IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO.4, NOVEMBER 2007 2249 Transmission Expansion Planning Using Contingency Criteria Jaeseok Choi, Senior Member, IEEE, Timothy D. Mount, and Robert J. Thomas, Fellow, IEEE Abstract—This paper proposes a methodology for choosing the best transmission expansion plan considering various types of security (operating reliability) criteria. The proposed method minimizes the total cost that includes the investment cost of transmission as well as the operating cost and standby cost of generators. The purpose of the study is development of new methodology for solving transmission system expansion planning problem sub) contingency criteria which are essentially extenject to (N sions of the (N-1) contingency criterion. The transmission expansion problem uses an integer programming framework, and the optimal strategy is determined using a branch and bound method that utilizes a network flow approach and the maximum flow-minimum cut set theorem. The characteristics of the proposed method are illustrated by applying it to a five-bus system and a 21-bus system. The results of these case studies demonstrate that the proposed method provides a practical way to find an optimal plan for power system expansion planning. Index Terms—Branch and bound method, investment cost, operating cost, security (reliability) criteria, standby cost, transmission expansion planning. I. INTRODUCTION RANSMISSION expansion planning with open access to the grid has become a hot issue in the electric utility industry in recent years [1], [2]. The recent blackouts that have occurred in countries worldwide suggest that more reliable grid structures may be needed to establish successful deregulated electricity markets. These incidents call for the development of new tools that can address system uncertainties and significantly enhance the effectiveness of transmission planning [3], [4]. However, the basic objective of strengthening a transmission grid is relevant for most countries. T Manuscript received December 13, 2005; revised July 24, 2007. This work was supported in part by the Consortium for Electric Reliability Technology Solutions (CERTS) program in the U.S. Department of Energy through the Power System Engineering Research Center (PSERC), Cornell University, Ithaca, NY, and in part by the Electrical Power Reliability/Power Quality Research Center (EPRRC), Ministry of Commerce, Industry and Energy (MOCIE), Korea. The supporting parties are not responsible for any conclusions and remaining errors. Paper no. TPWRS-00799-2005. J. Choi is with the School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850 USA, and also with the Department of Electrical Engineering, ERI Gyeongsang National University, Chinju, Korea (e-mail:
[email protected];
[email protected]). T. D. Mount is with the Department of Applied Economics and Management, Cornell University, Ithaca, NY 14850 USA (e-mail:
[email protected]). R. J. Thomas is with School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14850 USA (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2007.908478 Transmission expansion planning addresses the problem of augmenting an existing generation and transmission network to optimally serve a growing electric load while satisfying a set of economic and technical constraints. The problem is to minimize the cost of expansion subject to the constraints needed to meet an explicit reliability level [5]. Various techniques, including branch and bound, sensitivity analysis, Bender decomposition, simulated annealing, genetic algorithms, tabu search, and greedy randomized adaptative search procedure (GRASP), have been used to study the problem [6]–[15]. Since it is difficult to obtain the optimal solution for a realistic system considering both generators and transmission lines simultaneously, transmission expansion planning is usually performed after generation expansion planning. Typically, deterministic reliability criteria such as the (N-1) or (N-2) contingency criteria and load balance constraints are used in practice for transmission expansion planning because they are computationally tractable [16]. In a typical power system planning problem, adequacy or security standards may be used initially in order to select the reasonable plans from draft scenarios suggested from the view point of strategic policy is called a first macro stage. More detail technical analysis, which is mainly contingency analysis, fault analysis, and stability analysis, are applied in order to check the engineering feasibility of the plans. This is called a second micro stage. The conventional work procedure for power system planning is shown in part A of the Appendix. A deterministic reliability criterion such as load balancing constraints (adequacy) is often used in the first stage. This paper proposes a methodology for choosing the best transmission expansion plan using an adequacy-based security contingency criterion [17] done criterion based on an by eliminating contingencies with probabilities lower than a prescribed probability limit. An contingency is a single contingency with