An Approach for the Modeling of an Autonomous Induction Generator[1]

Volume 4, Issue 1 2005 Article 1052International Journal of Emerging Electric Power Systems An Approach for the Modeling of an Autonomous Induction Generator Taking Into Account the Saturation Effect Dr. Rekioua Djamila, Department of Electrical Engineering, University of Bejaia, (Algeria) Pr. Rekioua Toufik, Department of Electrical Engineering, Univeristy of Bejaia, (Algeria) Idjdarene Kassa Jr., Department of Electrical Engineering, Univeristy of Bejaia, (Algeria) Dr. Tounzi Abdelmounaim , Laboratoire D’Electrotechnique et D’Electronique de Puissance de Lille, L2EP (France) Recommended Citation: Djamila, Dr. Rekioua; Toufik, Pr. Rekioua; Kassa, Idjdarene Jr.; and Abdelmounaim , Dr. Tounzi (2005) "An Approach for the Modeling of an Autonomous Induction Generator Taking Into Account the Saturation Effect," International Journal of Emerging Electric Power Systems: Vol. 4 : Iss. 1, Article 1052. Available at: http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 ©2005 by the authors. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress, which has been given certain exclusive rights by the author. International Journal of Emerging Electric Power Systems is produced by Berkeley Electronic Press (bepress). An Approach for the Modeling of an Autonomous Induction Generator Taking Into Account the Saturation Effect Dr. Rekioua Djamila, Pr. Rekioua Toufik, Idjdarene Kassa Jr., and Dr. Tounzi Abdelmounaim Abstract This paper deals with a model to simulate the operating of an autonomous induction generator. The model used is a diphase one obtained by the application of the Park transform. This model permits, when adopting some simplifying hypothesis, to take account of the saturation effect. This is achieved using a variable inductance function of the magnetising current. The non linearity is then based on the approximation of the magnetising inductance with regards to the current. In our case, we use a polynomial function, of 12th degree to perform it. This approach is simple and very accurate. The developed model has been used to study the operating of an induction machine when a capacitive bank is connected to the stator windings. The simulation calculation was achieved using MATLAB®-SIMULINK® package. This paper presents transient analysis of the self-excited induction generator. In order to simulate the voltage build-up process and the dynamic behaviour of the machine, we first establish the machine's model based on a d-q axis considering the machine’s saturation effect. Secondly, effect of excitation capacitors or load imbalances on voltage build-up process is investigated. Simulations results for a 5.5 kWinduction generator are presented and discussed. Several experimentations are presented to validate simulations and verify the effectiveness of the developed model. KEYWORDS: Autonomous induction generator, Saturation effect, Modelisation, Magnetising inductance 1. INTRODUCTION It is well known that induction machines may generate power if sufficient excitation is provided [1, 2]. The squirrel induction machines are widely used in the wind energy conversion in the case of isolated or faraway areas from grid distribution [3, 4, 5]. Theses structures have a lot of advantages. They are robust, need few maintenance and do not cost so much. When operating as an autonomous generator, the induction machine has to be magnetised by an external supply [6]. The simple way to achieve this consists in connecting its stator windings to a capacitive bank in parallel to the load. Hence, for a given rotation speed, the remaining magnetic flux yields a low electromotive force. Then when the capacitances are well designed, the magnetising current through the capacitive bank yields the built up of the electromotive force and its increase to an useful value. A lot of works dealt with the study of the autonomous induction generator. They concerned the calculation of the required capacitance value or the performances of the device using the equivalent monophase model [7, 9] taking into account the saturation effect. These last twenty years, different authors use models to study also the transient operating of the device [10, 13]. These models take account of the non linearity of the magnetic material by different approaches more or less accurate and easy to implement. Hence, in references [12] and [13], a variable magnetising inductance, using the saturation degree function, permits to the saturation phenomena to be taken into consideration. However, this method, which is very accurate, needs the knowledge of the linear and saturated components of the magnetising flux. Besides, others authors do not use the approximation of the magnetising inductance but utilise determination techniques of the parameters (voltage, current…) to achieve the study of the induction generator [1, 14]. In our approach, the model used is a diphase one obtained by the application of the Park transform. This model permits, when adopting some simplifying hypothesis, to take account of the saturation effect. In this case, the non linearity is based on the approximation of the magnetising inductance with regards to the current. We use a polynomial function, of 12 th degree [15, 16] to achieve this approximation. This approach is simple and very accurate. In this case, we can apply easily control methods in closed loop. 1 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 In this paper, the developed model is used to study the autonomous generator running of an induction machine. First, we present the machine which has been used as an experimental test bench. Then, we perform calculation as no load and when the generator is loaded. For both cases, we compare the simulation results to the experiment. 2. PROPOSEDSTUDIEDSYSTEM Figure 1. shows the three-phase connection diagram of the self-excited induction generator (SEIG). Fig. 1: Proposed structure. To analyse the behaviour of the SEIG under several asymmetrical conditions, the dynamic equations of generator must be established. 