INDIAN INSTITUTE OF TECHNOLOGY, KHARAGUR 730, DECEMBER 79, 00 35 Reactive wer Cntrl f Islated WindDiesel Hybrid wer Systems fr Variable Slip R.C. Bansal, T.S. Bhatti, and D.. Kthari Abstract In this paper autmatic reactive pwer cntrl f islated winddiesel hybrid pwer system having an inductin generatr as a pwer cnversin device fr wind pwer generatin is presented. The mathematical mdel f the system using reactive pwer flw uatins is develped. The dynamic vltage stability evaluatin is based n small signal analysis cnsidering a typical Static VAR Cmpensatr (SVC) and IEEE typei excitatin system. It is shwn that a variable reactive pwer surce like SVC is a must t meet the varying demand f reactive pwer by inductin generatr and lad and t btain a very gd vltage regulatin f the system with minimum fluctuatins. Integral square errr (ISE) criterin is used t evaluate the ptimum setting f gain parameters. Finally the dynamic respnses f the pwer systems cnsidered with ptimum gain setting are als presented. Index Terms: inductin generatr, islated system, static VAR cmpensatr. INTRODUCTION In recent years, much emphasis has been placed n the squirrel cage inductin machine as the electrmechanical energy cnverter in generatin schemes invlving renewable energy surces []. The advantages f the inductin generatr ver the synchrnus generatr are lw cst, rbustness, n mving cntacts, i.e., slip rings, n synchrnizatin ruired and n need fr d.c. excitatin. But the inductin machine ruires a reactive pwer supprt fr its peratin [34]. A large number f papers have appeared in the literature n the subject and a few papers investigate the capacitance ruirement f selfexcited inductin generatr under steady state cnditins nly [4]. It has practical significance as it enables the design and peratin engineers t select the prper value f excitatin capacitance fr a specific machine. In a standalne hybrid pwer system, the reactive pwer device has t fulfill the variable reactive pwer ruirement f the inductin generatr and f the lad. In the absence f prper reactive device and cntrls the system may be subjected t large vltage fluctuatins, which is nt desirable. The device used fr this functin in cnventinal pwer systems is knwn as static var cmpensatr (SVC) [56] can als be emplyed fr the hybrid system. In cnventinal pwer system the pwer is exprted n transmissin lines t lad centres. The reactive pwer devices R.C. Bansal is with the Electrical & Electrnics Engg. Department, Birla Institute f Technlgy & Science, ilani, Rajasthan (India), 33303 email: rcbansal@htmail.cm T.S. Bhatti (email: tsb.ces.iitd.ernet.in) and D.. Kthari (email: dkthari@ces.iitd.ernet.in) are with the Centre fr Energy Studies, Indian Institute f Technlgy, Delhi, Hauz Khas, New Delhi (India) are emplyed in such a way t have minimum reactive pwer flw n the transmissin lines s that maximum pwer can be exprted with minimum transmissin lses. In hybrid systems the lad is directly cnnected t the generatr terminals itself. Therefre the bjective f the reactive pwer device in this case is t supply the reactive pwer ruired by the lad and the inductin machine under varying lad cnditins. An islated winddiesel hybrid pwer system has been cnsidered fr study having inductin generatr fr wind pwer cnversin and synchrnus alternatr with autmatic vltage regulatr (AVR) fr diesel unit. A new innvative scheme, namely, autmatic reactive pwer cntrl, similar t autmatic generatin cntrl [7] has been evlved. The scheme is applicable t islated hybrid pwer systems. The system state uatins have been derived with transfer