Fuzzy Coordination of FACTS Controllers for Damping Power System Oscillations

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1 Fuzzy Coordnaton of FACS Controllers for Dampng Poer System Oscllatons Ljun Ca István Erlch Electrcal Engneerng Department Electrcal Engneerng Department Unversty of Dusburg Unversty of Dusburg 757 Dusburg Germany 757 Dusburg Germany Abstract hs paper concerns the optmzaton and coordnaton of the conventonal FACS (Flexble AC ransmsson Systems) dampng controllers n multmachne poer system. Frstly, the parameters of FACS controller are optmzed. hen, a hybrd fuzzy logc controller for the coordnaton of FACS controllers s presented. hs coordnaton method s ell sutable to seres connected FACS devces lke UPFC, CSC etc. n dampng mult-modal oscllatons n mult-machne poer systems. Dgtal smulatons of a mult-machne poer system subjected to a de varety of dsturbances and dfferent structures valdate the effcency of the ne approach. Keyords: FACS, Fuzzy Logc, Coordnaton, Fuzzy- Coordnaton Controller, Dampng, Stablty. INRODUCION Noadays, FACS devces can be used to control the poer flo and enhance system stablty. hey are playng an ncreasng and major role n the operaton and control of poer systems. he UPFC (Unfed Poer Flo Controller) s the most versatle and poerful FACS devce []. he parameters n the transmsson lne,.e. lne mpedance, termnal voltages, and voltage angle can be controlled by UPFC. It s used for ndependent control of real and reactve poer n transmsson lnes. Moreover, the UPFC can be used for voltage support and dampng of electromechancal oscllatons [2~]. In ths paper, a multmachne system th UPFC s smulated. Dampng of electromechancal oscllatons beteen nterconnected synchronous generators s necessary for secure system operaton [5]. A ell-desgned FACS controller can not only ncrease the transmsson capablty but also mprove the poer system stablty. A seres of approaches have been made n developng dampng control strategy for FACS devces. he researches are mostly based on sngle machne system. Hoever, FACS devces are alays nstalled n mult-machne systems. he coordnaton beteen FACS controllers and other poer system controllers s very mportant. Fuzzy-coordnaton controller s presented n ths paper for the coordnated of tradtonal FACS controllers. he fuzzy logc controllers are rule-based controllers n hch a set of rules represents a control decson mechansm to adjust the effect of certan cases comng from poer system. Furthermore, fuzzy logc controllers do not requre a mathematcal model of the system. hey can cover a der range of operatng condtons and they are robust [6]. hs paper focuses on the optmzaton of conventonal poer oscllaton dampng (POD) controllers and fuzzy logc coordnaton of them. By usng fuzzy-coordnaton controller, the coordnaton objectves of the FACS devces are qute ell acheved. he paper s organzed as follos. Follong the ntroducton, n secton 2, three-machne system model and a UPFC model are ntroduced. hen n secton 3 the control schemes for UPFC are dscussed. In secton the parameters optmzaton and fuzzy-coordnaton controller desgn are proposed. he smulaton results are gven n secton 5. Fnally, bref conclusons are deduced. 2. SYSEM MODEL 2.. Poer System Model A three machne nne bus nterconnected poer system s smulated n ths paper. here are to UPFCs n the poer system: beteen Bus2 Bus3 and, Bus6 Bus7. he dagram of the poer system model s shon n Fg.. he system parameters are gven n Appendx. Bus Bus2 Bus3 Bus9 Bus Bus5 l l3 ~ ~ G UPFC l2 3 G3 L L Bus6 L3 UPFC2 Bus7 Bus8 Fg.. Poer system model 2.2. UPFC Model (UPFC heory) Bascally, the UPFC have to voltage source nverters (VSI) sharng a common dc storage capactor. It s connected to the system through to couplng transformers. One VSI s connected n shunt to the system va a shunt transformer. he other one s connected n seres through a seres transformer. he UPFC scheme s shon n Fg. 2. ~ 2 G2 L2

