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SVC BASED REACTIVE POWER CONTROL OF ISOLATED WIND-DIESEL HYBRID POWER SYSTEMS R.C. BANSAL1, T.S. BHATTI2, D.P. KOTHARI3 1 Electrical & Electronics Engg. Department, Birla Institute of Technology & Science, Pilani, (India) 2, 3 Centre for Energy Studies, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi - 110016 (India) 3 E-mail of Corresponding Author: [email protected] power requirement of the induction generator and of the load. In the absence of proper reactive device and controls the system may be subjected to large voltage fluctuations, which is not desirable. The device used for this function in conventional power systems is known as static var compensator (SVC) [11-16] can also be employed for the hybrid system. Abstract: In this paper automatic reactive power control of isolated wind-diesel hybrid power system having an induction generator as a power conversion device for wind power generation is presented. The mathematical model of the system using reactive power flow equations is developed. The dynamic voltage stability evaluation is based on small signal analysis considering a typical Static VAR Compensator (SVC) and IEEE type -I excitation system. It is shown that a variable reactive power source like SVC is a must to meet the varying demand of reactive power by induction generator and load and to obtain a very good voltage regulation of the system with minimum fluctuations. Integral square error (ISE) criterion is used to evaluate the optimum setting of gain parameters. Finally the dynamic responses of the power systems considered with optimum gain setting are also presented. In conventional power system the power is exported on transmission lines to load centres. The reactive power devices are employed in such a way to have minimum reactive power flow on the transmission lines so that maximum power can be exported with minimum transmission loses. In hybrid systems the load is directly connected to the generator terminals itself. Therefore the objective of the reactive power device in this case is to supply the reactive power required by the load and the induction machine under varying load conditions. An isolated wind-diesel hybrid power system has been considered for study having induction generator for wind power conversion and synchronous alternator with automatic voltage regulator (AVR) for diesel unit. The devices AVR and SVC have different functions but both operate on the voltage error signal caused by any disturbance in the system. The main function of the AVR is to maintain the voltage profile constant at the terminals. The alternator also provides partial reactive power to the load. Similarly the main function of SVC is to eliminate the mismatch of reactive power in the system. The SVC also partially helps in voltage maintenance at the terminals. A new innovative scheme, namely, automatic reactive power control, similar to automatic generation control [17,18] has been evolved. The scheme is applicable to isolated hybrid power systems. The system state equations have been derived with transfer function block diagram representation of the control system. The voltage deviation signal is used as area reactive power control error to eliminate the reactive power mismatch in the system. The integral square error (ISE) criterion is used to evaluate the optimum setting of gain parameters of the Keywords: reactive power control, hybrid power system, induction generator, static var compensator Introduction In recent years, much emphasis has been placed on the squirrel cage induction machine as the electromechanical energy converter in generation schemes involving renewable energy sources [1-4]. The advantages of the induction generator over the synchronous generator are low cost, robustness, no moving contacts, i.e., slip- rings, no synchronization required and no need for d.c. excitation. But the induction machine requires a reactive power support for its operation [5-10]. A large number of papers have appeared in the literature on the subject and a few papers investigate the capacitance requirement of self-excited induction generator under steady state conditions only [1-10]. It has practical significance as it enables the design and operation