Adaptive Power System Stabilizer Using ANFIS and Genetic Algorithms

Transcription

1 Procdings of th 44th IEEE Confrnc on Dcision and Control, and th Europan Control Confrnc 005 Svill, Spain, Dcmbr -5, 005 ThC0. Adaptiv Powr Systm Stabilizr Using ANFIS and Gntic Algorithms J. Frail-Ardanuy, TMmbr, IEEE and P.J.Zufiria. T Abstract This papr prsnts an adaptiv Powr Systm Stabilizr () using an Adaptiv Ntwork Basd Fuzzy Infrnc Systm (ANFIS) and Gntic Algorithms (GAs). Firstly, gntic algorithms ar usd to tun a convntional on a wid rang of oprating conditions and thn, th rlationship btwn ths oprating points and th paramtrs is larnd by th ANFIS. Th ANFIS optimally slcts th classical paramtrs basd on machin loading conditions. Th proposd stabilizr has bn tstd by prforming nonlinar simulations using a synchronous machin-infinit bus modl. Th rsults show th robustnss and th capability of th stabilizr to nhanc systm damping ovr a wid rang of oprating conditions and systm paramtr variations. P I. INTRODUCTION OWER systm control rquirs a continuous balanc btwn lctrical gnration and a varying load dmand, whil maintaining systm frquncy and voltag lvls. Th us of high prformanc xcitation systms is ssntial for maintaining stady stat and transint stability of modrn synchronous gnrators and provids fast control of th trminal voltag. Howvr, ths fast acting xcitrs with high gains can contribut to oscillatory instability in th powr systm. This typ of instability is charactrizd by low frquncy oscillations which can prsist or vn grow in magnitud [-]. Svral ral xampls hav bn rcordd and studid [3-4]. In ordr to avoid this ffct, supplmntary stabilizing signals hav bn proposd in th xcitation systms through lad/lag powr systm stabilizrs [5] or PI - PID powr systm stabilizrs [6]. Th computation of th fixd paramtrs of ths stabilizrs is basd on th linarizd modl of th powr systm around a nominal oprating point. Th oprating condition dos chang as a rsult of load variation and maor disturbancs, making th dynamic bhavior of th powr systm to bcom diffrnt, at diffrnt oprating points. Thus, if th paramtrs of th stabilizr ar kpt fixd, prformanc is dgradd whnvr th oprating point changs. J. Frail Ardanuy is with th Polytchnic Univrsity of Madrid, Spain. (phon: ; fax: ; -mail: far@ caminos.upm.s). P. J. Zufiria is with th Polytchnic Univrsity of Madrid, Spain (pzz@mat.upm.s) Thrfor, a good dsign must considr a trad-off btwn adaptability to th changs of th dynamics of th plant and asy dsign. From th svntis, dvlopmnts in digital tchnology hav mad possibl to implmnt nw controllrs using adaptiv control tchniqus [7-0]. Ths stabilizrs provid bttr dynamic prformanc ovr a wid rang of oprating conditions, but thy suffr from th maor drawback of rquiring paramtr modl idntification, stat obsrvation and fdback gain calculations in ral-tim. If thr is som rror in paramtr idntification, it can lad to gnrat incorrct control signals, rducing th robustnss. In last dcad, Fuzzy Logic Controllrs (FLCs) and Artificial Nural Ntwork Controllrs (ANNCs) bing usd as powr systm stabilizrs, hav bn dvlopd and tstd [-8]. Unlik othr classical control mthods, FLCs and ANNCs ar modl-fr controllrs; i. thy do not rquird an xact mathmatical modl of th controlld systm. Morovr, spd and robustnss ar th most significant proprtis in comparison to th othr classical schms. But ths controllrs prsnt som disadvantags. Thr ar not practical systmatic procdurs for th Fuzzy (F) dsign, so th ruls and th mmbrship functions of th controllr ar tund subctivly, making th dsign laborious and a tim-consuming task. With rspct to ANNCs, thy hav th capability of larning and adaptation, but thy work lik a 'black-box' and it is difficult to undrstand th bhaviour of th ntwork. In ordr to mak th dsign simplr, Gntic Algorithms (GAs) hav bn succssfully applid to dsign [9-]. GAs dfin a global optimization tchniqu basd on th mchanics of natural slction and survival-of-th-fittst. In th rsarch rportd in this papr, a convntional for a singl machin infinit bus systm is tund by an Adaptiv Ntwork basd Fuzzy Infrnc Systm (ANFIS) traind from th input-output data gnratd by a GA. Th advantags of this dsign ar: Th Gntic Algorithm uss a simpl obctiv function which dos not dpnd on th mathmatical modl of th lctric powr systm. Th ANFIS combins th advantags of FLCs and ANNCs, avoiding thir problms. Th paramtrs ar modifid on-lin, in ordr to gt a bttr rspons in th ntir rang of opration /05/$ IEEE 808