2.1 Induction machine model The linear model of the induction machine is widely known and used. It yields results relatively accurate when the operating point studied is not so far from the conditions of the model parameter identification. This is often the case when the motor operating, at rated voltage, is studied. As the air gap of induction machines is generally narrow, the saturation effect is not negligible in this structure. So, to improve the accuracy of simulation studies, especially when the voltage is variable, the non linearity of the iron has to be taken into account in the machine model. This becomes a necessary condition to study an autonomous induction generator because the linear model is not able to describe the behaviour of the system. Thus, only approaches, which take account of the saturation effect, can be utilized. This effect is not easy to yield with using three phase classical models. So, we usually SEIG C a C b C c Load Capacitive bank 2 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 adopt diphase approaches to take globally account of the magnetic non linearity. This evidently supposes some simplifying hypotheses. Indeed, the induction is considered homogenous in the whole structure. Moreover, the use of diphase model supposes that the saturation effect is considered only on the first harmonics and does not affect the sinusoidal behaviour of the variables. In our approach, we adopt the diphase model of the induction machine expressed in the stator frame. The classical electrical equations are written as follows: + + ÷ + + ÷ + + + + ÷ ÷ + ÷ ÷ ÷ ÷ = dt di dt di dt di dt di i i L L l i i i L l i i i L i i L L l l i i L L i i i L l i i i L i i L L l i i i i R L l R l L l R l R L R l L l R v v mq md sq sd m mq m m r m mq md m r m mq md m m md m m r r m mq m m m mq md m s m mq md m m md m m s mq md sq sd r m r r r r r m r r r r r r m s s s s m s s s s sq sd . . . . 0 . . . 0 . . . 0 . . . 0 . ) .( . ) .( . 0 . . . 0 . 0 0 2 ' ' ' 2 ' 2 ' ' ' 2 ' e e e e e e e e (1) Where R s , l s , R r and l r are the stator and rotor phase resistances and leakage inductances respectively, L m is the magnetizing inductance and O = e . p Besides, V sd , i sq , V sq and i sq are the d-q stator voltages and currents respectively, i md and i mq are the magnetizing currents, along the d and q axis, given by: rd sd md i i i + = (2) rq sq mq i i i + = (3) Where i rd and i rq are the d-q rotor currents i sd and i sq are the d-q stator currents. Thus, the saturation effect is taken into account by the expression of the magnetizing inductance L m with respects to the magnetizing current i m defined as: 2 2 mq md m i i i + = (4) To express L m in function of i m , we use a polynomial approximation, of degree 12 [15, 16]. 3 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 ( ) ( ) ¦ ¦ ¦ ¹ ¦ ¦ ¦ ´ ¦ = = = = = ¯ ¯ = ÷ = n j j m j m m m m m n j j m j m m i a j i f i d d i d dL L i a i f L 0 1 ' 0 . . . (5) 2.2 Load model The stator windings of the induction machine are connected to a star capacitive bank connected in parallel to a resistive load. Hence, at no load, the diphase stator voltages and currents are linked by the following expression: ÷ + = ds qs qs ds qs ds V V i i C C V V dt d . 0 0 . 1 0 0 1 e e (6) This takes, when the induction generator is loaded, this other writing: ÷ + ÷ ÷ = ds qs qch qs dch ds qs ds V V i i i i C C V V dt d . 0 0 . 1 0 0 1 e e (7) Where: i dch and i qch are the current through the equivalent diphase resistive load R. They can be expressed, from the stator voltages (Fig.2.). Fig.2: Induction machine model. The dynamic model of a three-phase balanced resistive load in the q-d axis arbitrary reference frame is given by ¹ ´ ¦ = = qch qs dch ds i R V i R V . . (8) Induction machine model i chd , i chd C Load R i sd , i sq v sd , v sq i Cd , i Cq 4 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 2.3 The global system The global differential system to solve is then written as follows: + + ÷ + + ÷ + + + ÷ ÷ O O O ÷ O ÷ = dt di dt di dt di dt di i i L L l i i i L l i i i L i i L L l l i i L L i i i L l i i i L i i L L l i i i i R R R R L p R l p L p l p R v v mq md sq sd m mq m m r m mq md m r m mq md m m md m m r r m mq m m m mq md m s m mq md m m md m m s mq md sq sd r r r r m s s m s s sq sd . . . . 0 . . . 0 . . . 0 . . . 0 . 0 0 0 0 0 . . . 0 . 0 0 2 ' ' ' 2 ' 2 ' ' ' 2 ' (9) To take into account the non linearity of the resolution, we use Runge Kutta algorithm to solve the system (7) and system (9) together. 3. RESULTS ANDDISCUSSION The developed model is used to study the autonomous generator running of an induction machine. First, we present the machine which has been used as an experimental test bench. Then, we perform calculation at no load and when the generator is loaded. For both cases, we compare the simulation results to the experiment. Fig 3: i m versus the phase applied voltage. P h a s e a p p l i e d v o l t a g e v s ( V ) Magnetizing current i m (A) 0 50 100 150 200 250 300 350 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 3.1 The experimental machine Experimental results were obtained from the implementation of the structure presented in Fig.1. using an induction machine of 5.5 kW (table.1) manufactured by CEN (Constructions Electriques -Nancy) (figure 4.). [16]. Fig 4: The experimental bench. Parameter Value Parameter Value P N 5.5 kW J 0,230 kg.m² U N 230/400 V f 0,0025 N.m/rad s-1 I N 23,8/13,7 Rs 1,07131 O f 50 Hz Rr 1,29511 O N N 690 rpm p 4 Table1. Machine parameters [16]. Then, from these data and the active power absorbed by the machine, one can determine the evolution of the magnetising inductance in function of i 0 . The obtained curve is drawn in figure 5-a. Lastly, to avoid the problem due to the absence of experimental inductance values outside the magnetising current range identification, we drawn a complementary part. This yield the evolution given in figure 5-b. 6 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 a: Measurement result b: Simulation result Fig.5: Magnetizing Curve. 3.2 No load tests. The experimental device is shown in figure 6. In this section, experimental and computed results are presented. Fig.6: The experimental device studied. The model introduced in the precedent paragraph has been used in the MATLAB SIMULINK environment to study the performance of the autonomous M a g n e t i z i n g i n d u c t a n c e L m ( H ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 a b Magnetizing current i m (A) 7 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 induction generator. The parameter of the model used are the ones of the experimental machine when the magnetizing inductance is the one given above, expressed by a proposed polynomial function. To simulate the remaining voltage, we take a non low initial value for the phase voltages. 3.2.1. Voltage build-up process under balanced conditions In order to validate the model of the induction generator, we study firstly the built up process of the stator voltage when the rotor of the induction machine is driven at 780 rpm under no-load conditions. The value of each self excitation is fixed to 100 µF [16]. Time [sec]. a: Simulated results. Time [sec]. b: Experimental results. Fig. 7: A phase voltage built up process under no-load conditions. For the same conditions, the evolution of a phase voltage calculated and measured is shown in the figure 7 (a and b respectively). We can notice the good agreement between both curves. We can observe that the voltage value before the P h a s e v o l t a g e V a [ V ] 0.14 0.2 0.42 0.56 0.70 0.84 0.98 0.00 -400 -300 -200 -100 0 100 200 300 400 P h a s e v o l t a g e V a [ V ] 100 V/div 0.14s/div 8 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 built-up is different for experimental test and for simulation. This is due to the initial conditions. The voltage build-up process is due to remaining field in the machine which can be different after every utilisation of the machine. We show also the calculation results related to a phase current (Fig.8) and the magnetizing current (Fig.9.) Time [sec] Fig.8: Evolution of a phase current. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 2 4 6 8 10 t (s) i 0 (A) Time [sec] Fig.9: Evolution of the magnetising current. 3.3 Other operating points. Other tests have been performed. The first one studies the effect, on the phase voltage, when the generator is loaded. In the figure 10a and b we show the simulated and measured evolution of a phase voltage respectively when the generator is connected to a resistive load of 50 O per phase. P h a s e c u r r e n t i a [ A ] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -8 -6 -4 -2 0 2 4 6 8 M a g n e t i s i n g c u r r e n t i 0 [ A ] 9 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 Time [sec]. a: Computed results. Time [sec]. b: Measured results. Fig.10: Evolution of a phase voltage when the generator is loaded (100uF–780 rpm) and R from · to 50 O. Once more, the results are in good agreement. The connection of the load yields a decrease of the phase voltage magnitude and a low variation of its frequency. Lastly, tests have been carried out to determine the evolutions of the phase voltage with regards to the capacitance, the speed rotation and the load values. Hence, for two capacitance values 100 µF and 110 µF, we drawn the curves V(R) for 3 values of the rotation speed (720, 750 and 780 rpm). In figure 11a and b, we give the simulation and experimental results respectively when the capacitance value is 100 µF. Figures 12a and b give the same evolutions for a capacitance of 110 µF. S t a t o r v o l t a g e V a [ V ] 100 V/div 0.14 s/div 1.42 1.5 1.58 1.66 1.74 1.82 1.9 -400 -300 -200 -100 0 100 200 300 400 S t a t o r v o l t a g e V a [ V ] 10 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 R[O] a: Simulation results. R[O] b: Experimental results Fig.11: Evolution of the rms phase voltage with respects to the R for 3 speed rotation values (100µF). P h a s e v o l t a g e V e f f [ V ] P h a s e v o l t a g e V e f f [ V ] 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 780 rpm 750 rpm 720 rpm 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 780 rpm 750 rpm 720 rpm 11 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 R[O] a: Simulation results R[O] b: Experimental results Fig.12: Evolution of the rms phase voltage with respects to the R for 3 speed rotation values (110µF). As we could expect, the magnitude of the phase voltage is an increasing function of both the capacitance and the speed rotation values. Furthermore, when the generator is highly loaded, the magnitude voltage decreases quickly. This well known characteristic, and problem, of the autonomous induction generator when connected to a simple capacitance bank in parallel. We drawn the evolution of the phase voltage with regards to the current (Fig.13, Fig14, Fig.15.) for three rotation speed values (780, 750 and 720 rpm) and two different values of capacitance (100µF, 110µF). P h a s e v o l t a g e V e f f [ V ] P h a s e v o l t a g e V e f f [ V ] 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 780 rpm 750 rpm 720 rpm 780 rpm 750 rpm 720 rpm 12 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 Current phase ia[A] C=100µF C=110µF a: Simulation b: Measurement Fig. 13: Variation of terminal voltage with current phase at constant speed (780 rpm). Current phase ia[A] C=100µF C=110µF a: Simulation, b: Measurement Fig.14: Variation of terminal voltage with current phase at constant speed. (750 rpm). 0 100 200 300 1 2 3 a b 0 1 2 3 4 5 a b 0 1 2 3 4 5 6 7 a b 300 200 100 300 200 100 0 1 2 3 4 5 6 a b 100 200 300 P h a s e v o l t a g e V e f f [ V ] P h a s e v o l t a g e V e f f [ V ] 13 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 Current phase ia[A] C=100µF C=110µF a: Simulation b: Measurement Fig. 15: Variation of terminal voltage with current phase at constant speed. (720 rpm). As we note, more the capacitance value increases and more the induction machine provides a constant voltage for a load current. We will find the same results for the two other speed values N. The curves have all the same shape of hook. We can add that more the rotor speed increases and more the stator voltage is high. Finally, all the curves are in the shape of hook. The higher capacity is the more one has a good behavior in voltage for a higher current. It will be necessary to choose the excitation capacity adapted for a given use of the induction machine. 3.4. Sudden disconnection of one capacitor We suddenly disconnected one of the excitation capacitors (C=100 uF), the corresponding simulated transient results are shown respectively on figures 16a, b and c. This test shows the good accuracy of the machine and the load model. 0 100 200 300 0 1 2 3 4 5 6 7 a b 0 1 2 3 4 5 a b 100 200 300 P h a s e v o l t a g e V e f f [ V ] 14 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 3 4 5 6 7 8 -200 -150 -100 -50 0 50 100 150 200 Time [sec]. a: Phase a. 3.9 4.1 4.3 4.5 -200 -150 -100 -50 0 50 100 150 200 Time [sec]. b: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -250 -200 -150 -100 -50 0 50 100 150 200 250 Time [sec]. c: Zoom on phase a, b and c. Fig. 16: Effect of a sudden disconnection of one capacitor (C=100 uF) on stator voltage. Naturally the transient behaviour of the SEIG will depend on the resulting remaining equivalent excitation capacitor. In fact, if the initial values of the capacitors are high, the voltage will not fall down under sudden disconnection of P h a s e v o l t a g e V a [ V ] P h a s e v o l t a g e V a b c [ V ] P h a s e v o l t a g e V a b c [ V ] 15 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 one capacitor. It will drops a little during transient and then return to a new steady-state operation point. The line current variation (Fig.17.) is similar to the one of voltage (Fig.16.). 3 4 5 6 7 8 -8 -6 -4 -2 0 2 4 6 8 Time [sec]. a: Phase a. 3.9 4.1 4.3 4.5 -8 -6 -4 -2 0 2 4 6 8 Time [sec]. b: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -8 -6 -4 -2 0 2 4 6 8 Time [sec]. c: Zoom on phase a, b and c. Fig. 17: Effect of a sudden disconnection of one capacitor (C=100 uF) on stator current. C u r r e n t p h a s e i a ( A ) C u r r e n t p h a s e i a b c ( A ) C u r r e n t p h a s e i a b c ( A ) 16 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 3.4 Influence of capacitor bank imbalance In order to show the influence of the capacitor bank imbalance (C=160 uF), we present respectively in figure 18. and figure 19. the variations of the stator voltage and current . 