simultaneous component failures. This objective function considers construction (investment) costs, operation/production costs, and generator standby costs [18], [19]. An assessment of congestion costs, caused by the non-coherency characteristics of generators on a grid and conflicting situations occurring under deregulation, may be considered because the operation/production cost of generators is included in the objective function [20], [21]. However, congestion rents and the shadow prices of transmission are not considered because the focus of this paper is on evaluating different contingency/security criteria for transmission expansion planning rather than on evaluating market designs. The transmission expansion problem in this paper is modeled in an integer programming framework [22]–[24], and determines the 0885-8950/$25.00 © 2007 IEEE the with with sum of the capacities of the first ckt through the th ckt connecting buses and . In general. Specifically A composite power system that includes generation and transrefers to the transmismission facilities is shown in Fig. Consequently. This paper considers production cost instead of the transmission line loss cost for the . NO. Fig. In the case of a competitive electricity market environment. A. A composite power system is designated as hierarchical level II (HLII) in this paper. can be (2) where set of all transformers and transmission lines. and is the number of load points. where construction cost of the th ckt connecting buses and . NOVEMBER 2007 construction costs of new lines and transformers. Some generators such as solar or wind power may be sited at a load point. II. VOL.2250 IEEE TRANSACTIONS ON POWER SYSTEMS. decision (integer) variable associated with the ckt connecting buses and (1 if the first ckt to the th ckt lines are to be constructed. or independent system operator (ISO). formulated as [18]. 1. Therefore. Fig. 22. optimum mix of additions to a transmission network using a branch and bound method based on a network flow approach and the maximum flow-minimum cut set theorem [25]–[29]. HLI is used to designate generation and load components only [30]. which are represented as nodes (points to which branches are connected in a network). Objective Function The conventional definition of cost in transmission expansion planning is to minimize the total construction costs plus the operating costs. capacity of the th ckt connecting buses and . Consequently. sion system. is the number of generators. TRANSMISSION EXPANSION PLANNING PROBLEM sum of construction costs of the first ckt through the th ckt of the new transformers and lines connecting buses and . offer-based operating (production) cost is calculated as the energy produced times the true marginal operating cost for each generator in this . [19] . stricter reliability criteria are expected to increase the construction cost because additional transmission lines will be required in order to increase reliability. This paper proposes a new definition of the total cost that includes the construction cost associated with investing in new transmission lines. which are represented as branches (segments connecting nodes) in a network model. (see parts A and B of the Appendix). as expressed in (1). 1. and the standby cost of generators. number of circuits (ckt) of new candidate branches (segments connecting nodes in a network) connecting buses and . 4. A network model and network flow method that neglects line loss are used in this paper [25]. Therefore. In this paper. a standard merit order method is used to evaluate the operating cost. or grid reliability committee will want to consider the problem of searching for a better plan from the point of view of a generation company (GENCO) as well as the grid owners. a grid owner. the objective is to minimize the total cost given by (1) 1) Construction Cost: The total cost of construction is the summation of the construction costs of new elements. and 0 otherwise). 2) Strategic Bidding-Based Operating (Production) Cost: Operating cost based on locational marginal prices (LMPs) in a competitive electricity market could also be evaluated. however. the operation/production cost . it is assumed that generator offers are based on their true marginal costs because this paper is focused not on LMPs but rather on the effects of various types of contingency criteria. Composite power system with nodal load duration curves. is the load duration curve at load bus. [31]. 1 illustrates the situation. 2. Constraints Fig. the standby cost is expected to decrease because the grid will have more flexibility for delivering energy. Fig. is the capacity of the minimum cut-set of the two subsets and containing source node and terminal node . study period time [hours]. at load bus . 