical wave propagation issue is well-discussed in (Thorp, 1998, Parashar, 2004, Phadke, 2008). They modeled a power system as a continuum. An online method for detection of loss of synchronism using an energy function criterion is developed in (Padiyar, 2006). Several methodologies are also available to solve the same problem, using artificial neural networks, heuristic algorithms and intelligent schemes. Emerging Phasor Measurement Units (PMUs) makes it possible to easily monitor the angle wave propagation throughout the power systems. They use Global Positioning Systems (GPS) to provide a synchronous time throughout the power systems which may be distributed through the continents. A methodology for islanding and identifying the weak links of a complex power system is proposed in (You, 2006 and Yang, 2006); they used the slow coherency approach. In this chapter, first as a background, the dif- ferent types of traveling waves in power systems and islanding control are addressed in Section 2. In Section 3, the problem at hand and the system modeling are described. In Sections 4 and 5, the islanding problem is re-analyzed concerning the wave propagation problem, and the proposed descriptive approach for power system stability assessment is explained. Some simulation results on two ring power system (64-bus and 200-bus), a 400-bus meshed system, and the 24-bus IEEE Reliability Test System (RTS-79) are presented. Further research directions are addressed in Sec- tion 6, and the chapter is concluded in Section 7. Finally, a new power system emergency control framework based on descriptive study of electrical mea- surements and electromechanical wave propagation in large electric power systems is introduced. Since, fast and accurate detection of instability is essential in initiating certain emergency control measures, the proposed methodology could be also useful to detect the contingency condition and performing the well-known islanding and load shedding techniques. The chapter is supplemented by some illustrative nonlinear simulations on large scale test systems. 295 A Descriptive Approach for Power System Stability and Security Assessment BACKGROUND Wave Propagation Wave propagation is a phenomenon appeared in many studying fields. In civil engineering, for example, it is used to study on propagation of earthquake waves through the structures com- ponents. Propagation of electromagnetic waves in different environments is an example of this phenomenon in physics and communication. When you move one end of a rope which another end is fixed, you can see a one-dimensional (1-D) wave that propagates through the rope and then back propagates. Indeed wherever there is a flex- ible material affected by a perturbation, the wave propagation phenomenon will appear. Observing the propagation of a wave through an environment makes it so useful for analyzing the related problems. Also wave propagation phenomenon is an interesting problem in study- ing of large scale power grids (Thorp, 1998, Parashar, 2004, Phadke, 2008, Wagner, 1950). A large electric power system can be introduced as a very complex and nonlinear dynamic system which is always subjected by small/large distur- bances. In many articles, it has been shown that the disturbances propagate through the system like a wave (Thorp, 1998, Parashar, 2004, Phadke, 2008, Wagner, 1950). Propagation of a disturbance through a power system may threat the stabil- ity if becomes large or if it passes through the weak lines/elements. Furthermore, it may cause undesirable tripping of some protection devices (Phadke, 2008). To study about electromechanical transients usually a large detailed model of the whole power system is needed. Preparing such system models and solving the heavy equations are so time-consuming; and often it will not give us a suitable sense on the global power system and its phenomenon such as electromechanical wave propagation. Studying a system based on wave propagation analysis is needed to observe an overall view of the system. Therefore, a descriptive approach could be considered as a good alternative to analyze a power system based on wave propagation. All performed studies on the wave propaga- tion over the years, can be categorized into two groups. The first group considers voltage wave propagation (Wagner, 1950, Sluis, 2001). The voltage-type wave propagation may be created following a switching or lighting. However, the second group is electromechanical wave propa- gation which is produced when a rotor angle of a synchronous generator deviates from its base frame following another disturbance. These phe- nomena are introduced in the below subsections. Voltage Wave Propagation Studying about power system stability can be di- vided into two general groups: static stability and transient stability. In static stability study, the goal is to verify the system stability when encountered with low-amplitude slow disturbances. However, in the transient stability problems, a large and suddenly disturbance is occurred. The dynamic stability is an improved form of static stability in the case of low amplitude disturbances with longer life time (Kundur, 1994). In static stability study the wave length is about 6000 Km for 50 HZ (Sluis, 2001). There- fore, in these studies a lumped model of a line is adequate. But for the transient stability problems, that the higher frequencies are exist, the traveling waves cannot be ignored. In other word, in this situation when a signal exists at one end of a line, there is no guarantee to appear it at another end of line, at the same moment. Indeed, the wave travels through the lines with a delay. This delay is actually because of charging the capacitance and inductance elements of the line (Sluis, 2001). In the lumped π-model, only two capacitors and one inductor are used; and in the T-model there are only two inductors and one capacitor. So, the voltage variations are immediately sensed at another end of line. But as shown in Figure 1, a 296 A Descriptive Approach for Power System Stability and Security Assessment distributed model contains a lot of elements that each element includes one inductor and one ca- pacitor. When a voltage source is applied at one end of the line, the first capacitor is immediately charged; but because of first inductor, the second capacitor charges when the inductor is charged, and it makes a delay. This delay also exists for the next elements. One of most important parameters in this issue is the characteristic impedance which is calcu- lated by Equation 1: Z L C = (1) where, L and C are defined as line inductance and capacitance values per length of line, respectively. When a voltage wave passes through a point in which the characteristic impedance is changed, the magnitude of reflected wave and the magnitude of the wave that lets trough are dependent on the value of characteristic impedances of two lines (for example when an overhead transmission line is connected to an underground cable). The wave propagation velocity is another important parameter that can be calculated with Equation 2. v LC = 1 (2) Rotor Angle Wave Propagation As discussed, the angle wave propagation which is called electromechanical wave propagation starts when a generator rotor deviates from its base frame. Then, it propagates throughout the power system. The velocity of angle wave propa- gation is slower than voltage wave propagation (Thorp, 1998 and Phadke, 2008). As has argued in (Phadke, 2008), the nature of this phenomenon is not completely clear. It seems to be the result of local inertias. As the waves may lead to loss of synchronism for under stressed power systems, studying of them is one of the interested issues in power systems stability analysis and security assessment. Formulation of wave motion as nonlinear partial differential equations in a two-dimensional surface is introduced in (Thorp, 1998). This for- mulation is in form of wave equations. The swing equation (Equation 3) of a generating unit can be expressed as follows: 2H D P P P a m e ω δ ω δ .. . + = = − (3) where, H, ω, D, , Pe , and Pm are inertia constant, angular speed, damping factor, rotor angle, elec- trical output power, and mechanical input power, respectively. The above swing equation is introduced as a second-order hyperbolic wave equation in (Thorp, 1998). Using of these equations lets us to intro- duce a power system as a continuum system. The Figure 1. Distributed model of a transmission line 297 A Descriptive Approach for Power System Stability and Security Assessment methodology of extracting the continuum model for a two-dimensional (2-D) power system is well-established in (Parashar, 2004). For a mesh network power system, which the generators and loads are located at distributed discrete points, introducing a 2-D continuum model needs to in- troduce the system parameters in form of smooth functions. To distribute the parameters, a Gaussian filter which is the most common smoothing tool can be suggested (Parashar, 2004). Islanding Control In fact, the angle instability is the loss of synchro- nism of the system synchronous generators. Angle instability is usually started when the synchronism between two generators which are located at two sides of a line is loosed. In other words, the angles of two generators are separated, may because of overloading a link which connects two generators, directly or indirectly. This link may be a weak link or a link which encountered a suddenly overload due to some connections in the network. There are many technical reports representing various methodologies for detection/prediction the angle instability situation. For example, using of energy function concept is suggested in (Padiyar, 2006). Based on this concept, for the purpose of stability, a system should be able to convert whole of kinetic energy achieved throughout a disturbance into potential energy. On the other words, when in a stable swing, the potential energy reaches its maximum value, the kinetic energy should be zero. In complex power systems, there are usu- ally more than one inter-islands connection line. Therefore, to validate the system stability, maintaining only one line is not adequate. Based on the given idea in (Padiyar, 2006 and Wang, 2004), the change of power in all lines belong- ing to a cutest called critical cutest determines the stability or instability situation. As argued in (Padiyar, 2006), the potential energy, under certain assumption, can be considered as sum of energies of the lines belonging to the cutest; and also, the kinetic energy is a function of voltage angle gradient of the cutest. When a power system is becoming unstable at the location of a cutest, it means that the angle of a portion of power system that connected to the system (with the critical cutest) moves in opposite direction of angle motion of the other parts of system. In this situation, the islanding control is the most effective control action. Therefore, the unstable part of system is separated by tripping the lines in the critical cutest. The detection of critical cutest/weak link is the first step, and the islanding control must be executed. Following the islanding process, we are in face of some islands with excess load or generation. Load-generation imbalance in an isolated island leads the island into another form of instability, but with a slower dynamic than angle instability. Therefore, the island formation may not be the final stabilizing step. However, it can be considered as a way to arrest the fast angle instability. Following the islanding, the other emergency control actions such as load shedding and generation tripping are usually needed (Tikdari, 2009 and Bevrani 2010). Slow coherency is a suitable and usual meth- odology for islanding formation (You, 2004). Fol- lowing a fault, there are some groups of generators based on their angle variations. The angle changes in a group are similar, but the different groups of generators behave in opposite directions. This is the concept of slow coherency theory. One may introduce every coherent group of generators as an island. The lines that connect the islands may also provide the power system weak links (You, 2004, Yang, 2006, Wang, 2004). Slow coherency is known as a good example for application of singular perturbation theory in power systems (You, 2004, Yang, 2006, Wang, 2004, Ourari, 2003 and Sowa, 2004). Using this method, the groups of generators with coherent angle behaviors can be determined. In transient stability issues, the slow coherency can be also used to find out the equivalent dynamic model of 298 A Descriptive Approach for Power System Stability and Security Assessment a power system (Ourari, 2003 and Sowa, 2004). In the slow coherency, it is assumed that state variables of an n-degree performance can be divided into two categories: r slowest states and n-r fast states. The r slowest states represent the groups of generators with slowest coherency. In slow coherency-based islanding, two assump- tions can be considered to simplify the process of finding coherent groups of generators: i) the groups of coherent generators are independent to size of disturbance; and ii) the groups of coherent generators are independent to the modeling ac- curacy of the generator unit. These assumptions are important to perform the continuum model of power system, which is main interest in the present chapter. PROBLEM ILLUSTRATION AND MODELING In this section, the problem that we are attempting to solve is described. Suppose a high stressed large scale power system which its elements are work- ing near their stability margins. When a system is explored near the stability limits, disturbances may easily force the system to a cascading failure and even blackout. The goal is to widely monitor system in order to effective protection against large disturbances. For this purpose, an online stability/security assessment program is needed. On the other hand, following a contingency, the voltage/angle deviations propagate through the power system. These traveling waves may pass through the high stressed elements and trigger an instability event. By using of wave propagation phenomenon, a descriptive approach for power system stability assessment can be proposed. In a power system, the operators and engineers will be able to use this descriptive tool to track the system dynamic behaviors, to validate the system performance against likelihood events, and to predict the next stable point. The methodology will be described in the next sections. As it can be seen, the main aim is looking for an approach to help the system operators to immediate identify the proper emergency action. Following dangerous events, the system operators have some choices as emergency control actions. Sometimes a load shedding scheme or a genera- tion rescheduling action can maintain the system stability. However, for very large disturbances, it may be needed to separate the system into two or more islands and control them separately. Solutions and Recommendations Based on power-voltage curves, there is a maximum value for transmission line loadability (Kundur, 1994 and Miller, 1982). A transmis- sion line may encounter overloading following a contingency. But, it is important to know that what happens when an overloading is appeared. The relation between angle and power across a line is shown in Equation 4 (Kundur, 1994 and Miller, 1982). P E E Z Sin Sin s r = 0 θ δ (4) where, is the length of transmission line in Radian; Es and Er are the voltage magnitudes at two ends of the line; Z0 is the characteristic impedance; P is the active power passes through the line; and is the angle difference between Es a nd Er. The is also known as transmission and load angle (Miller, 1982). Based on Equation 4, if a line active power increases, the angle across that link also increased. In this situation, if two synchronous machines are connected at two ends of the line, increasing of which is the difference between the positions of rotors of the machine may lead to loss of their synchronism. Therefore, there is also a maximum value for load angle of a line. Equation 4 shows that this 299 A Descriptive Approach for Power System Stability and Security Assessment maximum value is 90°. However, based on experi- ences it is not safe to let to increase more than 30° if the transmission line is not compensated (Miller, 1982). In transient stability studies, there are some approaches for the system stability assessment, following a contingency. For example Equal area criterion is one of them which is only used for one machine connected to an infinite bus or for two- machines system (Kundur, 1994). (Padiyar, 2006) used energy function criterion for online stability assessment of a large power system. Major of proposed criteria say that a system can stay stable if the generators can release the complete energy value that they obtained following a contingency. Because of oscillations and uncertainty in a real power system, the proposed algorithms for online stability assessment that uses instance values of power, angle and the other indices may need many considerations. While, in these situations it is needed to know the behavior of the indices that propagates through the power system like a wave. System Modeling A Ring System If the number of elements in a power system is large with a set of distributed generators parameters, the discrete model simulation results are also close to the continuum model (Thorp, 1998). Equation 5 and Equation 6 can be used for modeling of an N-bus ring power system: (see Box 1) The value of P k m can be achieved from steady states values of angles (k = k = 0). The steady state values of angles for an N-bus ring system can be calculated as (Equation 6): δ π k eq k N = 2 (6) Now, consider the 64-bus ring power system given in (Thorp, 1998). A Gaussian disturbance around line 15-16 can be implemented as follows (Equation 7). δ δ k k eq k e = + − − 1 2 0 1 15 5 2 . ( . ) (7) The simulation results are illustrated in Figure 2. This is a regeneration of the given example in (Thorp, 1998). In Figure 2, the wave propagation is illustrated versus time. However in Figure 3, the angle of wave is plotted versus bus number for different time slots. Figure 3b shows the normal- ized version of Figure 3a. As can be seen, when a deviation appears in rotor angle of a generator, it propagates and in the traveling path, it may encounter a weak link and may lead to a cascad- ing failure. 2-Dimensional System Now, consider a meshed power system with a configuration shown in Figure 4, in the Cartesian δ δ δ δ δ δ δ δ k k m k k k k k k k D P b .. . [ cos( ) cos( )] [sin( ) + = − − − − − − − − + − 2 1 1 1 ++ − = − + = − − − + sin( )]; , , ..., [ cos( .. . δ δ δ δ δ δ k k m N k N D P 1 1 1 1 1 2 3 1 2 for )) cos( )] [sin( ) sin( )] [ co .. . − − − − + − + = − − δ δ δ δ δ δ δ δ 1 2 1 1 2 2 b D P N N N m N ss( ) cos( )] [sin( ) sin( )] δ δ δ δ δ δ δ δ N N N N N N b − − − − − + − − − 1 1 1 1 (5) Box 1. 