Fuzzy Logic Control of Static Var Compensator for Power System Damping

Transcription

1 Fuzzy Logc Control of Statc Var Compensator for Power System Dampng N.Karpagam, D.Devaraj bstract Statc Var Compensator (SVC) s a shunt type FCTS devce whch s used n power system prmarly for the purpose of voltage and reactve power control. In ths paper, a fuzzy logc based supplementary controller for Statc Var Compensator (SVC) s developed whch s used for dampng the rotor angle oscllatons and to mprove the transent stablty of the power system. Generator speed and the electrcal power are chosen as nput sgnals for the Fuzzy Logc Controller (FLC). The effectveness and feasblty of the proposed control s demonstrated wth Sngle Machne Infnte Bus (SMIB) system and multmachne system (WSCC System) whch show mprovement over the use of a fxed parameter controller. Keywords FLC, SVC, Transent stablty, SMIB, PID controller. I. INTRODUCTION OWER System Stablty s the ablty of the system to Pregan ts orgnal operatng condtons after a dsturbance to the system. Power system transent stablty analyss s consdered wth large dsturbances lke sudden change n load, generaton or transmsson system confguraton due to fault or swtchng [1]. Dynamc voltage support and reactve power compensaton have been dentfed as a very sgnfcant measure to mprove the transent stablty of the system. Flexble C Transmsson Systems (FCTS) devces wth a sutable control strategy have the potental to ncrease the system stablty margn [2,3]. Shunt FCTS devces play an mportant role n reactve power flow n the power network. In large power systems, low frequency electro-mechancal oscllatons often follow the electrcal dsturbances. Generally, power system stablzers (PSS) are used n conjuncton wth utomatc Voltage Regulators (VR) to damp out the oscllatons [3]. However, durng some operatng condtons ths devce may not produce adequate dampng and other effectve alteratons are needed n addton to PSS [4,5]. nother means to acheve dampng s to use the same shunt FCTS devce Statc Var Compensator (SVC) desgned wth auxlary controllers [6]. Therefore SVC s more effectve and f accommodated wth supplementary controller, by adjustng N.Karpagam s wth rulmgu Kalasalngam College of Engneerng, nna Unversty, Inda., (correspondng author to provde phone: ; fax: ; e-mal: gaush02@ yahoo.com). D.Devaraj, Dr., s wth the Department of Electrcal and Electroncs Engneerng, rulmgu Kalasalngam College of Engneerng, nna Unversty, Inda (e-mal: deva230@yahoo.com). the equvalent shunt capactance, SVC wll damp out the oscllatons and mproves the overall system stablty [7]. The system operatng condtons change consderably durng dsturbances. Varous approaches are avalable for desgnng auxlary controllers n SVC. In [8] a proportonal ntegral dervatve (PID) was used n SVC. It was found that sgnfcant mprovements n system dampng can be acheved by the PID based SVC. lthough PID controllers are smple and easy to desgn, ther performances deterorate when the system operatng condtons vary wdely and large dsturbances occur. Fuzzy logc control approach s an emergng tool for solvng complex problems whose system behavor s complex n nature. n attractve feature of fuzzy logc control s ts robustness n system parameters and operatng condtons changes [9, 10]. Fuzzy logc controllers are capable of toleratng uncertanty and mprecson to a greater extent [11]. Ths paper presents a method based on fuzzy logc control for SVC controller whch damp out the oscllatons at a faster rate. Global nput sgnals such as machne speed () and electrcal power (Pe) are gven as nput to the fuzzy controller. Smulaton results for a Sngle Machne Infnte Bus System (SMIB) and a Mult machne system (WSCC system) are presented and dscussed. Fnally a comparatve study has been carred out between the PID controller and fuzzy controller. II. MODELING ND CONTROL OF SVC The Statc Var Compensator s bascally a shunt connected varable Var generator whose output s adjusted to exchange capactve or nductve current to the system. One of the most wdely used confguratons of the SVC s the FC- TCR type n whch a Fxed Capactor (FC) s connected n parallel wth Thyrstor Controlled Reactor (TCR). The magntude of the SVC s nductve admttance B L () s a functon of the frng angle and s gven by 2 2 sn 2 BL ( ) (1) X for /2 where X S S 2 S V V S = SVC bus bar voltage Q and Q L = MV ratng of reactor. s the SVC uses a fxed capactor and varable reactor combnaton (TCR- FC), the effectve shunt admttance s 1 BS BL ( ) (2) X C L 625