3) Standby Cost: In some situations. a no-shortage of power supply constraint can be expressed as follows [12]–[15]: (5) where variable for real power [MW]. B. The standby cost of generators. In a security constraint approach to adequacy. is the bus reserve/ marginal rate at load bus .CHOI et al. the criterion of no-shortage of power supply requires that the total capacity of the branches in the minimum cut-set under contingencies should be greater than or equal to the total load. and are the maximum arrival power and peak load. Deterministic operating/production energy of x-generator on load duration curve at k load bus. The demand constraint (5) can be expressed as maximum arrival of power delivered from generator to load bus [MW]. marginal operating cost of generator [$/MWh] Here. meeting load requires that the total capacity of the branches (segments connecting nodes in a network) in a minimum cut-set should be greater than or equal to the total load . Once again. . Therefore. respectively. . A reasonable payment (cost) for standby by a generator should. This is also referred to as the bottleneck capacity. The operating cost is formulated as (3) at the bottom of means the total arrival capacity at the the page. Therefore. when all nodes are separated by a minimum cutset. respectively. This is also referred to as the “bottleneck” capacity. reserve generating capacity of generator [MW]. This generator is not shutdown but is operated on a standby (reserve) basis to maintain the reliability of the power system. is formulated as (4) (6) where is the cut-set number and is the number of cut-sets. is the peak load at load bus . including the reserve rate. where th-load bus after generators #1 to # are loaded and 1) Minimum Cut-Set Flow Constraint: In a general deterministic approach. 2 shows the deterministic production of energy by generator at load bus using the merit order method (8760[hours] is used for T in the case studies). load duration curve at load bus . a generator may be committed but may not produce electrical energy to balance the load in real time. the constraint of no-shortage of power supply under contingencies can be expressed by (8) [2] (7) (3) .: TRANSMISSION EXPANSION PLANNING USING CONTINGENCY CRITERIA 2251 where marginal standby cost of generator [$/MWh]. be paid (called the standby cost in this paper). paper. which is defined as . merit order number of a generator. therefore. if a stricter reliability criterion is required. set of branches included with Therefore. Note that the summation of flows at all nodes except the source and terminal nodes in (10) is always zero by Kirchhoff’s first law [23]. from (source) to (terminal) in branch set. with a maximum of “ ”’ elements failing. it is necessary to evaluate whether or not the power flows under contingencies satisfy the peak load. etc. The under the security criterion system probability is formulated as [17]. is limited with a nonnegative real (transmission line) that is called the transmission line capacity (ratnumber ings) from node to node . III. the “ ” criterion considers contingencies in which one element fails out of “N” elements (generators. real power flow on the branch between nodes and . This problem can be solved by linear programming (LP). and . The maximum power flow using branch set under contingencies can be calculated by an LP. It can be bottleneck capacity under expressed as follows using the maximum flow minimum cut-set theorem [25]: set of branches not included with contingency. are proposed. the system security probability security criterion is formulated as (11) contingency. ALTERNATIVE TYPES OF CONTINGENCY CRITERIA (9) where set of security systems existing within the probability limit under contingencies. to use a security criterion stricter than (N-3) contingencies requires a substantial amount of computation for a realistic system. the actual occurrence of a deep contingency has a very low probability.01 and 500 lines each if the outages are mutuhaving a FOR of 0. 22. 4. IV. respectively. NO. For example. branch (generator and line) capacity between nodes and .). [25] (10) where flow under contingencies. the method used in this paper is to eliminate all contingencies with probabilities (Note that lower than a given probability limit was used in the case studies presented later in the paper. The criterion can be categorized in terms of the outage number. under contingencies can be formulated as a linear optimization problem in (10) [22]–[29]. .).2252 IEEE TRANSACTIONS ON POWER SYSTEMS. set of branches/lines under total load contingency. . respectively. the three types of contingency criteria. where describes the depth of the contingency. The maximum static power flow. In other words. by considering outages of selected elements only) is necessary in order to make deep contingency criteria practical. Based on this principle. defined in Table I. [33] (8) where forced outage rate of element (generators and lines). the occurrence of an (N-6) contingency in a power system with 100 generators each having a forced outage rate(FOR) equal to 0. Second. NOVEMBER 2007 where depth of a contingency. 