SIMULTANEOUS TUNING OF POWER SYSTEM STABILIZER PARAMETERS FOR MULTIMACHINE SYSTEM

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1 SIMULTANEOUS TUNING OF POWER SYSTEM STABILIZER PARAMETERS FOR MULTIMACHINE SYSTEM Mr.M.Svasubramanan 1 Mr.P.Musthafa Mr.K Sudheer 3 Assstant Professor / EEE Assstant Professor / EEE Assstant Professor / EEE VELTECH MULTITECH Dr RANGARAJAN Dr SAKUNTHALA ENGINEERING COLLEGE, AVADI, CHENNAI, INDIA ABSTRACT: Optmal multobjectve desgn of robust multmachne power system stablzers () usng genetc algorthms s presented n ths thess. A conventonal speed-based lead-lag PSS s used. The multmachne power system operatng at varous loadng condtons and system confguratons s treated as a fnte set of plants. The stablzers are tuned to smultaneously shft the lghtly damped and undamped electromechancal modes of all plants to a prescrbed zone n the s- plane. A multobjectve problem s formulated to optmze a composte set of objectve functons comprsng the dampng factor, and the dampng rato of the lghtly damped electromechancal modes. The problem of robustly selectng the parameters of the power system stablzers s converted to an optmzaton problem whch s solved by a genetc algorthm wth the egenvaluebased multobjectve functon. The effectveness of the suggested technque n dampng local and nterarea modes of oscllatons n multmachne power systems, over a wde range of loadng condtons and system confguratons, s confrmed through egenvalue analyss and nonlnear smulaton results Index Terms - Small sgnal stablty, genetc algorthms, multple objectve optmzaton, robustness, smultaneous stablzaton. 1. INTRODUCTION In mult-machne power systems wth several poorly damped modes of oscllatons, several power system stablzers (PSS) need to be on-lne and optmally tuned. present-day large-scale systems comprsng many nterconnected machnes, the problem of PSS tunng s not a straght-forward exercse, and n some cases can become relatvely too complex to resolve. The problem of PSS tunng s further complcated by the fact that operatng condtons n a power system are contnuously varyng. Therefore tunng the PSS such that, t would provde a satsfactory performance over the entre range of varatons s a rather exhaustve exercse. Research has been drected towards the desgn of adaptve (self-tunng), varable structure and other control strateges that provde robust tunng. However, mplementaton of such PSS requres contnuous on-lne calculaton of an dentfed model usng parameter estmaton and evaluaton of the control strategy. In recent years, research has been drected towards the applcaton of advanced numercal computaton methods such as neural networks and genetc algorthms (GA) to PSS tunng. Ths paper presents the desgn of a GA based PSS that uses a egen value based parameter optmzaton crteron to determne the ftness functon of an ndvdual wthn a populaton of possble solutons. Genetc algorthms are global search technques and provde a powerful tool for optmzaton problems by mmng the mechansms of natural selecton and genetcs. These operate on a populaton of potental solutons applyng the prncple of survval of the fttest to produce better and better approxmatons to a soluton. In each generaton, a new set of approxmatons s created by the process of selectng the ndvduals accordng to ther level of ftness n the problem doman and breedng them together usng operators borrowed from natural genetcs [1]. Thus, the populaton of solutons s successvely mproved wth respect to the search objectve, by replacng least ft ndvduals wth new ones (offset of ndvduals from the prevous generaton), better suted to the envronment, just as n natural evoluton. The performance (ftness) of each 9 P a g e