300 A Descriptive Approach for Power System Stability and Security Assessment Figure 3. Wave propagation; a) angle versus bus number for different time slots, and b) normalized plot Figure 2. Electromechanical wave propagation on 64-bus ring system 301 A Descriptive Approach for Power System Stability and Security Assessment characteristic. Each point represents a bus and each connection represents a transmission line. For simplicity, assume that each bus consist of a generator or a load, or nothing. To obtain the necessary equations, assume that a generator with a mechanical power of P A m is connected to the point A (Figure 4). Considering the connections, P A e is the sum of electrical powers transferred from bus A to its neighbor buses 1, 2, 3, and 4. Therefore, P A e can be calculated as Equation 8: P P P e A e Ak L A k = + = ∑ 1 4 (8) where (Equation 9), P V V x k e Ak A k Ak Ak = = sin , , , , δ 1 2 3 4 (9) Now, the swing equations can be easily written for each point (Bevrani and Tikdari, 2010). Us- ing above descriptions, an example is presented in Figure 5 which illustrates the propagation of angle wave through a 2-D power system. At t = 0, a disturbance occurs on the middle of the net- work then, it propagates throughout the system. The system situation following the disturbance is shown in a few time slots. PROPOSED METHODOLOGY This section describes the process of using island- ing formation, performing a continuum model for system stability assessment, and predicting suit- able emergency actions following a contingency. The overall view of the algorithm is demonstrated in Figure 6. Angle instability is a fast instability phenom- enon. Therefore, predicting its situation and performing suitable actions are very important. Having a continuum model of a power system can be helpful for predicting the trajectory of the disturbances, by using of disturbance conditions as initial states of the continuum model. Here, the power system continuum model is used to provide descriptive tool for stability analysis in emer- gency conditions. As introduced in the previous section, the slow coherency theory can be used to identify system islands. Determining the islands leads to identify the weak links or critical cutset. Having knowledge on system weak links/islands helps one Figure 4. Network configuration 302 A Descriptive Approach for Power System Stability and Security Assessment to determine most suitable connections/locations for performing a more carefully islanding plan, when the system needs to be separated. Here, a slow coherency is suggested to find weak links and islands. The weak links are used to check whether islanding is needed or not. The weak links can be considered as the locations should be tripped when the system operator recommends the islanding. It can be shown that following a contingency, if the weak links are not collapsed and the in- stability is also not observed in the links close to the contingency, the system remains stable. Therefore, the overall stability can be validated by monitoring of just few links (i.e. the weak links and the links near to the contingency loca- tion). Furthermore, observing the trajectory of bus voltage angles helps the operators to choose a suitable islanding plan. As already mentioned, following an islanding action, the power system is divided into some islands with excess load/ generation. Therefore, other emergency control actions (Bevrani and Tikdari, 2010, and Bevrani, 2009) such as load shedding and generation trip- ping should be performed as shown in Figure 6. Indeed, following a certain contingency, the most important goal of the proposed algorithm is to determine if islanding is needed or not. If the contingency is not very dangerous and the angle across a link does not excess from a certain value (for example 30° for non-compensated lines), Figure 5. Wave propagation through a network 303 A Descriptive Approach for Power System Stability and Security Assessment islanding is not needed. However, for the higher value of transmission angles, the other emergency action will not be able to restore the system sta- bility. For more clarification, assume the angle across a link is increasing and excess 90°. After that, decreasing of active power by, for example, load shedding could not restore the system because the angle may track the power at low side of P – curve; so, increases, thus instability occurs. If these circumstances to be predicted, the system will undoubtedly need to be separated. The critical angle values (thresholds) should be determined based on desire level of security. Operators and engineers can validate the power system stability at control rooms by observing the wave propagation at human machine interface (HMI). Three modes may be defined for this tool: real-time, prediction, and test modes. In real-time mode, the real-time data which are gathered from the network by the PMUs are shown as a surface. The operator can see the real- time states of whole the network. In prediction mode, the online data are used as initial values of a continuum model, and the system states at a certain time value later will be predicted. In the test mode, the operator or engineer can validate a certain contingency based on real states of the system. In this mode the system real-data are used as initial values of a continuum model and the certain test is used as a deviation from initial state; then the post contingency condition will be shown in HMI for a certain time interval. SIMULATION RESULTS A Ring System and Islanding To illustrate the concept of a coherent group of generators following a contingency, a 200-bus ring system is simulated. For simplicity, it is as- sumed that there is only one generator or one load Figure 6. Overall framework of the proposed methodology 304 A Descriptive Approach for Power System Stability and Security Assessment at each bus. All generators are similar with equal amount of power, and all loads are also equal. The number of generators (N G ) is equal to the number of loads (N L ), so N G = N L = 100. The system data is determined as follows (Equation 10): P P H D m L = = = = 0 3 0 3 1 0 2 . , . , , . (10) The system is examined under two different configurations. In the first configuration (con- fig-1), all generators and loads are distributed throughout the power system by a uniform random function. In the second configuration (config-2), the generators and loads are distributed in a three areas ring system, as shown in Figure 7. In this case, all line impedances are assumed to be fixed at 0.1 p.u., except three lines that their impedances are Z 75-76 = 0.2. Z 130-131 = 0.15, Z 200-1 = 0.3. For both configurations, a large disturbance (i.e. tripping line 200-1) is applied. The angle deviations are illustrated for config-1 and config-2 in Figure 8 (8.a and 8.b, respectively). The ring system is opened due to occurred disturbance. For both cases, the angle deviation behavior across link 75-76 is illustrated in Figure 9. As shown, for the unstable case (config-2), the angle across link 75-76 (i.e. 7 5-76 = 75 – 76) , i s con- tinually growing and finally this situation leads toward separation and instability. However, for the stable case (config-1); although the angle across link deviates, the system is remained in a limited boundary and moves to a constant value. The kinetic energy, potential energy, and total (kinetic plus potential) energy across link 75-76 are also depicted in Figure 10. As already men- tioned, the system to be stable if it can be able to convert all amount of its kinetic energy achieved during a contingency into potential energy. This simulation (Figure 10) also shows that following mentioned fault, config-2 is going to an unstable condition, while config-1 holds its stability. As another example, assume a Gaussian dis- tribution that affects the angles of a system de- picted in Figure 7 (config-2). Post-contingency wave propagation is illustrated in Figure 11. In this case, the center of disturbance is bus 60; however, it can be seen that the system is sepa- rated at line 75-76, which is a weak link. Actu- ally, when a disturbance reaches a weak link through its propagation trajectory, may lead to an unstable operating point. Figure 11b clearly shows the behavior of wave propagation when it reaches a weak links. For plotting this figure, the angle variations versus bus number for each time slot is calculated. As it can be seen, angle wave is reflected when it reaches to a transmission line without enough stability margin, and the system is separated ex- actly at the weak point. Application to 24-Bus Test System Here, the 24-bus reliability test system (RTS) is used to investigate the effectiveness of the proposed strategy. Single line diagram of RTS is illustrated in Figure 12. The RTS with its full data is introduced in (IEEE RTS Task Force 1979 and 1999); and the generators data are selected the same as given typical data in (Anderson, 2003). Here, the test system is divided into three areas. While most of the generation is located in area 1, most of the load is located in area 3. In area 2, load and generation are approximately the same. Area 1 delivers its over generation into area 2 and area 3 through three tie-lines: line 16-19, line 16-14, and line 24-3. As a serious fault, the connections between area 1 and area 2 are loosed. Now, the angle in- stability on link 24-3 can be considered as a good example to examine the proposed methodology. Assume lines 16-19 and 16-14 to be tripped at t = 2 seconds. Following this large disturbance, line 3-24 will be encountered with a high over- loading problem. This over-loading is larger than its angle stability limit. Therefore, as shown in Figure 13, the angles of generators G1 and G15 located at two sides of the line, are separated; and 305 A Descriptive Approach for Power System Stability and Security Assessment Figure 8. Wave propagation for: a) config-1; b) config-2 Figure 7. 200-bus ring system (config-2) 306 A Descriptive Approach for Power System Stability and Security Assessment the angle instability phenomena is immediately occurred. To save system in this dangerous condi- tion, one solution is the use of islanding control (You, 2003). The angle deviations reduced by PMUs from the system buses are illustrated in Figure 14. As it is shown, following the contingency the con- nection between area 1 and area 3 (link 3-24) is separated as well as separation of area 2 and area 1. It demonstrates that the islanding between area 1 and area 3 at link 3-24 is a good idea to protect the system stability. Figure 15 illustrates how an islanding improves the voltage behavior that has been suddenly depressed following the mentioned event. Figure 9. Angle across link 75 in a) config-1; b) config-2 Figure 10. Energy across link 75: a) kinetic energy for config-1; b) kinetic energy for config-2; c) po- tential and total energy for config-1; d) potential and total energy for config-2 307 A Descriptive Approach for Power System Stability and Security Assessment Therefore, the remaining tie-line may be tripped when appropriate algorithms are not used to stabilize the resulted two islands. To save an island with excess load, an under frequency load shedding (UFLS) algorithm, like those suggested by the Florida Reliability Coordinating Council (FRCC) (FRCC Automatic UFLS Program, 2009) or (Tikdari, 2009, Bevrani & Tikdari, 2010, and Bevrani, 2009) should be used. However, for the islands with excess generation, some loads must be switched on. FUTURE RESEARCH DIRECTIONS By using the PMUs, one can monitor the thorough behavior of a power system. The PMUs use Global Positioning Systems (GPS); so, they can offer a synchronous time for all of data gathered from the whole network. Therefore, it is possible to improve a continuum model to a trainable one, as a future work. The model uses the data gathered from the system at times t and t + 1. By comparing the output of the model and the actual values from the PMUs at time t + 1, the error can be computed. Figure 11. Wave propagation following a Gaussian disturbance which its center is bus 60 (the system is separated at link 75-76): a) 2D plot, and b) 3D plot 308 A Descriptive Approach for Power System Stability and Security Assessment Figure 13. Angles of generators: G 1 and G 15 Figure 12. 24-bus Reliability Test System (RTS) 309 A Descriptive Approach for Power System Stability and Security Assessment By using the error value, the continuum model can be trained and improved. There are many researches that offer optimal is- landing. As another future work, these approaches may be included into the proposed methodology to prepare a more effective approach. In order to use wave propagation studies as an automatic tool instead of descriptive tool by the power system operators, some additional algorithms may needed. Pattern recognition methods may be used in these situations. Some features can be extracted from the angle surface variation, following different contingencies. They can produce special patterns and may be used in stability assessment problems, more effectively. Moreover, some important research needs in future are the updating of existing emergency frequency control schemes for N-1 contingency, economic assessment/analysis the frequency regu- lation prices (considering various control strate- gies, penetration level, and installation location of renewable energy sources units), further study on frequency/voltage stability using dynamic demand control and ratios of renewable energy sources technologies, and quantification of reserve margin due to increasing renewable energy penetration. Figure 15. Voltage response following disturbance (at 2 sec) and islanding plan (at 2.4 sec) Figure 14. Bus voltage angles deviations following the contingency 310 A Descriptive Approach for Power System Stability and Security Assessment CONCLUSION In a power grid, when a propagation energy wave caused by a disturbance hits a weak link, a reflec- tion is appeared and a part of energy is transferred across the link. Based on this basic fact, the pres- ent chapter proposes an analytical descriptive methodology to study the dynamical stability and security of a large scale power system, following serious disturbances. The possibility of simulta- neous remote measurement of bus voltage, rotor angle and system frequency through synchronized PMUs and intelligent electronic devices empha- sizes the significance of the proposed descriptive scheme for real-world complex power systems. In this chapter, first an overview on the electro- mechanical waves in power systems, mathematical formulation and their interesting properties with a brief literature review is presented. The ampli- fication of a propagated wave due to reflections or in combination with waves initiated from other disturbances is studied and it is shown how the occurrence of a large disturbance in a power system may lead to an uncontrolled tripping of generators and cascading failures, and may finally result in a blackout; if proper actions are not taken. Finally, based on given descriptive study of electrical measurements and electromechanical wave propagation in large electric power systems, a power system emergency control scheme is in- troduced to detect possible plans. The chapter is supplemented by several simulations on standard 24-bus, 200-bus, and 400-bus test systems. ACKNOWLEDGMENT This work is financially supported by Research Office at University of Kurdistan. REFERENCES Anderson, P. M., & Fouad, A. A. (2003). Power system control and stability. USA: IEEE Press. Bank, J. N., Gardner, R. M., Tsai, S. J. S., Kook, K. S., & Liu, Y. (2007). 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Self-healing in power systems: An approach using islanding and rate of frequency decline based load shed- ding. IEEE Transactions on Power Systems, 18, 174–181. doi:10.1109/TPWRS.2002.807111 ADDITIONAL READING Abu-Elnaga, M. M., El-Kady, M. A., & Find- lay, R. D. (1988, Nov). Stability assessment of highly stressed power systems using the sparse formulation of the direct method. IEEE Transactions on Power Systems, 3, 1655–1661. doi:10.1109/59.192977 Bin Qiu Ling Chen Centeno, V. Xuzhu Dong Yilu Liu. (2001). Internet based frequency monitor- ing network (FNET). IEEE Power Engineering Society Winter Meeting.vol.3 (pp. 1166 – 1171). Cresap, R. L., & Hauer, J. F. (1981). Aril). Emer- gence of a New Swing Mode in the Western Power System. IEEE Transactions on Power Apparatus and Systems, PAS-100, 2037–2045. doi:10.1109/ TPAS.1981.316481 De La Ree, J., Centeno, V., Thorp, J. S., & Phadke, A. G. (2010, June). Synchronized Phasor Measurement Applications in Power Systems. IEEE Transactions on Smart Grid, 1, 20–27. doi:10.1109/TSG.2010.2044815 Delin Wang Xiaoru Wang Yi Fang Wenbin Hao. (2006, Oct.). Study on Dynamic Characteristics of Electromechanical Wave in the Continuum Model for Power System. International Conference on Power System Technology. Diduch, J. Y., & Chang, C. P. L. (2008, April). Islanding Detection Using Proportional Power Spectral Density. IEEE Transactions on Power Delivery, 23, 776–784. doi:10.1109/TP- WRD.2007.915907 Grobovoy, A., & Lizalek, N. (2002, April). As- sessment of power system properties by wave ap- proach and structure analysis. Fifth International Conference on Power System Management and Control (pp. 365 – 370). Kimbark, E. (1956). Power System Stability. New York: Dover. Kook, K. S., Liu, Y., & Bang, M. J. (2008, Septem- ber). Global behaviour of power system frequency in korean power system for the application of frequency monitoring network. IET Generation. Transmission & Distribution., 2, 764–774. Makarov, Y. V. Reshetov, V.I. Stroev, A. Voropai, I. (2005, Nov.). Blackout Prevention in the United States, Europe, and Russia. Proceedings of the IEEE. Vol. 93 (pp. 1942 – 1955). Murphy, R. J. (1996, Jan). Disturbance record- ers trigger detection and protection. IEEE Computer Applications in Power, 9, 24–28. doi:10.1109/67.475956 Pariz, N. Shanechi, H.M. Vaahedi, E. (2003, May). Explaining and validating stressed power systems behavior using modal series. IEEE Transactions on Power Systems, 18, 778–785. doi:10.1109/ TPWRS.2003.811307 Rajamani, K., & Hambarde, U. K. (1999, Jul). Islanding and load shedding schemes for cap- tive power plants. IEEE Transactions on Power Delivery, 14, 805–809. doi:10.1109/61.772318 313 A Descriptive Approach for Power System Stability and Security Assessment Semlyen, A. (1974, March) Analysis of Distur- bance Propagation in Power Systems Based on a Homogeneoue Dynamic Model. IEEE Trans- actions on Power Apparatus and Systems. Vol. PAS-93 (PP. 676 – 684). Senroy, N., Heydt, G. T., & Vittal, V. (2006, Nov.). Decision Tree Assisted Controlled Islanding. IEEE Transactions on Power Systems, 21, 1790–1797. doi:10.1109/TPWRS.2006.882470 Shu-Jen Tsai Li Zhang Phadke, A.G. Yilu Liu In- gram, M.R. Bell, S.C. Grant, I.S. Bradshaw, D.T. Lubkeman, D. Le Tang. (2007, Aug.). Frequency Sensitivity and Electromechanical Propagation Simulation Study in Large Power Systems. IEEE Transactions on Circuits and Systems. I, Regular Papers, 54, 1819–1828. doi:10.1109/ TCSI.2007.902542 Taylor, C. W., & Erickson, D. C. (1997, Jan). Recording and analyzing the July 2 cascading outage [Western USA power system]. IEEE Computer Applications in Power, 10, 26–30. doi:10.1109/67.560830 Thomas, A. J., & Mahajan, S. M. (2009, Oct.). Electromechanical Wave Analysis Through Tran- sient Magnetic Modeling. IEEE Transactions on Power Delivery, 24, 2336–2343. doi:10.1109/ TPWRD.2009.2027504 Thorp, J. S., Seyler, C. E., Parashar, M., & Phadke, A. G. (1998, Jan). The large scale elec- tric power system as a distributed continuum. IEEE Power Engineering Review, 18, 49–50. doi:10.1109/39.646962 Vanfretti, L. Aliyu, U. Chow, J.H. Momoh, J.A. (2009, July). System frequency monitoring in the Nigerian power system. IEEE Power & Energy Society General Meeting (pp. 1 – 6). Vittal, V., Rajagopal, S., Fouad, A. A., El-Kady, M. A., Vaahedi, E., & Carvalho, V. F. (1988, Feb). Transient stability analysis of stressed power systems using the energy function method. IEEE Transactions on Power Systems, 3, 239–244. doi:10.1109/59.43206 Wang Yuguo Zhao Wei Xie Yan. (2009, June). Dynamic feature extraction of power disturbance signal based on time-frequency technology. Con- trol and Decision Conference. CCDC ‘09. Chinese (pp. 2300 – 2303). Xu, G. Vittal, V. Meklin, A. Thalman, J. E. (2010) Controlled Islanding Demonstrations on the WECC System. IEEE Transactions on Power Systems. Vol. PP. Yilu, L. (2006). A US-Wide Power Systems Fre- quency Monitoring Network. IEEE Power Systems Conference and Exposition. (pp. 159 – 166). Yingchen Zhang Markham, P. Tao Xia Lang Chen Yanzhu Ye Zhongyu Wu Zhiyong Yuan Lei Wang Bank, J. Burgett, J. Conners, R.W. Yilu Liu. (2010, Sept.). Wide-Area Frequency Monitoring Network (FNET) Architecture and Applications. IEEE Transactions on Smart Grid. Vol. 1 (pp. 159 – 167). Zhian Zhong Chunchun Xu Billian, B.J. Li Zhang Tsai, S.-J.S. Conners, R.W. Centeno, V.A. Phadke, A.G. Yilu Liu. (2005, Nov.). Power system fre- quency monitoring network (FNET) implementa- tion. IEEE Transactions on Power Systems, 20, 1914–1921. doi:10.1109/TPWRS.2005.857386 KEY TERMS AND DEFINITIONS Angle Instability: Angle instability is a very fast instability that leads to loss of synchronism. Emergency Control: Control of a power sys- tem in dangerous conditions, where the system is going to the instability or blackout. 314 A Descriptive Approach for Power System Stability and Security Assessment Islanding Control: Separate of power system into some isolated sub-systems following large disturbances, in order to prevent a global black out. Load Shedding: An emergency control action to curtail a part of load, and is useful where the amount of load is larger than available generation. PMU: Power measurement unit is a device which uses GPS to collect data from the various points of network in a synchronous time. Slow Coherency: A method which is used in islanding control problems. Using this method- ology, the system islands and weak links can be identified. Wave Propagation: Propagation of a distur- bance through the power system network like a propagated wave. 315 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 11 DOI: 10.4018/978-1-61350-138-2.ch011 Rana A. Jabbar Rachna College of Engineering and Technology, Pakistan Muhammad Junaid Rachna College of Engineering and Technology, Pakistan M. A. Masood Rachna College of Engineering and Technology, Pakistan A. Bashir Rachna College of Engineering and Technology, Pakistan M. Mansoor Rachna College of Engineering and Technology, Pakistan Analyses and Monitoring of Power Grid ABSTRACT Power system analyses and monitoring of power system engineering are as essential as oxygen for human beings. This innovative approach deals with a 132 kV grid simulation in electrical transient analyzer program (ETAP). The existing power distribution system in Pakistan consists of approximately six thousand 11 kV feeders, which are mainly analyzed by software FDR-ANA (Feeder Analyses). This software does not have capability to provide comprehensive analyses for integrated power system. The case under study is 132 kV grid situated in Gujranwala electric power company (GEPCO), one of the distribution companies (DISCO’s) of Pakistan electric power company (PEPCO) which has been selected for comprehensive analyses using ETAP software. This software performs numerical calculations of large integrated power system with fabulous speed, besides generating output reports. In a developing country like Pakistan it is frst time that analyses based Off-line monitoring has been made, which includes load fow, harmonic, transient, short circuit and ground grid analyses. In load fow analysis, current fowing in every branch, power factor, active and reactive power fow, line losses, voltage magnitude with angle etc. have been calculated. During harmonic analysis, distorted current and voltage waveforms along with their harmonic spectrum caused by non-linear loads have been recorded. Transient analysis has been performed to record different waveforms like variation in bus frequency, bus real power loading, bus voltage angle, and bus reactive power loading for short interval of time during transient conditions. 