2 where X C =Capactve reactance. n SVC wth frng control system can be represented, for the sake of smplcty by a frst order model characterzed by a gan K SVC and tme constants T 1 and T 2 as shown n Fg.1 The controller send frng control sgnals to the thyrstor swtchng unt to modfy the equvalent capactance of the SVC. The fuzzy controller provdes a auxlary control, whch s n addton to the voltage feedback loop. Fg.1 Block representaton of SVC control The auxlary control loop of the SVC uses stablzng sgnals, such as speed, frequency, phase angle dfference etc... to mprove the dynamc performance of the system. III. REVIEW OF FUZZY LOGIC Fuzzy set theory provdes an excellent means for representng uncertanty due to vagueness n the avalable data or unknown behavor of a system. It can represent the human control processes and also allows expermental knowledge n adjustng the controller parameters.. Fuzzy sets fuzzy set s a collecton of dstnct elements wth a varyng degree of relevance or ncluson. If X s a set of elements, then a fuzzy set n X s defned to be a set of ordered pars, {( x, ( x)) x X} where (x) s called the membershp functon of x n. Ths membershp functon can take (x) denotes the degree to whch x belongs to and s normally lmted to values between 0 and 1. hgh value of (x) mples that t s very lkely for x to be n. B. Fuzzy If Then rules In the fuzzy model the knowledge relatng the nput features and the output class are represented by the fuzzy f then rules of the form R j : f x pl s jl and x pn s jn, then class C j wth CF = CF j where j1, jn are antecedent fuzzy sets n the unt nterval [0,1], C j s one of the class codes and CF j s the grade of certanty of the rule. collecton of such statements replace the usual mathematcal model of system theory. The knowledge requred to generate the fuzzy f then rules can be derved from an expert operator and a desgn engneer or by an off lne smulaton. C. Fuzzy Inference system Wth cause effect relatonshp expressed as a collecton of fuzzy f then rules, n whch the precondtons uses lngustc varables and the consequent have class labels, qualtatve reasonng s performed to nfer the results. In our model Mamdan nference system wth product t-norm and max t-co norm s used. Here, the set of sensor nput s matched aganst the f part of each f then rule, and the response of each rule s obtaned through fuzzy mplcaton operaton. The response of each rule s weghted accordng to the extent to whch each rule fres. The response of all the fuzzy rules for a partcular output class are combned to obtan the confdence wth whch the sensor nput s classfed to that fault class. D. Defuzzfcaton The output of a fuzzy rule based system s generally mprecse and fuzzy. s a fuzzy set cannot drectly be used to take the decsons, the fuzzy conclusons of rule based systems have to be converted n to precse quantty. Ths s called Defuzzfcaton. There are varous methods lke centrod method, weghted average method and max-membershp method etc for ths purpose. IV. FLC BSED DMPING CONTROLLER DESIGN Fg.2 shows the schematc dagram of a SVC along wth Fuzzy logc based dampng controller. Generator speed devaton () and (P) are taken as the nput sgnals of the fuzzy controller. Fg. 2 Block dagram of proposed Fuzzy logc controller The number of membershp functons for each varable determnes the qualty of control whch can be acheved usng fuzzy logc controllers. In the present nvestgaton, fve membershp functons are defned for the nput and output varables. Fg.3 shows the membershp functons defned. The mentoned membershp functons are used to specfy a set of rules called a rule base. The rules developed are based on the knowledge and experence. Wth two nputs and fve lngustc terms, 25 rules were developed whch s gven n Table 1. In nference mechansm all the rules are compared to the nputs to determne whch rules apply to the current stuaton. fter the matchng process the requred rules are fred. The controlled output Bsvc s determned for the dfferent nput condtons. The defuzzfcaton produces the fnal crsp output of FLC wth the fuzzfed nput. Centrod method s employed where the output wll be calculated as O / P 5 b ( ) ( ) (3) 626