2 and II. GENETIC ALGORITHMS AND ANFIS A. Gntic Algorithms Gntic Algorithms copy th procss of th natural volution. Th principls of GAs wr firstly publishd by Holland [3]. In GAs, th faturs charactrizing an individual ar oftn binary codd in bits and concatnatd as a string. Th string packag mad from diffrnt combinations of bits is rfrrd to as a point in th solution spac. Th fundamntal oprations of a GA ar: Initialization. Th GA dos not work with a singl string but with a population of strings, which volvs itrativly by gnrating nw individuals taking th plac of thir parnts. To bgin, th individuals of th initial population ar gnratd randomly. In our application, ach string dos cod a st of paramtrs. Obctiv Function. Th prformanc of ach structur is valuatd according to its 'fitnss', which is dfind as th non-ngativ figur of mrit to b maximizd. Gntic Oprations. With th valuation of th fitnss function of all individuals, th GA gnrats a nw and improvd population from th old on. Most commonly usd oprations ar th following: Rproduction. It is an opration whrby an old string is copid into a 'mating pool' according to its fitnss. Mor highly fittd strings rciv a highr numbr of copis in th nxt gnration. Crossovr. Crossovr xchangs gntic matrial from two parnt chromosoms, allowing thir bnficial gns to b combind in thir offspring. Mutation. It is an opration which is abl to crat nw gntic matrial in th population, changing som chromosoms according to a probabilistic law. B. ANFIS ANFIS was proposd by [4]. In this nural fuzzy control systm, th consqunts of th Takagi-Sugno (TS) fuzzy ruls ar linar combinations of thir prconditions. Th TS fuzzy ruls ar in th following forms: Rul : IF B xb is A AND xbb is A AND xbnb is A n THEN y = f = a0 + a x + a x an xn () ANFIS is composd of six functional layrs, as shown in Fig. : In layr, vry nod is an input nod that ust passs xtrnal signals to th following layr. In layr, vry nod is an adaptiv on with a nod function dfind by: µ () x A i i whr xbib is th input to th ith-nod and A i is th linguistic labl (larg, small, tc.) associatd with this nod. Th output of this nod spcifis th dgr to which th givn B xbi satisfis th quantifir A i. In this study, th function µ is th bll-shapd function with a maximum valu x A i i qual to and a minimum valu qual to 0, with th following paramtrs{ a i, bi, ci }: b i xi ci µ = + xi (3) Ai ai x x A A A A µa (x) Π µa (x) µa (x) µa (x) Π LAYER LAYER LAYER 3 LAYER 4 LAYER 5 Fig.. Architctur of ANFIS systm. w w w w N N w w x x f x x f w f w f Σ LAYER 6 y=w f + w f Paramtrs in this layr ar rfrrd to as prmis or prcondition paramtrs B SB can b traind using th ANFIS hybrid larning algorithm. Evry nod in layr 3 is a fixd nod which multiplis th incoming signals. Each nod output rprsnts th firing strngth of a rul, hnc, th nods prform th fuzzy AND opration. = µ ( x ). µ ( x ), =, (4) A A Nods in layr 4 ar fixd nods and calculat th ratio of th firing strngth of th -th rul to th sum of all firing strngths of th ruls: = (5) = In layr 5, vry nod in this layr is an adaptiv nod and has th following output: ( p x + q x + r ) whr { p q, r } (6), is rfrrd to as th consqunt paramtr st SB B. Thy can also b traind using ANFIS larning algorithms. Th singl nod in th layr 6 is a fixd nod that computs th ovrall output as th summation of all incoming signals, i.., y = f (7) Th ANFIS hybrid larning algorithm is composd of a forward pass and a backward pass. In th forward pass, kping constant th availabl valus of th prmis paramtrs st SBB, functional signals go forward until layr four and th consqunt paramtr vctor { p, q, r } is idntifid by mans of th last squars stimat (LSE), solving th ovr constraind simultanous linar quations shown in (8). 809