316 Analyses and Monitoring of Power Grid INTRODUCTION This book chapter comprises of two interna- tional conferences research papers published in ELECO’09 and PCO’10 in which first time in the history of Pakistan a practical 132 kV grid containing a large distribution network has been simulated for analyses purpose using ETAP soft- ware (Jabbar Khan et al, 2009; Bashir et al, 2010). For the last few years electrical engineers have been focusing on the power system studies using software tools. Recent advances in engineering sciences have brought a revolution in the field of electrical engineering after the development of powerful computer based software. This research work high-lights the effective use of ETAP soft- ware for analyses of large electrical power system which comprises of large power distribution net- work emanating from 132 kV power grid (Lei et al, 2002; Inoue, 2007; Takimoto, 2005; Nagata & Inoue, 2008; Brown et al, 1990; Zhongxi & Xiaoxin, 1998; Stagg& El-Abiad, 1968). Motivation to conduct the research work is to develop a prototype model which can be used as bench mark for comprehensive simulation of integrated network at national grid level to ad- dress power system stability under normal and abnormal operating conditions. PEPCO, the only power sector utility in Pakistan, consists of nine power distribution companies along with national transmission and power dispatch company but unfortunately no ON/OFF line monitoring is currently being performed. For this purpose a 132 kV grid station has been simulated using ETAP. PEPCO has been experiencing severe power shortage for last many years. Resultantly, the country is facing repeated and astonishing black outs. Despite the shortage of electricity, one of the main reasons of this energy crisis is deficiency in the field of analyses and monitoring of electrical power network. Keeping in view the above scenario, Rachna College of Engineering & Technology (RCET) Pakistan, has analyzed the complete 132 kV grid network which contains 11 kV feeders and rest of distribution network to predict the actual effects of load on the entire power system. These analyses include load flow analysis, harmonic analysis, transient analysis, ground grid analysis and short circuit analysis. The data used for analyses purpose is in the form of one line diagram of complete power system network starting from power transformer at grid up-till the load. The ratings of power/dis- tribution transformers are taken as they actually exist. Moreover, the conductors/cables, circuit breakers, CT’s, PT’s, and rest of power system elements are also modelled according to their actual ratings in ETAP. This 132 kV Grid located in GEPCO region, having 6 power transformers, 32 feeders, 48 cir- cuit breakers, 42 current transformers, 8 potential transformers and 2 incoming lines. Practical power system under study is a very antique grid which was inaugurated in 1952 and a centralized grid which feeds power supply to the other grids in this region, all the analyses and monitoring are concentrated on this grid (WAPDA, 2006). A powerful computational software ETAP is used in this research paper for modeling and simu- lation purpose. The complete power system from grid to tail end load is modeled in this software. Although MATLAB is also used for power system In ground grid modeling, step, and touch potentials have been calculated in comparison with set stan- dards. While performing short circuit analysis, all the possible short circuit faults like line to ground, double line to ground, 3-phase faults etc. on ½ cycle, 1.5 to 4 cycle, and 30 cycle networks have been performed to record the short circuit currents. These analyses have been executed using ETAP software, based upon historical data obtained from original system that will be very helpful for system security and reliability. 317 Analyses and Monitoring of Power Grid simulation world widely, but ETAP has preferred here due to strong built-in properties regarding power system studies (Sybille & Hoang, 2002; Qinghuaz et al, 2009; Kjølle et al, 2002; Gatta et al, 2003; Gonen, 1968) Earlier, considerable work has been done on transient stability studies, but power system of developing countries like Pakistan have never been simulated using software technique like ETAP on such a large scale. The major purpose for transient stability studies on this power system is to find dynamic performance which has great impact in the design and operation of the system. After transient stability studies on 132 kV grid, machine power angles and speed deviations, system electri- cal frequency, real and reactive power flows of the machines and buses, power flow of lines and transformers, as well as the voltage level of the buses in the power system have been determined thoroughly (Hongbin et al, 2002; IEEE 1995). A ground grid study is first time addressed in this research for a large power system. The touch and step potential measurement will really be helpful for safety of both grid staff and equip- ment. It is worth mentioning that in this analysis three-dimension view grid grounding scheme has been used on such a large scale using ETAP. In short circuit analyses on 132 kV grid mo- mentary, steady-state, short circuit and other fault interruption currents on ½ cycle network (sub transient network), 1.5 to 4 cycle network (tran- sient network), and 30 cycle network at different buses have also been determined (Osahenvemwem & Omorogiuwa, 2008). BACKGROUND Introduction to ETAP Software ETAP software is used for simulation purpose which provides a fully graphical user interface (GUI) for constructing one-line diagram. Here elements can graphically add, delete, relocate, connect, zoom in or out, display grid off or on, change element size, change element orientation, change symbols, hide or show protective devices, enter properties and set operating status, etc. ETAP’s electrical system diagram is a one-line representation of a three-phase system. The one- line diagram is the starting point for all studies. The electrical system can be constructed graphically by connecting the buses, branches, isolators, circuit breakers and protective devices in any order from the one-line diagram edit toolbar. Single Line Diagram of the System Figure 1 shows the single line diagram of the complete power system which is under study. It is clear that there are two incoming lines of 132 Figure 1. Single line diagram of 132 kV grid 318 Analyses and Monitoring of Power Grid kV supplying power to six power transformers of different ratings at 132 kV grid station, and these power transformers are connected with 11 kV power distribution network (11 kV feeders). Monitoring Points are also marked on the same single line diagram to discuss different results while performing simulation. In Figure1, point A is taken at secondary of power transformer, point B is taken at primary distribution side (i.e. 11 kV feeder) and point C is taken on a feeder where furnace load is connected. This large system is sub divided into sections according to their load behavior for analyses and monitoring purpose. Power transformers installed at the grid are given in Table 1. Circuit breakers (CB) of different ratings have been installed at the grid. Some of them are of SF6 circuit breakers and remaining are oil, air and vacuum circuit breakers. These CB’s type, voltage ratings and current ratings are given in the Table 2. Simulation of 132 Kv Grid The system under study is simulated in ETAP as shown in Figure 2. Simulation of 11 Kv Feeders For simplicity of analyses, only one power trans- former named T1 has been selected for simulation. Following the practical system, feeders are divided into two different categories, one for furnace load and other for usual distributed load which may include static, inductive, dynamic and dc load etc. Figure 3 shows that 7 no. feeders are emanat- ing from power transformer T1. Three furnaces are being supplied from feeder 7. The simulated network for general purpose feeder is shown in Figure 4. Load Modeling Following the real time data, load modeling is performed by considering 70% static and dy- namic load in addition to 30% dc load. Figure 5 and Figure 6 show the simulated model of load connected with 200 kVA and 50 kVA distribution transformers respectively. For the modeling of furnace load, ETAP pro- vides the provision for exact modeling of such large electronic load in which rectification and inversion phenomenon. Figure 7 shows one of the three furnaces connected to the feeder. All the three furnaces are of different ratings, Furnace-1 which takes a load of 62.2 A from the Table 1. Power transformers at 132 kV grid Power Transformers MVA rating T-1 40 T-2 26 T-3 26 T-4 26 T-5 37 T-6 13 Table 2. Circuit breakers at 132 kV grid CB Types Rated Voltage (kV) Rated Current (A) V-15F-31 (Vacuum) 12 630 3AF2721-4B (Vacuum) 12 630 WPV-25-O (Vacuum) 12 2500 V-15V-31 (SF6) 145 3150 JB429FORM (Oil) 66 4380 319 Analyses and Monitoring of Power Grid Figure 2. Simulated diagram of 132kV grid using ETAP Figure 3. Simulated diagram of power transformer T1 320 Analyses and Monitoring of Power Grid Figure 4. Distribution network in ETAP for general purpose feeder Figure 5. Load modeling for 200 kVA distribution transformer Figure 6. Load modeling for50 kVA distribution transformer 321 Analyses and Monitoring of Power Grid system. Similarly, Furnace-2 and Furnace-3 take loads of 161.2 A and 136.5 A respectively (Jabbar et al, 2008a; Jabbar et al, 2008b). SOLUTIONS AND RECOMMENDATIONS Load Flow Analysis Load flow studies have been carried out on com- plete power system using ETAP. However for detailed monitoring purpose three important points are selected as shown in Figure 1. Point A is the secondary side of power transformer T1. Point B is at 11 kV side of general purpose feeder. Point C is at the 11 kV side of furnace feeder. Consequent results after performing load flow analysis are given in Table 3 and Table 4 accordingly. Table 4 clearly shows that real power on swing buses is 16.789 MW while reactive power is 11.970 MVAR. Power factor is 81.4% which is less than the standard set by the utility (i.e. 92%). ETAP Alerts during Load Flow Analysis While performing load flow analysis ETAP provides various alerts which need immediate attention for smooth running of the system, some of the critical alerts regarding under voltages are detailed in Table 5. Over-Loaded Transformers Loading wise power system under study was normal (not over loaded) but it is interesting due to involvement of large electronic load (i.e. furnace) another loss is involved in the system which is known as distortion power loss due to which system becomes over loaded in some branches, some of these over loaded transformers are indicated in Table 6. Voltage Drop Table 7 shows the % voltage drop in different distribution transformers (only few are given here). Magnitude of voltage drop standard set by utility is 5% which is significantly violated here. Figure 7. Load modeling for furnace feeder Table 3. Load flow results Monitoring Points kV MW MVAR % PF Grid (Bus 3) 132 36.68 23.10 84.6 A 11 5.520 3.793 83.1 B 11 0.379 0.253 83.0 C 11 0.717 0.471 83.6 322 Analyses and Monitoring of Power Grid Technical Losses Technical losses calculated while performing simulation are given in Table 8 at some branches. Harmonic Analysis A detailed harmonic analysis (HA) has been performed on the entire system using ETAP. The results include current/voltage waveforms and their harmonic spectrums at different points of the power system under consideration. In addition total and individual harmonic distortion in voltage and current (i.e. [% THDv], [% IHDv], [% THDi] and [% IHDi]) has also been obtained. Table 9 shows the different results which are recorded after harmonic studies on different monitoring points. These results clearly show that % THDv at Point Table 6. Some over loaded transformers in the system TF ID Capability (MVA) Loading (input) MVA Loading (input) % Loading (output) MVA Loading (output) % T114 0.200 1.251 625.3 0.952 476.2 T797 0.200 0.352 175.8 0.330 165.12 T122 0.200 0.452 225.9 0.416 208.231 T618 0.200 0.352 175.8 0.330 165.1 T803 0.200 0.452 225.9 0.416 208.3 T807 0.200 1.195 597.3 0.926 462.3 T809 0.200 0.352 175.8 0.330 165.3 Table 5. Under voltage alerts during load flow results Device ID Rating Calculated % Value Alert Condition Bus 210 0.415 kV 0.314 kV 73.2 Under Voltage Bus 675 11 kV 10.531 kV 96 Under Voltage Bus 674 0.415 kV 0.387 kV 93.2 Under Voltage Bus 700 11 kV 10.615 kV 96.5 Under Voltage Bus 238 11 kV 11 kV 10.604 Under Voltage Bus 239 0.415 kV 0.391 kV 94.1 Under Voltage Bus 698 11 kV 10.671 kV 97 Under Voltage Bus 638 11 kV 10.623 kV 96.6 Under Voltage Bus 695 11 kV 10.558 kV 96 Under Voltage Table 4. Summary report of total demand and losses Points for Discussion MW MVAR MVA % PF Swing Bus 16.789 11.970 20.619 81.4 (lag) Total Demand 16.789 11.970 20.619 81.4 (lag) Total Motor Load 15.413 7.068 16.956 90.9 (lag) Total Static Load 0.555 0.393 Apparent Losses 0.821 4.510 323 Analyses and Monitoring of Power Grid C has exceeded the limit set by IEEE std. 519- 1992 (i.e. 5% at the point of common coupling). The current waveform and its harmonic spec- trum captured at the monitoring point A are shown in Figure 8 and Figure 9 respectively. Voltage waveform and its harmonic spectrum captured at monitoring point A are shown in Figure 10 and Figure 11. The below waveshape is at the 11kV bus bar which shows the significant presence of 5th and 7th harmonic componets that also contribute very much in the disturbing the power quality of the system. Similarly, the current waveform and har- monic spectrum captured at point B are shown in Figure 12 and Figure 13 respectively. Voltage waveform with harmonic spectrum at point B is given in Figure 14. Table 7. % Voltage drop in few sections/branches CKT/Branch ID % Bus Voltage from % Bus Voltage to %Voltage drop (Mag.) T114 73.7 96.8 23.08 T624 89.1 96.12 7.58 T625 90.4 96.2 6.27 T628 75 96.7 21.77 T797 90.8 96.7 5.89 T803 89.1 96.12 7.58 T819 75 96.7 21.77 T821 90.7 96.8 5.88 T831 75 96.7 21.77 T833 90.7 96.8 5.88 T839 89.1 96.12 7.58 Table 8. Losses in kW & kVAR in few sections/branches CKT/Branch ID Losses kW Losses kVAR T114 83.6 426.3 T624 10.9 55.7 T625 6.7 19.5 T628 76.2 388.7 T797 6.6 33.7 T803 10.9 55.7 T807 76.2 388.7 T819 76.2 388.7 T821 6.6 33.7 T831 76.2 388.7 Table 9. % THDv & % THDi at monitoring points Monitoring Points % THDv %THDi A 2.13 3.41 B 3.0 2.25 C 13.1 15 324 Analyses and Monitoring of Power Grid Figure 8. Current waveform at point A Figure 9. Current spectrum at point A Figure 10. Voltage waveform at point A 325 Analyses and Monitoring of Power Grid Figure 11. Voltage waveform spectrum at point A Figure 12. Current waveform at point B Figure 13. Current spectrum at point B 326 Analyses and Monitoring of Power Grid Figure 14. Voltage waveform at point B Figure 15. Voltage waveform spectrum at point B Figure 16. Current waveform at point C 327 Analyses and Monitoring of Power Grid Figure 17. Current spectrum at point C Figure 18. Votage waveform at point C Figure 19. Votage spactrum at point C 328 Analyses and Monitoring of Power Grid Due to presence of dc load voltage waveform is also distorted as a result of current waveform distortion. FFT spectrum is shown in Figure 15, at the monitoring point B, which shows that 5th, 7th, 11th and 13th harmonic components contrib- ute very much. Figure 16 and Figure 17 are the current wave- form and its harmonic spectrum at point C which is more distorted as compared to points A and B. The reason behind this distorted pattern is sig- nificant presence of 5 th , 7 th , 11 th and 13 th etc. harmonic contents in the current waveform drawn by the furnace load. Similarly, the voltage waveform and har- monic spectrum at point C are given in Figure 18 and Figure 19 respectively. Harmonic analysis has been performed on complete system but due to space limitation it is not possible to discuss here any more. Transient Stability Analysis During transient stability analysis for the system under consideration given in Figure 1, the stability limits of the power system can be inspected before, during and after system changes. Figure 20 is the Figure 20. Simulated network in ETAP Figure 21. Bus frequency variations at selected time interval 329 Analyses and Monitoring of Power Grid section of power system modeled in ETAP which is selected for transient analysis, where a group of different motors is connected to a distribution transformer. Figure 21 shows bus frequency variation at specific time interval (0.5 – 0.7 sec) when group of different motors is connected to bus 232 during transient stability analysis. It is clear from the Figure 3 that before 0.5 sec the system frequency was 50 Hz. (i.e. 100%), after 0.5 sec – 0.7 sec during transient the system frequency decreases significanly and system becomes normal after that transient interval. It is observed, during the transient stability analysis on the selected bus that real and reactive power loading of the bus changes abruptly during transient phase. Figure 22 and Figure 23 show real and reactive power loading at specific time interval when group of different motors is con- nected to the system. During the switching of the motor load to the power system it is observed that magnitude in bus voltage and angle is distorted very firmly which causes for the instability problems in the power system. Figure 24 and Figure 25 show bus voltage magnitude and angle variations at perticular instant Figure 22. Abrupt changes in bus real power loading Figure 23. Bus real power loading at particular instant of time 330 Analyses and Monitoring of Power Grid Figure 24. Variation in bus voltage Figure 25. Bus voltage angle variation Figure 26. Variation in bus voltage per Hz 331 Analyses and Monitoring of Power Grid of time when group of different motors con- nected to the bus are switched on. Magnitude of bus voltage variation with respect to frequency of the power system when dynamic load is switched on also causes the instability problems in the power system. This voltage mag- nitude variation versus freequency of the power system is expresed in Figure 26. The consequences of instability issues dis- cussed earlier may result in temporary, permanent loss to electrical installations, mal-operation of protective devices and power blackouts etc. Ground Grid Analysis For ground grid analysis, power transformer T1 at 132 kV grid has been selected. The exact area in grid where power transformer and its other related components like bus bar, circuit break- ers, isolators etc. are situated is measured. The exact no. of horizontal and vertical rods used for mesh grounding is also recorded. The same is implemented in ETAP for ground grid analysis to evaluate step and touch potential exactly. Ground Grid Layout The ground grid layout is consisted of three types of different views named as top view, soil view and 3D view which are shown in Figure 27, Figure 28 and Figure 29 respectively. Calculation of Touch and Step Potential The step and touch potential measurements on 132 kV grid provide safety limits for grid equipment as well as staff. Table 10 shows the different potential measurements located at x-axis and y-axis of 132 kV Grid against tolerable limits. It is clear from the Table that calculated value of touch potential is 1946.6 volts which is beyond the tolerable limits i.e 427.1 volts. Similarly, step potential is also out of tolerable limits. The situ- ation is alarming due to this out of range potential. It is recommended here, to increase the number of vertical rods to over come this problem. These step and touch potentials are also ex- pressed in 3-D view highlighting the limits and ranges in Figure 30 and Figure 31 respectively. Figure 27. Top view of 132 kV ground grid 332 Analyses and Monitoring of Power Grid Figure 28. Soil view of 132 kV ground grid Table 10. Calculated step potential and touch potential on tolerable limits Touch potential Step Potential Calculated volts 1949.6 1368.5 Tolerable volts 427.1 1216.4 Location x(axis) 51.9 48.3 Location y(axis) 33.2 4.4 Figure 29. 