3 Fg.5 SIMULINK model of FLC controller for SVC Fg. 3 Membershp functons of, P and Bsvc TBLE 1 FUZZY INFERENCE RULES Output (B SVC ) P NB NS Z PS PB NB NB NS NB NS Z NS NS NB Z Z PS Z NS Z Z PS PS PS Z Z PS PS PS PB Z PS PS PS PB When the SVC wth conventonal PID controller s placed at bus 1 and the same fault condton s smulated, t s observed that the dampng s mproved but stll oscllatons are present. Wth the FLC based SVC the oscllatons are fully damped out and the system comes back to orgnal steady state. Fgs 6 and 7 show the dynamc response of the power angle and the speed devaton, under fault condtons wth dfferent controllers. V. SIMULTION RESULTS To assess the effectveness of the proposed controller, smulaton studes are carred out for the most severe fault condtons and overload condtons n both SMIB system and Mult machne system. The detals of the smulaton are presented here...smib system SMIB system, equpped wth Generator, Transmsson lne and SVC at the mdpont of the lne s shown n Fg.4 The SVC wth ts controller s place at the mdpont of the transmsson lne. The fuzzy dampng controller for the SVC s developed usng MTLB / SIMULINK and ts block dagram s shown n Fg.5. three phase fault s smulated at the load end at t= 0.1 sec. and cleared after 0.05 sec. The system response wthout SVC s oscllatory and leads to nstablty. E V V jx1 m jx2 Fg.6 Varaton n rotor angle for dfferent controllers of SVC B. Multmachne system The same SVC controller wth FLC s mplemented n the 3 machne nne bus system (WSCC system). The one lne dagram of WSCC system s gven Fg.8. SVC Fg.4 SMIB system wth SVC - sngle lne dagram 627

4 Fg.7 Varaton n speed devaton () for dfferent controllers of SVC Power system data s gven n [8]. Power system stablzers wth IEEE type DC1 excter are equpped wth the generators. Fg.9. Dampng of rotor angle oscllatons for FLC- SVC for three phase fault at bus 7 From Fg.10, t s observed that the bus voltage of SVC wth the proposed FLC s reduced durng fault condtons. If PID controllers employed, the SVC voltage ncreases durng fault perod whch causes addtonal voltage njecton n the system nstead of current njecton. Ths wll be the remarkable advantage whle usng a FLC based controller. Fg. 8 One lne dagram of WSCC system Case 1: The FLC based SVC s nstalled at bus 8 near the generator 2. Wth the ntal power flow condtons, a three phase to ground short crcut was smulated near bus 7. In Fgs 9 to 12 the varaton of rotor angle, SVC voltage, speed devaton, and the suceptance Bsvc of SVC wth PID controller and wth FLC based SVC controller are plotted. In ths study case, fault condton at 0.3 seconds, exstng for the perod of 0.1 second and cleared at 0.4 seconds s shown n Fg.9. It s clear that the rotor angle dampng usng fuzzy controller s more effectve than PID controller. The settlng tme of both controllers s found to be same, but the ampltude of rotor angle s reduced n FLC controller. Fg.10 SVC voltage n p.u fault wth FLC for 3 phase fault at bus 7 From Fg.11, t s dentfed that the angular speed devatons wll be same for the two controllers and n post fault perod, the angular speed devatons are quckly reduced usng FLC controller. 628