3 4 5 6 7 8 -300 -200 -100 0 100 200 300 Time [sec]. a: Phase a. 3.9 4.1 4.3 4.5 -300 -200 -100 0 100 200 300 Time [sec]. b: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -300 -200 -100 0 100 200 300 Time [sec]. c: Zoom on phase a, b and c. Fig. 18: Influence of capacitor bank imbalance (C=160 uF) on Stator voltage. V o l t a g e p h a s e v a ( V ) V o l t a g e p h a s e v a b c ( V ) V o l t a g e p h a s e v a b c ( V ) 17 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 3 4 5 6 7 8 -15 -10 -5 0 5 10 15 Time [sec]. a: Phase a. 3.9 4.1 4.3 4.5 -15 -10 -5 0 5 10 15 Time [sec]. b: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -15 -10 -5 0 5 10 15 Time [sec]. c: Zoom on phase a, b and c. Fig. 19: Influence of capacitor bank imbalance (C=160 uF) on Stator current. 3.6. Influence of a sudden disconnection of the load We can notice that the disconnection of a purely resistive load, involves a voltage variation but the steady-state is reached after a delay of about 1 s. The same C u r r e n t p h a s e i a ( A ) C u r r e n t p h a s e i a ( A ) C u r r e n t p h a s e i a ( A ) 18 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 phenomenon can be observed on stator currents. Simulation results show the validity of the adopted modelling approach. 3 4 5 6 7 8 -300 -200 -100 0 100 200 300 Time [sec]. a: Phase a 3.9 4 4.1 4.2 4.3 4.4 4.5 -300 -200 -100 0 100 200 300 Time [sec]. b: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -200 -150 -100 -50 0 50 100 150 200 Time [sec]. c: Zoom on phase a, b and c. Fig. 20: Stator voltages of phases a, b and c under unbalanced load conditions. V o l t a g e p h a s e v a b c ( A ) V o l t a g e p h a s e v a b c ( A ) V o l t a g e p h a s e v a ( A ) 19 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 3.9 4 4.1 4.2 4.3 4.4 4.5 -10 -5 0 5 10 Time [sec]. a: Phase a, b and c. 3.98 4 4.02 4.04 4.06 4.08 4.1 -10 -8 -6 -4 -2 0 2 4 6 8 10 Time [sec]. b: Zoom on phase a, b and c. Fig.21: Stator currents of phases a, b and c under unbalanced load conditions. 3.7. Influence of an unbalanced load. The aim of this test is to show the resistive load unbalance effect on the behaviour of the stator voltages and currents. The resistive load parameters are R a =R b =50 Ÿ, R c =80 Ÿ and each excitation capacitors is equal to 100 µF. The obtained results are presented respectively on figures 22 and 23. C u r r e n t p h a s e i a b c ( A ) C u r r e n t p h a s e i a ( b c A ) 20 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 4 4.02 4.04 4.06 4.08 4.1 -200 -100 0 100 200 Time [sec]. Fig. 22: Stator voltages of phases a, b and c under unbalanced load condition. 4 4.02 4.04 4.06 4.08 4.1 -8 -6 -4 -2 0 2 4 6 8 Time [sec]. Fig. 23: Stator current of phases a, b and c under unbalanced load condition. The influence on stator voltage is negligible while the chosen load imbalance induces a consequent variation of the peak current value. 4. CONCLUSION The paper examines the dynamic performances of an autonomous induction generator, taking the saturation effects into account, by the means of a variable magnetising inductance, has been presented. This magnetising inductance is expressed, using a polynomial function, of degree 12, as a function of the magnetising current. The proposed model has been used, in a MATLAB SIMULINK simulation environment to study an induction machine in autonomous generator operating. V o l t a g r e p h a s e v a b c ( A ) C u r r e n t p h a s e i a b c ( A ) 21 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 Obtained results of the SEIG under voltage build-up process, balanced or unbalanced network load side conditions are presented and compared. Excessive conditions like disconnection of one self-excitation capacitor or sudden disconnection of the load are also analysed. The analysis presented is validated by experimental results. The comparison of all these results shows a very good agreement between the experimentation and simulation. The amplitudes of the signals, their shapes as their duration present practically the same values for both simulation and experimentation. The coherence between computed and measured results is very good as well for dynamic conditions as for steady state. This concordance between the experimentation and simulation confirms the validity of the developed model. 5. REFERENCES [1] E. G. Marra and J.A.Pomilio, “Self excited induction generator controlled by a VS-PWM bi-directional converter for rural applications,” IEEE transactions on industry Applications, Vol 35, N°4, July/August 1999, pp: 877-883. [2] T. Ahmed, E. Hiraki, M. Nakaoka and O.Noro, “Three phase self excited induction generator driven by variable speed prime mover for clean renewable energy utilizations and its terminal voltage regulation, Characteristics by static VAR compensator,” IEEE transactions on industrial Applications 2003 pp: 693-700. [3] A. M. Alsalloum, A. I. Alolah and R. M. Hamouda, “Operation of three- phase self-excited induction generator under unbalanced load,” In the Proceeding of Electrimacs 2002, August 18-21, pp: 1-5. [4] B. Robyns and M. Nasser, “Modélisation et simulation d’une éolienne à vitesse variable basée sur une génératrice asynchrone à cage,” In the Proceeding of Electrotechnique du Futur EF’2001, Nancy, France, 14-15 Nov 2001, pp: 77-82. [5] E. Muljadi, K. Pierce and P. Migliore, “Control strategy for variable-speed, stall-regulated wind turbines,” In the Proceeding of American Controls Conference, Philadelphia, PA , 24-26 June, 1998, pp: 1-8. [6] A. Tounzi , “Utilisation de l’énergie éolienne dans la production de l’électricité,” Journées du club EEA, 28-29 janvier 1998, Paris (France), pp 1-14. [7] N. Ammasaigounden, M. Subbiah and M.R. Krishnamurthy, “Wind-driven Self-Excited Pole-Changing Induction Generators.,” In the IEE Proc., Vol. 133, Pt. B, No. 5, Sept 1986, pp: 315-321. 