2 ndvdual n the problem doman s assessed through an objectve functon that ultmately establshes the bass for the based selecton process. Hgher the ndvduals ftness s, hgher s ts chance to pass on genetc nformaton to successve generatons. The selected ndvduals are then modfed through the applcaton of genetc operators, n order to obtan the next generaton. Thus GA based optmzaton of PSS parameters s more lkely to converge to the global optma than a conventonal optmzaton, snce they search from a populaton of possble solutons, and are based on probablstc transton rules. Moreover, by tunng the PSS smultaneously, the egenvalue drft problem s elmnated. In the recent lterature, applcaton of genetc algorthm to tune the parameters of PSS has been reported [1], [], [7]. A GA based optmzaton method has been used n [] to tune the parameters of a rule-based PSS. Ths way, the advantages of the rule-based PSS such as ts robustness, less computatonal burden and ease of realzaton are mantaned. Introducton of GA helps obtan an optmal tunng for all PSS parameters smultaneously, whch thereby takes care of nteractons between dfferent PSS. In [] smultaneous tunng for all the PSS n the system usng a GA based approach has been developed. The GA seeks to shft all egenvalues of the system wthn a regon n the stable doman.. APPLICATION OF GENETIC ALGORITHM TO PSS DESIGN Each ndvdual n the ntal populaton has an assocated objectve functon value. Usng the objectve functon nformaton, the GA then produces a new populaton. The applcaton of a genetc algorthm nvolves repettvely performng two steps: 1. The calculaton of the objectve functons for each of the ndvduals n the current populaton. To do ths, the system egenvalues must be computed.. The genetc algorthm then produces the next generaton of ndvduals usng the selecton, crossover and mutaton operators. These two steps are repeated from generaton to generaton untl the populaton has converged, producng the optmum parameters. A genetc algorthm (GA)-based approach to robust PSS desgn, n whch several operatng condtons and system confguratons are smultaneously consdered n the desgn process, s presented. The advantage of the GA technque s that t s ndependent of the complexty of the performance ndex consdered. It suffces to specfy the objectve functon and to place fnte bounds on the optmzed parameters. Intally, the robust PSS desgn was formulated as a sngle objectve functon problem, and not all PSS parameters were consdered adjustable. However, n practce, one s typcally confronted wth multple objectve functons and these objectve functons are generally of dverse natures. In ths thess, the problem of robust PSS desgn s formulated as a multobjectve optmzaton problem and GA s employed to solve ths problem. Moreover, unlke [], all PSS parameters were consdered adjustable, and more severe dsturbances were used to assess the potental of the multobjectve approach. Robustness s acheved by consderng several operatng condtons and system confguratons smultaneously. The multobjectve problem s concocted to optmze a composte set of two egenvaluebased objectve functons comprsng the desred dampng factor, and the desred dampng rato of the lghtly damped and undamped electromechancal modes. The use of the frst objectve functon wll result n that shft the lghtly damped and undamped electromechancal modes to the left-hand sde of a vertcal lne n the complex s-plane; hence, mprovng the dampng factor. The use of the second objectve functon wll yeld settngs that place these modes n a wedge-shape sector n the complex s-plane, thus mprovng the dampng rato of these modes. Consequently, the use of the multobjectve functon wll therefore guarantee that the relatve stablty and the tme doman specfcatons are concurrently secured. The proposed desgn approach has been appled to a multmachne power system. The egenvalue analyss and the nonlnear smulaton results have been carred out to assess the effectveness of the proposed under dfferent dsturbances, loadng condtons, and system confguratons. 3. CONTROLLER TUNING: The problem of selectng the parameters of the controllers that would assure maxmum dampng performance over the consdered set of operatng ponts s solved va a GAs optmzaton procedure wth an egenvalue based performance ndex. 30 P a g e