2. In a contingency analysis. This is the solution to the shortest path problem to determine the contingencies [25]. In this paper.001 is less than ally independent. The power flow in the network of each arc This paper proposes various new kinds of contingency criteria. . when all nodes are separated by a minimum cut-set contingencies. VOL. This type of rare contingency can be ignored for planning purposes. lines. for the where under is the maximum power flow for branch set contingencies. First. transformers and switching gear. the “ ” criterion considers all possible contingencies with depths 1. MAXIMUM FLOW UNDER CONTINGENCY ANALYSIS FOR SECURITY CONSTRAINT In order to consider the security constraints from the view point of adequacy in this study. capacity of the minimum cut-set of two subsets ( and ) containing source node and terminal node . Development of a modified or simplified method (for example. set of nodes connected with a source (or terminal) node. under 2) Security State Probability Constraint: Generally. the “ ” criterion considers all possible contingencies for generators as well as all possible contingencies for transmission lines up to a maximum elements failing. transmission lines. if set . The “NN” column is the ckt of elements (generators or lines). If not. 7) If the . where represent the generators. . 3. 1) Check the “need” for transmission expansion for the system and the “possibility” of meeting load using the candidate lines. the parentheses for and are omitted for convenience. . In what follows. 3. 3. Case Study I: Five-Bus System The method presented in Section V was applied to a five-bus sample system. and it is called a Branch in a solution graph. the new system is named the system. In Table II. 6) If the system has already been considered in the solution graph. The cost unit. Otherwise. Fig. 600 MW and 650 MW at load bus 2. Transmission companies (TRANSCOs) should respond to this decision by generators and determine how to strengthen the grid in order to deliver the electrical energy reliably to meet the higher load. 5) Select a branch/line of the candidate branches/lines set in the minimum cut-set and add it to the system. CASE STUDIES A. Table III shows the forced outage rates of the generators and transmission lines. and are the start and end buses of a line. and . Otherwise. The proposed solution algorithm uses the following steps. 4 shows the inverted load duration . 12) Set 13) Add this solution to the solution graph. the solution graph has been constructed 16) For has the lowest cost fully and the optimal solution . and go to step 13. shown in Fig. is the maximum number of branches that should be searched in a solution graph. This initial system satisfies at least the (N-3) contingency criterion. 9) If . and are the capacity and cost of the existing line that connects nodes and . appearing in (2) and (6).CHOI et al. have 14) If all the candidate branches/lines in the cut-set been considered. . Five-bus sample system (present year). 3) If . the “ ” criterion considers all possible contingencies for generators combined with all possible contingencies for transmission lines up to a maximum of elements failing. go to step 15. and loads. . three candidate lines are considered. set and go to step 5. where is a parameter of the optimal solution in a solution graph for the branch and bound. The TRANSCOs identify the candidate elements for con. 4) Calculate the minimum cut-set using the maximum flow method for system ( solution in the solution graph). branch and bound. is a parameter that indicates whether a branch can be terminated in a solution graph (If it is 1. and . 8) Calculate the total cost for the system and evaluate the security level of the system. These can be checked for a given reliability criterion by considering the system with no candidate lines and with all candidate lines. 11) Check the security criterion. . . and go to step 14. Fig.). VI. set 15) If and go to step 4. Since the branch and bound method has significant merit for problems with many constraints. In this study. with 1530 MW of generation capacity and 900 MW of peak load.: TRANSMISSION EXPANSION PLANNING USING CONTINGENCY CRITERIA TABLE I ALTERNATIVE DEFINITIONS OF (N 2253 0 ) CONTINGENCIES (where. respectively. SOLUTION ALGORITHM The proposed integer programming problem for transmission expansion planning could be solved by any one of implicit enumeration. V. and it also satisfies the required security criterion in step 11. respectively. continue to the next step. the system is an end node at which the branch operation of branch and bound is finished (bound) in a solution graph. . After ten years. It is assumed that all generators have decided to increase existing generating capacity by 50%. it is forecasted that loads will increase from the initial level of 300 MW to 550 MW. or the Gomory cutting planes methods [22]. and 4. and structing new lines shown in Table II. there is no need to consider any of the other graphs following the system. . 10) Set . M$ in this table stands for millions of dollars. go to step 14. . go to step 12. Go to step 13. 2) Set (initial system). respectively. the current system ( ) with a cost of may be optimal. go to step 14. the branch is bounded. G and T present generators and transmission lines) Third. In this situation. it is used in this paper. 