22 International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052 http://www.bepress.com/ijeeps/vol4/iss1/art1052 DOI: 10.2202/1553-779X.1052 [8] Ching-Huei Lee and Li Wang, “A Novel Analysis of Parallel Operated Self- Excited Induction Generators,” IEEE Trans. on Energy Conversion, Vol. 13, No. 2, June 1996, pp: 117-123. [9] Li Wang and Ching-Huei Lee, “A Novel Analysis on the Performance of an Isolated Self-Excited Induction Generator.,” IEEE Transactions on Energy Conversion, Vol. 12, No. 2, June 1997, pp. 109-117 [10] F. Poitiers, M. Machmoum, M.E. Zaim and R. Le Doeuff, “Performances and Limits of an Autonomous Self-Excited Induction Generator.,” In the Proceeding of UPEC Conference, University of Wales, Swansea, Sept 2001, CD-ROM proceedings. [11] F. Poitiers, M. Machmoum, M. E. Zaim and T. Branchet, “Transient performance of a self-excited induction generator under unbalanced conditions.,” In the Proceeding of ICEM Conference, Aug 2002, Brugge, Belgium, CD-ROM proceedings. [12] R. Ibtiouen, A. Nesba, S. Mekhtoub and O. Touhami, “An approach for the modeling of saturated induction machine.,” In the Proceeding of. International Conference on Electrical Machines and Power Electronics ACEMP'01, Kasudasi-Turkey, 27-29 June, 2001, pp: 269-274. [13] R. Ibtiouen, M. Benhaddadi, A. Nesba, S. Mekhtoub and O. Touhami, “Dynamic performances of a self excited induction generator feeding different static loads.,” In the Proceeding of ICEM Conference , Aug 2002, Brugge, Belgium, CD-ROM proceedings. [14] C. Grantham and H. Tabatabaei-Yazdi, “Rapid Parameter Determination for use in the control High Performances Induction Motor drives,” In the Proceeding of IEEE International Conference on Power Electronics and Drive systems, 1999, pp: 267-272. [15] D.Aouzellag, “Optimisation of the frequency technical control for the asynchronous electric actuators with the whole of fixed requirements and limitations.” Thèse de P.H.D, Université Nationale d’Aéronautique, Kiev, Ukraine, 2001. [16] K.Idjdarene, D.Rekioua, “Modeling, and Simulation of wind conversion power system based on an induction generator taking the saturation into account», 3rd conference on Electrical Engineering (CEE'04), Batna, Algeria, October 2004. [17] J. O. Ojo, A. Consoli and T. A. Lipo, “An improved model of saturated induction machine,” In IEEE Trans. on Industry Applications, Vol. 26, No. 2, pp. 212-222, March /April 1990. 23 Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator Published by Berkeley Electronic Press, 2005 An Approach for the Modeling of an Autonomous Induction Generator Taking Into Account the Saturation Effect Dr. Rekioua Djamila, Pr. Rekioua Toufik, Idjdarene Kassa Jr., and Dr. Tounzi Abdelmounaim Abstract This paper deals with a model to simulate the operating of an autonomous induction generator. The model used is a diphase one obtained by the application of the Park transform. This model permits, when adopting some simplifying hypothesis, to take account of the saturation effect. This is achieved using a variable inductance function of the magnetising current. The non linearity is then based on the approximation of the magnetising inductance with regards to the current. In our case, we use a polynomial function, of 12th degree to perform it. This approach is simple and very accurate. The developed model has been used to study the operating of an induction machine when a capacitive bank is connected to the stator windings. The simulation calculation was achieved using MATLAB®-SIMULINK® package. This paper presents transient analysis of the self-excited induction generator. In order to simulate the voltage build-up process and the dynamic behaviour of the machine, we first establish the machine's model based on a d-q axis considering the machine’s saturation effect. Secondly, effect of excitation capacitors or load imbalances on voltage build-up process is investigated. Simulations results for a 5.5 kW induction generator are presented and discussed. Several experimentations are presented to validate simulations and verify the effectiveness of the developed model. KEYWORDS: Autonomous induction generator, Saturation effect, Modelisation, Magnetising inductance A lot of works dealt with the study of the autonomous induction generator. Then when the capacitances are well designed. When operating as an autonomous generator. The squirrel induction machines are widely used in the wind energy conversion in the case of isolated or faraway areas from grid distribution [3. in references [12] and [13]. We use a polynomial function. 9] taking into account the saturation effect. In our approach. They are robust. Hence. However. 14]. for a given rotation speed. This model permits. the remaining magnetic flux yields a low electromotive force.: An Approach for the Modeling of an Autonomous Induction Generator 1. current…) to achieve the study of the induction generator [1. permits to the saturation phenomena to be taken into consideration. 4. Besides. INTRODUCTION It is well known that induction machines may generate power if sufficient excitation is provided [1. 2005 1 . In this case. need few maintenance and do not cost so much. when adopting some simplifying hypothesis. These last twenty years. 16] to achieve this approximation. In this case. 5]. Published by Berkeley Electronic Press. 13].Djamila et al. of 12th degree [15. 2]. which is very accurate. others authors do not use the approximation of the magnetising inductance but utilise determination techniques of the parameters (voltage. These models take account of the non linearity of the magnetic material by different approaches more or less accurate and easy to implement. the induction machine has to be magnetised by an external supply [6]. needs the knowledge of the linear and saturated components of the magnetising flux. Theses structures have a lot of advantages. to take account of the saturation effect. They concerned the calculation of the required capacitance value or the performances of the device using the equivalent monophase model [7. we can apply easily control methods in closed loop. a variable magnetising inductance. this method. using the saturation degree function. Hence. the magnetising current through the capacitive bank yields the built up of the electromotive force and its increase to an useful value. the model used is a diphase one obtained by the application of the Park transform. different authors use models to study also the transient operating of the device [10. The simple way to achieve this consists in connecting its stator windings to a capacitive bank in parallel to the load. This approach is simple and very accurate. the non linearity is based on the approximation of the magnetising inductance with regards to the current. we usually http://www. can be utilized. the saturation effect is not negligible in this structure. 2. First. SEIG Ca Cb Cc Load Capacitive bank Fig. we compare the simulation results to the experiment. the non linearity of the iron has to be taken into account in the machine model. shows the three-phase connection diagram of the self-excited induction generator (SEIG). Thus. which take account of the saturation effect. To analyse the behaviour of the SEIG under several asymmetrical conditions. Then. to improve the accuracy of simulation studies. 4 [2005].International Journal of Emerging Electric Power Systems. we present the machine which has been used as an experimental test bench. 