3 A. MODEL AND CONTROL STRUCTURE Equatons 1 descrbe a lnear model of power system extracted around a certan operatng pont. x Ax Bu (1) y Cx Du The controller s a lead-lag type descrbed by: V( s) K( s) y( s ) () where K(s) s the transfer functon of the controller, y(s) s the measurement sgnal and V (s) s the output sgnal from the controller whch wll provde addtonal dampng by movng modes to the left. Equaton can be expressed n the statespace form as: xk Ak xk Bk y (3) u Ck xk Dk y where x k s the state vector of the controller. Combnng Equatons 1 and 3 wth Equatons 1 and a closed loop system gven n Equaton 4 s obtaned. pont. The relatve stablty s determned by the value of 0. In many cases, certan tme-doman control system specfcatons such as maxmum overshoot, rse tme and steady-state error goals can be realzed by placng the closed-loop egenvalues of the system wthn a regon bounded by mnmum of the dampng coeffcents n the left-half of the complex s-plane. In order to do ths, the objectve functon of (7) s changed to: J [ 0, j] (7) j 1 where s the dampng rato of the -th egenvalue of the j-th operatng pont. Ths wll place the closed-loop egenvalues n a wedge-shape sector n whch as shown n Fg. 4. xcl Acl x cl (4) Let j be the -th egenvalue (mode) of the closed loop matrx. Then, the dampng coeffcent ( ) of the -th egenvalue s defned by The structure of PSS s gven below. (5) st (1 st ) (1 st ) U s K s w 1 3 ( ) ( ) 1 stw (1 st ) (1 st4 ) B. OBJECTIVE FUNCTION Very often, the closed loop modes are specfed to have some degree of relatve stablty. In ths case, the closed-loop egenvalues are constraned to le to the left of a vertcal lne correspondng to a specfed dampng factor. Select the parameters of the PSS to mnmze the followng objectve functon: J 1 [ 0, j] (6) j 1 where s the number of operatng ponts consdered n the desgn process, and s the real, j part of the -th egenvalue of the j-th operatng Fg.1 Interested regon of pole locatons n s-plane These sngle objectve problems may be converted to a multple objectve problem by assgnng dstnct weghts to each objectve. In ths case, the condtons and are mposed smultaneously. The parameters of the PSS may be selected to mnmze the followng objectve functon: 31 P a g e

4 J J1 aj (8) [ 0, j ] [ 0, j ] j 1 j 1 J a Ths wll place the system closed-loop egenvalues n the D-shape sector as shown n Fg.4.3. The desgn problem can be formulated as the followng constraned optmzaton problem, where the constrants are the PSS parameter bounds: Mnmze J subject to K K K,mn,max 1,mn 1 1,max,mn,max 3,mn 3 3,max 4,mn 4 4,max (9) The mnmzaton of the objectve functon J wll result n a PSS structure that satsfes the tme-doman performance specfcatons as well as relatve stablty. It s necessary to menton here that f only partcular egenvalues need to he relocated, then only those egenvalues should be taken nto consderaton n the computaton of the objectve functon. Ths s usually the case n dynamc stablty where t s desred to relocate the electromechancal modes of oscllatons. The proposed approach employs GA to solve ths optmzaton problem and search for optmal or near optmal set of PSS parameters, K, T1, T, T3, T for =1 to m, where 4 m s the number of machnes. C. CONTROL PARATMETERS AND GA PARAMETERS A two stage lead/lag compensator structure was chosen for the PSS. Hence all the fve parameters (K, T 1, T, T 3 and T 4 ) are taken as control parameters. Gan K s bounded between 0.5 and 150 and all Tme constants are bounded between 0.01 and 1.5 seconds. These parameterbounds were defned on the bass of conventonal control desgn for nomnal operatng condton. In GA mplementaton, the crossover and mutaton probabltes of 0.95 and 0.033, respectvely, are found to be qute satsfactory. The number of ndvduals n each generaton s selected to be 00. In addton, the search wll termnate f the best soluton does not change for more than 50 generatons or the number of generatons reaches 100 for sngle objectve functon and 00 for multobjectve functon respectvely. 4. TEST SYSTEM AND PSS DESIGN The one-lne dagram of the test system s gven n Fg.. Ths two-area power system, whch as a benchmark system for nter-area oscllatons studes consst of two generators n each area, connected va a 0 km te lne. All generators are equpped wth smple excters and have the same parameters. Dampng control s provded at all four generators. Fg. Two Area 4 Machne Power System To desgn the proposed, two dfferent operatng condtons that represent the system under severe loadng condtons and crtcal lne outages n addton to the base case are consdered. These condtons are extremely harsh from the stablty vewpont [6]. Two system confguratons, whch s heavly loaded wth 400 MW of power flowng from area 1 to area, were analyzed: Operatng Condton 1 System wth two lnes between bus 3 and 101 Operatng Condton System wth a sngle lne between bus 3 and 101 There are 30 parameters to be optmzed, namely K, T, T, T, T 1,,3. The tme constant T w s set to be 5 s [7]. In ths study, 0 and 0 are chosen to be 1.0 and 0.0, respectvely. Fg. 3 Convergence for objectve functon J 1 3 P a g e