4. it is interesting to note that although the marginal cost of the generator at bus 5 is the lowest. The reason for this is that the delivery capacity of the grid is still TABLE V CONFIGURATION OF ENERGY DELIVERED FROM GENERATORS TO LOADS FOR THE NEW SYSTEM OF CASE 1 [(N-1) CONTINGENCY]: [GWh/YEAR] limited for generator #5. VOL. 5 and 6 show the optimal systems for the (N-1) and (N-2) criteria. part of this generator’s capacity should be operated on standby and the standby cost (22. Optimal system under (N-2) contingency security criterion (case 2). it is interesting to see that Cases 4–6 have higher costs than Cases 1–3. and operating cost for the optimal system using the (N-1) criterion are shown in Tables IV–VI. (a) Bus 2. 22. From these tables. energy delivered. . For example. 4. FUTURE LOAD AND CAPACITY. even though a new line is constructed in the optimal plan. Configurations of the power dispatched. (8 ) at the load buses. Optimal system under (N-1) contingency security criterion (case 1). 5. as the contingency/security criterion gets stronger. the bus reserve rate in (5) is set to zero.2254 IEEE TRANSACTIONS ON POWER SYSTEMS. respectively) TABLE III OPERATING AND STANDBY MARGINAL COSTS OF GENERATORS AND FOR Fig. the grid expansion problem is “what is the optimal/best line choice (solution) with the minimum total cost under a security criterion constraint for the increased load?” Initially. . for Cases 1–15. Table VII shows the components of cost for the optimal expansion plans for different contingency criteria. Inverted load duration curves 3. respectively. and the total cost is higher. NOVEMBER 2007 TABLE II NEW GENERATION CAPACITY. Therefore. NO. (c) Bus 4.776[M$/year]) should be paid to the generator’s owner. Figs. 6. (SB #0 and EB #6 represent source and terminal nodes. respectively. Case 0 corresponds to an (N-0) criterion that meets only the constraint to balance load. TABLE IV CONFIGURATION OF POWER DELIVERED FROM GENERATORS TO LOADS FOR THE NEW SYSTEM OF CASE 1 [(N-1) CONTINGENCY]: [MW] Fig. and the effects of setting are evaluated in Cases 16–18. where the dotted line and bold number represent the new construction of generators and lines. The results show that the number of new construction elements increases. AND COST DATA ) AND OF SYSTEM CANDIDATE LINES ( 1P( ) : (MW) 1C( ) : (M$) Fig. (b) Bus curves at the load buses for the higher forecast loads. However. The security probability is lower for Case 10 because fewer contingency events are considered compared to Case 6. OC : operating cost. SC : stand by cost) respectively.397[M$/year] for (N-2) and (N-3) contingencies. The following inequalities can be determined from the reis the total cost for contingencies.456[M$/year] and 166. For example. as expected. In general. Cases 11–15 are omitted for convenience because the costs are identical to Cases 1. this does not mean that it is necessarily the most reliable. while the operating cost is 199. Testing (N-4) contingencies for the five-bus system failed because the candidate lines cannot support a feasible solution. respectively. where and show. as the security criterion gets stronger. the investment cost increases substantially while the operating cost decreases slightly.99995) was obtained for Case 6 [(N-3G-3T) contingencies]. The highest security probability (0. that the deeper contingency criteria require higher total costs for transmission expansion planning: (where CC : construction cost. and the results are shown in the last column of Table VII. Costs variation due to security criterion types (cases). 8. Security criteria using composite contingencies of the type generally require higher total costs than the simpler criteria using contingencies. 4.CHOI et al. sults. and 3. it is 171. The expansion plans for Case 10 [(N-2G-3T) contingencies] and Case 6 [(N-3G-3T) contingencies] are identical. 2. These characteristics do not always hold because of the non-coherency of the composite power system. The security probabilities for all contingency criteria were evaluated. Cases 7–10 present results using the more complex criteria of contingencies.: TRANSMISSION EXPANSION PLANNING USING CONTINGENCY CRITERIA TABLE VI CONFIGURATION OF OPERATING COST FROM GENERATORS TO LOAD FOR THE NEW SYSTEM OF CASE 1 [(N-1) CONTINGENCY]: [M$/YEAR] 2255 TABLE VIII ALTERNATIVE SECURITY CRITERIA RANKED BY TOTAL COST (FIVE-BUS SYSTEM) TABLE VII OPTIMAL EXPANSION PLANS AND COSTS USING ALTERNATIVE SECURITY CRITERIA (FIVE-BUS SYSTEM) Fig. Although the (N-3G-3T) criterion has the highest security probability. 7. 7 shows how the components of total cost vary for the different security criteria.281[M$/year] for (N-1) contingencies. Fig. respectively. Table VIII ranks the security criteria according to the total cost. because congestion costs are lower when the grid is more flexible. Cases 11–15 present results for contingencies. It is interesting to note how much the operating costs decrease with the stronger contingency criteria. and they are both equally reliable. the ranking of the security criteria in . defined in (5) and below in (12). B. One alternative criterion uses the bus reserve rate index . In Cases 16–18. at load bus . (b) ILDC at bus 2. Inverted load duration curves at the buses with the four largest loads. After specifying a forecast of the future system load. (a) ILDC at bus 17. VOL. the alterative criteria were applied and the results compared [15]. Using the criterion with (N-1) contingencies in Case II-1. 