1. PROPOSED STUDIED SYSTEM Figure 1.1 Induction machine model The linear model of the induction machine is widely known and used. It yields results relatively accurate when the operating point studied is not so far from the conditions of the model parameter identification. Vol.2202/1553-779X. we perform calculation as no load and when the generator is loaded. 1052 In this paper. This is often the case when the motor operating. 2. So.com/ijeeps/vol4/iss1/art1052 DOI: 10. For both cases. Art. only approaches. 1: Proposed structure. at rated voltage. is studied. Iss. This becomes a necessary condition to study an autonomous induction generator because the linear model is not able to describe the behaviour of the system. the dynamic equations of generator must be established. As the air gap of induction machines is generally narrow. especially when the voltage is variable.bepress. This effect is not easy to yield with using three phase classical models. the developed model is used to study the autonomous generator running of an induction machine.1052 2 . So. the use of diphase model supposes that the saturation effect is considered only on the first harmonics and does not affect the sinusoidal behaviour of the variables. the induction is considered homogenous in the whole structure. di md dt 2 . Lm is the magnetizing inductance and Besides. we use a polynomial approximation. im 2 2 di sd dt di sq dt . isq .r s s 0 i ' md Lm Lm . Indeed. Published by Berkeley Electronic Press. im imq Lm . inductances respectively.i ' md mq Lm . given by: i md i sd ird (2) (3) imq i sq irq Where ird and irq are the d-q rotor currents isd and isq are the d-q stator currents.( r r lr 0 i ' md Lm Lm . im i . im ' Rs . Vsd. 2005 3 .lr 0 . The classical electrical equations are written as follows: ls vsd vsq 0 0 Rs l s.i ' md mq Lm . Vsq and isq are the d-q stator voltages and currents respectively. ls. im imq ' Lm Lm . along the d and q axis.i ' md mq Lm .Lm isd isq . In our approach.Djamila et al. s Rr l r. im ' Rr di mq dt lr Lm (1) Where Rs. imd and imq are the magnetizing currents. 16].l 0 s . im i . imd imq 0 lr imd.L m s . Moreover. Rr and lr are the stator and rotor phase resistances and leakage p.: An Approach for the Modeling of an Autonomous Induction Generator adopt diphase approaches to take globally account of the magnetic non linearity. im lr 2 i . the saturation effect is taken into account by the expression of the magnetizing inductance Lm with respects to the magnetizing current im defined as: im imd 2 imq 2 (4) To express Lm in function of im. This evidently supposes some simplifying hypotheses.imq Lm . of degree 12 [15.( r Lm) l Rr 0 ls r Rr l Lm) r . Thus. we adopt the diphase model of the induction machine expressed in the stator frame. 1 dt 0 V qs i qs 0 V ds C This takes. Hence. vsq C Load R Induction machine model Fig. (7) 1 dt 0 V qs 0 i qs i qch V ds C Where: idch and iqch are the current through the equivalent diphase resistive load R. when the induction generator is loaded.aj . They can be expressed. the diphase stator voltages and currents are linked by the following expression: 1 V ds i ds 0 V qs 0 d C (6) .2 Load model The stator windings of the induction machine are connected to a star capacitive bank connected in parallel to a resistive load. Iss.com/ijeeps/vol4/iss1/art1052 DOI: 10. this other writing: 1 V ds 0 i ds i dch V qs 0 d C . 4 [2005]. .2: Induction machine model. iCq vsd. 1052 n Lm f im j 0 aj . im j (5) Lm ' dL d m f im d im d im n j.International Journal of Emerging Electric Power Systems. Art. 1. isd. . ichd iCd.).bepress. isq ichd. The dynamic model of a three-phase balanced resistive load in the q-d axis arbitrary reference frame is given by V ds R . i qch http://www. Vol.1052 4 . from the stator voltages (Fig.i dch (8) V qs R . im j 0 j 1 2.2. at no load.2202/1553-779X. imq im 2 di mq dt (9) To take into account the non linearity of the resolution. ' imd im 2 Lm . 0 Rr imd imq 0 lr L.imq im lr Lm L . we present the machine which has been used as an experimental test bench.imq im ' di sd dt 2 isd isq 0 ls Lm . ' imd. we compare the simulation results to the experiment. Then. di md dt lr 0 lr Lm Lm .: An Approach for the Modeling of an Autonomous Induction Generator 2.imq im ' m imd. imd im Lm .Lm 0 . Published by Berkeley Electronic Press.ls Rr 0 p . ' m 0 Lm Lm .imq im ' Lm Lm . we use Runge Kutta algorithm to solve the system (7) and system (9) together. For both cases. 2 imq im di sq dt . 350 Phase applied voltage vs (V) 300 250 200 150 100 50 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Magnetizing current im (A) Fig 3: im versus the phase applied voltage. 2005 5 .ls Rs 0 Rr 0 p . 3.3 The global system The global differential system to solve is then written as follows: ls vsd vsq 0 0 p Rs . we perform calculation at no load and when the generator is loaded.Djamila et al. First. RESULTS AND DISCUSSION The developed model is used to study the autonomous generator running of an induction machine.Lm Rr 0 p . ' imd. ' imd. bepress.m² 230/400 V f 0. using an induction machine of 5.230 kg. Then.1) manufactured by CEN (Constructions Electriques -Nancy) (figure 4. Iss. Machine parameters [16]. [16].International Journal of Emerging Electric Power Systems. 4 [2005]. This yield the evolution given in figure 5-b. we drawn a complementary part.29511 690 rpm p 4 Table1. 1.0025 N. from these data and the active power absorbed by the machine. Fig 4: The experimental bench.7 Rs 1.1 The experimental machine Experimental results were obtained from the implementation of the structure presented in Fig. 1052 3. one can determine the evolution of the magnetising inductance in function of i0.5 kW J 0.1.m/rads-1 23. Vol. to avoid the problem due to the absence of experimental inductance values outside the magnetising current range identification. Lastly.com/ijeeps/vol4/iss1/art1052 DOI: 10. Art. The obtained curve is drawn in figure 5-a.1052 6 . Parameter PN UN IN f NN Value Parameter Value 5.8/13.5 kW (table. http://www.07131 50 Hz Rr 1.2202/1553-779X.). 01 0 0 b a Magnetizing inductance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Magnetizing current im(A) a: Measurement result b: Simulation result Fig.02 0. The model introduced in the precedent paragraph has been used in the MATLAB SIMULINK environment to study the performance of the autonomous Published by Berkeley Electronic Press.10 0.04 0. 2005 7 .: An Approach for the Modeling of an Autonomous Induction Generator 0.08 0.2 No load tests.05 0.07 0.Djamila et al. The experimental device is shown in figure 6.09 0.03 0.13 0.5: Magnetizing Curve. 3.6: The experimental device studied. Fig.11 0.06 0. In this section.12 Lm (H) 0. experimental and computed results are presented. Voltage build-up process under balanced conditions In order to validate the model of the induction generator. 