3-D view of 132 kV ground grid 333 Analyses and Monitoring of Power Grid Short Circuit Fault Analysis Three-Phase Fault Calculations at Different Buses For short circuit analysis some of the buses are selected where an artificial short circuit fault is created. An equivalent voltage source at the fault location is replaced by all external voltage sources and machines internal voltage sources. Three different impedance networks are formed for each faulted bus where calculations are made to calculate for sub transient, transient and steady state short circuit currents. These networks are ½ cycle network (sub transient network), 1.5 - 4 cycle network (transient network) and 30 cycle network (steady state network). Figure 30. Step potential profile of 132 kV grid Figure 31. Touch potential profile of 132 kV grid 334 Analyses and Monitoring of Power Grid Sub-Transient Network (Half-Cycle Network) This type of network is used to calculate sub transient currents at different buses in the sys- tem. Detail of short circuit sub transient currents calculations are given in the Table 11. It is important to note that bus 232 is rated at 0.415 kV and remaining buses are rated at 11 kV. Transient Network (1.5 - 4 Cycle Network) Transient currents at selected buses in the power system are represented by using 1.5 to 4 cycle network in EATP. Transient calculations are given in Table 12 at different buses. Thirty-Cycle Network This network is used to calculate the steady state short circuit current at the faulty buses. Table Table 11. 3-phase short circuit current calculations in half cycle network Fault Bus ID ½ Cycle (kA Real) ½ Cycle (kA Imag) Imag/ Real kA symm Magnitude 232 5.661 -112.818 19.9 112.960 240 2.851 -12.084 4.2 12.416 693 0.881 -2.5588 2.9 2.705 695 0.993 -2.963 3.0 3.125 696 0.864 -2.503 2.9 2.648 700 2.045 -17.159 8.4 17.280 Table 12. 3-phase short circuit current calculations in 1.5 to 4 cycles network Fault Bus ID 1.5-4 Cycle (kA Real) 1.5-4 Cycle (kA Imag) Imag/ Real kA symm Magnitude 240 2.632 -11.828 4.5 12.117 693 0.868 -2.548 2.9 2.692 695 0.977 -2.950 3.0 3.107 696 0.852 -2.494 2.9 2.635 700 1.747 -16.596 9.5 16.688 Table 13. 3-phase short circuit current calculations in 30 cycles network Fault Bus ID 30 Cycle (kA Real) 30 Cycle (kA Imag) X/R Ratio kA Symm Magnitude 232 3.712 -61.298 16.5 61.140 240 2.491 -11.509 4.6 11.775 693 0.858 -2.535 3.0 2.676 695 0.963 -2.932 3.0 3.086 696 0.842 -2.481 2.9 2.620 700 1.621 -15.964 9.8 16.046 335 Analyses and Monitoring of Power Grid 13 shows steady state short circuit currents at selected buses. Three-Phase LG, LL, and LLG (1/2 Cycle Network) Fault Currents at Selected Buses The purpose of this analysis on the faulty buses is to calculate line-to-ground, line-to-line, double- line-to-ground, three-phase short-circuit fault cur- rents and sequence voltages at ½ cycles networks. Table 14 shows 3-phase fault currents and their respective sequence voltages at the faulty buses. Three-phase symmetrical short circuit current at faulty buses are shown in Table 15 as: Three-Phase LG, LL, AND LLG (1.5 - 4 Cycle Network) Fault Currents at Different Buses Line-to-ground, line-to-line, double-line-to- ground, three-phase short-circuit fault currents Table 16. 3-phase short circuit current and sequence voltages at faulty buses in transient networks Fault Bus ID 3 Phase Fault %V kA Symm Line-Ground Fault (%V from Bus) Va Vb Vc 232 0.0 112.960 0.00 100.75 100.57 240 0.0 12.416 0.00 173.21 173.21 693 0.0 2.705 0.00 173.21 173.21 695 0.0 3.125 0.00 173.21 173.21 696 0.0 2.648 0.00 173.21 173.21 700 0.0 17.280 0.00 173.21 173.21 Table 15. 3-phase symmetrical short circuit current calculations in 1/2 cycles network (sub transient network) Fault Bus ID Line-Ground Fault (kA Symm rms) Ia 3Io 232 110.73 110.731 240 0.00 0.00 693 0.00 0.00 695 0.00 0.00 696 0.00 0.00 700 0.00 0.00 Table 14. 3-phase short circuit current & sequence voltages at faulted buses in sub transient networks Fault Bus ID 3 Phase Fault %V kA Symm Line-Ground Fault (%V from Bus) Va Vb Vc 232 0.0 112.960 0.00 100.12 100.88 240 0.0 12.416 0.00 173.21 173.21 693 0.0 2.705 0.00 173.21 173.21 695 0.0 3.125 0.00 173.21 173.21 696 0.0 2.3648 0.00 173.21 173.21 700 0.0 17.280 0.00 173.21 173.21 336 Analyses and Monitoring of Power Grid and sequence voltage values in 1½ - 4 cycles are represented through this study on the faulty buses. Table 16 and Table 17 indicates 3-phase fault currents along with their respective sequence voltages and 3-phase symmetrical short circuit current calculations in 1.5 - 4 cycles network (transient network) at the selected faulted buses respectively. Three-Phase LG, LL & LLG (30 Cycle Network) Fault Currents at Different Buses Three-phase line-ground, line-line and double- line-ground fault is calculated for 30-cycle net- work are summarized in Table 18 and Table 19 respectively. Table 17. 3-phase symmetrical short circuit current calculations in 1.5-4 cycles network (transient network) Fault Bus ID Line-Ground Fault (KA Symm rms) Ia 3Io 232 110.259 110.259 240 0.00 0.00 693 0.00 0.00 695 0.00 0.00 696 0.00 0.00 700 0.00 0.00 Table 18. 3-phase short circuit current & sequence voltages at faulty buses in transient networks Fault Bus ID 3 Phase Fault %V kA Symm Line-Ground Fault (%V from Bus) Va Vb Vc 232 0.0 61.410 0.00 79.73 79.64 240 0.0 11.775 0.00 173.21 173.21 693 0.0 2.676 0.00 173.21 173.21 695 0.0 3.086 0.00 173.21 173.21 696 0.0 2.626 0.00 173.21 173.21 700 0.0 16.046 0.00 173.21 173.21 Table 19. 3-phase symmetrical short circuit current calculations in 30-cycles network (transient network) Fault Bus ID Line-Ground Fault (KA Symm rms) Ia 3Io 232 86.370 86.73 240 0.00 0.00 693 0.00 0.00 695 0.00 0.00 696 0.00 0.00 700 0.00 0.00 337 Analyses and Monitoring of Power Grid FUTURE RESEARCH DIRECTIONS Research conducted during this work is based upon the historical data of a practical grid which has further been implemented in ETAP for off- line monitoring. Keeping in view the latest trends, on-line monitoring can also be performed on same network using same software tool along with hardware setup. For accurate monitoring and analyses purpose, real time monitoring has been recommended in future. Moreover, protec- tive equipment installed at grid and sensitive load equipment can also be modelled for relay coordination analysis in ETAP. CONCLUSION ETAP Software based simulation of integrated electric power system comprising of 132 kV grid including load flow, harmonics, transient, ground grid and short circuit analyses reveals innovative contribution to the power industry stake holders to access in-advance knowledge for acquiring the security and quality of supply. Overloading of power/distribution transformers, line conduc- tors/cables current carrying ability, power factor, supply demand gap, voltage drop at the tail end, technical losses, active and reactive power flow, voltage and current magnitudes, THD in voltage and current etc. can be analyzed and monitored at any desired location using this innovative ap- proach. Moreover, the novel approach of ground grid 3D analysis is really interesting and will be helpful for evaluating the exact value of step and touch potential for safety purpose. Simulation con- ducted in this research work can be implemented successfully at any desired section of the power system network for above mentioned parameters. REFERENCES Bashir, A., Jabbar Khan, R. A., Junaid, M., & Asghar, M. M. (2010). ETAP software based transient, ground Grid and short circuit analyses of 132 kV Grid. 3 rd Global Conference on Power Control and optimization (PCO 2010). 2-4 Feb- ruary, 2010, Gold Coast, Queensland, Australia. Brown, K., Shokooh, F., Abcede, H., & Don- ner, G. (1990). Interactive simulation of power system: ETAP techniques and applications (pp. 1930–1941). IEEE. ETAP. (n.d.). Enterprise software solution for power systems (Electrical Transient Analyzer Program). Retrieved from http://etap.com/training /tutorials-training-videos.htm Gatta, F. M., Iliceto, F., Lauria, S., & Masato, P. (2003). Modeling and computer simulation of dispersed generation in distribution networks: Measures to prevent disconnection during system disturbances. IEEE PowerTech Conference. June 2003, Italy. Gonen, T. (1986). Electric power transmission system engineering (pp. 87–93). New York, NY: Wiley. Hongbin, Z., Renmu, H., & Jian, Z. (2002). Ap- plication of different load models for the transient stability calculation. Proc. 2002 IEEE Power Engineering Society Transmission and Distribu- tion Conf., (pp. 2014-2018). IEEE Task Force on Load Representation for Dynamic Performance. (1995). Bibliography on load models for power flow and dynamic perfor- mance simulation. IEEE Transactions on Power Systems, 10. 338 Analyses and Monitoring of Power Grid Inoue, T. (2007). Dynamic simulations of electric power systems under long-term change in system generations and loads. The Seventh IASTED International Conference on Power and Energy Systems (EuroPES 2007), (pp. 232-237). August 2007, Spain. Jabbar, R. A., Akmal, M., Junaid, M., & Masood, M. A. (2008b). Operational and economic impacts of distorted current drawn by the modern induc- tion furnaces. Proceedings of AUPEC’08. IEEE. 14-17 December, 2008, UNSW, Sydney, Australia. ISBN 978-0-7334-2715-2 Jabbar, R. A., Akmal, M., Masood, M. A., Junaid, M., & Akram, F. (2008a). Voltage waveform distortion measurement caused by current drawn by modern induction furnaces. Proceedings of 13th ICHQP, IEEE PES. 07 November 2008, University of Wollongong, Australia. ISBN 978- 1-4244-1771-1 Jabbar Khan, R. A., Junaid, M., & Asghar, M. M. (2009). Analyses and monitoring of 132 kV Grid using ETAP software. 6th International Confer- ence on Electrical and Electronics Engineering (ELECO 2009). IEEE. 5-8 November 2009, Bursa, Turkey. Kjølle, G. H., Aabø, Y., & Hjartsjø, B. T. (2002). Fault statistics as a basis for designing cost- effective protection and control solutions. Proc. 2002 CIGRE Session, Paris, August 2002. Lei, X., Buchholz, B., Povh, D., & Retzmann, D. (2002). Power system analysis-software approach and real-time simulation, vol 2 (pp. 1011-1016). Power Engineering Society Winter Meeting, 2002. IEEE. ISBN 0-7803-7322-7 Nagata, M., & Inoue, T. (2008). An efficient voltage and reactive power control simulation using long term dynamics simulation. 16 th Power Systems Computation Conference 2008, June 2008, Scotland. Osahenvemwem, A. O., & Omorogiuwa, O. (2008). Electric transmission line faults in Nigeria: A cause study of Benin-Irrua 132kV transmission line. International Journal of Electrical and Power Engineering, 2(6), 384-388. ISSN 1990-7958 Pakistan Water and Power Development Author- ity (WAPDA). (2006-07). Annual report. July 2006- June 2007. Qinghuaz, N. N., Jian Wu Haupt, T., & Srivastava, A. K. (2009). Power system decoupled simulation in MATLAB/Simulink, (pp. 1-8). ISBN: 978-1- 4244-4283-6 Stagg, G. W., & El-Abiad, A. H. (1968). Computer methods in power system analyses (pp. 110–127). New York, NY: McGraw-Hill. Sybille, G., & Hoang, L. (2002). Digital simulation of power systems and power electronics using the MATLAB/Simulink power system blockset, (pp. 2973–2981). Power Engineering Society Winter Meeting, 2000. IEEE. ISBN: 0-7803-5935-6 Takimoto, A. (2005). Time domain simulation based preventive control method for transient stability. The International Conference on electri- cal Engineering 2005, July 2005, China. Zhongxi, W., & Xiaoxin, Z. (1998). Power system analyses software package (PSASP)-An integrated powersystem analyses tool (pp. 7-11). ISBN: 0-7803-4754-4 ADDITIONAL READING Das, J. C. (2002). Power System Analysis: Short- Circuit Load Flow and Harmonics (1st ed.). Power Engineering. Glover, J. D. (2008). Sarma.M.S (4th ed.). Power System Analysis and Design. 339 Analyses and Monitoring of Power Grid Grainger, J. J., & Stevenson, W. (1994). Power System Analysis. McGraw-Hill Science/ Engg/ Math. (2002). Natarajan (1st ed.). Computer Aided Power System. CRC. Tleis, N. (2007). Power Systems Modelling and Fault Analysis: Theory and Practice Book. ISBN: 0750680741 340 Analyses and Monitoring of Power Grid APPENDIX 1: KEY TERMS, CONCEPTS, AND EQUATIONS Load Flow Analysis: Calculates the bus voltages, branch power factors, currents, and power flows throughout the electrical system. Unlike traditional circuit analysis, a power flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various forms of AC power rather than voltage and current. It analyzes the power systems in normal steady-state operation. Load Flow Calculation Methods: ETAP provides three load flow calculation methods: Newton- Raphson, Fast-Decoupled, and Accelerated Gauss-Seidel. Newton-Raphson method has been used during the simulation. ∆ ∆ ∆ ∆ P Q J J J J V = 1 2 3 4 δ (1) Fast-Decoupled Method: Derived from the Newton-Raphson method. It takes the fact that a small change in the magnitude of bus voltage does not vary the real power at the bus appreciably, and likewise, for a small change in the phase angle of the bus voltage, the reactive power does not change apprecia- bly. Thus the load flow equation from the Newton-Raphson method can be simplified into two separate decoupled sets of load flow equations, which can be solved iteratively (Equation 2): ∆ ∆ ∆ ∆ P J Q J V = = 1 4 δ (2) Gauss-Seidel Method: From the system nodal voltage equation (Equation 3): l Y V BUS = (3) P jQ V Y V T BUS + = (4) Data Required for Load Flow Analysis: Following data is required during load flow analysis: • Bus Data • Branch Data • Power Grid Data • Synchronous Generator Data • Inverter Data • Synchronous Motor Data • Induction Motor Data • Static Load Data • Capacitor Data • Lumped Load Data • Charger & UPS Data 341 Analyses and Monitoring of Power Grid Harmonic Analysis: Due to the wide and ever increasing applications of power electronic devices, such as variable speed drives, uninterruptible power supplies (UPS), static power converters, etc., power system voltage and current quality has been severely affected in some areas. In these areas components other than that of fundamental frequency can be found to exist in the distorted voltage and current waveforms. These components usually are the integer multipliers of the fundamental frequency, called harmonics. In addition to electronic devices, some other non-linear loads, or devices including saturated transformers, arc furnaces, fluorescent lights, and cyclo-converters are also responsible for the deteriora- tion in power system quality. Harmonic Analysis Calculation Methods: ETAP harmonic analysis program fully complies with the latest version of the following standards: • IEEE Standards 519, IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems • IEEE Standards 141, IEEE Recommended Practice for Electric Power Distribution for Power Plants • ANSI/IEEE Standard 399, IEEE Recommended Practice for Power System Analysis THD F F i = ∑ 2 2 1 ϑ (5) Individual Harmonic Distortion (IHD): Simply calculates the ratio of the harmonic component to the fundamental component. This value is sometimes used to track the effect of each individual harmonic and examine its magnitude. IHD is determined by (Equation 6): IHD F F i = 1 (6) Root Mean Square (RMS) Total: This is the square root of the sum of the squares of the magnitudes of the fundamental plus all harmonics in the system. For a system with no harmonics at all, the total RMS should be equal to the fundamental component RMS. The total RMS is determined by (Equation 7): RMS F i = ∑ 2 1 ϑ (7) Transient Stability Analysis: ETAP transient stability analysis program is designed to investigate the stability limits of a power system before, during and after system changes or disturbances. The program models dynamic characteristics of a power system, implements the user-defined events and actions, solves the system network equation and machine differential equations interactively to find out system and machine responses in time domain. 342 Analyses and Monitoring of Power Grid Power System Stability: The property of a power system which insures that it remains in electro- mechanical equilibrium throughout any normal and abnormal operating conditions. Stability Limits: There are two types of stability limit for a power system, namely steady-state stability limit and transient stability limit. Steady-State Stability Limit: defined as the stability of a system under conditions of gradual or small changes in the system. This stability can be either found by the load flow calculation for a steady-state operation, or determined by a transient stability study if there are system changes or disturbances involved. Transient Stability Limit: defined as the stability of a system during and after sudden changes or disturbances in the system, such as short-circuits, loss of generators, sudden changes in load, line trip- ping, or any other similar impact. The system is said to be transient stable if following a severe distur- bance, all synchronous machines reach their steady-state operating condition without prolonged loss of synchronism or going out of step with other machines. Causes of Instability Problems: The major causes to industrial power system instability problems include: • Short-circuits • Loss of a tie connection to a utility system • Loss of a portion of in-plant co-generation (generator rejection) • Starting a motor that is large relative to the system generating capacity • Switching operations of lines, capacitors, etc. • Impact loading (motors and static loads) • A sudden large step change of load or generation Consequences of Instability Problems: • Area-wide blackout • Interruption of loads • Low-voltage conditions • Damage to equipment • Relay and protective device malfunctions Ground Grid Systems: Since the early days of the electric power industry, the safety of personnel in and around electric power installations has been a primary concern. With ever increasing fault cur- rent levels in today’s interconnected power systems, there is renewed emphasis on safety. The safety of personnel is compromised by the rise in the ground potential of grounded structures during unbalanced electric power faults. At such times, humans touching grounded structures can be subjected to voltages. However, the magnitude and duration of the electric current conducted through the human body should not be sufficient to cause ventricular fibrillation Years of research on the effects of electric current on the human body have lead to the development of standards of permissible values to avoid electrocution. The ground grid systems program utilizes the following four methods of computation: • FEM: Finite Element Method • IEEE 80-1986 343 Analyses and Monitoring of Power Grid • IEEE 80-2000 • EEE 665-1995 Calculations during Ground Grid Analysis: Following are the calculations performed during this analysis: • The Step and Touch potentials for any rectangular/triangular/L-shaped/T-shaped confguration of a ground grid, with or without ground rods (IEEE Std 80 and IEEE Std 665). • The tolerable Step and Mesh potentials and compares them with actual, calculated Step and Mesh potentials (IEEE Std 80 and IEEE Std 665). • Graphic profles for the absolute Step and Touch voltages, as well as the tables of the voltages at various locations (Finite Element Method). • The optimum number of parallel ground conductors and rods for a rectangular/triangular/L- shaped/T-shaped ground grid. The cost of conductors/rods and the safety of personnel in the vi- cinity of the substation/generating station during a ground fault are both considered. • The Ground Resistance and Ground Potential rise (GPR). Short Circuit Analysis: ETAP short-circuit analysis program analyzes the effect of three-phase, line-to-ground, line-to-line, and line-to-line-to-ground faults on the electrical distribution systems. The program calculates the total short-circuit currents as well as the contributions of individual motors, generators, and utility ties in the system. Fault duties are in compliance with the latest editions of the ANSI/IEEE standards (C37 series) and IEC standards (IEC 909 and others). 3-Phase Faults: Device Duty: This study calculates momentary symmetrical and asymmetrical RMS, momentary asymmetrical crest, interrupting symmetrical RMS, and interrupting adjusted symmetrical RMS short-circuit currents at faulted buses. 