2 Lne V V se V 2 I sh V sh I + - I v dc C I2 V se [9]. hus, as shon n Fg., the dampng control of the UPFC s the same as a CSC POD control scheme []. By the control of the magntude of V se, the seres compensaton dampng control can be acheved. V V se V 2 Fg. 2 UPFC scheme he UPFC has several operatng modes. o control modes are possble for the shunt control: [2,7,8] ) VAR control mode: the reference nput s an nductve or capactve Var request 2) Automatc voltage control mode: the goal s to mantan the transmsson lne voltage at the connecton pont to a reference value. By the control of seres voltage, UPFC can be operated n four dfferent ays [2,7,8]: ) Drect voltage njecton mode: the reference nputs are drectly the magntude and phase angle of the seres voltage 2) Phase angle shfter emulaton mode: the reference nput s phase dsplacement beteen the sendng end voltage and the recevng end voltage 3) Lne mpedance emulaton mode: the reference nput s an mpedance value to nsert n seres th the lne mpedance ) Automatc poer flo control mode: the reference nputs are values of P and Q to mantan on the transmsson lne despte system changes. Generally, for dampng of poer system oscllatons, UPFC ll be operated n the drect voltage njecton mode. he mathematc model of UPFC for the dynamc smulaton s shon n Fg. 3. I lne V se V V 2 V sh Fg 3. UPFC model 3. CONROL SCHEME 3.. radtonal FACS Dampng Control Scheme Under a large dsturbance, lne mpedance emulaton mode ll be used to mprove frst sng stablty. For dampng of the subsequent sngs, as suggested before, UPFC ll be operated n the drect voltage njecton mode. In ths mode, the UPFC output s the seres compensaton voltage V se. hs voltage s perpendcular to the lne current I lne and the phase angle of I lne s ahead of I lne Fg.. Seres compensaton mode 3.2. POD Controller Commonly the POD controllers nvolve a transfer functon consstng of an amplfcaton lnk, a ashout lnk and to lead-lag lnks []. A block dagram of the conventonal POD controller s llustrated n Fg. 5. In ths paper the actve poer of the transmsson lne s used as nput sgnal. P Lne K 2 Fg. 5. UPFC POD controller he UPFC POD controller orks effectvely n sngle machne system. In order to mprove the dynamc performance of a mult-machne system, the behavor of the controllers must be coordnated. Otherse the poer system ll be deterorated Fuzzy Logc Control In order to keep the advantage of the exstng POD controller and to mprove ts control performance n multmachne systems, the hybrd fuzzy coordnated controller s suggested n ths paper. Fuzzy logc controller s one of the most practcally successful approaches for utlzng the qualtatve knoledge of a system to desgn a controller [6]. In ths paper the man functon of the fuzzy logc control s to coordnate the operaton of FACS controllers. In secton the desgn of the fuzzy logc coordnated controller s presented n detal.. PARAMEER OPIMIZAION AND CONROLLER DESIGN.. Parameter Optmzaton for a Sngle Machne POD Controller In order to ork effectvely under dfferent operatng condtons, many researches are made on the controller parameter optmzaton []. Parameters of the POD controller can be adjusted ether by tral and error or by 3 V mn V max V se lm