7: A phase voltage built up process under no-load conditions.42 0.1. Vol.84 0.bepress. expressed by a proposed polynomial function.14s/div Phase voltage Va [V] Time [sec]. the evolution of a phase voltage calculated and measured is shown in the figure 7 (a and b respectively).1052 8 . 1. The parameter of the model used are the ones of the experimental machine when the magnetizing inductance is the one given above.98 a: Simulated results.00 0.com/ijeeps/vol4/iss1/art1052 DOI: 10. we take a non low initial value for the phase voltages. 400 300 Phase voltage Va [V] 200 100 0 -100 -200 -300 -400 0. The value of each self excitation is fixed to 100 µF [16].14 0. 100 V/div 0. we study firstly the built up process of the stator voltage when the rotor of the induction machine is driven at 780 rpm under no-load conditions.2.70 0. b: Experimental results. Art. For the same conditions.International Journal of Emerging Electric Power Systems. 4 [2005]. We can notice the good agreement between both curves. We can observe that the voltage value before the http://www. 3. 0.2202/1553-779X. Iss. 1052 induction generator.56 Time [sec].2 0. To simulate the remaining voltage. Fig. 8 Time [sec] t (s) 2 Fig. The voltage build-up process is due to remaining field in the machine which can be different after every utilisation of the machine. Published by Berkeley Electronic Press.7 0.4 0.: An Approach for the Modeling of an Autonomous Induction Generator built-up is different for experimental test and for simulation. 2005 9 . The first one studies the effect.6 1.9: Evolution of the magnetising current.9.1 0.3 Other operating points.8) and the magnetizing current (Fig. We show also the calculation results related to a phase current (Fig.2 0.3 0.5 0. Other tests have been performed.2 0. 10 Magnetising current i0 [A] i0 (A) 8 6 4 2 0 0 0.8 0.4 1.9 Time [sec] 1 Fig.4 0.6 0. when the generator is loaded.) 8 6 4 Phase current ia [A] 2 0 -2 -4 -6 -8 0 0.6 0.8: Evolution of a phase current.2 1. In the figure 10a and b we show the simulated and measured evolution of a phase voltage respectively when the generator is connected to a resistive load of 50 per phase. This is due to the initial conditions.8 1 1. 3.Djamila et al. on the phase voltage. com/ijeeps/vol4/iss1/art1052 DOI: 10. a: Computed results.1052 10 . tests have been carried out to determine the evolutions of the phase voltage with regards to the capacitance. the results are in good agreement.74 1. b: Measured results. Lastly.66 1.2202/1553-779X.9 Time [sec]. the speed rotation and the load values.bepress. 750 and 780 rpm). 1. for two capacitance values 100 µF and 110 µF.82 1. Art.14 s/div Stator voltage Va [V] Time [sec]. we give the simulation and experimental results respectively when the capacitance value is 100 µF.5 1. In figure 11a and b. http://www. Fig.58 1. Iss.International Journal of Emerging Electric Power Systems. The connection of the load yields a decrease of the phase voltage magnitude and a low variation of its frequency. Hence. Figures 12a and b give the same evolutions for a capacitance of 110 µF. we drawn the curves V(R) for 3 values of the rotation speed (720. Once more. 4 [2005]. 1052 400 300 Stator voltage Va [V] 200 100 0 -100 -200 -300 -400 1.10: Evolution of a phase voltage when the generator is loaded (100 F–780 rpm) and R from to 50 . 100 V/div 0.42 1. Vol. : An Approach for the Modeling of an Autonomous Induction Generator 300 780 rpm Phase voltage Veff [V] 750 rpm 720 rpm 250 200 150 100 50 450 400 350 300 R[ ] 250 200 150 100 50 0 a: Simulation results. Published by Berkeley Electronic Press. 2005 11 .11: Evolution of the rms phase voltage with respects to the R for 3 speed rotation values (100µF).Djamila et al. 780 rpm Phase voltage Veff [V] 750 rpm 720 rpm 300 250 200 150 100 50 0 450 400 350 300 250 200 150 100 R[ ] 50 0 b: Experimental results Fig. 750 and 720 rpm) and two different values of capacitance (100µF.15. We drawn the evolution of the phase voltage with regards to the current (Fig.2202/1553-779X. Furthermore. when the generator is highly loaded.13. the magnitude voltage decreases quickly.bepress.12: Evolution of the rms phase voltage with respects to the R for 3 speed rotation values (110µF).com/ijeeps/vol4/iss1/art1052 DOI: 10. Vol. and problem. 4 [2005]. Iss. 1052 300 780 rpm 750 rpm 720 rpm Phase voltage Veff [V] 250 200 150 100 50 0 450 400 350 300 250 R[ ] 200 150 100 50 0 a: Simulation results 780 rpm 300 750 rpm 720 rpm 250 200 150 100 50 0 Phase voltage Veff [V] 450 400 350 300 250 R[ ] 200 150 100 50 0 b: Experimental results Fig. Art. Fig.International Journal of Emerging Electric Power Systems. Fig14. of the autonomous induction generator when connected to a simple capacitance bank in parallel.) for three rotation speed values (780. the magnitude of the phase voltage is an increasing function of both the capacitance and the speed rotation values. http://www. 110µF).1052 12 . As we could expect. 1. This well known characteristic. b: Measurement Fig.: An Approach for the Modeling of an Autonomous Induction Generator 300 300 b b Phase voltage Veff [V] 200 a a 200 100 100 0 1 2 3 4 5 0 1 2 3 4 5 6 7 Current phase ia[A] C=100µF C=110µF a: Simulation b: Measurement Fig. 13: Variation of terminal voltage with current phase at constant speed (780 rpm). Published by Berkeley Electronic Press. 300 Phase voltage Veff [V] 300 b b 200 a a 200 100 100 0 1 2 3 0 1 2 3 4 5 6 Current phase ia[A] C=100µF C=110µF a: Simulation. 2005 13 . (750 rpm).14: Variation of terminal voltage with current phase at constant speed.Djamila et al. 4 [2005]. Finally. 15: Variation of terminal voltage with current phase at constant speed. We can add that more the rotor speed increases and more the stator voltage is high. (720 rpm).com/ijeeps/vol4/iss1/art1052 DOI: 10. 1052 300 b Phase voltage Veff [V] 200 a 300 b 200 a 100 100 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 Current phase ia[A] C=100µF C=110µF a: Simulation b: Measurement Fig.2202/1553-779X.4. b and c. Sudden disconnection of one capacitor We suddenly disconnected one of the excitation capacitors (C=100 F). The curves have all the same shape of hook. Iss. 1. Vol. 3.1052 14 . As we note. The higher capacity is the more one has a good behavior in voltage for a higher current. all the curves are in the shape of hook.bepress. http://www. We will find the same results for the two other speed values N. Art. the corresponding simulated transient results are shown respectively on figures 16a. It will be necessary to choose the excitation capacity adapted for a given use of the induction machine.International Journal of Emerging Electric Power Systems. This test shows the good accuracy of the machine and the load model. more the capacitance value increases and more the induction machine provides a constant voltage for a load current. c: Zoom on phase a.5 Time [sec].1 Phase voltage Vabc[V] Time [sec].04 4. b: Phase a. b and c.3 4. Naturally the transient behaviour of the SEIG will depend on the resulting remaining equivalent excitation capacitor. Fig. the voltage will not fall down under sudden disconnection of Published by Berkeley Electronic Press.: An Approach for the Modeling of an Autonomous Induction Generator 200 150 Phase voltage Va[V] 100 50 0 -50 -100 -150 -200 3 4 5 6 7 8 Time [sec].Djamila et al. a: Phase a. 200 150 Phase voltage Vabc[V] 100 50 0 -50 -100 -150 -200 3. In fact. b and c.1 4.98 4 4. if the initial values of the capacitors are high. 16: Effect of a sudden disconnection of one capacitor (C=100 F) on stator voltage. 