5 Fg.11 ngular speed devaton n p.u for 3 phase fault at bus 7 From Fg.12, the njecton of B SVC durng fault condton s demonstrated. When the fault occurs, the suceptance njected wll be at maxmum of 1.25 p.u and due to the frng angle control through FLC, t was mmedately thrown of to nductve effect from capactve effect. Fg.13 Dampng of rotor angle oscllatons for FLC- SVC for loadng condton of 1.5 p.u For the tme nterval of 0.5seconds, the suceptance s ncluded and at the perod of 1 second, the capactve effect s changed over to nductve effect and regans ts orgnal state at qucker tme wth the presence of FLC SVC controller. Fg. 14 Control of Bsvc for loadng condton of 1.5 p.u Fg.12. Control of Bsvc wth FLC based SVC for three phase Fault at bus 7 Case 2: In ths case, wth the same locaton of SVC at bus 8, power of load bus 7 s ncreased to 1.5 p.u at 0.5 second wth 0.5 second duraton. The system response s studed wth both PID and FLC based SVC controller. For ths overloaded condton also, SVC supples reactve power durng ths perod and quckly mantans the system stablty. From the Fg.13, t can be seen that, complete dampng of rotor angle oscllatons occur at 2.25 seconds only wth PID controller whereas wth FLC controller damp out the oscllatons at 1.5 seconds. From the Fg.14, t can be observed that the suceptance Bsvc ncluded n the system s ncreased from 0.5 p.u to 1.0 p.u at 0.5 second at whch the dsturbance s occurrng. VI. CONCLUSION Ths paper presents the applcaton of a fuzzy logc based auxlary control for an SVC to acheve transent stablty enhancement. The proposed FLC for SVC s proved to be very effectve and robust n dampng power system oscllatons and thereby enhancng system transent stablty. Fuzzy rules are easly derved from the measurable global sgnals lke lne actve power flow, and remote generator speed devaton. The performance of varous controllers s then compared based on non lnear smulaton results whch are shown n Fg.6 to 14. mong these the performance of the proposed controller s found to be better and damp out the system oscllatons at faster rate. It was also observed that for both SMIB system and multmachne system, SVC controller works accurately. Dgtal computer smulatons were performed usng MTLB/ SIMULINK software. 629

6 PPENDIX I. Modelng of Power System Components. Generator The generator s represented by thrd order model comprsng the electromechancal swng equaton and the generator nternal voltage equatons [10] are 0 (4) 1 ( Pm G K d Pe ) (5) M 1 E q [ E ( ) ] fd xd xd d Eq T (6) do where =Rotor angle n degrees = angular speed n rad/sec P m =Mechancal power developed by the generator K d = Dampng constant of the generator P e = Electrcal Power delvered n p.u X d, X q = Drect and quadrature axs reactance of the generator n p.u E d, E q = Drect and quadrature axs voltages behnd the transent reactance n p.u B. Excter and PSS The block dagram representng IEEE type 1 DC excter and Power System Stablzer (PSS) accommodated wth the generator s shown n Fg.15 whch s modeled wth the followng equatons K E fd E fd ( Vref Vt U PSS ) T T (7) Pe vd d vqq (8) and Vt ( vd vq ) (9) wth v E sn ( x ) D and v q d Eq x d d q q s K G2 G ( K ) G1 (10) 1 st Fg.15. IEEE type DC1 excter G 1 st1 1 st3 U PSS (11) K P 1 st2 1 st4 where K and T = gan and tme constants of the excter V ref = reference voltage n p.u V t = Termnal voltage n p.u E fd = Feld voltage of the generator n p.u K G1, K G2 = Gan constants of the Governor K P= Gan of the PSS T 1,T 2,T 3 and T 4 = Tme constants of the PSS Ds = Dampng coeffcent of PSS U PSS = Output of PSS n p.u II. Soluton for Multmachne Systems In the multmachne system model, the loads are assumed to be constant mpedance and converted n to admttances as ( PL jql ) y L where -1,.m. (12) 2 V The network equatons for the new augmented network can be wrtten as I Y YB E (13) 0 YC YD VB whch can be reduced to I 1 Y YBYBYD YC E Y E Where the elements of the j( / 2) nt I and E are (14) I ( I ji ) e (15) E d E q (16) The elements of Y j j Y nt j are G jb (17) For the smulaton of mult machne system, frst the admttance matrx (Y) of the system s calculated and the complexty of transent stablty analyss s reduced by consderng all the rotor angles of synchronous machnes concdes wth angle of the voltage behnd the transent reactance and all the machnes are assumed to swng at coherent. The power flow equaton of th machne s calculated by m j Pe E E Yj cos( j j ) j1 nd the swng equaton s 2 m H d P cos( ) 2 m E E j Yj j j f dt 0 j1 III. System data Synchronous machne data X d =1.8 X d =0.3 X d =0.15 Xq=1.8 X q =0.0 X q =0.15 T do =6.0 T do 0.04 H=4 T qo =0.2 T do =0.0 R=0.002 X 1 =0.0 K d =0.0 (18) (19) 630