engineers to select the proper value of excitation capacitance for a specific machine. In a stand-alone hybrid power system, the reactive power device has to fulfil the variable reactive 1 QL = C1Vq controller. Finally transient responses are shown for different disturbance conditions. where C1 is the constant of the load and the exponent q depends upon the type of load. For small perturbations equation (6) can be written as Incremental Reactive Power Balance Analysis QL /V = q (QLo / Vo) QSG + QSVC - QL - QIG = 2 EMo / (Vo QR) d/dt (V) + DV V (8) In equation (8) QR divides only one term as all the other terms are already in pu kVAR. The term E Mo / QR can be written as where QSG = reactive power generated by diesel generator set, QSVC = reactive power generated by SVC, EMo / QR = 1/ (4 π f kR) = HR = reactive power load demand, and For the incremental reactive power balance analysis of the hybrid system, let the hybrid system experience a reactive power load change of magnitude QL. Due to the action of the AVR and SVC controllers the system reactive power generation increases by an amount QSG+QSVC. The reactive power required by the system will also change due to change in voltage by V. The net reactive power surplus in the system, therefore, equals QSG + QSVC - QL - QIG and this power will increase the system voltage in two ways: by increasing the electromagnetic energy absorption EM of the induction generator at the rate d/dt (EM), by an increased reactive load consumption of the QSG + QSVC – QL - QIG = 2 HR / Vo d/dt (V) + DV V (10) In Laplace form the state differential equation, from equation (10), can be written as V(s) = KV /(1 + s TV) [QSG(s) + QSVC(s) - QL(s) QIG(s)] (11) Under transient condition QSG is given by system due to increase in voltage. QSG = (E'q V cos - V2)/ X'd This can be expressed mathematically as Taking Laplace transform of both sides we get (3) where XM is the magnetizing reactance of the induction generator. Equation (3) can be further written as EM = V2 / (4πf XM) and (4) QSG(s) = K3 E'q(s) + K4 V(s) (14) where K3 = V cos / X'd (15) K4 = (E'q cos - 2V ) / X'd (16) The reactive power supplied by the SVC is given by From equation (4), EM can be written as EM = EM – EMo = 2 (EMo / Vo) V (12) where E'q = change in the internal armature emf proportional to the change in the direct axis field flux under transient condition. For small perturbation equation (12) can be written as QSG = V cos / X'd E'q + (E'q cos - 2V)/ X'd V (13) (2) The electromagnetic energy stored in the winding of the induction generator is given by EM = ½ LM IM2 = ½ LM(V / XM)2 (9) where HR is a constant of the system and its units are sec. and kR is the ratio of system reactive power rating to rated magnetizing reactive power of induction generator. Substituting the value of EMo / QR from equation (9) in equation (8) we get QIG = reactive power required by generator. QSG + QSVC - QL - QIG = d/dt (EM) + DV V (7) In equation (2), DV can be calculated empirically using equation (7). Let QR be the system reactive power rating. Using equation (5), equation (3) can be written as A wind-diesel system is considered for mathematical modeling, where diesel generator (DG) set acts as a local grid for the wind energy conversion system connected to it. The system also has a SVC to provide the required reactive power in addition to the reactive power generated by the synchronous generator. The reactive power balance equation of the system under steady state condition is Q SG+ QSVC = Q L+ QIG (1) QL (6) QSVC = V2 BSVC (5) (17) For small perturbation equation (17), taking Laplace transform, can be written as QSVC(s)= K6 V(s) + K7 BSVC(s) (18) With increase in voltage all the connected loads experience an increase by DV = QL / V pu kVAR /pu kV. The parameter DV can be found empirically. The composite loads are expressed in the exponential voltage form as where 2 K6 = 2 V BSVC and K7 = V2 (19) The optimum value of the parameters corresponds to the minimum value of the performance index. In the studies carried out in this paper is evaluated over a time period of 2 seconds. The performance index curve for 1 % step increase in reactive load demand is shown Fig.2. The minimum value of the gain parameter obtained is KR = 337. The Flux Linkage Equation