INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 73, DECEMBER 7-9, 47 of Power System Osilltions using Unified Power Flow Controller (UPFC) Neelim Tmey M. L. Kothri Astrt--This pper presents systemti pproh for designing Unified Power Flow Controller (UPFC) sed dmping ontrollers for dmping low frequeny osilltions in power system. Detiled investigtions hve een rried out onsidering four lterntive UPFC sed dmping ontrollers. The investigtions revel tht the dmping ontrollers sed on UPFC ontrol prmeters δ E nd δ B provide roust performne to vritions in system loding nd equivlent retne Xe. Keywords-- Power system Stility, of power system osilltions, UPFC, FACTS ontrollers. I. INTRODUCTION The power trnsfer in n integrted power system is onstrined y trnsient stility, voltge stility nd smll signl stility. These onstrints limit full utiliztion of ville trnsmission orridors. Flexile AC Trnsmission System (FACTS) is the tehnology tht provides the needed orretions of the trnsmission funtionlity in order to fully utilize the existing trnsmission filities nd hene, minimizing the gp etween the stility limit nd therml limit. Unified Power Flow Controller (UPFC) is one of the FACTS devies, whih n ontrol power system prmeters suh s terminl voltge, line impedne nd phse ngle. It n lso e used for dmping power system osilltions. Reently reserhers hve presented dynmi models of UPFC in order to design power flow, voltge nd dmping ontrollers [4-]. Wng [8-], hs presented modified linerised Heffron-Phillips model of power system instlled with UPFC. He hs ddressed the si issues pertining to the design of UPFC dmping ontroller, i.e., seletion of roust operting ondition for designing dmping ontroller; nd the hoie of prmeters of UPFC (suh s m B, m E, δ B nd δ E ) to e modulted for hieving desired dmping. No effort seems to hve een mde to identify the most suitle UPFC ontrol prmeter, to e modulted for hieving roust dynmi performne of the system following wide vritions in loding ondition. In view of the ove, the min ojetives of the reserh work presented in the pper re,. To present systemti pproh for designing UPFC sed dmping ontrollers. Neelim Tmey is persuing her Ph.D t Indin Institute of Tehnology, Delhi,Indi (e-mil: neelu_tmey@yhoo.om) Prof. M.L. Kothri is with Eletril Engineering Deptt, Indin Institute of Tehnology, Delhi, Indi.(e-mil : mohnkothri@hotmil.om). To exmine the reltive effetiveness of modulting lterntive UPFC ontrol prmeters (i.e. m B, m E, δ B nd δ E ), for dmping power system osilltions. 3. To investigte the performne of the lterntive dmping ontrollers, onsidering wide vritions in loding onditions nd system prmeters in order to rrive t most effetive dmping ontroller. II. SYSTEM INVESTIGATED A single-mhine-infinite-us (SMIB) system instlled with UPFC is onsidered (Fig. ). A stti exittion system model type IEEE-STA hs een onsidered. The UPFC onsidered here is ssumed to e sed on pulse width modultion (PWM) onverters. The nominl loding ondition nd system prmeters re given in Appendix-. I t X te X E V o I B I E ET VSC - E V d VSC - B V B m E δ E m B δ B UPFC V BT Fig.. UPFC instlled in SMIB system. III. UNIFIED POWER FLOW CONTROLLER Unified power flow ontroller (UPFC) is omintion of stti synhronous ompenstor (STATCOM) nd stti synhronous series ompenstor (SSSC) whih re oupled vi ommon d link, to llow i-diretionl flow of rel power etween the series output terminls of the SSSC nd the shunt output terminls of the STATCOM nd re ontrolled to provide onurrent rel nd retive series line ompenstion without n externl eletri energy soure. The UPFC, y mens of ngulrly unonstrined series voltge injetion, is le to ontrol, onurrently or seletively, the trnsmission line voltge, impedne nd ngle or lterntively, the rel nd retive power flow in the line. The UPFC my lso provide independently ontrollle shunt retive ompenstion. Viewing the opertion of UPFC from the stndpoint of onventionl power trnsmission sed on retive shunt ompenstion, series ompenstion nd phse shifting, the UPFC n fulfill ll these funtions nd thery meet multiple ontrol ojetives. X BV V