3 of and ar and ar r () () () () () () p ϖ ϖ x... ϖ x d () () () () () () q ϖ ϖ x... ϖ x = d. (8) : : : : r : p p p p p p ϖ x... x p ϖ ϖ d q whr ( k ( ) ( k [ x, x )), d ] k ar th k-th training pair, with k=,,..p, and ϖ ( k ) and ϖ ( k ) ar th third-layr outputs associatd with th input ( k ( ) ( k x x ), ). In th backwards pass, th rror rats propagat backward and th prmis paramtrs ( k ) B SB, ϖ and ( k ϖ ), ar updatd by th gradint dscnt [4]. III. PROPOSED ADAPTIVE Th proposd is shown in Fig., whr th ANFIS systm adusts th paramtrs procssing th oprating points data dfind by th activ powr output, PBtB, ractiv powr output, QBtB, and th trminal voltag, VBtB th gnrator. A widly usd convntional lad-lag is considrd in this papr: T + st V = K (9) + st + st whr TB B is st to b.0 s. ANFIS outputs ar th optimal paramtrs gnratd by th gntic algorithm in this particular oprating point dfind by th inputs. Convntional Wash-out filtr lad-lag controllr T K +st +st +st Oprating Conditions P t Q t V t Fig.. Proposd Adaptiv. ANFIS V adaptiv paramtrs: K, T and T Th dsign is dividd in two diffrnt parts: A. Tuning th convntional using GA in diffrnt oprating points, storing th optimal paramtrs and th oprating conditions. B. Training th ANFIS systm with th stord data. A. Collcting th training data Firstly, a GA is usd to adust th paramtrs on a wid spctrum of oprating conditions, i.., th gnrator powr output ranging from 0. p.u. to. p.u., and th powr factor ranging from 0.7 lad to 0. lag. Similarly, a wid rang of possibl disturbancs is usd for th training. Ths disturbancs ar: rfrnc voltag in th rang of 0. to 0.5 p.u., input mchanical torqu variation from 0. p.u. to 0. p.u., on transmission lin outag and thr phas fault on on of th doubl circuit transmission lins connctd to th gnrator. Starting in a particular oprating point, th GA sarchs th paramtrs that optimiz th fitnss function: f k = (0) t + t () t dt t whr B B tb tb th study tim limits and (t) rprsnts th spd dviation of th gnrator. Th paramtrs KB B, B TBB TB slctd so as to maximiz th obctiv function fbkb. Th advantag of th slctd fitnss function as opposd to othr functions proposd in [0], [] and [5], is that minimal dynamic plant information is ndd. It is only ncssary to masur th spd dviation of th gnrator instad of idntifying on-lin th lctric powr systm modl paramtrs, ndd to dsign th by a polplacmnt tchniqu. For a givn oprating point, th obctiv function is valuatd with an initial population randomly gnratd. Each individual in th initial population has an associatd fitnss function valu. Using this information, GA oprations ar applid to produc th nxt gnration. Ths two stps, valuation of th obctiv function and gnration of th nw population, ar rpatd from gnration to gnration until th population dos convrg, producing th optimum paramtrs for this particular oprating point. Onc th paramtrs ar tund, ths data ar stord togthr with th loading condition and th algorithm starts again in a diffrnt oprating point. All th data collctd constitut th training st. B. ANFIS Training A total of 5000 input-output data pairs wr obtaind for th training of th ANFIS. Th ANFIS transforms a fuzzy infrnc ngin into an adaptiv ntwork that larns th rlationship btwn inputs, dfind by th oprating conditions, and outputs, dfind by th paramtrs. Ths rlationships ar larnd indpndntly for ach paramtr, using 3 ANFIS, in ordr to improv th convrg spd of th ANFIS hybrid larning algorithm. Choosing th corrct numbr of mmbrship functions is a fundamntal qustion oftn raisd in ths applications. Usually this numbr is dtrmind xprimntally in a similar way to choosing th numbr of nurons in th hiddn layr of an artificial nural ntwork. But thr ar othr mthods basd on pruning or growing th ntwork. Pruning algorithms start with a largr ntwork and thn prun it to dsird siz [7], [8]. On th opposit, growing algorithms start with a small ntwork and gradually incras it to appropriat siz [9]. In this papr, th numbr of mmbrship functions for ach input variabl is dtrmind 8030