5 5. SMALL SIGNAL AND LARGE SIGNAL TESTS Small-sgnal analyss provdes a mean to compare the dampng of the dfferent system modes. Table II. Egenvalues and Dampng ratos of electromechancal modes wth and wthout Case KL Case K1L Fg. 4 Convergence for objectve functon J Several values for the weght a were tested; t was found that the effect of varyng a on the fnal goals s mnmal. The results presented here are for a=10. The convergence rate of the sngle objectve functons and, and the multobjectve functon are shown n Fg. 4, 5 and 6. The fnal value of the objectve functons J 1 and J s 0, ndcatng that all of the electromechancal modes have been shfted to the left of the vertcal lne 0 = -1 and 0 =0. respectvely. The fnal value of the objectve functon J= J 1 +aj s J=0, ndcatng that all of the electromechancal modes have been shfted to the specfed D-shape sector n the s-plane. out J 1 J J j j To better understand the results, we have completed the small sgnal analyss of the tuned PSS was performed on the system for both sngle te-lne (K1L) and on two te-lnes (KL) confguratons. The system electromechancal modes, for the base case and the two operatng condtons (cases K1L KL), wthout and wth the tuned usng J 1, J and J are lsted n Table II. Fg. 5 Convergence for objectve functon J Table I Tuned PSS parameters for Objectve functon J 1, J and J. Obj Gen K T 1 T T 3 T 4 J 1 G G G G J G G G G G J G G G Fg. 6 Egenvalues assocated wth modes of J In assessng PSS, small-sgnal performance s not enough. Good performance durng large perturbatons and good robustness wth respect to changng operatng condtons are 33 P a g e

6 other crtera of an equal mportance. To demonstrate the effectveness of the tuned usng the proposed multobjectve functon over a wde range of operatng condtons, the followng dsturbance s consdered for nonlnear tme smulatons. Test case C Table III. Test Cases for Large Sgnal Assessment TEST CASE NAME A B C SYSTEM CONFIGURATION KL SYSTEM KL SYSTEM K1L SYSTEM CONTINGENCY DESCRIPTION 5 cycle, three phase fault at bus 101 wth the outage of 30 KV lne. 5 cycle, three phase fault at bus 1 wth no equpment outage. 3 cycle, sngle phase fault at bus 10 wthout outage. It s clear that the system response from Fg.7 that, the tuned usng the multobjectve functon J settles faster, and provdes superor dampng n comparson wth the case when ether of J 1 or J s used. Ths ndcates that the tme doman specfcatons were smultaneously met. Test case A Test case B Fg. 7 Responses for Test case A, B and C respectvely. (a) Angular Devaton ( 14) between (M1-M4) n Degrees (b) Speed ( 1) of M1 n pu. (c) Termnal voltage (V t ) of M1 n pu (d) PSS output for M1 n pu. 7. CONCLUSION In ths thess, optmal multobjectve desgn of robust multmachne power system stablzers () usng GAs s proposed. A conventonal speed-based lead-lag PSS s used n ths work. The multmachne power system operatng at varous loadng condtons and system confguratons s treated as a fnte set of plants. The stablzers are tuned to smultaneously shft the lghtly damped electromechancal modes of all plants to a prescrbed zone n the s-plane. A multobjectve problem s formulated to optmze a composte set of objectve functons comprsng the dampng factor, and the dampng rato of the lghtly damped electromechancal modes. The problem of robustly selectng the parameters of the power system stablzers s converted to an optmzaton problem whch s solved by a GA wth the egenvalue-based multobjectve functon. The egenvalue analyss and non lnear tmedoman smulatons, confrms that the closed-loop plant performance s consstent wth the desgn requrements n spte of changes n the operatng condtons, and reveals the superorty of the tuned usng the multobjectve functon n dampng local and nter-area modes of oscllatons. 34 P a g e

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