7 Excter IEEE Type DC 1 Data (p.u) K =200 T =0.02 K F =0.028 T F =0.92 K E =0.0 T E= 0.05 SVC data K SVC =100 T 1 =0.0 T 2 = 0.05 Bsvc=±1.5 CKNOWLEDGMENT The authors would lke to acknowledge the management, head of the Insttuton for ther contnuous support to complete ths work. REFERENCES [1] P.Kundur, Power System Stablty and Control, Mc Graw Hll, Newyok, [2] T.thay, R.Podmore and S.Vrman, Robust control strategy for shunt and seres reactve compensators to damp electromechancal oscllatons IEEE Transactons on Power Delvery,vol.16, No.4.pp ,Oct,2001. [3] M..bdo, nalyss and assessment of STTCOM based dampng stablzers for Power system stablty enhancement Electrc Power System Research,73, ,2005.E.Lerch, D.Povh, dvanced SVC control for dampng powersystem oscllatons IEEE Transactons on Power Systems, vol.16,no.2,may 1991,pp [4] E.H.Zhou., pplcaton of Statc Var Compensator to ncrease Power System Dampng, IEEE Transactons on Power Systems,Vol.8, No.2,May [5] M.E. boul.ela,..sallam, J.D.Mc Calley, et.al, Dampng controller desgn for power system oscllaton usng global sgnals, IEEE Transactons on Power systems,vol.11.no.2,1996, pp [6] Yong Chang, Zhen Xu, novel SVC supplementary controllers basd on wde area sgnals,electrc Power Systems Research, 77( ), [7] Qun Gu, nupama Pandey and Shell K. Starrett, Fuzzy logc control schemes for statc VR compensator to control system dampng usng global sgnal Electrc Power Systems Research,67,2003, [8] J.Lu, M.H.Nehrr,and D..Perre, fuzzylogc based adaptve dampng controller for statc VR compensator,electrc Power Systems Research,68,113-18,2004. [9] Takash Hyama,Wald Hubb,Thomas H. Ortmayer, Fuzzy logc Control Scheme wth Varable gan for Statc Var Compensator to enhance Power System Stablty, IEEE Transactons on Power Systems, vol.14, No.1, Feb,1999. [10] K. Phorang, M. Leelajndakrareak and Y Mzutan, Dampng mprovement of oscllaton n power system by fuzzy logc based SVC stablzer, sa Pacfc. IEEE/PES Transmsson and Dstrbuton Conference and Exhbton 2002, Vol.3, Oct. 2002, pp [11] D. Z. Fang, Yang Xao dong; T. S. Chung and K. P.Wong, daptve fuzzy-logc SVC dampng controller usng strategy of oscllaton energy descent, IEEE Trans. on Power Systems, Vol.19(3), ug. 2004, pp [12] K. L. Lo and Khan Laq, Fuzzy logc based SVC for power system transent stablty enhancement, Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and Power Technologes (DRPT 2000), prl 2000, pp [13] P.K.Dash, S.Mshra, Dampng of multmodal power system oscllatons by FCTS devces usng non lnear Takag Sugeno fuzzy controller, Electrc Power Systems Research,25, ,2003. [14].Ghafor, M.R.Zolghadr and M.Ehsan, Fuzzy controlled STTCOM for mprovng the Power System Transent Stablty, IEEE nternatonal conference on Power system pp , [15] Ghadr Radman, Reshma S.Raje, Dynamc model for power systems wth multple FCTS controllers Electrc Power Systems Research, 78, , [16] N.Mdhulananthan, C..Canzares, Comparson of PSS, SVC and STTCOM controllers for dampng Power System Oscllatons, IEE Transactons on Power Systems, vol.18,no.2, May [17] Vladmro Mranda, n mproved Fuzzy Inference System for Voltage / VR control IEEE Transactons on Power Systems, vol.22,no.4, November N.Karpagam receved the M.E degree n Power Systems Engneerng from Madura Kamaraj Unversty, Madura, Tamlnadu, Inda n 2000,. Currently, she s a Research Scholar n Electrcal Engneerng Department of nna Unversty, Chenna, Taml nadu, Inda. She s an ssstant Professor n the Department of Electrcal and Electroncs Engneerng, rulmgu Kalasalngam College of Engneerng, Krshnan kol, Taml nadu, Inda. Her areas of research nclude power system stablty, FCTS, optmzaton technques, Fuzzylogc and G applcatons to power systems. Dr.D.Devaraj receved the M.E degree n Power Systems Engneerng from Madura Kamaraj Unversty, Madura, Tamlnadu, Inda n 1993 and Ph.D n Power System Engneerng at IIT, Madras, Inda n Currently, he s Senor Professor n the Department of Electrcal and Electroncs Engneerng, rulmgu Kalasalngam College of Engneerng, Krshnan kol, Taml nadu, Inda. Hs areas of research nclude power system securty, FCTS, optmzaton technques, Fuzzy logc and G applcatons to power systems.. 631