3-Phase Faults: 30 Cycle Network: This study calculates short-circuit currents in their RMS values after 30 cycles at faulted buses. LG, LL, LLG, & 3-Phase Faults: ½ Cycle: This study calculates short-circuit currents in their RMS values at ½ cycle at faulted buses. LG, LL, LLG, & 3-Phase Faults: 1.5 to 4 Cycle: This study calculates short-circuit currents in their RMS values between 1.5 to 4 cycles at faulted buses. LG, LL, LLG, & 3-Phase Faults: 30 Cycle: This study calculates short-circuit currents in their RMS values at 30-cycles at faulted buses. 344 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 12 INTRODUCTION In order to deal with the vagueness of human thought, Zadeh (1965) first introduced fuzzy set theory. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership function which assigns to each object a grade of membership ranging between zero and one (Zadeh, 1965). A fuzzy set is an extension of a crisp set. Crisp sets only allow full membership or non-membership, whereas fuzzy sets allow partial membership. In other words, an element may partially belong to a fuzzy set (Ertugrul and Karakasoglu, 2006; Liang, 2008; Peidro et. al, 2010). Fuzzy sets and fuzzy logic are powerful mathematical tools for Pandian Vasant University Technology Petronas, Malaysia Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms and Hybrid Genetic Algorithms Pattern Search Approaches ABSTRACT In this chapter a solution is proposed to a certain nonlinear programming diffculties related to the pres- ence of uncertain technological coeffcients represented by vague numbers. Only vague numbers with modifed s-curve membership functions are considered. The proposed methodology consists of novel genetic algorithms and a hybrid genetic algorithm pattern search (Vasant, 2008) for nonlinear program- ming for solving problems that arise in industrial production planning in uncertain environments. Real life application examples in production planning and their numerical solutions are analyzed in detail. The new method suggested has produced good results in fnding globally near-optimal solutions for the objective function under consideration. DOI: 10.4018/978-1-61350-138-2.ch012 345 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms modeling: uncertain systems in industry, nature and humanity; and facilitators for commonsense reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematical methods, especially when the goal is to find a good approximate solution (Bojadziev and Bo- jadziev, 1998; Zamirian et. al, 2009). Modeling using fuzzy sets has proven to be an effective way for formulating decision problems where the information available is subjective and imprecise (Zimmermann, 1992; Jimenez et. al, 2008). A linguistic variable is a variable whose values are words or sentences in a natural or artificial language (Zadeh, 1975). As an illustration, Age is a linguistic variable if its values are assumed to be the fuzzy variables labeled young, not young, very young, not very young, etc. rather than the numbers 0, 1, 2, 3. (Bellman and Zadeh, 1977). The concept of a linguistic variable provides a means of approximate characterization of phe- nomena which are too complex or too ill-defined to be amenable to description in conventional quantitative terms. The main applications of the linguistic approach lie in the realm of humanistic systems—especially in the fields of artificial in- telligence, linguistics, human decision processes, pattern recognition, psychology, law, medical diagnosis, information retrieval, economics and related areas (Zadeh, 1975). In this paper a novel, genetic algorithm (GA) approach is reported that was successfully used for solving problems originating from the uncertainty of the technological coefficients in production planning in industrial engineering. The main reason for GA method is adopted in solving this problem is given below. Some of the advantages of GA over classical optimization methods include (Deb, 2001): 1. GA is less susceptible to the complexity of the problem at hand than non-evolutionary methods; 2. They deal with multiple solutions in one run. This is useful to achieve solutions rapidly in the presence of a large number of parameters; 3. They allow the exploration of multiple local optima; 4. GAs have successfully been applied to various optimization problems that involve a large number of parameters, multiple criteria, and complex criteria relationships. It is commonly believed that the main driving principle behind the natural evolutionary process is the Darwin’s survival-of-the-fittest principle (Eldredge, 1989). In most scenarios, nature ruth- lessly follows two simple principles: 1. If by genetic processing an above-average offspring is created, it usually survives longer than an average individual and thus has more opportunities to produce offspring having some of its traits than an average individual. 2. If, on the other hand, a below-average off- spring is created, it usually does not survive longer and thus gets eliminated quickly from the population. The two important main characteristics of genetic algorithms are provided: Exploration: The process of visiting entirely new regions of a search space, to see if anything promising may be found there. Unlike exploita- tion, exploration involves leaps into the unknown. Problems which have many local maxima can sometimes only be solved by this sort of random search. Exploitation: When traversing a search space, exploitation is the process using information gathered from previously visited points in the search space to determine which places might be profitable to visit next. An example is hill climbing, which investigates adjacent points in the search space, and moves in the direction giving the great- est increase in fitness. Exploitation techniques 346 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms are good at finding local maxima (Maric, 2010; Stanimrovic, 2010). Employing a GA is a global stochastic method based on the mechanism of natural selection and evolutionary genetics and is used in various fields. For a specific problem such as nonlinear programming, the combination of GA and other methods such as the gradient based method can outperform the GA alone. This can be illustrated by experimental results (Honggang and Jianchao, 1997; Jeya Mala et. al, 2010). Hybrid genetic al- gorithms have been adopted in this research work. The GA approach that has been used in this research work has some disadvantages regarding global optimization. The major drawback of the technique in this research work is that it is un- able to locate the global optimum for a nonlinear problem with uncertain technological coefficients for industrial production planning. Therefore we are motivated to use a more superior technique of hybrid evolutionary computation to solve nonlin- ear industrial production planning problems with uncertain technological coefficients. The rest of this paper is structured as follows: Section 2 describes the membership function for the technological coefficients for the mathemati- cal model of the problem. It’s followed by a brief review of previous work on the GA approach for production planning problems in Section 3. Sec- tion 4 provides a description of the case study of chocolate manufacturing problems. Illustration on the problem formulation and mathematical model for the case study is given in Section 5. Section 6 explains the computational results and findings on the solutions of the optimization problems of production planning in an uncertain environment. The paper ends with a conclusion in Section 7. FUZZY MEMBERSHIP FUNCTION In applications it is often convenient to work with s-curve membership functions for the fuzzy numbers because of their computational flex- ibility, and because they are useful in promoting representations and information processing in a fuzzy environment. In this study an s-curve membership function for the fuzzy numbers in uncertain technological coefficients of the fuzzy optimization is adopted (Vasant, 2003; Vasant & Barsoum, 2006). Decision-makers face up to the uncertainty and vagueness with subjective perceptions and experiences in the decision-making process (Er- tugrul and Karakasoglu, 2006). By using the fuzzy optimization approach, uncertainty and vagueness from subjective perception and the experiences of a decision maker can be effectively represented and a more effective decision reached (Sanchez, Jimenez and Vasant, 2007). A quadratic objective function for a production planning problem was considered by Turabieh, Sheta and Vasant (2007). In order to describe the real world problem of production planning, a non-linear cubic function is considered in this research work. We formulate a non-linear cubic function for the fuzzy optimization problem of industrial pro- duction planning. This problem cannot be solved by the fuzzy linear programming approach. There- fore in this research work global optimization techniques using genetic GAs have been adopted. GENETIC ALGORITHMS FOR PRODUCTION PLANNING PROBLEMS Since the late 1980s there has been a growing interest in Genetic Gas (stochastic optimization algorithms based on the principles of natural [Darwinian] evolution). These have been used widely for parameter optimization, classification and learning. More recently, production plan- ning has emerged as an area to which GAs can be applied. A detailed introduction to GAs can be found in Goldberg (1989). One of the earliest reported applications of GAs to production was reported by Davis (1985). It is a characteristic of 347 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms the robust optimization process that once fairly good solutions have been formed their features will be carried forward into better solutions and lead ultimately to optimal solutions. It is in the nature of GAs that new solutions are formed from the features of known good solutions. Therefore, it follows that GAs are particularly attractive for production planning. Compared with other opti- mization methods, GAs are suitable for traversing large search spaces since they can do this relatively rapidly and because the mutation operator diverts the method away from local minima, which will tend to become more common as the search space increases in size. Suitability for large search spaces is a useful advantage when dealing with produc- tion problems of increasing size, since the solution space grows very rapidly, especially when this is compounded by such features as alternative profit production optimization. It is important that these large search spaces are traversed as rapidly as possible to enable the practical and useful imple- mentation of automated production optimization. If the optimization is done quickly, production managers can try out ‘what-if’ scenarios and detailed optimization analyses besides being able to react to ‘crises’ as soon as possible. Traditional approaches to production planning optimization such as mathematical programming and ‘branch and bound’ are computationally very slow in such a massive search space. Researchers have found that a key advantage of a GA is that it provides a ‘general purpose’ solution to the optimization problem, with the peculiarities of any particular example being accounted for in the fitness func- tion without disturbing the logic of the standard optimization (GA) routine. This means that it is a relatively straightforward and convenient to adapt the software implementation of the method to meet the needs of particular applications. Case Study Chocolate Manufacturing Due to limitations in resources for manufacturing a product and the need to satisfy certain conditions in manufacturing and demand, a problem of fuzzi- ness occurs in industrial systems. This problem occurs, for example, in chocolate manufacturing when deciding a mixed selection of raw materials to produce varieties of products. This is referred here to as the product-mix selection problem (Tabucanon, 1996). There are a number of products to be manu- factured by mixing different raw materials and using several varieties of processing. There are limitations in raw material resources and facility usage for the different types of processing. The raw materials and facilities usage required for manufacturing each product are expressed by means of fuzzy coefficients. There are also some constraints imposed by the marketing department such as product-mix requirements, main product line requirements and lower and upper limits of Table 1. Profit Coefficients c i , d i and e i (Profit function in US $ per 10 3 units) Product (x i ) Synonym c i d i e i x 1 = Milk chocolate, 250g MC 250 c 1 = 180 d 1 = 0.18 e 1 = 0.01 x 2 = Milk chocolate, 100g MC 100 c 2 = 83 d 2 = 0.16 e 2 = 0.13 x 3 = Crunchy chocolate, 250g CC 250 c 3 = 153 d 3 = 0.15 e 3 = 0.14 x 4 = Crunchy chocolate, 100g CC 100 c 4 = 72 d 4 = 0.14 e 4 = 0.12 x 5 = Chocolate with nuts, 250g CN 250 c 5 = 130 d 5 = 0.13 e 5 = 0.15 x 6 = Chocolate with nuts, 100g CN 100 c 6 = 70 d 6 = 0.14 e 6 = 0.17 x 7 = Chocolate candy CANDY c 7 = 208 d 7 = 0.21 e 7 = 0.18 x 8 = Chocolate wafer WAFER c 8 = 83 d 8 = 0.17 e 8 = 0.16 348 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms demand for each product. It is necessary to obtain maximum profit with a certain degree of satisfac- tion for the decision-maker. Problem Formulation Optimization techniques are primarily used in production planning problems in order to achieve optimal profit; a certain objective function is maximized by satisfying a number of constraints. The first step in an optimal production planning problem is to formulate the underlying nonlinear programming (NLP) problem with uncertain tech- nological coefficients by writing the mathematical functions relating to the objectives and constraints. Given a degree of possibility (μ), the fuzzy constrained optimization problem can be formu- lated (Vasant, 2006) as a nonlinear constrained optimization problem shown. Tables 1, 2, 3, and 4 provide the input data for Equation 1 in the problem statement and the values for c i , d i , e i , a ij h , a ij l , r i , u i and b j . The mathematical formulation (Equation 1), of the problem is now described. The eight deci- sion variables are: 250g of Milk Chocolate (x 1 ), 100g of Milk Chocolate (x 2 ), 250g of Crunchy Chocolate (x 3 ), 100g of Crunchy Chocolate (x 4 ), 250g of Chocolate with Nuts (x 5 ), 100g of Choc- olate with Nuts (x 6 ), Chocolate Candy (x 7 ), and Chocolate Wafer (x 7 ). The objective is to find an optimal profit value for the production planning problem with uncertain technological coefficients. The production planning problem is subject to a number of constraints imposed by raw material availability, facility capacity, and the sales depart- ment. An upper and lower limit is imposed on each of the decision variables (refer to Table 3). In Equation 1 there are 21 other inequality con- straints, as follows: (i) 17 constraints of facility capacity (refer to Table 2) and resource variables (refer to Table 4) (ii) 4 constraints by the sales department (refer to Table 3). The optimization formulation is, Maximize Subject to: ( ) c i x i d i x i e i x i i a ij l a ij h a ij l − − = ∑ ÷ − í 2 3 1 8 α (( · · · · · · ·· \ ) í ( · · · · \ ) l l l l l l l − = ln 1 1 1 C B i µ 88 0 1 2 17 0 15 1 6 7 8 0 1 0 6 2 0 ∑ − ≤ = − = ∑ = ∑ ≤ − ≤ x i b j j r i x i r i x i i i x x , , ,..., . . xx x x x x i u i i C B 3 0 6 4 0 5 0 6 6 0 0 1 2 8 0 00 00 00 − ≤ − ≤ ≤ ≤ = = = . . , , ,..., . , , 1 1 1 1 . £ £ . , £ £ . 0 00 0 1 99 and 1 45 m a (1) In the non-linear programming problem (Equation 1), the variable vector x represents a set of variables x i , i = 1, 2,…, 8. The optimization problem contains eight continuous variables and 21 inequality constraints. A test point x i satisfying constraints is either feasible, or infeasible. The set satisfying the constraints is called the feasible domain. The aim of the optimization is to maxi- mize the total production profit for the industrial production planning problem. The practical mean- ing of the constraints is available in Tabucanon (1996). The vagueness factor γ represents fuzzy numbers in uncertain technological parameters. The objective function appears in work by Lin (2007) and Chaudhuri (2007). The objective function represents the profit. COMPUTATIONAL RESULTS Experimental studies are carried out for GAs and hybrid GA pattern search (HGAPS) approaches. In the following sections, the simulation results for the GA approach is provided in detail and the improved results of the HGAPS approach are provided as well. In this research work MATLAB ® toolboxes have been utilized for computation, simulation, 2D and 3D plots. 349 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Results and Discussion for Genetic Algorithm Approach The GA approach mimics biological processes in evolving optimal or near optimal solutions to problems. In this section a practical application to challenging industrial problems of production planning are investigated to exploit the full po- tential of GA to look for a promising near global optimal solution. The results for the industrial production plan- ning problems were obtained by using the follow- ing genetic algorithm. Algorithm Initialization: Generate an initial population. Initialize parameters and define fitness function. Crossover: Perform crossover using arithme- tic crossover. Mutation: Perform mutation using adaptive feasibility. Selection: Evaluate the fitness of each indi- vidual in the population. Choose N best chromo- somes to form the next generation. Termination Criteria: If stopping criteria are satisfied, then terminate. Otherwise, select the next generation and go to Step 2. Table 2. Raw material and Facility usage required (per 10 3 units) (ã ij = [a l ij , a h ij ]) and Availability (b j ) Material or Facility MC 250 MC 100 CC 250 CC100 CN250 CN100 Candy Wafer Cocoa (kg) [66, 109] [26, 44] [56,9] [22,37] [37,62] [15,25] [45, 75] [9, 21] Milk (kg) [47, 78] [19, 31] [37,6] [15,25] [37,62] [15,25] [22, 37] [9, 21] Nuts (kg) [0, 0] [0, 0] [28,4] [11,19] [56,94] [22,37] [0, 0] [0, 0] Cons. sugar (kg) [75, 125] [30, 50] [66,109] [26,44] [56,94] [22,37] [157,262] [18,30] Flour (kg) [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [54,90] Alum. foil (ft 2 ) [375,625] [0, 0] [375,625] [0, 0] [0, 0] [0, 0] [0, 0] [187,312] Paper (ft 2 ) [337,562] [0, 0] [337,563] [0, 0] [337,562] [0, 0] [0, 0] [0, 0] Plastic (ft 2 ) [45, 75] [95, 150] [45, 75] [90,150] [45,75] [90, 150] [1200,200] [187,312] Cooking(ton- hours) [0.4, 0.6] [0.1, 0.2] [0.3, 0.5] [0.1, 0.2] [0.3,0.4] [0.1, 0.2] [0.4, 0.7] [0.1,0.12] Mixing (ton- hours) [0, 0] [0, 0] [0.1, 0.2] [0.04,0.07] [0.2, 0.3] [0.07, 0.12] [0, 0] [0, 0] Forming(ton- hours) [0.6, 0.9] [0.2, 0.4] [0.6, 0.9] [0.2, 0.4] [0.6, 0.9] [0.2, 0.4] [0.7, 1.1] [0.3, 0.4] Grinding(ton- hours) [0, 0] [0, 0] [0.2, 0.3] [0.07, 0.12] [0, 0] [0, 0] [0, 0] [0, 0] Wafer making (ton-hours) [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [0, 0] [0.2, 0.4] Cutting (hours) [0.07,0.2] [0.07,0.12] [0.07,0.12] [0.07, 0.12] [0.07, 0.12] [0.07, 0.12] [0.15, 0.25] [0, 0] Packaging1 (hours) [0.2, 0.3] [0, 0] [0.2, 0.3] [0, 0] [0.2, 0.3] [0, 0] [0, 0] [0, 0] Packaging2 (hours) [0.04,0.6] [0.2, 0.4] [0.04, 0.06] [0.2, 0.4] [0.04, 0.06] [0.2, 0.4] [1.9, 3.1] [0.1, 0.2] Labour (hours) [0.2, 0.4] [0.2, 0.4] [0.2, 0.4] [0.2, 0.4] [0.2, 0.4] [0.2, 0.4] [1.9, 3.1] [1.9, 3.1] 350 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Output the best solutions. Description of the Genetic Algorithm Parameter Setting Fitness function (Equation 2): Maximize ( ) c i x i d i x i e i x i i − − = ∑ 2 3 1 8 (2) The fitness function is the objective function that has to be maximized. Mutation functions make small random changes in individuals in the population, which provide genetic diversity and enable the GA to search a broader space. A step length is chosen along each direction so that linear constraints and bounds are satisfied. Crossover combines two individuals, or par- ents, to form a new individual, or child, for the next generation. The following has been specified that performs the crossover in the crossover func- tion field. Arithmetic crossover creates children that are the weighted arithmetic mean of the two parents. Children are feasible with respect to linear constraints and bounds. Stopping Criteria Options The stopping criteria determines what causes the algorithm to terminate. The following options have been considered in the simulation of the GA. Generations specifies the maximum number of iterations the GA performs. Time Limit specifies the maximum time in sec- onds the genetic algorithm runs before stopping. Table 3. Demand (u k ) and Revenues/Sales (r k ) in US $ per 10 3 units Product (x k ) Synonym Demand (u k ) Revenues/Sales (r k ) x 1 = Milk chocolate, 250g MC 250 u 1 = 500 r 1 = 375 x 2 = Milk chocolate, 100g MC 100 u 2 = 800 r 2 = 150 x 3 = Crunchy chocolate, 250g CC 250 u 3 = 400 r 3 = 400 x 4 = Crunchy chocolate, 100g CC 