The flux linkage equation of the round rotor synchronous machine for small perturbation is d/dt (Eq) = (Efd - Eq)/T'do (20) where Eq = change in the internal armature emf proportional to the change in the direct axis field flux under steady state condition. T'do = direct axis open circuit transient time constant The transient response curves of the system for 1% step increase in reactive load for optimum gain settings are shown in Fig. 3. It is observed that the deviation in the system voltage and firing angle vanishes in 150 msec. The deviation in voltage behind transient reactance Δ E'q takes maximum time of 3 sec. to vanish as shown in Fig. 3 (b). It is clear from the Fig. 3 that the reactive demand by load and induction generator ΔQL + ΔQIG is met by reactive power ΔQSVC supplied by the SVC with negligible reactive power ΔQSG supplied by the synchronous generator. The system returns to steady state conditions in 7½ cycles of the supply frequency following a step load disturbance of 1 %. In equation (20) Eq is given by Eq = (Xd / X'd) E'q - (Xd - X'd)/ X'd V cos (21) For small changes equation (20), using equation (21) and taking Laplace transform can be written as (1+ sTg) E'q (s) = K1 Efd(s) + K2 V(s) (22) where Tg = X'd T'do /Xd (23) K1 = X'd/ Xd (24) K2 = (Xd – X'd) cos / Xd (25) Mathematical system Modelling of It indicates that AVR controls the voltage of the system and the SVC controls the reactive power of the system. Wind/diesel Conclusions The block diagram of the system using the Laplace transfer function equations (11), (14), (18) and (22) with typical SVC scheme and IEEE type I excitation system is shown in Fig 1. The state equations in a standard form can be written as x =Ax+Bu+Cp (26) • where x, u and p are state, control and disturbance vectors and A, B and C are system, control and disturbances matrices, respectively. The vectors are given by x =[ Efd Va Vf E'q B'SVC BSVC V]T A dynamic voltage stability study has been presented in this paper for the hybrid wind-diesel isolated power system considering transfer function model based on small signal analysis. The automatic reactive power control model using reactive power flow equations have been developed for the first time for hybrid systems. The integral square error criterion has been used to evaluate the optimum gain settings. It has been shown that SVC is essential for an isolated hybrid system to meet the varying demand of reactive power by induction generator and load and to have minimum voltage fluctuations. Finally some of the system transient responses have been shown for optimum gain settings. (27) u = [Vref ] (28) p = [QL ] (29) The elements of the associated matrices are given in Appendix I. References [1] B.T. Ooi, R.A.David, "Induction Generator/Synchronous Condenser System for Power Systems", IEE Proceedings, Vol. 126, No.1, Jan. 1979, pp. 69 -74. [2] S.S. Murthy, O.P. Malik and A.K. Tandon, "Analysis of Self Excited Induction Generator", IEE Proceedings 129, Pt. C, No. 6, Nov. 1982, pp. 260-265. [3] M.A. Elsharkawi, J.T. Williams and J. N. Butlar, "An Adaptive Power Factor Controller for Three-Phase Induction Generators", IEEE Trans. on PAS, Vol. PAS-104, No. 7, July 1985, pp. 1825-1831. Computer Simulation and Results The data of the wind-diesel power system considered for simulation is given in Appendix -II. The gains are optimized using the Liapunov technique for continuous linear systems with the performance index based upon the integral square error criterion (ISE) and is given by = [V(t)]2 dt (30) 3 [4] A.H. Al-Bahrani, N.H.Malik, "Steady-State Analysis and Performance Characteristic of a 3-Phase Induction Generator Self-Excited with a single capacitor", IEEE Transactions on Energy Conversion, Vol.5, No. 4, 1990, pp. 725-732. [5] T.F.Chan, "Capacitive Requirements of Self-Excited Induction Generators", IEEE Trans. on Energy Conversion, Vol. 08, No. 2, June 1993, pp. 304-311. [6] N.H. Malik and A.A. Mazi, "Capacitive Requirements for Isolated Self-Excited Induction Generators", IEEE Trans. on Energy Conversion, Vol. EC-2, No. 1, March 1987, pp. 62-69. [7] L. Shridhar, B.Singh, C.S.Jha, 1995, "Transient Performance of the Self-Regulated Short-Shunt Self Excited Induction Generator", IEEE Trans. on Energy Conversion, Vol.10, No. 