functin blck diagram representatin f the cntrl system. The vltage deviatin signal is used as area reactive pwer cntrl errr t eliminate the reactive pwer mismatch in the system. The integral square errr (ISE) criterin is used t evaluate the ptimum setting f gain parameters f the cntrller. Finally transient respnses are shwn fr different disturbance cnditins. II. INCREMENTAL REACTIVE OWER BALANCE ANALYSIS A winddiesel system is cnsidered fr mathematical mdeling, where diesel generatr (DG) set acts as a lcal grid fr the wind energy cnversin system cnnected t it. The system als has a SVC t prvide the ruired reactive pwer in additin t the reactive pwer generated by the synchrnus generatr. The reactive pwer balance uatin f the system under steady state cnditin is Q SG Q SVC = Q L Q IG () where Q SG = reactive pwer generated by diesel generatr set, Q SVC = reactive pwer generated by SVC, = reactive pwer lad demand, and Q L Q IG = reactive pwer ruired by generatr. Fr the incremental reactive pwer balance analysis f the hybrid system, let the hybrid system experience a reactive pwer lad change f magnitude Q L. Due t the actin f the AVR and SVC cntrllers the system reactive pwer generatin increases by an amunt Q SG Q SVC. The reactive pwer ruired by the system will als change due t change in vltage by V. The net reactive pwer surplus in the system, therefre, uals Q SG Q SVC Q L Q IG and this pwer will increase the system vltage in tw ways:
36 NATIONAL OWER SYSTEMS CONFERENCE, NSC 00 by increasing the electrmagnetic energy absrptin E M f the inductin generatr at the rate d/dt ( E M ), by an increased reactive lad cnsumptin f the system due t increase in vltage. This can be expressed mathematically as Q SG Q SVC Q L Q IG = d/dt ( E M ) D V V () The electrmagnetic energy stred in the winding f the inductin generatr is given by E M = ½ L M I M = ½ L M (V / X M ) (3) where X M is the magnetizing reactance f the inductin generatr. Equatin (3) can be further written as E M = V / (4πf X M ) (4) Frm uatin (4), E M can be written as E M = E M E M = (E M / V ) V (5) With increase in vltage all the cnnected lads experience an increase by D V = Q L / V pu kvar /pu kv. The parameter D V can be fund empirically. The cmpsite lads are expressed in the expnential vltage frm as Q L = C V q (6) where C is the cnstant f the lad and the expnent q depends upn the type f lad. Fr small perturbatins uatin (6) can be written as Q L / V = q (Q L / V ) (7) In uatin (), D V can be calculated empirically using uatin (7). Let Q R be the system reactive pwer rating. Using uatin (5), uatin (3) can be written as Q SG Q SVC Q L Q IG = E M / (V Q R ) d/dt ( V) D V V (8) In uatin (8) Q R divides nly ne term as all the ther terms are already in pu kvar. The term E M / Q R can be written as E M / Q R = / (4 π f k R ) = H R (9) where H R is a cnstant f the system and its units are sec. and k R is the rati f system reactive pwer rating t rated magnetizing reactive pwer f inductin generatr. Substituting the value f E M / Q R frm uatin (9) in uatin (8) we get Q SG Q SVC Q L Q IG = H R / V d/dt ( V) D V V (0) In Laplace frm the state differential uatin, frm uatin (0), can be written as V(s) = K V /( s T V ) [ Q SG (s) Q SVC (s) Q L (s) Q IG (s)] () Under transient cnditin Q SG is given by Q SG = (E' q V csδ V ) / X' d () where E' q = change in the internal armature emf prprtinal t the change in the direct axis field flux under transient cnditin. Fr small perturbatin uatin () can be written as Q SG = V cs δ / X' d E' q (E' q cs δ V)/ X' d V (3) Taking Laplace transfrm