7 is based on the total cost. the basic criterion is (N-1) contingencies. The basic objective is to provide additional intermediate criteria between (N-2) and (N-3) contingencies. and this is not necessarily the same as ranking the level of reliability. Fig. respectively. Fig. 9. 4. (d) ILDC at bus 13. Therefore. (c) ILDC at bus 21. The deterministic reliability (reserve) constraint for a specified load bus increases when Fig. to represent situations in which customers at a particular load bus ask for additional reliability. Table IX shows the results for three case studies using the modified security criterion. [19]. The optimal expansion plan has a total cost of 1. (12) where is and and are the maximum arrival power and peak load. the step from (N-2) to (N-3) contingencies may be too ambitious because meeting an (N-3) criterion is too expensive and computationally demanding for real systems. NO. Fig. the modified constraint in (12) with can be used as an alternative criterion to give greater reliability than the simple criterion of (N-1) contingencies. and in addition. 9 shows the inverted load duration curves for the four largest loads. In practice. Case Study II: 21-Bus System The proposed reliability criteria were also tested on the 21-bus system shown in Fig. Comparing the results in Table IX with Case 1 in Table VII shows that more candidate lines are connected directly or indirectly with load bus when . respectively.254. The marginal operating costs. and the capacity and construction costs are shown in Tables XVI –XVIII.81[M$] and the new transmission lines are . NOVEMBER 2007 TABLE IX OPTIMAL EXPANSION PLANS BY COMBINING AN (N-1) CONTINGENCY CRITERION WITH BRR = 20 AT BUSES 2–4 (where BRR = (AP 0 L ) 2 100=L ) Fig. for example. of part C of the Appendix. The 21-bus model system. the forced outage rates.2256 IEEE TRANSACTIONS ON POWER SYSTEMS. when the former is considered too weak and the latter too strong. 8 that is part of the grid in the southeastern region (Youngnam) of Korea. respectively. 22. 8. at load busses 2–4. This paper evaluates a number of modified contingency/security criteria as alternatives to the standard criterion of contingencies. 10 shows the new system with the dotted lines presenting the three new lines that were required to meet reliability and the higher forecasted load. 11. 2257 Fig. . The optimal expansion plan in Case II-2 has a total cost of 1. . It also implies that the initial system in Fig. The table shows also . This suggests that transmission lines may be more important than generators for maintaining reliability in this particular system. 10. 8 has a transmission system that is relatively weak given the amount and location of installed generation capacity. and . and Fig. . Comparing Cases II-1 and II-2 in Tables X and XI. Optimal system by the N-2 security criterion approach (case II-2). Therefore. This ranking is consistent with the results for the five-bus system in Table VIII and shows that the following inequalities hold. Evaluating the relative importance for system reliability between adding new transmission lines or new generators to a given system is an interesting topic for future research. .: TRANSMISSION EXPANSION PLANNING USING CONTINGENCY CRITERIA Fig. and G20 are substantially different. . 11 shows the new system. even though the total generation and the total reserve capacity remain unchanged. and . the distributions of both generation and reserve capacity change when the reliability criterion changes. 8 (Case II-2). Table XII shows a summary of the components of the total cost of the optimal expansion plans using different security criteria.81[M$]. Table XIII summarizes the results in Table XII by ranking Cases II-0 through II-7 by the total cost. Optimal system using an (N-1) criterion (case II-1). the pattern of deliveries from G3 and the levels of generation for G10.CHOI et al. and the new transmission lines are . It is interesting to note that the results are identical for (N-2G1T) and (N-1G-1T) contingencies and for (N-1G2T) and (N-2) [which could also be written as (N-2G2T)] contingencies. 10.979. G18. The criterion with (N-2) contingencies was applied to the same initial system shown in Fig. TABLE X CONFIGURATION OF POWER DELIVERED FROM GENERATORS TO LOADS FOR THE OPTIMAL SYSTEM IN CASE II-1 [MW] TABLE XI CONFIGURATION OF POWER DELIVERED FROM GENERATORS TO LOAD FOR THE NEW SYSTEM OF CASE II-2 (N-2 CONTINGENCY): [MW] . Table X shows the configuration of power delivered from generators to loads for the new system in Fig. Table XI shows the configuration of power delivered from generators to loads in Case II-2. . . The various case studies for a five-bus and a 21-bus system show that substantially different expansion plans are optimal for the same level of system load when different security criteria are used. modified security criteria of the form . the standby cost model proposed in this paper implicitly puts a value on reliability using a deterministic approach. These results also confirm that setting for a load is a practical way to augment the reliability of a conventional (N-1) criterion using a larger. It shows that the computation time is increased exponentially more as the applied contingency criterion is stronger Table XIV shows the results from four case studies using in (12) to 20% and 30% (N-1) contingencies and setting at the two main load buses. 