2, 1995, pp. 261-267. [8] S.M. Alghuwainem, "Steady State Analysis of an Induction Generator Self-Excited by a Capacitor in Parallel with a Saturable Reactor", Electric Machines and Power Systems, Vol. 26, 1998, pp. 617-625. [9] Bhim Singh, L. B. Shilpakar, "Analysis of a Novel Solid State Voltage Regulator for a Self-Excited Induction Generator", IEE Proceedings- Generation Transmission Distribution, Vol. 145, No. 6, Nov. 1998. [10] A. A. Shaltout, M.A. Abdel-Halim, "Solid-State Control of Wind Driven Self-Excited Induction Generator", Electric Machines and Power Systems, Vol. 23, 1995, pp. 571-582. [11] S.E. Haque, N.H. Malik, W. Shepherd, "Operation of a Fixed Capacitor-Thyristor Controlled Reactor (FC-TCR) Power Factor Compensator", IEEE Trans. on PAS, Vol. PAS-104, No. 6, June 1985, pp. 1385-1390. [12] P. V. Balasubramanyam, A.S.R. Murthy and P. Parameswaran," Design of Variable Structure Controller for Static VAR Compensator," Electric Machines and Power Systems, Vol. 26, 1998, pp. 431-450. [13] A.E. Hammad, "Analysis of Power System Stability Enhancement by Static VAR Compensators", IEEE Transactions on Power Systems, Vol. PWRS-1, No. 4, November 1986, pp. 222-227. [14] K.R. Padiyar, R.K. Verma, "Static VAR System Auxiliary Controllers for Improvement of Dynamic Stability", Electrical Power and Energy Systems, Vol. 12, No. 4, Oct. 1990, pp. 287-297. Dispatcher Training Simulator", IEEE Transactions on Power Systems, Vol. 10, No. 3, August 1994, pp. 12341242. [17] O.I. Elgerd, "Electric Energy System Theory An Introduction", a book, Tata McGraw Hill, New Delhi, 1982, pp. 299-361. [18] A.A.F. Al-ademi, "Load-Frequency Control of Stand-Alone Hybrid Power Systems Based on Renewable Energy Sources", Ph. D. Thesis, IIT Delhi, India, July 1996. Appendix - I The elements of the system, control and disturbance matrices are given below: A (1,1) = -KE/TE A (1,2) = 1/TE A (2,1) = -KF KA/(TF TA) A (2,2) = -1/TA A (2,3) = KA/TA A (2,8) = -KA/TA A (3,1) = KF/(TF TF) A (3,3) = -1/TF A (4,1) = K1/TG A (4,4) = -1/TgA (4,8) = K2/Tg A (5,5) = -1/Td A (5,6) = 1/Td A (6,6) = -1/T A (6,7) = K/T A (7,7) = -1/TR A (7,8) = -KR/TR A (8,4) = K3 KV/TV A (8,5) = KV K9/TV A (8,8) = -1/TV + KVK4/TV + KVK8/TV-KVK5/TV B (2,1) = KA/TA B (5,1) = KR/TR C (8,1) = -KV/TV where K5 = 2 V Xeq/(R2y + X 2eq) K = 2(1.0-cos (2 ))/(πXR) Appendix-II Table I. Ratings and data of the typical example of the isolated power system studied. Generation Capacity (kW) Load (kW) Wind 150.0 150.0 Diesel 150.0 100.0 Total 300.0 250.0 System Parameters Eq = 1.1136 pu X'd = 0.15 pu TE = 0.55 sec. KF = 0.5 TA= 0.05 sec. QL = 0.75 pu = 2.443985 T= 0.02/4 sec [15] R. Raghunatha, R. Ramanujam, K. Parthasarthy, and D. Thakuram, " Incorporation of Static VAR Compensators and Power System Stabilizers for Dynamic Stability Evaluation", 6th NPSC Conference at IIT Bombay, June 4-7, 1990, pp. 435-4439. [16] Ning Zhu, Subramanian Vadari, Davis Hawang, "Analysis of Static VAR Compensator Using the 4 = 21.05 E'q = 0.9603 pu KA = 40.0 KE = 1.0 TR = 0.05 sec. RY = 4.06415 pu q = 2.0 Td = 0.02/12 sec. Xd = 1.0 pu T'do = 5.0sec. TF = 0.715 sec. KR = 337.0 Xeq = 1.12 pu BSVC = 0.73 pu XR = 1.0/0.85 pu SVC Model (s) Vref(s) + o + B'SVC(s) 1 + s1Td KR K 1 + s TR 1 + s T QSVC (s) 1 + s TV QIG (s) + K5 + E'q (s) 1 K7 QL (s) KV ((((V9s0 1 + s Td B SVC(s) /2 o + V(s) 1 K3 + + QSG(s) + + K6 K4 1 + s Tg + K2 + K1 s KF SF 1 + s TF V Vref (s) ref(s) + KA Va(s) + 1 + s TA 1 Efd(s) KE + s TE Fig. 1 Transfer function block diagram for reactive power control of wind/diesel hybrid power system. 5 0.0005 0.00024 0 V Performance Index, 0.001 0.000245 0.000235 -0.0005 0 50 100 150 200 Time ( msec.) 0.00023 -0.001 0.000225 300 325 350 375 -0.0015 400 KR (a) Fig. 2 Optimization of SVC amplifier gain . 2.5 -0.000005 0 Time (msec.) 0.5 1 1.5 2 Time (sec.) -0.00001 Time (msec.) 2.49 2.48 2.47 Eq' 0 2.46 -0.000015 2.45 -0.00002 2.44 0 50 100 150 200 -0.000025 0.02 b 0.015 QSVC Time ) (msec.) 0.005 0 -0.005 Time c(msec.) 0 50 100 150 0.005 200 0 -0.005 (d) 50 100 150 200 ( Fig. 3 Transient responsese of the system for 1 % step disturbance in ) reactive power load. 0.00015 0.0001 0.00005 50 100 150 200 -0.0001 -0.00015 0 (e) (d) 0 -0.00005 0 ) 0.01 -0.01 QIG ( 0.015 0.01 QSG (c) ( (b) Time (msec.) -0.0002 (f) ( f ) 6