f bth sides we get Q SG (s) = K3 E' q (s) K4 V(s) (4) where K3 = V cs δ / X' d (5) and K4 = (E' q cs δ V ) / X' d The reactive pwer supplied by the SVC is given by (6) Q SVC = V B SVC (7) Fr small perturbatin uatin (7), taking Laplace transfrm, can be written as Q SVC (s)= K 8 V(s) K 9 B SVC (s) (8) where K 8 = V B SVC and K 9 = V (9) III. THE FLUX LINKAGE EQUATION The flux linkage uatin f the rund rtr synchrnus machine fr small perturbatin is d/dt ( E q ) = ( E fd E q )/T' d (0) where E q = change in the internal armature emf prprtinal t the change in the direct axis field flux under steady state cnditin. T' d = direct axis pen circuit transient time cnstant In uatin (0) E q is given by E q = (X d / X' d ) E' q (X d X' d )/ X' d V cs δ () Fr small changes uatin (0), using uatin () and taking Laplace transfrm can be written as ( st g ) E' q (s) = K E fd (s) K V(s) () where T g = X' d T' d /X d (3) K = X' d / X d (4) K = (Xd X' d ) cs δ / X d (5) The real pwer input, IW and reactive pwer, Q IG absrbed by the inductin generatr can be written in terms f generatr terminal vltage, slip and generatr parameters. These uatins can be written fr small perturbatin, by eliminating deviatin in slip, s as Q IG (s)=k 6 m (s)k 7 V(s) (6) where X K 6 = (7) R R X / R = X ( Y ) Y V K 7 = R Y X R X (8) Y ( R ( R X )/ R ) Y Where r ' R = ( s) s (9) R Y = R R (30) R =r r ' (3) X =x x ' (3) IV. MATHEMATICAL MODELLING OF WIND/DIESEL SYSTEM The blck diagram f the system using the Laplace transfer functin uatins (), (4), (8) and () with typical SVC scheme and IEEE type I excitatin system is shwn in Fig. The state uatins in a standard frm can be written as x = A x B u C p (33)
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGUR 730, DECEMBER 79, 00 37 where x, u and p are state, cntrl and disturbance vectrs and A, B and C are system, cntrl and disturbances matrices, respectively. The vectrs are given by x = [ E fd V a V f E' q α B' SVC B SVC V] T (34) u = [ V ref ] (35) p = [ Q L ] (36) The elements f the assciated matrices are given in Appendix I. V. COMUTER SIMULATION AND RESULTS The data f the winddiesel pwer system cnsidered fr simulatin is given in Appendix II. The gains are ptimized using the Liapunv technique fr cntinuus linear systems with the perfrmance index based upn the integral square errr criterin (ISE) and is given by η = [ V(t)] dt (37) The ptimum value f the parameters crrespnds t the minimum value f the perfrmance index. In the studies carried ut in this paper η is evaluated ver a time perid f secnds. The perfrmance index curve fr % step increase in reactive lad demand is shwn Fig.. The minimum value f the gain parameter btained is K R = 575. The transient respnse curves f the system fr % step increase in reactive lad fr ptimum gain settings are shwn in Fig. 3. It is bserved that the deviatin in the system vltage and firing angle vanishes in abut 0.3 sec. It is clear frm the Fig. 3 that the reactive demand by lad and inductin generatr Q L Q IG is met by reactive pwer Q SVC supplied by the SVC with negligible reactive pwer Q SG supplied by the synchrnus generatr. The system returns t steady state cnditins in 7½ cycles f the supply fruency fllwing a step lad disturbance f %. It indicates that AVR cntrls the vltage f the system and the SVC cntrls the reactive pwer f the system. VI. CONCLUSIONS A dynamic vltage stability study has been presented in this paper fr the hybrid winddiesel islated pwer system cnsidering transfer functin mdel based n small signal analysis. The autmatic reactive pwer cntrl mdel using