3 optmzaton technque. In ths paper the parameters of the POD controller are optmzed usng a nonlnear programmng algorthm. Orgnally, the am of the parameter optmzaton s to damp oscllatons of poer systems here the UPFCs are nstalled. hs objectve can be formulated as the mnmzaton of a nonlnear programmng problem expressed as follos: mn. s. t. f ( A( = B( here f ( s the objectve functon, x are the parameters of the POD controller. A ( are the equalty functons and B ( are the nequalty functons respectvely. Partcularly B ( ndcate the restrctons of the POD parameter. (.e. the restrctons of lead-lag lnks and ash-out lnks). In ths smulaton, only the nequalty functons B ( are necessary. he objectve functon s extremely mportant for the parameter optmzaton. In ths paper the objectve functon s defned as follos: t = () f ( δ ( t, dt (2) here δ ( t, s the poer angle curve of the generator and t s the tme range of the smulaton. Wth the varaton of the controller parameters x, the δ ( t, ll also be changed. he poer system smulaton program PSD (Poer System Dynamc) [5] s employed n ths smulaton to evaluate the performance of the POD controller. Equaton () s a general parameter-constraned nonlnear optmzaton problem and can be solved successfully. In ths paper the Matlab Optmzaton oolbox s appled [2]. he optmzaton starts th the pre-selected ntal values of the POD controller. hen the nonlnear algorthm s used to teratvely adjust the parameters, untl the objectve functon (2) s mnmzed. hese so determned parameters are the optmal settngs of the POD controller. he flo chat of the parameter optmzaton s shon n Fg. 6 he proposed optmzaton algorthm as realzed n a sngle machne poer system. In ths optmzaton the prefault state and post-fault state are the same, here δ ( ) = δ ( ). he optmzed parameters are gven n Appendx Fuzzy Logc Coordnated Controller Desgn Most of the FACS POD controllers belong to the PI (proportonal ntegral) type and ork effectvely n sngle machne system [3]. Especally, after the parameter optmzaton, the dampng of poer system oscllatons s perfectly acheved. Hoever the performance of the above mentoned POD controllers deterorates n mult-machne system. herefore the coordnaton beteen POD controllers must be taken nto account. Begn Intalzaton Intal Values x Constraned Nonlnear Parameter Optmzaton: Fmncon [ ] Optmzed Parameter Set x End PSD Nonlnear Smulaton: δ ( t, Calculate objectve functon: t f ( = δ ( t, dt Fg. 6. Flo chart of the parameter optmzaton o cope th the coordnaton problem, the optmzaton based coordnaton [] and the feedback sgnal based coordnaton [] have been developed. Also fuzzy logc has successfully been appled to coordnaton [3]. he method used n [3] s usng the fuzzy logc controller to coordnate the nput sgnal of the FACS controller. In ths paper the fuzzy logc controller s to coordnate the parameters of FACS controllers. he structure of the proposed fuzzy-coordnaton controller s shon n Fg. 7. P UPFC P UPFC 2 Fuzzy-coordnaton POD Controller Fuzzy-coordnaton POD Controller 2 2 Fg. 7. UPFC fuzzy-coordnaton controller here the nputs P and UPFC P are the actve poer UPFC 2 flo through the UPFC and UPFC2. he output sgnals are command sgnals adjusted to the UPFC controllers and 2. In ths ay, the conventonal POD controllers are tuned by usng fuzzy-coordnaton controllers. he fuzzycoordnaton controller nvolves Fuzzfcaton, Inference and Defuzzfcaton unt. 2 Valdate Inequalty Constran B( Control Sgnal to UPFC 3 3 V mn V mn lm Control Sgnal to UPFC 2 lm V max V max V se V se2