2005 15 .9 4.02 4.08 4. 250 200 150 100 50 0 -50 -100 -150 -200 -250 3.06 4. bepress. c: Zoom on phase a. 4 [2005]. http://www. Fig.1 4.17.com/ijeeps/vol4/iss1/art1052 DOI: 10. b: Phase a. It will drops a little during transient and then return to a new steady-state operation point. Iss. 8 6 Current phase iabc(A) 4 2 0 -2 -4 -6 -8 3. Art.2202/1553-779X. b and c.3 4.02 4.5 Time [sec]. Vol. 17: Effect of a sudden disconnection of one capacitor (C=100 F) on stator current. a: Phase a.). 8 6 Current phase iabc(A) 4 2 0 -2 -4 -6 -8 3. 1.16. 8 6 Current phase ia(A) 4 2 0 -2 -4 -6 -8 3 4 5 6 7 8 Time [sec].1052 16 .9 4.06 4.International Journal of Emerging Electric Power Systems.) is similar to the one of voltage (Fig. The line current variation (Fig.98 4 4.1 Time [sec]. b and c.04 4.08 4. 1052 one capacitor. c: Zoom on phase a. 18: Influence of capacitor bank imbalance (C=160 F) on Stator voltage.4 Influence of capacitor bank imbalance In order to show the influence of the capacitor bank imbalance (C=160 F).Djamila et al. 2005 17 .08 4.02 4. b and c. Published by Berkeley Electronic Press.98 4 4.5 Time [sec]. b and c. a: Phase a.04 4. 300 200 Voltage phase vabc(V) 100 0 -100 -200 -300 3. b: Phase a.: An Approach for the Modeling of an Autonomous Induction Generator 3.06 4. the variations of the stator voltage and current .3 4. and figure 19. we present respectively in figure 18. 300 Voltage phase vabc(V) 200 100 0 -100 -200 -300 3.1 4. Fig.1 Time [sec].9 4. 300 200 Voltage phase va(V) 100 0 -100 -200 -300 3 4 5 6 7 8 Time [sec]. Vol. Art. c: Zoom on phase a.98 4 4.9 Current phase ia(A) 4. 4 [2005]. b: Phase a.06 4.com/ijeeps/vol4/iss1/art1052 DOI: 10.04 4. 3. The same http://www.08 4. Iss.2202/1553-779X. a: Phase a.02 4. Influence of a sudden disconnection of the load We can notice that the disconnection of a purely resistive load. 19: Influence of capacitor bank imbalance (C=160 F) on Stator current.1 Time [sec]. 15 10 5 0 -5 -10 -15 3.3 4.1052 18 .5 Time [sec].International Journal of Emerging Electric Power Systems. b and c. 1. 15 10 Current phase ia(A) 5 0 -5 -10 -15 3. 1052 15 10 5 0 -5 -10 -15 Current phase ia(A) 3 4 5 6 7 8 Time [sec]. Fig.1 4.bepress. b and c.6. involves a voltage variation but the steady-state is reached after a delay of about 1 s. 98 4 4.06 4.9 Voltage phase vabc(A) 4 4. 20: Stator voltages of phases a. 300 200 100 0 -100 -200 -300 Voltage phase va(A) 3 4 5 6 7 8 Time [sec].1 4. b and c.4 4. b: Phase a. 2005 19 .: An Approach for the Modeling of an Autonomous Induction Generator phenomenon can be observed on stator currents. Published by Berkeley Electronic Press. a: Phase a 300 200 100 0 -100 -200 -300 3. Fig. c: Zoom on phase a.5 Time [sec].08 4.1 Time [sec].Djamila et al. b and c.3 4. 200 150 Voltage phase vabc(A) 100 50 0 -50 -100 -150 -200 3.2 4. b and c under unbalanced load conditions.02 4.04 4. Simulation results show the validity of the adopted modelling approach. Fig. The obtained results are presented respectively on figures 22 and 23.9 4 4.1052 20 .08 4.International Journal of Emerging Electric Power Systems.1 4. b: Zoom on phase a.5 Time [sec].98 4 4. Vol.04 4. 4 [2005]. Rc=80 and each excitation capacitors is equal to 100 µF. Influence of an unbalanced load. b and c under unbalanced load conditions.7. 1. The resistive load parameters are Ra=Rb=50 .bepress.1 Current phase ia(bcA) Time [sec]. http://www. Iss.2202/1553-779X. 10 8 6 4 2 0 -2 -4 -6 -8 -10 3.3 4. a: Phase a. b and c. The aim of this test is to show the resistive load unbalance effect on the behaviour of the stator voltages and currents.4 4. 3.2 4.02 4.21: Stator currents of phases a. 1052 10 Current phase iabc(A) 5 0 -5 -10 3. Art. b and c.06 4.com/ijeeps/vol4/iss1/art1052 DOI: 10. 04 4.Djamila et al. has been presented.08 4.: An Approach for the Modeling of an Autonomous Induction Generator 200 Voltagre phase vabc(A) 100 0 -100 -200 4 4.08 4.1 Time [sec]. The influence on stator voltage is negligible while the chosen load imbalance induces a consequent variation of the peak current value. Fig.02 4. taking the saturation effects into account.06 4. using a polynomial function. b and c under unbalanced load condition. as a function of the magnetising current.1 Time [sec]. 4. b and c under unbalanced load condition. 23: Stator current of phases a. 8 6 Current phase iabc(A) 4 2 0 -2 -4 -6 -8 4 4.06 4. in a MATLAB SIMULINK simulation environment to study an induction machine in autonomous generator operating. CONCLUSION The paper examines the dynamic performances of an autonomous induction generator. of degree 12.02 4. Fig.04 4. This magnetising inductance is expressed. 22: Stator voltages of phases a. 2005 21 . by the means of a variable magnetising inductance. The proposed model has been used. Published by Berkeley Electronic Press. Hamouda. pp: 315-321. 5.R.International Journal of Emerging Electric Power Systems. K.bepress. E. The comparison of all these results shows a very good agreement between the experimentation and simulation. Vol. “Self excited induction generator controlled by a VS-PWM bi-directional converter for rural applications.1052 22 . 133. N. Paris (France).” In the Proceeding of American Controls Conference. Vol 35. Nakaoka and O. T. 5. 14-15 Nov 2001.” In the IEE Proc. REFERENCES [1] E. Sept 1986. N°4. 24-26 June. balanced or unbalanced network load side conditions are presented and compared. Marra and J. Nancy.. I. Hiraki. Krishnamurthy. Excessive conditions like disconnection of one self-excitation capacitor or sudden disconnection of the load are also analysed. pp: 877-883. pp: 77-82. This concordance between the experimentation and simulation confirms the validity of the developed model.com/ijeeps/vol4/iss1/art1052 DOI: 10. pp 1-14. The coherence between computed and measured results is very good as well for dynamic conditions as for steady state. “Operation of threephase self-excited induction generator under unbalanced load.” IEEE transactions on industrial Applications 2003 pp: 693-700. 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