1. 4.4 GHz) computational time for the various criteria. NOVEMBER 2007 TABLE XII OPTIMAL EXPANSION PLANS AND COSTS USING ALTERNATIVE SECURITY CRITERIA (21-BUS SYSTEM) TABLE XIV OPTIMAL EXPANSION PLANS BY COMBINING AN (N-1) CONTINGENCY CRITERION WITH BRR = 20 AND 30 AT BUSES 6 AND 17 (where BRR = (AP 0 L ) 2 100=L ) that the optimal expansion plans have more candidate lines conin nected directly or indirectly to the load bus with order to satisfy the higher reliability requirements of that load. a stronger security criterion is associated with . and dynamics in more detail [32]. bus 6 and bus 17. and are proposed as intermediate steps between the typical and criteria (for ). and standby costs (reserve generating capacity) of the system. The implicit assumption is that the cost and computational burden of the N-c-1 criterion are too great. OC : operating cost.2258 IEEE TRANSACTIONS ON POWER SYSTEMS. VII. but the security provided by the N-c criterion is too low. The proposed procedure represents the first macro-evaluation stage in the process of selecting a transmission expansion plan that would be followed by additional dynamic analyses. NO. It is challenging to consider these three costs simultaneously when searching for an optimal expansion plan. The results show This paper presents a methodology for choosing the best transmission expansion plan using alternative security criteria based on different specifications of contingencies. The optimal locations and capacities of new transmission lines can be determined using the proposed method. more realistic system. SC : standby cost) TABLE XIII ALTERNATIVE SECURITY CRITERIA RANKED BY TOTAL COST AND COMPUTATIONAL TIME FOR THE CRITERIA (21-BUS SYSTEM) (Pentium M. This paper presents a practical approach to planning that should serve as a useful guide for decision makers in selecting a reasonable expansion plan prior to checking system stability. In this paper. In general. The proposed method minimizes the total cost the investment. The computation time is introduced in Table XIII. Specifically. CONCLUSIONS (where CC : construction cost. quality. This is similar to the practice of including outage costs using a probabilistic approach. VOL. 22. operation. if the (N-2) criterion requires too much investment. and transmission expansion and AC load flow. . It is difficult to check for a shortage of power supply in the system because these elements are presented as nodes in a system model. B. Fig. Fig. Aspects of a shortage of power supply according to a bottleneck are given in Table XV. such as a criterion covering (N-1G-1T) contingencies. and load points have limited capacities. the operating cost may be slightly lower due to less congestion on the grid. Network model. This paper concludes that the modified security criteria can be used effectively for transmission expansion planning in both regulated and deregulated electricity markets. 12 system. 12. nodal reliability criteria. Power system. for example. Traditional Work Procedure for Power System Planning Fig.CHOI et al. simultaneous generation. as a sensible way to find a transmission expansion plan that is more reliable than a plan based on the (N-1) criterion and less expensive than a plan based on the (N-2) criterion. This paper proposes a more flexible security criterion. The objective of future research will be to extend the methodology in this paper to consider probabilistic operating/production costs. Network Modeling of Power System Generators. it is useful to consider intermediate security criteria between the (N-1) criterion and the (N-2) criterion. a higher investment cost. 14. [25].: TRANSMISSION EXPANSION PLANNING USING CONTINGENCY CRITERIA 2259 TABLE XV VARIOUS ASPECTS OF POWER SUPPLY BOTTLE NECK (where F : maximum flow of the network G: total power generation L: total system load) Fig. but at the same time. Network modeling of the system makes it convenient to check a shortage of power supply because the network elements mentioned above are presented as branches with capacity limitations [23]. Since grid operators are often asked to adopt a stronger security criterion. such as a criterion covering (N-2) contingencies rather than the conventional (N-1) contingencies. substations. [26]. and minimum cut-set of Fig. TABLE XVI OPERATING MARGINAL COST AND STANDBY MARGINAL COST OF GENERATORS APPENDIX A. Traditional work procedure for power system planning. 13. stronger security criteria. cut sets. 12 shows the traditional work procedure for power system planning. S. Power Syst. Aug. and D. IEE Power & Energy Series 44. Silva. Fang and D. Romero and A. 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