4 by trial and rror for simplicity. In this study, fiv linguistic variabls for ach input variabl wr us to gt th dsird prformanc. IV. SIMULATION STUDIES To dmonstrat th ffctivnss of th proposd whos paramtrs ar adaptd by th ANFIS, tim domain simulations wr prformd for th gnrator undr maor disturbanc conditions ovr a wid rang of loading conditions. Tst cass ar similar to thos proposd in [- 3] and [5-], to vrify th bhavior. Th considrd systm is a synchronous machin connctd to an infinit bus through two paralll transmission lins as shown in Fig. 3. stp chang, P= p.u. and pf=0.97 p.u. Changing th oprating point to 0.6 p.u. gnratd powr and a powr factor lad of 0.8, a 5 % stp dcras in input torqu rfrnc was applid at t=0. s. Th spd dviation for th proposd and th convntional ar shown in Fig. 5. Th proposd shows bttr damping. v t R X E b G R X Proposd Excitr and AVR v Convntional v t Fig. 3. Singl machin infinit bus systm with two transmission lins. Th nonlinar modl quations usd to simulat th gnrating unit, AVR and convntional (C) ar givn in th Appndix. Th C is adustd to giv optimal prformanc for th oprating point of p.u. gnratd powr, and 0.97 powr factor lag. A. Input Torqu Rfrnc Stp Chang With th gnrator oprating at an activ powr of p.u. and powr factor lag of 0.97, a 5% stp dcras in th input torqu rfrnc was applid at t=0. s. Th spd dviation of th gnrator for th proposd and th convntional ar shown in Fig. 4. With th slctd paramtrs, th C and th proposd rsponss wr vry clos to ach othr. v rf 0 Fig. 5. Spd dviation for a 0.5 p.u. mchanical input torqu rfrnc stp chang, P=0.6 p.u. and pf=-0.8 p.u. B. Switching of on lin At an oprating point of 0.9 p.u., 0.98 powr factor lag, on circuit of th doubl circuit transmission lin was switchd off at t=9 s. Bfor th lin disconnction, 0. p.u. stp incras in th input torqu rfrnc was applid at t= s and rmovd at t=5 s. A scond 0. p.u. stp incras in th input torqu rfrnc was applid at t=3 s. and rmovd at t=7 s. during th transmission lin fault. Th rspons of th systm with both convntional and th proposd is shown in Fig. 6. Th rspons with th proposd shows lss oscillations than th convntional and dmonstrats bttr prformanc. Fig. 6. Powr angl for a ±0. p.u. input torqu rfrnc stp chang at P=0.9 p.u. and pf=0.98 p.u. during th switching of on of th transmission lins. Fig. 4. Spd dviation for a 0.5 p.u. mchanical input torqu rfrnc 803

5 ar is Th paramtrs slctd valus of th proposd during this simulation ar shown in Fig. 7. Fig. 7. Proposd tund paramtrs. C. Thr phas to ground fault Thr phas to ground fault locating at 50 % of th distanc along lin is applid at t=0.5 s. and th fault is clard at t=0.773 s. Rsponss without stabilizr and with convntional and proposd ar shown in Fig. 8. Systms without stabilizr and with convntional ar both unstabl. Th systm with proposd is highly oscillatory, but it is stabl. Fig. 8. Thr phas to ground fault. V. CONCLUSION An adaptiv powr systm stabilizr basd on an Adaptiv-Ntwork-Basd Fuzzy Infrnc Systm and Gntic Algorithms is prsntd in this papr. Th ffctivnss of this schm has bn invstigatd through nonlinar simulations. Th following conclusions ar drivd from th rsults: Sinc paramtrs ar adustd by a gntic algorithm, minimal knowldg about th systm is rquird and thr is no nd for systm modl linarization. Du to th slctd fitnss function, opposit to othr functions proposd in othr paprs, thr is no nd to idntify th powr systm modl paramtrs. So this dsign, which is not basd on a pol-placmnt tchniqu, savs tim and rducs th complxity of th dsign. Th ANFIS combins th advantags of artificial nural ntworks and fuzzy logic controllrs, that is, adaptation and robustnss. Sinc th proposd dsign modifis th paramtrs of th installd classical, thr is no nd to chang th actual in th gnrator. Tst rsults for various oprating conditions and disturbations show that th proposd stabilizr is abl to provid good damping ovr a wid oprating rang and improvs th ovrall systm prformanc. APPENDIX Systm Modl: dδ d = 0, = ( Tmch D T lc ) (A.) dt dt M whr, T mch and T lc ar th input (mchanical) and output (lctrical) torqus of th gnrator, rspctivly; M is th inrtia constant and DB B is th damping cofficint, δ y ar th rotor angl and spd, rspctivly. Th intrnal voltag quations ar: deq = ( E FD Eq ( xd x d ) id ) (A.) dt Td0 ded = ( Ed ( xq xq ) iq ) (A.3) dt T lc q0 d d q q ( xq xd ) iqid T = E i + E i + (A.4) ( x + x )( x + x ) Z = r + (A.5) q id r + rs x + x q Ed = i q Z ( x + ) + xd r rs E q (A.6) E + s + b r r x xq sin δ Z x + xd r + rs cosδ Th IEEE Typ-ST xcitation systm is considrd in this study: de FD K A EFD = ( Vrf Vt + V ) (A.7) dt TA TA whr B KBA and B TBA th gain and tim constant of th xcitation systm, VBrfB is th rfrnc voltag and VBtB th trminal voltag. For th convntional, th following transfr function is considrd: T + st V = K (A.8) + st + st whr TB B is th wash-out filtr tim constant. d 803

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