4 .2. Fuzzfcaton Fuzzfcaton s a process hereby the nput varables are mapped onto fuzzy varables (lngustc varables). Each fuzzfed varable has a certan membershp functon. he nputs are fuzzfed usng three fuzzy sets: B (bg), M (medum) and S (small), as shon n Fg. 8. µ( S M B P UPFC2 P UPFC able Inference system S M B S B M S M B M S B M S S K-N K K+N Fg. 8. Membershp functon he membershp functon of the small set s: x.2.3 Defuzzfcaton he output varables of the nference system are lngustc varables. hey must be converted to numercal output. he fuzzy-coordnaton controller uses centrod method. he output of the fuzzy-coordnaton controller s u 9 c = = 9 µ ( u ) u = µ ( u ) c (6) µ ( = S x + K N x < K N K N x K x > K (3) here u corresponds to the value of control output for hch the membershp values n the output sets are equal to unty. here x, namely P or UPFC P, s the nput to the fuzzy UPFC 2 controller. Smlarly the bg set membershp functon s: x K µ B ( = N x < K K x K + N x > K + N And the medum set membershp functon s: x + N K µ = N M ( x + N + K N x < K N K N x K K x K + N x > K + N he parameters L and K, as shon n Appendx 3, are determned basng upon the rated values of UPFCs. hese parameters can also be optmzed by usng the smulaton results..2.2 Inference Control decsons are made based on the fuzzfed varables. Inference nvolves rules for determnng output decsons. Due to the nput varables havng three fuzzfed varables, the fuzzy-coordnaton controller has nne rules for each UPFC controller. he rules can be obtaned from the system operaton and the knoledge of the operator. able shos the nference system. o determne the degree of membershps for output varables, the Mn-Max nference s appled. Both of the to UPFC controllers use the same nference system. Only the nput of them are exchanged. (as shon n Fg. 7) () (5) 5. SIMULAION RESULS 5.. Parameter optmzaton he parameter optmzaton s made n sngle machne system. Fg. 9 demonstrates the mprovement n dampng of poer system oscllaton. he ntal and optmzed values of the POD controller are gven n Appendx Wthout Optmzaton Optmzed POD Controller me [s] Fg. 9. Parameter optmsaton n a sngle machne nfnte bus system 5.2. Smulaton n mult-machne system Usng the mult-machne poer system shon n Fg., dfferent dsturbances and dfferent netork parameters are

5 smulated. he performance of the fuzzy-coordnaton controller for UPFC n dampng poer system oscllatons s examned. he follong smulatons are made for evaluatng the performance of the proposed controller. In ths paper machne G3 s taken as the reference. Case : hree-phase fault at Bus 2 A three-phase fault of ms duraton s smulated at Bus 2. Fg. presents the results of the examned poer system th fuzzy-coordnaton controller. From Fg. t can be seen that th the proposed controller, the dynamc performance of the poer system s qute mproved. he pre-fault operatng condton (n p. s: P=.5, P2=.85. Fg.. Fuzzy-coordnaton controller smulaton case Case 2: Changng of operaton condtons (hree-phase fault at Bus 3) o valdate the robustness of fuzzy-coordnaton controller the pre-fault operatng condtons of the poer netork s changed to P=.95, P2=.28. Moreover the fault type s also dfferent: a three-phase fault of ms duraton s smulated at Bus 3. Fg. shos the results of the smulaton. he proposed controller acts pretty ell th the varaton of operaton condton δ me [s] δ 3 δ 3 δ 23 δ 23 δ 23 δ 3 δ me [s] Fg.. Fuzzy-coordnaton controller smulaton case2 Case 3: Changng of netork parameters (hree-phase fault at Bus 9) In order to verfy the performance of the fuzzycoordnaton controller for the changng of system parameters, the reactance of transformers and 2 are ncreased by 2%. A three-phase fault of ms s smulated at Bus 9. he smulaton results, as shon n Fg. 2, llustrate that the proposed controller s robust n parametrc change. he pre-fault operatng condton (n p. s: P=., P2= δ me [s] Fg. 2. Fuzzy-coordnaton controller smulaton case 3 6. CONCLUSIONS he paper presents a ne fuzzy-coordnaton controller for the FACS devces n a mult-machne poer system to