reactive pwer flw uatins have been develped fr the first time fr hybrid systems. The integral square errr criterin has been used t evaluate the ptimum gain settings. It has been shwn that SVC is essential fr an islated hybrid system t meet the varying demand f reactive pwer by inductin generatr and lad and t have minimum vltage fluctuatins. Finally sme f the system transient respnses have been shwn fr ptimum gain settings. VII. REFERENCES [] S.S. Murthy, O.. Malik and A.K. Tandn, "Analysis f Self Excited Inductin Generatr", IEE rceedings 9, t. C, N. 6, Nv. 98, pp. 6065. [] M.A. Elsharkawi, J.T. Williams and J. N. Butlar, "An Adaptive wer Factr Cntrller fr Threehase Inductin Generatrs", IEEE Trans. n AS, Vl. AS04, N. 7, July 985, pp. 8583. [3] A.H. AlBahrani, N.H.Malik, "SteadyState Analysis and erfrmance Characteristic f a 3hase Inductin Generatr Self Excited with a single capacitr", IEEE Transactins n Energy Cnversin, Vl.5, N. 4, 990, pp. 7573. [4] S.M. Alghuwainem, "Steady State Analysis f an Inductin Generatr SelfExcited by a Capacitr in arallel with a Saturable Reactr", Electric Machines and wer Systems, Vl. 6, 998, pp. 6765. [5] A.E. Hammad, "Analysis f wer System Stability Enhancement by Static VAR Cmpensatrs", IEEE Transactins n wer Systems, Vl. WRS, N. 4, Nvember 986, pp. 7. [6] K.R. adiyar, R.K. Verma, "Static VAR System Auxiliary Cntrllers fr Imprvement f Dynamic Stability", Electrical wer and Energy Systems, Vl., N. 4, Oct. 990, pp. 8797. [7] O.I. Elgerd, "Electric Energy System Thery An Intrductin", a bk, Tata McGraw Hill, New Delhi, 98, pp. 9936. Appendix I The elements f the system, cntrl and disturbance matrices are given belw: A (,) = K E /T E A (,) = /T E A (,) = K F K A /(T F T A ) A (,) = /T A A (,3) = K A /T A A (,8) = K A /T A A (3,) = K F /(T F T F ) A (3,3) = /T F A (4,) = K /T g A (4,4) = /T g A (4,8) = K /T g A (5,5) = /T d A (5,6) = /T d A (6,6) = /T α A (6,7) = K α /T α A (7,7) = /T R A (7,8) = K R /T R A (8,4) = K 3 K V /T V A (8,5) = K V K 9 /T V A (8,8) = /T V K V K 4 /T V K V K 8 /T V K V K 5 /T V B (,) = K A /T A B (5,) = K R /T R C (8,) = K V /T V where K 5 = V X /(R y X ) K α = (.0cs ( α))/(πx R ) AppendixII Table I. Ratings and data f the typical example f the islated pwer system studied. Generatin Capacity (kw) Lad (kw) Wind 50.0 50.0 Diesel 50.0 00.0 Ttal 300.0 50.0 System arameters E q =.36 pu δ =.05 X d =.0 pu X' d = 0.5 pu E' q = 0.9603 pu T' d = 5.0sec. T E = 0.55 sec. K A = 40.0 T F = 0.75 sec. K F = 0.5 K E =.0 K R = 337.0 T A = 0.05 sec. T R = 0.05 sec. X =. pu Q L = 0.75 pu R Y = 4.0645 pu B SVC = 0.73 pu α =.443985 q =.0 X R =.0/0.85 p T α = 0.0/4 sec T d = 0.0/ sec
38 NATIONAL OWER SYSTEMS CONFERENCE, NSC 00 Type I SVC mdel α 0 α π V ref (s) K R st R α 0 α π B K SVC (s) α α(s) st d st α B SVC (s) π/ α π/ 0 α α 0 α V(s) K V st V Q L (s) Q SVC K 9 K 7 Q IG (s) K 6 Q SG (s) K 8 IW (s) E q (s) st G K 3 K 4 K K V a (s) V f (s) saturatin functin skf st F S F V ref (s) K A st A K E st E E fd (s) Fig.. Transfer functin blck diagram fr reactive pwer cntrl f wind/diesel hybrid pwer system with variable slip
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGUR 730, DECEMBER 79, 00 39 erfrmance Index, η.70e03.60e03.50e03 500 550 600 650 K R V.00E03.00E03 0.00E00.00E03 Time ( sec.).00e03 (a) Fig. Optimizatin f SVC amplifier gain.53.00e04.49 E q '.45 0.00E00 0 0.05 0. 0.5 0. 0.5 0.3.4 (b) α.50e0 (c).00e0 Q SG 0.00E00 0 0.05 0. 0.5 0. 0.5 0.3.00E0 (d) Q SVC.00E0 0 5.00E03 0. 0. 0.3 (e) 3.0E03 Q IG 3.00E03 Fig. 3 Transient respnses f the system fr % step disturbance in.80e03 (f)