100 u 4 = 600 r 4 = 160 x 5 = Chocolate with nuts, 250g CN 250 u 5 = 300 r 5 = 420 x 6 = Chocolate with nuts, 100g CN 100 u 6 = 500 r 6 = 175 x 7 = Chocolate candy CANDY u 7 = 200 r 7 = 400 x 8 = Chocolate wafer WAFER u 8 = 400 r 8 = 150 Table 4. Raw material availability (b j ) Material or Facility Availability Cocoa (kg) 100000 Milk (kg) 120000 Nuts (kg) 60000 Cons. sugar (kg) 200000 Flour (kg) 20000 Alum. foil (ft 2 ) 500000 Paper (ft 2 ) 500000 Plastic (ft 2 ) 500000 Cooking (ton-hours) 1000 Mixing (ton-hours) 200 Forming (ton-hours) 1500 Grinding (ton-hours) 200 Wafer making (ton-hours) 100 Cutting (hours) 400 Packaging 1 (hours) 400 Packaging 2 (hours) 1200 Labour (hours) 1000 351 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Fitness Limit: If the best value is less than or equal to the value of Fitness Limit, the algorithm stops. Stall Generations: If the weighted average change in the fitness function value over Stall Generations is less than Function Tolerance, the algorithm stops. Stall Time Limit: If there is no improvement in the best fitness value for an interval of time in seconds specified by Stall Time Limit, the algorithms stops. Function Tolerance: If the cumulative change in the fitness function value over Stall Generations is less than Function Tolerance, the algorithm stops. Among the above options, the final results show that the Fitness Limit option has been utilized successfully in the simulation results. Number of Runs: 20, 26, 31 and 95. Equation 1 was solved by the using the GA with the following parameters. μ = Degree of possibility Table 5. Optimal value for Objective Function γ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 f time (s) 0.001 0.69 2.26 0.00 0.00 0.41 2.79 0.00 0.00 559.8 0.012 0.1 0.51 0.00 0.78 0.00 0.00 0.00 0.00 1.31 320.4 0.058 0.2 1.47 0.00 0.00 0.00 0.00 0.04 0.00 0.00 268.3 0.057 0.3 0.35 0.00 0.23 0.15 0.00 0.00 0.25 0.00 161.5 0.056 0.4 0.22 0.00 0.00 0.00 1.78 0.06 0.75 0.00 430.3 0.055 0.5 0.71 0.34 0.56 0.00 1.03 0.00 0.00 0.00 375.0 0.055 0.6 0.53 0.00 0.00 0.47 0.70 0.00 1.06 0.00 441.0 0.055 0.7 0.00 0.51 0.00 0.00 0.79 0.70 0.68 0.00 336.7 0.055 0.8 0.16 0.00 0.00 0.00 1.91 0.27 0.99 0.95 583.0 0.056 0.9 0.76 0.16 0.00 0.00 0.78 0.00 1.38 0.85 250.2 0.055 0.99 1.08 0.80 0.00 0.00 0.78 0.00 1.38 0.85 719.6 0.056 Table 6. Optimal value for Fitness function γ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 f time (s) 0.001 0.18 0.00 0.00 0.00 1.46 1.80 0.00 0.39 379.2 0.420 0.1 0.00 0.11 0.81 0.00 0.00 0.28 0.29 0.00 213.5 0.212 0.2 0.00 0.90 0.00 0.00 0.72 0.30 1.55 0.00 510.6 0.201 0.3 0.00 0.00 0.00 0.93 0.00 0.00 0.00 0.78 131.8 0.200 0.4 0.60 0.94 0.00 0.00 0.08 0.00 0.00 0.00 197.3 0.205 0.5 1.35 2.14 0.17 0.00 0.28 0.39 0.00 0.18 523.7 0.202 0.6 0.00 0.00 0.82 0.00 0.00 0.00 0.00 0.69 182.5 0.233 0.7 0.00 0.32 0.51 0.00 0.10 0.00 0.69 1.88 416.5 0.210 0.8 0.32 0.00 0.03 0.00 0.00 0.48 0.00 0.39 128.9 0.203 0.9 0.05 0.00 0.24 0.72 0.15 0.13 0.00 1.31 236.2 0.207 0.99 1.20 0.00 0.00 0.39 0.00 0.00 2.64 0.00 791.4 0.310 352 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms γ = Level of satisfaction α = Vagueness factor f = Objective function or fitness function x i = Decision variables Time in seconds = CPU (s) The best optimal solution for the fitness func- tion and the best feasible solution for the decision variables with respect to the level of satisfaction γ is reported in Table 5. Figure 1, Figure 2, and Figure 3 provide solutions for α = 13.813. The Total CPU time for the above results is 0.57 s and the average CPU time is 0.052 for γ = 1 to γ = 0.99. Number of runs = 50, population size = 15 and number of generation = 20. Figure 1. Fitness value f and level of satisfaction γ Figure 2. Fitness value (scores) and final population 353 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Figure 3. Final population for γ = 0.99 Figure 4. Fitness value f and generation Figure 5. Fitness value f and level of satisfaction γ 354 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Figure 4 and Figure 5 show the simulation results for number of runs = 20, population size = 100 and generation = 10000. The computed results for best optimal value for fitness function, best feasible solutions for decision variables with respect to γ is reported in Table 6. Experimental simulation results for Figure 6, total CPU time = 2.603 seconds and average CPU time = 0.237 seconds. Further experiments were carried out by increasing the number of runs by 31 with population size = 100 and number of generation = 10000. Table 7 reports the best optimal solution for fitness function f, and the best feasible decision variables with respect to γ. The total CPU time = 3.155 seconds and average CPU time = 0.287 seconds for running the simulation. Figure 6. Fitness value f and level of satisfaction γ Figure 7. Current best individual solutions x i at γ = 0.99 355 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms The best individual solution for the decision variables is shown in Figure 7 for the experiment with increased population size = 100 and number of generation = 10000. Table 8 reports the best optimal value of fitness function at γ = 0.99 is 1222.6 and total CPU time = 1.981 seconds with average CPU time = 0.180 seconds. There is a tremendous improvement in the fitness function value when the population size is increased to 100. A thorough investigation was carried out with following parameter settings in the genetic algo- rithms techniques: Population size = 100; Generation = 10000; Elite Count = 20; Selection = Uniform, roulette and tournament; Fitness scaling = proportional, top and shift linear; Crossover functions = Inter- mediate, heuristic, arithmetic, single point, two point and Mutation function = Adaptive feasible. Table 9 reports very important information on the simulation results obtained for α = 1 to α = 25 by independent runs. The total CPU time (s) Table 7. Optimal value for Fitness function γ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 f time (s) 0.001 0.63 0.00 1.49 0.00 0.00 0.00 0.00 0.00 340.7 0.220 0.1 0.40 1.44 0.00 0.00 0.00 0.69 0.00 0.00 240.4 0.199 0.2 0.00 0.00 0.31 0.68 0.00 0.00 0.00 0.00 96.20 0.466 0.3 0.56 0.00 0.00 0.00 0.00 0.44 0.88 0.71 375.1 0.208 0.4 0.00 0.00 1.33 0.00 1.20 0.13 0.00 0.53 412.6 0.670 0.5 0.00 1.18 1.76 1.70 0.00 0.00 0.00 0.00 489.2 0.191 0.6 0.00 0.00 0.41 0.60 0.00 0.00 0.02 0.00 110.1 0.195 0.7 0.00 0.58 0.61 0.00 0.95 0.00 0.00 0.00 265.6 0.207 0.8 0.00 0.03 0.00 0.00 1.01 1.63 0.00 0.37 277.6 0.192 0.9 1.36 0.00 0.00 0.62 0.00 0.00 0.00 0.13 299.3 0.404 0.99 1.09 0.47 1.27 1.18 0.21 0.00 0.00 0.46 579.9 0.203 Table 8. Optimal value for Fitness function γ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 f time (s) 0.001 0.62 0.00 0.00 0.00 1.26 0.86 0.00 0.00 336.0 0.194 0.1 0.55 0.00 0.00 0.00 0.49 0.00 0.08 0.00 180.3 0.183 0.2 0.00 0.00 0.00 0.00 0.00 0.00 1.09 1.32 337.1 0.178 0.3 0.00 0.00 0.21 0.00 0.06 0.00 1.69 0.33 418.5 0.179 0.4 0.72 1.60 0.00 0.00 0.18 0.53 0.00 0.30 345.9 0.176 0.5 0.00 0.00 0.00 0.96 0.00 0.00 0.00 0.28 92.00 0.179 0.6 0.00 1.60 0.57 0.32 0.00 0.31 1.34 0.00 545.1 0.180 0.7 1.30 0.00 0.00 0.88 0.58 0.00 0.00 0.57 419.7 0.179 0.8 0.00 0.00 0.00 0.00 0.00 0.00 0.29 0.00 60.40 0.179 0.9 1.31 0.66 0.00 0.00 0.00 0.00 0.37 0.90 444.0 0.177 0.99 1.28 0.00 0.61 1.95 2.26 0.00 2.24 0.00 1222.6 0.177 356 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms and an average CPU time (s) for each α from 1 to 41 with respect to the range γ = 0.001 to γ = 0.99 provided in the last two rows of the Table 9. Unfortunately, there is no solution for the fitness function for α = 45 at γ = 0.99. This is the draw back of this GA algorithm for the higher value of α in an independent run. A 3D plot for the fitness value, vagueness factor and level of satisfaction for α = 1 to α = 41 is shown in Figure 8. The result obtained for α = 45 at γ = 0.99 motivates to further investigate this simulation with a single run for α = 1 to α = 41. Figure 9 shows a 3D solution obtained with a single run of the GA for α = 1 to α = 41. The optimal value for the fitness function is 1086 at α = 41 and γ = 0.99. The solution for the problem is further investigated for α values between 39 and 59. Figure 9 was obtained for the solution of fitness function f. Population size of 2000 and number of gen- eration of 100000 with arithmetic cross over and adaptive feasible mutation have been used in the above result. The optimal solution for the fitness function is 925.53 at α = 41 and γ = 0.2. Compu- tational time for this solution is 0.148 seconds. Figure10 shows the solution for a run number of 26. In this case, the number of generations used is 1000000 and the population size is 100. Figure 11 shows the optimal results for α values from 39 to 57. The optimal value occurs at α = 41 and γ = 0.5 with fitness value 1302.59. The CPU time for this solution is 0.056 seconds. The simulation was carried out for 95 runs and the following result obtained by using a popula- tion size of 200 and the number of generations equal to 1,000,000. The number of runs carried out in this simula- tion results for the optimal fitness function value are 20, 26, 31 and 95. This is the largest number of runs that have been considered in these simu- lation results. The optimal value for the fitness function is 1302.59, obtained at α = 41 and γ = 0.5 and the computational time is 0.055 seconds. The simulation was run for α = 1 to α = 41 and the results for the fitness function is 1302.59 at α = 21 and γ = 0.9. The computational time for running this solution is 0.056. Figure 12, Figure 13, Figure 14, and Figure 15 give complete views of the various dimensions of the solutions. Table 9. Optimal values of Fitness function for α = 1 to α = 45 γ α= 1 α= 5 α= 9 α=3 α=17 α=21 α=25 α=29 α=33 α=37 α=41 α=45 0.01 370.1 352.8 412.7 352.8 412.7 48.70 216.3 352.8 370.1 352.8 412.7 216.3 0.1 287.2 392.7 562.0 392.7 562.0 36.10 547.7 392.7 287.2 392.7 562.0 547.7 0.2 518.0 81.60 925.5 81.60 925.5 433.3 616.6 81.60 518.0 81.60 925.5 616.6 0.3 360.0 348.3 248.1 348.3 248.1 445.4 408.8 348.3 360.0 348.3 248.1 408.8 0.4 605.7 154.8 207.8 154.8 207.8 254.2 801.0 154.8 605.7 154.8 207.8 801.0 0.5 205.7 418.1 485.7 418.1 485.7 492.1 154.9 418.1 205.7 418.1 485.7 154.9 0.6 351.2 431.4 453.3 431.4 453.3 414.6 550.6 431.4 351.2 431.4 453.3 550.6 0.7 295.9 47.70 539.5 47.70 539.5 441.5 707.2 47.70 295.9 47.70 539.5 707.2 0.8 475.5 194.4 442.5 194.4 442.5 420.7 551.1 194.4 475.5 194.4 442.5 551.1 0.9 337.2 198.2 408.2 198.2 408.2 88.60 372.4 198.2 337.2 198.2 408.2 372.4 0.99 366.4 311.6 243.1 311.6 243.1 288.1 703.1 311.6 366.4 311.6 243.1 0.000 TT 6.234 3.338 4.312 4.393 3.761 4.051 4.128 2.058 8.306 3.556 3.487 2.128 AT 0.567 0.303 0.392 0.399 0.342 0.368 0.375 0.187 0.755 0.323 0.317 0.193 TT = Total time and AT = Average time 357 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms The contour in Figure 16 clearly explains the situation where by the optimal solution for the fitness function is stuck at 1221 for α = 39 and α = 59. In order to to escape from this solution, another hybrid method is needed to further improve the final optimal solution. Results and Discussion for Hybrid Genetic Algorithm Pattern Search Approach The hybrid GA and general pattern search is a combination of a GA and a general pattern search. Below is the algorithm for this approach. • Step 1: Initial population: Generate initial population randomly. • Step 2: Genetic operators: Selection: sto- chastic uniform, Crossover: arithmetic crossover operator Mutation, Adaptive fea- sible mutation operator • Step 3: Evaluation: Best offspring and ft- ness function. • Step 4: Stop condition: If a pre-defned maximum generation number, time limit, ftness limit reached or an optimal solution is located during the genetic search pro- cess, then stop; otherwise, go to Step 2. • Step 5: Continue with general pattern search techniques (Vasant & Barsoum, 2009). • Step 6: End Figure 17 provides the best optimal solution for the fitness function with respect to a level of satisfaction of α = 13.813. Table 10 provides the solution for the best fitness function and the decision variables at α = 13.813. The CPU time to run the simulation for α = 13.813 is 16 minutes. The best optimal solu- tion for the fitness function is 180776.1 at γ = 0.1. Figure 18. explains the detailed solution for the decision variables versus level of satisfaction. The CPU time for α = 13.813 at γ = 0.99 is 78.375 seconds. The solution for the decision variable x 8 is unrealistic since for the majority values of γ, x 8 is zero. Therefore, this solution needs some improve- ment. For this purpose, the following hybrid methods is thoroughly investigated. Figure 8. Fitness value, vagueness and level of satisfaction 358 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Figure 9. Fitness value f and level of satisfaction γ Figure 10. Fitness value f and level of satisfaction γ Figure 11. Fitness value f and level of satisfaction γ 359 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Fitness values for various values of α from 1 to 41 are given in Figure 19. The optimal value for the fitness function occurs at α = 9 and γ = 0.99 is 197980.93. The total CPU time for the simulation of Figure 19 is 2 hours 18 minutes. Figure 20 provides a holistic view of the 3D mesh plot solution for various values of α, and γ with respect to the level of satisfaction. The CPU time for the 3D mesh plot is 2 hours 52 minutes. The main contribution of the hybrid HGAPS approach is that it is able to locate the best near global optimal solution for the fitness function which is far superior to the GA alone. On the other hand, it is unable to provide a reasonable computational CPU time for the fitness function values. Figure 12. Fitness value f, vagueness factor α and level of satisfaction γ Figure 13. Vagueness α and level of satisfaction γ 360 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Figure 14. Fitness value f and level of satisfaction γ Figure 15. Fitness value f and vagueness factor α 361 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms CONCLUSION The HGAPS algorithm drives the solution to the optimal point where all constraints are satisfied. Moreover, for problem having a moderate type of constraints such as a linear constraint, the HGAPS simulation results guarantee an accurate and robust solution with less computational time and greater convergence stability than classical optimization techniques such as line search (Vasant, 2008). The outcomes of the simulation of the GA algorithm were not satisfactory for a moderate non-linear fitness function with 21 inequality linear constraints and 8 bound constraints for a production planning problem. The simulation was carried out for various numbers of runs and generations. Most of the time, the simula- tion for the GA algorithm produced very poor feasible solutions for the decision variables and local optimal solutions for the fitness function. Figure 16. Contour plots for vagueness α and level of satisfaction γ Table 10. Optimal value for Fitness Function (f) γ x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 f 0.001 0.62 0.80 0.94 0.00 0.21 0.24 0.00 0.00 366.4 0.1 346.7 580.5 276.2 460.4 148.7 247.9 189.2 4.54 180776.1 0.2 0.43 0.90 0.73 0.58 0.04 0.68 0.57 0.00 475.5 0.3 314.8 577.5 291.0 485.7 104.2 173.7 175.9 5.34 173329.7 0.4 0.00 0.00 0.00 0.61 0.51 1.69 0.59 0.00 351.2 0.5 278.2 466.2 282.0 521.1 156.5 260.8 164.2 0.00 170805.1 0.6 280.6 497.6 269.3 493.6 146.5 244.2 161.4 0.00 169598.1 0.7 258.1 602.6 260.3 472.7 128.5 214.2 153.6 0.00 166739.9 0.8 305.2 512.4 238.8 398.0 136.8 228.1 159.4 0.00 166566.4 0.9 257.7 444.3 269.2 450.5 146.1 243.6 148.2 0.00 163208.3 0.99 283.8 566.7 153.1 255.2 106.4 177.3 123.5 0.00 144803.8 362 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms To overcome these major drawbacks, a hybrid approach has been adopted in this study for the global optimal solutions. The major drawback of the GA algorithms is that is not able to provide a global optimal solution for the fitness function. This is possibly due to premature convergence. Further investigation has been carried out by the hybridize technique HGAPS in order to find a global optimal solution for the objective func- tion. The final optimal solution for the objective function is very promising and is superior to the GA approach alone. The major goal of this paper is finally achieved successfully. Figure 17. Fitness value f and level of satisfaction γ Figure 18. Decision variables x i and level of satisfaction γ 363 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Figure 19. Fitness value f and level of satisfaction γ Figure 20. Mesh plot for fitness value f, α and γ 364 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms REFERENCES Bellman, R. E., & Zadeh, L. A. (1977). Local and fuzzy logics. 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ADDITIONAL READING Abraham, A., Vasant, P., & Bhattacharya, A. (2008). Neuro-Fuzzy Approximation of Multi- Criteria Decision-Making QFD Methodology. In Kahraman, C. (Ed.), Fuzzy Multi-Criteria Decision Making Theory and Applications with Recent Developments (pp. 301–324). Springer. doi:10.1007/978-0-387-76813-7_12 Aliev, R. A., Fazlollahi, B., Guirimov, B. G., & Aliev, R. R. (2007). Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Information Sciences, 177, 4241–4255. doi:10.1016/j.ins.2007.04.012 Bhattacharya, A., Abraham, A., & Vasant, P. (2008). FMS Selection Under Disparate Level- of-Satisfaction of Decision Making Using an Intelligent Fuzzy-MCDM- Model. In Kahraman, C. (Ed.), Fuzzy Multi-Criteria Decision Making Theory and Applications with Recent Develop- ments (pp. 263–280). Springer. doi:10.1007/978- 0-387-76813-7_10 Bhattacharya, A., Vasant, P., & Susanto, S. (2007). Simulating theory of constraint problem with a novel fuzzy compromise linear programming model. In A. Elsheikh, A. T. Al Ajeeli, & E. M. Abu-Taieh. Simulation and Modeling: Current Technologies and Applications (pp. 307-336). IGI Publisher. Buckley, J. J., & Feuring, T. (2000). Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming. Fuzzy Sets and Systems, 109, 35–53. doi:10.1016/S0165-0114(98)00022-0 Elamvazuthi, I., Vasant, P., & Ganesan, T. (2010). Fuzzy linear programming using modified logistic membership function. International Review of Automatic Control, 3(4), 370–377. Jen, M., Ida, K., Lee, J., & Kim, J. (1997). Fuzzy nonlinear goal programming using genetic algo- rithm. Computers & Industrial Engineering, 33, 39–42. doi:10.1016/S0360-8352(97)00036-3 Jimenez, F., Cadenas, J. M., Verdegay, J. L., & Sanchez, G. (2003). Solving fuzzy optimization problems by evolutionary algorithms. Information Sciences, 152, 303–311. doi:10.1016/S0020- 0255(03)00074-4 Jimenez, F., Sanchez, G., & Vasant, P. (2008). Fuzzy Optimization via Multi-Objective Evolu- tionary Computation for Chocolate Manufactur- ing. In Kahraman, C. (Ed.), Fuzzy Multi-Criteria Decision Making Theory and Applications with Recent Developments (pp. 523–538). Springer. doi:10.1007/978-0-387-76813-7_20 Liang, T. F. (2008). Interactive multi-objective transportation planning decisions using fuzzy linear programming. Asia Pacific Journal of Operational Research, 25, 11–31. doi:10.1142/ S0217595908001602 Madronero, M. D., Peidro, D., & Vasant, P.Vendor selection problem by using an interactive fuzzy multi-objective approach with modified s-curve membership functions. Computers & Mathemat- ics with Applications (Oxford, England), 60, 1038–1048. doi:10.1016/j.camwa.2010.03.060 Modal, S., & Maiti, M. (2002). Multi-item fuzzy EOQ models using genetic algorithm. Comput- ers & Industrial Engineering, 44, 105–117. doi:10.1016/S0360-8352(02)00187-0 367 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms Peidro, D., Mula, J., & Poler, R. (2010). Fuzzy linear programming for supply chain planning under uncertainty. International Journal of In- formation Technology & Decision Making, 9, 373–392. doi:10.1142/S0219622010003865 Sasaki, M., & Gen, M. (2003). Fuzzy multiple objective optimal system design by hybrid ge- netic algorithm. Applied Soft Computing, 2(3F), 189–196. doi:10.1016/S1568-4946(02)00068-6 Varela, L. R., & Ribeiro, R. A. (2003). Evaluation of simulated annealing to solve fuzzy optimiza- tion problems. Journal of Intelligent & Fuzzy Systems, 14, 59–71. Vasant, P. (2010). Hybrid simulated annealing and genetic algorithms for industrial production management problems. International Journal of Computational Methods, 7(2), 279–297. doi:10.1142/S0219876210002209 Vasant, P. (2010). Innovative hybrid genetic algorithms and line search method for indus- trial production management. In Chis, M. (Ed.), Computation and Optimization Algorithms in Software Engineering: Application and Tech- niques (pp. 142–160). Hershey, PA: IGI Global. doi:10.4018/978-1-61520-809-8.ch008 Vasant, P. (2010). Hybrid optimization techniques for industrial production planning. Journal of Computer Science & Technology, 10(3), 150–151. Vasant, P., & Barsoum, N. (2009). Hybrid genetic algorithms and line search method for indus- trial production planning with non-linear fitness function. Engineering Applications of Artificial Intelligence, 22, 767–777. doi:10.1016/j.engap- pai.2009.03.010 Vasant, P., & Barsoum, N. (2010). Hybrid pattern search and simulated annealing for fuzzy produc- tion planning problem. Computers & Mathemat- ics with Applications (Oxford, England), 60, 1058–1067. doi:10.1016/j.camwa.2010.03.063 Vasant, P., Barsoum, N., Kahraman, C., & Di- mirovski, G. (2007). Application of fuzzy optimi- zation in forecasting and planning of construction industry. In Vrakas, D., & Vlahavas, I. (Eds.), Artificial Intelligent for Advanced Problem Solv- ing Technique. IGI publisher. Vasant, P., Bhattacharya, A., & Abraham, A. (2008). Measurement of Level-of-Satisfaction of Decision Maker in Intelligent Fuzzy-MCDM Theory: A Generalized Approach. In Kahraman, C. (Ed.), Fuzzy Multi-Criteria Decision Making Theory and Applications with Recent Develop- ments (pp. 235–262). Springer. doi:10.1007/978- 0-387-76813-7_9 Vasant, P., Elamvazuthi, I., & Webb, J. F. (2010). Fuzzy technique for optimization of objec- tive function with uncertain resource variables and technological coefficients. International Journal of Modeling, Simulation, and Scien- tific Computing, 1(3), 349–367. doi:10.1142/ S1793962310000225 Vasant, P., & Kale, H. (2007). Introduction to fuzzy logic and fuzzy linear programming. In A. Frederick & P. Humphreys (Eds.), Encyclopedia of Decision Making and Decision Support Tech- nologies. IGI publisher. Yang, L., Jones, B. F., & Yang, S. H. (2007). A fuzzy multi-objective programming for op- timization of the fire station locations through genetic algorithms. European Journal of Op- erational Research, 181, 903–915. doi:10.1016/j. ejor.2006.07.003 Zamirian, M., Kamyad, A. V., & Farahi, M. H. (2009). A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation. Physics Letters. [Part A], 373, 3439–3449. doi:10.1016/j.phys- leta.2009.07.018 368 Solving Fuzzy Optimization Problems of Uncertain Technological Coeffcients with Genetic Algorithms KEY TERMS AND DEFINITIONS Adaptive Feasible Mutation: A significant operator in genetic algorithm which provide di- versification in search for optimal solution. Arithmetic Crossover: A dynamic back ground operator which organized by itself. Degree of Satisfaction: Measure of level of satisfaction by the decision makers. Genetic Algorithms: An artificial intelligent technique using evolutionary ideas of natural selection and genetic. Pattern Search: A very useful direct search algorithms for non-derivative, nosy and discrete objection function in optimization problems. Uncertain Coefficients: Imprecise technical coefficients in fuzzy optimization problems. Vagueness Factor: Measure of imprecise variables in uncertain environment. 369 About the Contributors Pandian Vasant was born in Sungai Petani, Malaysia in 1961. Currently, he is a Senior Lecturer of Engineering Mathematics for Electrical & Electronics Engineering Program and Fundamental & Applied Sciences Department at University Technology Petronas in Tronoh, Perak, Mlaysia. He has graduated in 1986 from University of Malaya (MY) in Kuala Lumpur, obtaining his BSc Degree with Honors (II Class Upper) in Mathematics, and in 1988 also obtained a Diploma in English for Business from Cam- bridge Tutorial College, Cambridge, England. In the year 2002 he has obtained his MSc (By Research) in Engineering Mathematics from the School of Engineering & Information Technology of University of Malaysia Sabah, Malaysia, and has a Doctoral Degree (2008) from University Putra Malaysia in Malaysia. After graduation, during 1987-88 he was Tutor in operational research at University Science Malaysia in Alor Setar, Kedah and during 1989-95 he was Tutor of Engineering Mathematics at the same university but with Engineering Campus at Tronoh, Perak. There after during 1996-2003 he became a lecturer in Advanced Calculus and Engineering Mathematics at Mara University of Technology, in Kota Kinabalu. He became Senior Lecturer of Engineering Mathematics in American Degree Program at Nilai International College (Malaysia), during 2003-2004 before taking his present position at Univer- sity Teknologi Petronas in Tronoh. His main research interests are in the areas of Optimization Methods and Applications to Decision Making and Industrial Engineering, Fuzzy Optimization, Computational Intelligence, and Hybrid Soft Computing. Vasant has co-authored 200 research papers and articles in national journals, international journals, conference proceedings, conference paper presentation, and special issue guest editor, lead guest editor for book chapters’ project, conference abstract, edited book and book chapters. In the year 2009, Vasant was awarded top reviewer for the journal Applied Soft Computing (Elsevier). He has been Co-editor for AIP Conference Proceedings of PCO (Power Control and Optimization) conferences since 2008 and editorial board member of international journals in the area of Soft Computing, Optimization and Computer Applications. Currently he’s a lead managing editor for GJTO (Global Journal Technology & Optimization) and organizing committee member (PCO Global) for PCO Global conferences. Nader Barsoum obtained his PhD from University of Newcastle upon Tyne, UK, 1989 in Eclectic Machines and Drives, and his first three degrees from Alexandria University, Egypt in Power Engineer- ing 1976, Applied Mathematics 1979 and Engineering Mathematics 1983. He has academically jointed University Sains Malaysia, University Malaysia Sabah, University of Western Sydney, and Curtin Uni- versity of Technology in the past 20 years. He obtained School Research and Developments Excellence Award 2010, Highest Research Performance Incentive Award 2010, Best Researcher Award 2009, ANAK Sarawak Award 2009, and University Encouragement Award 1992. He completed several funded projects About the Contributors such as: Implementation of an Optimal Energy Saving System with solar tracker 2010, Development of Smart Drive Build in AC Motors for Optimal Operations 2010, Investigation of Electrical Properties of Palm Oil Using Kerr-effect Technique 2009, Hardware design of body sensor device 2008, Low cost hydrogen fuel cell for hybrid renewable energy system 2006, and Simulation of Micro-Controller for Induction Motor Drive 1995. Besides supervising many Master and PhD degrees, he selected several times as an external examiner and published over 86 papers in both international scientific journals and conferences. He is the President of Malaysian Solar Energy Society since 2010, Editor In Chief of Global Journal Of Technology and Optimization since 2010, General Chairman of an Annual Global Conference on Power Control and Optimization since 2008, and Guest Editor of International Journal Of Computers & Mathematics With Applications. Jeffrey Webb has a Ph.D. degree in photothermal physics from Strathclyde University, Scotland, U.K. He is now an Associate Professor in the School of Engineering, Computing and Science, Swin- burne University of Technology, Sarawak (Malaysia). His research experience is in the areas of optics, electromagnetic waves, ferroelectric materials, and nanoelectronics. * * * Muhammad Mansoor Asghar did his BSc Electrical Engineering from University of Engineering & Technology, Lahore, Pakistan in 2009. He is also student in MSc Electrical Engineering. Currently he is serving as Lecturer/Lab Engineer in Rachna College of Engineering & Technology, Gujranwala, Pakistan. He has published more than five international research papers. His research interests include power system analysis, renewable technologies, power electronics, et cetera. Adnan Bashir did his BSc and MSc Electrical Engineering from University of Engineering & Tech- nology, Lahore, Pakistan in 2006 and 2009, respectively. Currently he is serving as Lecturer in Rachna College of Engineering & Technology, Gujranwala, Pakistan. He has published more than three inter- national research papers. His research interests include power system analysis, renewable technologies, power electronics, et cetera. Roman V. Bershanskiy (M’ 2002) graduated from Moscow Power Institute as an engineer-electrician in 2002 and since that time has been working with Joint Stock Company “System Operator of Unified Energy System”, JSC, SO UES, Moscow, Russia. Now he is a postgraduate student at Energy Systems Institute, Russian Academy of Sciences, Irkutsk. His scientific interests are connected with real-time control problems, using FACTS and WAMS for control of power systems, detection of weak nodes, and cut sets. Hassan Bevrani received the M.Eng. (Hons.) degree from K. N. Toosi University of Technology, Tehran, Iran, in 1997, and the Ph.D. degree from Osaka University, Osaka, Japan, in 2004, both in electri- cal engineering. From 2004 to 2006, he was a Postdoctoral Fellow at Kumamoto University, Kumamoto, Japan. From 2007 to 2008, he was a Senior Research Fellow at Queensland University of Technology, Brisbane, Qld., Australia. From 2000, he has been an academic member of University of Kurdistan. Cur- rently, he is a Professor in Kumamoto University (Japan). His special fields of interest include intelligent 370 About the Contributors and robust control applications in power system and power electronic industry. Prof. Bevrani is a senior member of Institute of Electrical and Electronics Engineers (IEEE), and a member of the Institute of Electrical Engineers of Japan (IEEJ) and the Institution of Engineering and Technology (IET). Selcuk Cebi received his MSc degree on mechanical engineering from Karadeniz Technical University in 2004 and he received his PhD degree on industrial engineering from Istanbul Technical University in 2010. His academic career started in Karadeniz Technical University in 2002 as a research assistant until 2004. Then, he worked at Istanbul Technical University as a research assistant between 2005 and 2010. Now, he is working at Karadeniz Technical University as an Assistant Professor. Dr. Cebi has interests in decision support systems, multiple criteria decision making, and design topics, and he has over 20 publications in SCI indexed journals during his academic career. Muhammad Ali Masood Cheema was born in Gujranwala, Pakistan, in 1984. He did his BSc and MSc Electrical (Power) Engineering with Honours from University of Engineering & Technology, Lahore, Pakistan in 2008 and 2010, respectively. He was awarded two Gold Medals during his BSc in Electrical Engineering. He served in Pakistan’s largest transformer manufacturing company, PEL, for one year as Design Engineer. Currently he is serving as Lecturer in Rachna College of Engineering & Technology, Gujranwala, Pakistan. He has published more than twelve international research papers including IEEE PES, Springer Journal, and Elsevier Journal. His research interests include power qual- ity, electric machine design, control systems, power system analysis, distributed generation and load modeling, et cetera. Vo Ngoc Dieu received his B.Eng. and M.Eng. degrees in electrical engineering from Ho Chi Minh City University of Technology, Ho Chi Minh city, Vietnam, in 1995 and 1999, respectively, and his D.Eng. degree in energy from Asian Institute of Technology (AIT), Pathumthani, Thailand in 2007. He is Research Associate at AIT and lecturer at Department of Power Systems, Faculty of Electrical and Electronic Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam. His interest is applications of AI in power system optimization. Dmitry N. Efimov is a senior researcher in the Energy Systems Institute of the Russian Academy of Science (ESI SB RAS), Irkutsk, Russia. He was born in 1961 in Irkutsk. He graduated from Irkutsk State Technical University in 1987. Since then he has been with ESI SB RAS. He received his degree of Candidate of Technical Sciences from the ESI SB RAS in 1998. From 1998 till 2000, D.N.Efimov was an Executive Director of the International Research Energy Laboratory, Budapest, Hungary. His research interests include simulation of transients in electric power systems, development, operation, and dynamic properties of the large power interconnections. Alexander Z. Gamm graduated from the Electrotechnical Institute, Novosibirsk, Russia, where he received the Ph.D and D.Sc. degrees. During 1961-1962, he was a scientific worker in the Transport Power Institute, Novosibirsk. Since then, he has been with the Energy System Institute (ESI), Russian Academy of Sciences, Irkutsk. At present, he is a Chief Researcher. His special fields of interest include state estimation, optimization, and real-time control problems. Dr. Gamm is an Academician of the Rus- sian Academy of Electrical Sciences and member of International Energy Academy. 371 About the Contributors Anna M. Glazunova graduated from the Irkutsk Polytechnical Institute in 1982. Since 1986 she has been working as a researcher at Energy Systems Institute. She received her PhD in 2002. Her research interest is methods of state estimation of electricity use. Irina I. Golub (M’1995, SM’1997) graduated from Moscow Power Institute as an engineer-elec- trician. She has been working at Siberian Energy Institute, Irkutsk since 1972. Her scientific interests are connected with real-time control problems, especially in the field of observability of electric power systems and allocation of measurements of operating parameters of electric networks. She is a leading researcher, University Professor, and Doctor of technical sciences. U. Häger received his diploma degree in Electrical Engineering in 2006 from the Univ. of Dortmund, Germany. He is working at Technische Universität Dortmund, Institute of Power Systems and Power Economics, on his doctoral degree in the field of wide area congestion management by use of fast power flow controllers. Mahmoud-Reza Haghifam received his B.Sc., M.Sc., and Ph.D. degrees in 1988, 1990, and 1995, respectively, all in electric power engineering. Currently, he is the Full Professor of electrical engineering at Tarbiat Modares University, Tehran, Iran and worked on Electric Distribution Systems’ Reconfiguration during several essays and projects. He is a senior member of IEEE and research fellow of Alexander Van Humboldt, Germany. His research interest includes electric distribution analysis and planning, electric distribution system operation and automation, power system analysis and planning, development of soft computing and bio-inspired computing techniques for power system planning, power system reliability and reactive power control. Muhammad Junaid was born in Gujranwala, Pakistan, in 1981. He did his BSc, MSc Electrical (Power) Engineering with Honours from University of Engineering & Technology, Lahore, Pakistan in 2008 and 2010 respectively. Currently he is serving as Lecturer in Rachna College of Engineering & Technology (RCET), Gujranwala. He has published more than fifteen international research papers including IEEE PES, Springer Journal, and Elsevier Journal. He is also author of International Book Chapter titled “Harmonics Modelling & Simulation.” During 4 th Global Conference on Power Control & Optimization held in Malaysia, he was declared Best Presenter. Keeping in view his valuable research contributions, RCET has given him Best Research award. His research interests include power quality, power system analysis, power system operation & control, power electronics, et cetera. Cengiz Kahraman received his MSc and PhD degrees in industrial engineering from Istanbul Technical University. He is in the editorial board of some journals such as Journal of Human and Ecological Risk Assessment, International Journal of Computational Intelligence Systems, New Mathematics and Natural Computation, Journal of Enterprise Information Management, Technological and Economic Development of Economy, Baltic Journal on Sustainability, International Journal of Strategic Property Management, Journal of Multiple Valued Logic and Soft Computing, and he has made the guest editorships of special issues of some international journals such as Information Sciences, Journal of Enterprise Information Management, and International Journal Of Approximate Reasoning. He is the editor of such Springer books as “Fuzzy Applications in Industrial Engineering,” “Fuzzy Multicriteria Decision Making: Theory and Applications with Recent Developments,” and “Fuzzy Engineering Economics with Applications.” 372 About the Contributors Fouad Kamel is a Senior Lecturer at the University of Southern Queensland in Toowoomba, Faculty of Engineering and Surveying, Department of Electrical and Computer Engineering since February 2008. He graduated Diploma Engineer and PhD in photovoltaic systems from Hanover University in Germany 1984, Dr. Fouad worked as a Lecturer and Associate Professor at the Suez Canal University in Egypt during 1985-1999. In 1999, he moved to New Zealand and worked there between 2000 and 2007 for tertiary education and research at Christchurch Polytechnic Institute of Technology and the Southern Institute of Technology. Dr. Fouad has a history of publications in different renewable energy areas. Rana Abdul Jabbar Khan graduated from University of Engineering and Technology, Lahore, Pakistan in 1991. He completed ME from University of Wollongong, Australia in 1995 and PhD from RMIT University Melbourne, Australia in 2003. He has been serving as SDO and XEN in Water and Power Development Authority (WAPDA), largest organization of Asia, responsible for generation, transmission, and distribution of electricity country wide. Currently he is on deputation and serving Rachna College of Engineering and Technology (RCET) as Principal since 2005. He is principal author of an open access book chapter, titled “Harmonics Modelling and Simulation”. He is a senior member of IEEE, IEAust, IEE, and PEC. He has published several papers in IEEE journals. Honoring his valu- able research contribution he has been nominated for Presidential Award 2009 by the government of Pakistan. His research interest includes power quality, power system simulation, renewable technologies and deregulation of electricity, et cetera. İhsan Kaya is currently an Assistant Professor in Yıldız Technical University Department of Industrial Engineering. He received his MSc and PhD degrees on industrial engineering from Selçuk University and Istanbul Technical University, respectively. His main research areas are fuzzy set theory, process capability analyses, quality control, decision making, and fuzzy statistics. Irina N. Kolosok graduated from St. Petersburg Technical University. Since 1972 she has been with Energy Systems Institute (ESI), Russian Academy of Sciences, currently as a leading researcher. She received the PhD (1986) and DSc (2004) degrees. Her scientific interests are: real-time control prob- lems, especially in the field of state estimation of electric power systems (EPS), SCADA systems, and application of AI-methods for on-line EPS control. Elena S. Korkina graduated from Irkutsk Polytechnic Institute on speciality of an engineer-economist in 1978. Since 1987 she has been working at the Siberian Energy Institute of the Siberian Branch of Russian Academy of Sciences in the laboratory of electric power system operation control problems. Her scientific interests are: real-time control problems, SCADA systems, and up-to-date Information Technologies. Victor G. Kurbatsky (M’08) was born on May, 27th, 1949 in Russia. He is PhD, Professor, and Doctor of Science. He is Leading Researcher at the Energy Systems Institute of the Russian Academy of Sciences, Irkutsk, Russia. Victor Kurbatsky received his degree of Candidate of Technical Sciences at SibNIIE (Novosibirsk) in 1984 and Doctor of Technical Sciences at the Energy Systems Institute (Ir- kutsk) in 1997. His research interests include: electromagnetic compatibility and power quality in electric networks and application of artificial intelligence techniques in power systems. Professor Kurbatsky is the author of several monographs and manuals and more than 280 scientific papers. 