damp the electromechancal oscllatons. he fuzzycoordnaton controller s desgned based on the conventonal POD controllers. he amplfcaton part of the conventonal controller s modfed by the fuzzycoordnaton controller. he performance of the proposed method s smulated over a de range of operatng condtons and dsturbances and ts robustness s proved. Both nter-area and local modes oscllatons are qute damped usng ths ne controller. he proposed control scheme adopts the advantages of the conventonal POD controller and t s not only robust but also smple and beng easy to be realzed n poer system. APPENDIX Appendx : poer system model δ 3 δ 23 Wth Coordnaton Base Value: V B = 22KV S B = MVA Generators: 2H = 2H 2 = 8s 2H 3 = D = D2 = D2 =. d = d 2 =. 9s d 3 = 6s δ 3 Wth Coordnaton

6 X d d 2 =.56( p. X d 3 = 2( p. X q q2 =.6( p. X =. q3 9 ' ' ' X d d 2 =.7( p. X d 3 =.25( p. ransformers: X 2 3 = j.35 (p. ransmsson lnes: Z = Z = Z =..25 (p. l l 2 l3 + j UPFCs: V Oper = 22KV V = semax. V Oper Vsemn =. V Oper Loads: L = L = L =.5 ( p..) L =.65 ( p..) 2 3 u Appendx 2: parameter optmzaton u Parameter Value K = 3 2 = Vmax Vmn Intal Optmzed Appendx 3: Fuzzy-coordnaton controller K=.7, N=.2 REFERENCE [] L. Gyug, Unfed Poer flo concept for flexble AC transmsson systems, IEE Proc. vol. 39, no., pp , 992. [2] M. Noroozan, L. Angqust, M. Ghandar, and G. Anderson, Use of UPFC for optmal poer flo control, IEEE rans. on Poer Systems, vol. 2, no., 997, pp [3] A. Nabav-Nak and M.R. Iravan, Steady-state and dynamc models of unfed poer flo controller (UPFC) for poer system studes, IEEE 96 Wnter Meetng, 996, Paper 96. [] C.D. Schauder, D.M. Hama, and A. Edrs. Operaton of the Unfed Poer Flo Controller (UPFC) under Practcal constrants, IEEE rans. on Poer Delvery. vol. 3, No. 2. Aprl 998, pp. 63~639. [5] M. Noroozan, L. Angqust, M. Ghandar, and G. Anderson, Improvng poer system dynamcs by seres-connected FAC s devces, IEEE rans. on Poer Systems, vol. 2, no., 997, pp [6] S. Lmyngcharone, U. D. Annakkage, and N. C. Pahalaaththa, Fuzzy logc based unfed poer flo controllers for transent stablty mprovement, IEE Proc. vol. 5, No. 3, 998, pp [7] D. Mennt, and A. Pennarell, Modellng of Unfed Poer Flo Controller nto Poer Systems usng P- Spce, IPS Conference, Ro de Janeo, Brazl, June 2-28, 2, Paper 25. [8] A. J. F. Ker, X. Lombard, and A. A. Edrs, Unfed Poer Flo Controller (UPFC): Modellng and Analyss, IEEE rans. on Poer Delvery, vol., No. 2, Aprl 999, pp [9] Zhengyu Huang, Yxn N, C. M. Shen, Felx F. Wu, Shousun Chen, and Baoln Zhang, Applcaton of Unfed Poer Flo Controller n Interconnected Poer Systems Modelng, Interface, Control Strategy, and Case Study, IEEE rans. on Poer Systems, vol. 5, No. 2, 2, pp [] X. Le, D. Jang, and D. Retzmann, Stablty Improvement n Poer Systems th Non-Lnear CSC Control Strateges, EEP, vol, No. 6, November/December 998, pp [] Xanzhang Le, Edn N. Lerch, and Dusan Povh, Optmzaton and Coordnaton of Dampng Controls for Improvng System Dynamc Performance, IEEE rans. on Poer Systems. vol. 6, No. 3. August 2, pp [2] homas Coleman, Mary Ann Branch, and Andre Grace. Optmzaton oolbox for Use th Matlab, he Mathorks Inc, 999. [3] P. K. Dash, S. Mshra, and G. Panda, Dampng Mult-modal Poer System Oscllaton Usng a Hybrd Fuzzy Controller for Seres Connected FACS Devces, IEEE rans. on Poer Systems, vol. 5, No., November 2, pp [] H.F. Wang, Selecton of Robust Installng Locatons and Feedback Sgnals of FACS-based Stablzers n Mult-machne Poer Systems, IEEE rans. On Poer Systems, vol., No. 2, May 999, pp [5] I. Erlch and H. Pundt. Dgtal Program for the Smulaton of Electromechanc ransents n the Medum and Long-erm Range., 8 th. PSCC Helsnk, 9-2, August, 98.