373 About the Contributors Gerard Ledwich received the Ph.D. degree in Electrical Engineering from the University of Newcastle, Newcastle, Australia, in 1976. He has been the Chair Professor in Power Engineering at Queensland University of Technology, Brisbane, Australia, since 2006. Previously, he was the Chair in Electrical Asset Management from 1998 to 2005 at the same university. He was the Head of Electrical Engineering at the University of Newcastle from 1997 to 1998. Previously, he was associated with the University of Queensland from 1976 to 1994. His interests are in the areas of power systems, power electronics, and controls. Prof. Ledwich is a Fellow of the Institution of Engineers Australia (I.E.Aust.). Igor Litvinchev received his M.Sc. degree from Moscow Institute of Physics and Technology (Fizteh), Moscow, Russia, and Ph.D. and Dr.Sci. degrees in systems modelling and optimisation from Computing Centre, Russian Academy of Sciences, Moscow. He has held visiting positions at universities in Brazil, Mexico, as well as positions at various universities and research centres in Russia. His research focuses on large-scale system modelling, optimisation, and control. Dr. Litvinchev is a member of Russian Academy of Natural Sciences and Mexican Academy of Sciences. Marwan Marwan received the B.Eng. degree from Hasanuddin University, Makassar, Indonesia, and the M.Eng. degree from the Queensland University of Technology, Brisbane, Australia, in 2000 and 2006, respectively, all in electrical engineering. He is working at The State Polytechnic of Ujung Pandang Makassar Indonesia as a Lecturer in Energy Conversion Department from 2001 to the present. Presently, he is preparing Ph.D. at the University of Southern Queensland in Toowoomba, Australia. Armin Ebrahimi Milani received his B.Sc. degree (Electric Power Engineering) from Islamic Azad University, South Branch, Tehran, Iran, in 2006 and M.Sc. degree in Electric Power Engineering from Islamic Azad University, Science and Research Branch, Tehran, Iran, in 2010. He worked his thesis on Electric Distribution Systems’ Reconfiguration. Currently, he is with department of Electrical Engineering, Azad University, Iran. He is a member of IEEE and senior member of Young Researchers Club, Tehran, Iran. His research interest includes power system optimization and control, electric distribution systems, power system restructuring, development of soft computing and bio-inspired computing techniques for power system planning, operation, and control applications. J. Zambujal-Oliveira received M.S. degrees in Economics at New University of Lisbon (FE) and in Management Science at Technical University of Lisbon (ISEG). In 2007, he received a Ph.D. degree in Management Science from the Technical University of Lisbon (ISEG). Before coming to the Department of Engineering and Management at Technical University of Lisbon (IST), Prof. J. Zambujal-Oliveira was employed as a Systems Engineer at banks, insurance companies and consulting firms, and as an Assistant Professor of management at the University of Madeira in Funchal. Prof. J. Zambujal-Oliveira’s research interests include real options analysis and international taxation. In particular, he enjoys work- ing with graduate students and colleagues in developing, analyzing, and testing numerical methods for solving stochastic differential equations, developing and analyzing models in transfer prices systems and developing, analyzing, and testing computational methods in mathematical finance. Abdeen Mustafa Omer (BSc, MSc, PhD) is a qualified Mechanical Engineer with a proven track record within the water industry and renewable energy technologies. He has been graduated from 374 About the Contributors University of El Menoufia, Egypt, BSc in Mechanical Engineering. His previous experience involved being a member of the research team at the National Council for Research/Energy Research Institute in Sudan and working director of research and development for National Water Equipment Manufactur- ing Co. Ltd., Sudan. He has been listed in the WHO’S WHO in the World 2005, 2006, and 2007. He has published over 200 papers in peer-reviewed journals, 50 review articles, and 40 chapters in books. Weerakorn Ongsakul received his B.Eng. degree in electrical engineering from Chulalongkorn University, Bangkok, Thailand, in 1988, and his M.S. and Ph.D. degrees in electrical engineering from Texas A&M University, College Station, in 1991 and 1994, respectively. Currently, he is an Associate Professor of Energy Field of Study, and Dean of School of Environment, Resources and Development at Asian Institute of Technology (AIT), Pathumthani, Thailand. His interests are in computer applica- tions to power systems, parallel processing applications, AI applications in power systems, and power system deregulation. Alexei S. Paltsev graduated from Irkutsk State Technical University specializing in computer science in 2005. Since 2000 he has been with the Energy Systems Institute (ESI), Russian Academy of Sciences, currently as a leading Engineer. He finished his postgraduate courses at ESI in 2008. His scientific in- terests are multi-agent systems and EPS state estimation. Daniil A. Panasetsky (SM’07) is a postgraduate student at the Energy Systems Institute m of the Russian Academy of Sciences, Irkutsk, Russia. He graduated with honors from Irkutsk State Technical University specializing in electrical engineering in 2006. His research interests include stability analy- sis of power systems, emergency control, FACTS devices, and application of artificial intelligence to power systems. Dmitri B. Popov is a leading engineer of Energy Systems Institute (Siberian Energy Institute until 1997) of the Russian Academy of Sciences, Irkutsk, Russia. He was born in 1967 in Irkutsk. In 1984 he was granted the certificate in mathematical programming at the Institute of System Dynamics and Control Theory of Russian Academy of Sciences. In 1995 he graduated from Irkutsk State Technical University specializing in electrical engineering. D.B. Popov joined the Siberian Energy Institute in 1989. His research interests are transient stability analysis, database application development, users interface design, program interface development, asynchronous conditions, and prevention by customization of automatic equipment. Socorro Rangel received her M.Sc. degree from Campinas State University (UNICAMP), Campinas, Brazil, and Ph.D. degree from Brunel University, Uxbridge, England. She is currently an Associate Pro- fessor at the State University of São Paulo (UNESP), São José do Rio Preto, Brazil. Her main research interests lies on large-scale system modelling and optimisation. Christian Rehtanz received his diploma degree in Electrical Engineering in 1994 and his Ph.D. in 1997 at Technische Universität Dortmund, Germany. From 2000 he was with ABB Corporate Research, Switzerland and from 2003, Head of Technology for the global ABB business area Power Systems. From 2005 he was Director of ABB Corporate Research in China. From 2007 he is Professor and Chair 375 About the Contributors for power systems and power economics at Technische Universität Dortmund. His research activities include technologies for network enhancement and congestion relief like stability assessment, wide-area monitoring, protection, and coordinated FACTS- and HVDC-control. Mohammad Saleh received B.Sc. and MSc degrees in electrical engineering from Tarbiat Moallem University (Tabriz), and University of Kurdistan (Sanandaj), Iran, in 2007 and 2011, respectively. His current research interests include Grid integration of wind energy converters. Ghasem Tikdari was born on 1985 in Tikdar, Kerman, Iran. He received the B.S. degree from Bahonar University, Kerman, Iran in 2007 in Electronic Engineering and received the M.S. degree from University of Kurdistan, Sanandaj, Iran in 2009 in Electrical Power System Engineering. His research interests are on power system emergency control, renewable energy sources, artificial intelligence techniques, and electronic and power electronic device designing. He also experienced in some industrial works which use Distributed Control System (DCS), Supervisory Control and Data Accusation (SCADA), and field- bus communication protocols. Nikita V. Tomin, PhD, (M’08) was born on December 18th in 1982, in Russia. Dr. Tomin is a Senior Researcher at the Energy Systems Institute of the Russian Academy of Science, Irkutsk, Russia. In 2007 he defended his PhD thesis at the Energy Systems Institute SB RAS (Irkutsk). Dr. Tomin specializes in the field of artificial intelligence technologies in electric power systems. He is the author and co-author of more than 60 scientific papers. Nikolai I. Voropai (M’1996, SM’1998; F’2009) is Director of the Energy Systems Institute (Siberian Energy Institute until 1997) of the Russian Academy of Sciences, Irkutsk, Russia. He is also Head of Department at Irkutsk Technical University. He was born in Belarus in 1943. He graduated from Len- ingrad (St. Petersburg) Polytechnic Institute in 1966 and has been with the Siberian Energy Institute since. N.I. Voropai received his degree of Candidate of Technical Sciences at Leningrad Polytechnic Institute in 1974, and Doctor of Technical Sciences at the Siberian Energy Institute in 1990. His research interests include: modeling of power systems; operation and dynamic performance of large intercon- nections; reliability, security and restoration of power systems; development of national, international and intercontinental electric power grids. N.I. Voropai is a member of CIGRE, a Fellow of IEEE, and a member of PES. He is the IEEE PES Region 8 Zone East Representative. 376 377 Index Symbols 30 Cycle Network (Thirty-Cycle Network) 317, 333-334, 336, 343 3-Phase Faults 316, 343 A acid rain 103, 109, 121 active power fow 23, 25, 36 adaptive feasible mutation 356-357, 368 agricultural zones 108 Analytic Hierarchy Process (AHP) 166, 171, 173, 181-182, 186, 190-192, 194, 197 angle instability 294, 297, 301, 304, 306, 313 Ant Colony Optimization (ACO) 170, 186, 189, 195 Ant Colony Search Algorithm (ACSA) 59, 91 arithmetic crossover 349-350, 357, 368 Artifcial Intelligence (AI) 3-5, 13, 20-21, 54, 56, 59, 67, 80, 189-191, 193, 195-196, 269, 280, 345, 367 Artifcial Neural Networks (ANN) 21-23, 50, 166, 169, 176, 186, 189-190, 192-194, 294 B bad data 7, 9-10, 12, 22-23 binomial options pricing model 264 biomass energy 127-128, 135 boundary branch 16-18 boundary nodes 7-13 box agents 38 branch data 340 bus data 340 C calculated scheme 7-9, 12-13, 19, 50 capacitor data 340 capacity factor 138-139, 157, 198, 206, 219 Carbon Dioxide (CO2) 95-98, 100, 103-105, 108, 112-113, 120, 127, 136, 164, 181, 184, 251, 253, 255-260 carbon dioxide content 97 characteristic impedance 296, 298 Circuit Breakers (CB) 316-318, 331 climate change 100-101, 103, 108-110, 112-113, 121, 126, 129, 136, 162, 165, 178, 181 combined cycle 248-249, 253, 255, 259-260, 264 confguration 117, 195, 268-273, 283, 285, 287- 289, 292, 299, 301, 304, 343 consumption nodes 6 control system 2, 32, 34, 37, 43, 46, 50, 55-56, 203-204 Cost Effciency (CE) 96, 138, 242 critical cutest 297 current 5-7, 9, 13, 21, 24-25, 32-33, 35, 39-40, 43- 45, 49, 52, 87, 95-98, 126, 139-140, 147, 158, 163, 165, 185, 203-204, 231, 240, 254, 274, 315-316, 318, 322-328, 334-338, 340-342, 354, 366 current quality 341 D degree of satisfaction 348, 368 device duty 343 Differential Evolution (DE) 51, 59, 90-91, 169, 188, 206, 220, 243, 261, 312 Direct Load Control (DLC) 141 Discount Cash Flow (DCF) 248-249, 252, 255-259 Distribution Companies (DISCO’s) 315-316 Divandarreh 204-210 Double-Line Ground (LLG) 335-336, 343 Doubly-Fed Induction Generator (DFIG) 199-201, 203, 209, 215 drive train model 202 Dual-Input Power System Stabilizer Model (PSS2A) 209 378 Index E Earth energy 117 economic load dispatch 57-58, 88, 91, 93-94 electrical circuit 10, 163 electrical component 163 electrical energy 135, 137-138, 148-150, 156-158, 160-161, 187, 201, 210, 289, 291 electrical generation 163 Electrical Transient Analyzer Program (ETAP) 315- 322, 328-329, 331, 337-338, 340-341, 343 electrical vehicle 162-163 electric distribution network 287, 292 electricity network 145, 163, 200 Electricity Price (EP) 59, 90-91, 96, 140, 147, 149, 152-154, 159, 161, 163, 169, 206, 208, 249- 257, 259 electric motors 163 Electric Power Research Institute (EPRI) 140 Elimination and Choice Expressing Reality (ELEC- TRE) 171, 176, 184, 187-188, 194 emergency control 1-6, 20, 32, 34, 43, 46, 49, 51, 54-56, 214, 294, 297-298, 302, 310, 313-314 Emergency Demand Response Program (EDRP) 141-142, 158 Emerging Energy Technology (EET) 167, 169, 176, 185-186, 197 Enercon E-53 206 energy cost analysis 207 Energy Effciency (EE) 55, 96-97, 110, 112, 118- 120, 122, 124, 126-127, 129-130, 133, 145, 159, 162, 165, 181, 183, 192 energy function 44, 54, 57, 60-62, 65-67, 69-70, 74, 81, 88, 90, 94, 293-294, 297, 299, 311, 313 energy management 137, 154, 162-163, 263-264 Environmental Performance (EP) 59, 90-91, 96, 110, 159, 169, 206, 208, 253, 256 equal area criterion 51, 299 ETAP software 315-317, 337-338 Evolutionary Programming (EP) 59, 90-91, 96, 159, 169, 206, 208, 256 exergy 122-124, 188 F fast-decoupled method 340 Feeder Analyses (FDR-ANA) 315 Fixed-Speed Induction Generator (FSIG) 199, 209 Fixed Speed Wind Turbine (FSWT) 201, 217, 219 Florida Reliability Coordinating Council (FRCC) 307, 311 forecasting model 22 Fuel Constrained Economic Load Dispatch (FELD) 57, 72-73, 88, 94 functional decomposition 1, 7, 9, 13, 49 fuzzy logic 55, 59, 91, 166, 169, 188, 196, 344, 364, 367 fuzzy optimization 344, 346, 364-368 fuzzy sets 54, 188-189, 192, 196-197, 289, 344- 345, 364-366 fuzzy set theory 344, 366 fuzzy TOPSIS 171, 174, 188, 364 G Gaussian Filter 297 Gauss-Seidel Method 340 generalized assignment problem 220, 228, 243-246 generator agent 35-38 generator node 26-27, 30 Genetic Algorithms (GA) 21-22, 52, 59, 91, 128, 169-170, 176, 186, 189-190, 193, 269, 279- 281, 283, 288, 291, 344-351, 355-357, 359, 361-362, 364-365, 367-368 geothermal energy 117, 130, 133, 135 geothermal power 127, 129, 133, 135 global warming 95-98, 100, 103-104, 113, 127, 129, 133, 164-165 Graphical User Interface (GUI) 317 greenhouse effect 95, 97, 103, 113, 136 greenhouse gases 96, 108, 118, 127, 136, 165 ground grid analysis 316, 331, 343 ground grid systems 342 Gujranwala Electric Power Company (GEPCO) 315-316 H harmonic analysis calculation methods 341 Harmonic Analysis (HA) 315-316, 322, 328, 341 Heating, Ventilating and Air-Conditioning (HVAC) 96 historical volatility 254-255, 257, 264 hopfeld lagrange network 57, 61-62, 64, 94 Hopfeld Neural Network (HNN) 57, 59-61, 69, 80, 84, 90-94 Human Machine Interface (HMI) 303 Hybrid GA Pattern Search (HGAPS) 348, 359, 361-362 hybrid genetic algorithms 344, 346, 367 hydropower 135 hydrothermal economic load dispatch 88, 94 379 Index I Individual Harmonic Distortion (IHD) 322, 341 Indoor Environmental Quality (IEQ) 96-97 induction motor data 340 information axiom 166, 171, 175-176, 188, 191, 196-197 Integrated Gasifcation Combined Cycle (IGCC) 259-260 interconnection 3, 20, 43-44, 200 inverter data 340 Iran 198-199, 201, 213, 216, 268, 293, 311 islanding control 294, 297, 306, 314 J Jacobi matrix 24-27, 29-30 JADE platform 38 K kinetic energy 43, 135, 213, 297, 304, 306 Kurdistan Electric Network 198-199, 209, 216 kyoto protocol 100-101, 125 L Lagrangian dual 220-222, 225, 228-230, 237, 242, 246-247 Lagrangian dual problem 222, 237, 246-247 Lagrangian function 57, 59, 61-62, 67, 74, 88, 90, 94, 221, 241-242, 246 Lagrangian heuristic 242, 244, 246 Lagrangian multipliers 62, 228, 233, 242, 246 Lagrangian relaxation 59, 61, 94, 221, 225-227, 245-247 Lagrangian relaxation bounds 246 large scale power grids 295 Levelised Cost of Electricity (LCOE) 205, 207-208, 219 lignocellulosics 113 Line-Ground (LG) 335-336, 343 Line-Line (LL) 335-336, 343 load agent 36-37 load fow 13, 15-16, 19, 23, 26, 52, 54, 91, 273- 277, 283, 289-292, 315-316, 321-322, 337-338, 340, 342 load fow analysis 315-316, 321, 340 load fow calculation methods 340 load shedding 34-37, 40, 43, 45-46, 214, 294, 297- 298, 302-303, 307, 310-312, 314 localization 223-228, 241-242, 244 lumped load data 340 M MACBETH 177-178, 187 many-to-many assignment problem 222, 227, 246 market conditions 109, 137, 163, 248-250, 257 Market Introduction of New Energy Technologies (EMINENT) 184, 195 Master Problem (MP) 226-227, 229-230, 240 maximal cost component 231 Maximum Power Point Trajectory (MPPT) 188, 202-203 meta-heuristic methods 59 modifed Lagrangian bounds 220, 222, 236 monitoring 1-6, 8, 20-21, 23, 49-54, 56, 121, 124, 127, 302, 312-313, 315-316, 318, 321-323, 328, 337-338 Monte Carlo simulation 250, 252, 261, 264 multi-agent systems 1-2, 51, 53 Multi Attribute Decision Making (MADM) 171, 197 Multi Criteria Decision Making (MCDM) 166, 171, 176-179, 185-186, 188, 190, 194, 197 Multi Objective Decision Making (MODM) 171, 192, 197 N Natural Gas Combined Cycle (NGCC) 253, 259 Natural Gas (NG) 97-99, 114, 187, 251, 253-259, 261-262, 264, 275, 304 neural network 2, 21-23, 57, 59-65, 69, 75-76, 80, 82-85, 88, 90-94, 187-188, 190-191, 193, 195 Newton-Raphson Method 340 nodal admittance matrix 25-26 nodal voltages 9, 12, 24-26 Nonlinear Programming (NLP) 344, 346, 348, 364 Nordex 77 206 North American Electric Reliability Corporation (NERC) 6 O objective copy constraint 236, 238, 241 on-site renewable energy 145, 157-158, 163 operating control 1, 200 operational management 2 optimal ftness function 356 optimal primal-dual pair 221, 241 optimization problem 34, 58, 60, 62, 65, 77, 94, 195, 220-222, 269, 273, 279, 283, 285, 288, 292, 346-348 380 Index organic sulphur 113, 130 P Pakistan Electric Power Company (PEPCO) 315- 316 Particle Swarm Optimization (PSO) 59, 90-92, 169 pattern search 169, 344, 348, 357, 365, 367-368 Permanent Magnet Synchronous Generator (PMSG) 199, 201, 203-204 Phasor Measurement Units (PMUs) 2, 7-14, 16-19, 47, 53, 294, 303, 306-307, 310 power factor 203, 211, 315, 321, 337 power grid data 340 power system control 2, 33, 52-53, 199, 218, 310 power system dynamic stability 1 power system stability 44, 51, 198, 212, 218, 293- 295, 298, 303, 310-312, 316, 342 power system voltage 37, 341 Preference Ranking Organisation Method for En- richment Evaluations (PROMETHEE) 171, 188 Probability Density Function (PDF) 159, 161, 275- 279, 283-286, 292 protection 4, 32-34, 43-44, 53-54, 97, 121, 128-129, 131-133, 270-271, 295, 298, 312, 338 Q quadratic programming 61, 90-91, 93 R Rachna College of Engineering & Technology (RCET) 316 radial schemes 15-16, 18-19 reactive power fow 315, 337 Real Options Analysis (ROA) 248-250, 253, 256, 258-260, 264 Reconfguration 109, 268-273, 286-292 regional electric network 198 Reliability Test System (RTS-79) 294, 304, 308, 311 renewable energies 95-97, 101, 117, 126, 198, 201 renewable energy 3, 95-96, 99-102, 106-107, 117- 118, 122-129, 132-133, 135, 137, 144-145, 150, 157-158, 160, 162-163, 165, 176-178, 184, 187-191, 193-195, 198-199, 214-217, 289, 293, 309, 311 resource management 121, 135 risk-adjusted discount rate 251-252, 255, 264 Root Mean Square (RMS) 341, 343 S Sanandaj power plant 209-210 short circuit analysis 316, 333, 343 sigmoid function 60-63, 68-69, 82, 90, 94 Simple Additive Weighting Method (SAW) 171 Simulated Annealing (SA) 10, 22, 59, 91-92, 131, 134, 169-170, 269, 365, 367 slow coherency 294, 297-298, 301-302, 312, 314 smart grid 3, 51, 54, 137, 139, 144-146, 160-163, 312-313 Soft Computing (SC) 92, 164, 166-169, 171, 176- 178, 185-188, 191, 194-197, 365, 367 solar energy 97, 117, 135, 158-160, 162, 188-190, 194 spark spread 250, 263-264 stability assessment 293-294, 298-299, 301, 309, 312 stability limits 199, 294, 298, 328, 341-342 STATCOM-based control approach 198 State Estimation (SE) 1, 5-10, 12-14, 16-19, 21, 34, 49-53, 55-56, 255 state variables 2, 6, 13, 21-22, 25, 35, 44, 47, 50, 275, 298 static load data 340 static power converters 341 Static Synchronous Compensator (STATCOM) 198- 199, 211-212, 214-219 steady-state stability limit 26, 342 stratospheric ozone 95, 103 subgradient technique 220, 222, 233, 239-242 surrogate localization 225, 227 sustainable development 95-96, 100, 104, 106, 110, 120, 122-124, 128-129, 131-135 switch 147, 163, 250-251, 268-269, 272-273, 285, 292 switch types 268-269, 272-273, 292 synchronous generator data 340 synchronous motor data 340 T Tabu Search (TS) 59, 91, 124, 166, 169, 171, 186, 189, 289 Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) 164, 166, 171-172, 174, 184, 188-189, 194, 196-197, 364 tie-lines 7, 304 Total Harmonic Distortion (THD) 337 trace metals 108 transfer function 63, 68-69, 94, 169 381 Index transient stability 44-46, 209, 211, 214-216, 218, 295, 297, 299, 313, 317, 328-329, 337-338, 341-342 transient stability analysis 215, 313, 328-329, 341 transient stability limit 342 transmission system 32, 35, 37, 60, 90, 150, 163, 270, 337 Two-Dimensional (2-D) 296-297, 301 U uncertain coeffcients 368 Under Frequency Load Shedding (UFLS) 307 Uninterruptible Power Supplies (UPS) 43, 51, 340- 341 V vagueness factor 348, 352, 356, 359-360, 368 Variable Speed Wind Turbine (VSWT) 201-203, 218-219 VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) 171, 191, 194 voltage magnitudes 7, 10, 13, 16, 273, 298 W WAMS (Wide-Area Measurement System) 7-8, 21 water privatisation 107 Weibull Distribution 198, 219 Western European Union for the Coordination of Transmission of Electricity (UCTE) 6, 43, 45 wholesale markets 5 wind energy 130, 135, 189, 198-202, 204, 210, 213-219 wind farms 198-200, 209-211, 214-218 Wind Power Systems (WPSs) 199-200, 207-208, 210, 212-214, 219, 310 wind rose diagram 204, 219 World Energy Council (WEC) 96-98, 130, 132