48 NATIONAL POWER SYSTEMS CONFERENCE, NPSC IV. MODIFIED HEFFRON-PHILLIPS SMALL PERTURBATION TRANSFER FUNCTION MODEL OF A SMIB SYSTEM INCLUDING UPFC Fig. shows the smll perturtion trnsfer Funtion lok digrm of mhine-infinite us system inluding UPFC relting the pertinent vriles of eletri torque, speed, ngle, terminl voltge, field voltge, flux linkges, UPFC ontrol prmeters, nd d link voltge. This model hs een developed y Wng [8], y modifying the si Heffron-Phillips model inluding UPFC. This liner model hs een developed y linerising the nonliner model round nominl operting point. The onstnts of the model depend on the system prmeters nd the operting ondition. K Te T m Ms D ω s δ [K pu ] K K 6 K 4 K 5 K pd Eq' K 3 st do ' K st V ref K 8 [K qu ] K qd [K vu ] K vd [K u ] V d s K 9 [ u] K 7 Fig.. Modified Heffron-Phillips model of SMIB System with UPFC. In the ove trnsfer funtion model [ u] is the olumn vetor while [Kpu], [Kqu], [Kvu] nd [Ku] re the row vetors s defined elow, [ u] = [ me δe mb δb] T, [Kpu] = [Kpe Kpδe Kp Kpδ], [Kqu] = [Kqe Kqδe Kq Kqδ] [Kvu] = [Kve Kvδe Kv Kvδ] [Ku] = [Ke Kδe K Kδ] The ontrol prmeters of the UPFC re :. m B pulse width modultion index of series inverter. By ontrolling m B, the mgnitude of series injeted voltge n e ontrolled.. δ B Phse ngle of series inverter whih when ontrolled results in the rel power exhnge. 3. m E pulse width modultion index of shunt inverter. By ontrolling m E, the voltge t us where UPFC is instlled, is ontrolled through retive power ompenstion. 4. δ E Phse ngle of the shunt inverter, whih regultes the d voltge t d link. V. ANALYSIS ) Computtion of Constnts of the Model The initil d-q xes voltge nd urrent omponents nd torque ngle for the nominl operting ondition needed for omputing onstnts of the model re lulted nd re given elow: Q =.67 pu E do =.733 pu e do =.3999 pu E qo =.68 pu e qo =.966 pu i do =.479 pu δ o = 47.3 i qo =.6665 pu
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 73, DECEMBER 7-9, 49 The onstnts of the model omputed for nominl operting ondition nd system prmeters re, K =.356 K p =.333 K pδe =.935 K =.4567 K q =.4 K qδe = -.44 K 3 =.65 K v = -.9 K vδe =.8 K 4 =.96 Kpe =.964 K =.763 K 5 = -.7 K qe =.4984 K e =.8 K 6 =.834 K ve = -.5 K δ = -.47 K 7 =.6854 K pδ =.94 K δe =.4937 K 8 =.35 K qδ = -.5 K pd =.68 K 9 = -.83 K vδ =.6 K qd =.6 K vd = -.536 ). Design of Controllers For this operting ondition, the eigen-vlues of the system re otined (Tle ) nd it is lerly seen tht the system is unstle. The dmping ontrollers re designed to produe n eletril torque in phse with speed devition.the four ontrol prmeters of the UPFC (i.e. m B, m E, δ B nd δ E ) n e modulted in order to produe the dmping torque. The speed devition is onsidered s the input to the dmping ontrollers. The four lterntive UPFC sed dmping ontrollers re exmined in the present work. ontroller sed on UPFC ontrol prmeter m B shll heneforth e denoted s ontroller (m B ). Similrly dmping ontrollers sed on m E, δ B nd δ E shll heneforth e denoted s ontroller (m E ), ontroller (δ B ), nd ontroller (δ E ) respetively. denoted s GEPA. The time onstnts of the phse ompenstor re hosen so tht the phse lg/led of the system is fully ompensted. For the nominl operting ondition, the nturl frequeny of osilltion ω n = 4.974 rd./se. The trnsfer funtion relting Te nd m B is denoted s GEPA. For the nominl operting ondition, phse ngle of GEPA i.e. GEPA =.3 lgging. The mgnitude of GEPA i.e. GEPA =.348. To ompenste the phse lg, the time onstnts of the led ompenstor re omputed [] nd re otined s T =.36 se. nd T =.975 se. Following the sme proedure, the phse ngle to e ompensted y the other three dmping ontrollers re omputed nd re given in Tle. The ritil exmintion of Tle revels tht the phse ngle of the system i.e. GEPA, is negtive for ontrol prmeter m B nd m E However, it is positive for δ B nd δ E. Hene the phse ompenstor for the ontroller (m B ) nd ontroller (m E ) is led ompenstor while for ontroller (δ B ) nd ontroller (δ E ) is lg ompenstor. The gin settings (K d ) of the ontrollers re omputed ssuming dmping rtio ξ =.5. Tle. Gin nd phse ngle of the trnsfer funtion GEPA. GEPA GEPA GEPA (degrees) Te / m E.368-8.47 Te / δ E.899.6357 Te / m B.348 -.73 Te / δ B.958 8.843 K d Gin s T w s T w Signl Wshout G(s) = s T s T Phse ompenstor Fig. 3. Struture of UPFC sed dmping ontroller. The struture of UPFC sed dmping ontroller is shown in Fig. 3. It onsists of gin, signl wshout nd phse ompenstor loks. The signl wshout is the high pss filter tht prevents stedy hnges in the speed from modifying the UPFC input prmeter. The vlue of the wshout time onstnt T w should e high enough to llow signls ssoited with osilltions in rotor speed to pss unhnged. From the viewpoint of the wshout funtion, the vlue of T w is not ritil nd my e in the rnge of to seonds. T w equl to seonds is hosen in the present studies. The prmeters of the dmping ontroller re otined using the phse ompenstion tehnique []. The trnsfer funtion of the system relting the eletril omponent of torque ( Te) nd UPFC ontrol prmeter is u Tle. Eigen-vlues of the losed loop system. Tle 3 shows the prmeters (Gin nd Time onstnts) of the four lterntive dmping ontrollers. Tle 3 lerly shows tht the gin setting of the ontroller (m B ) nd ontroller (δ B ) re muh higher s ompred to gin setting of ontroller (δ E ) nd ontroller (m E ). System without ny dmping ontroller Eigen-vlues ω n of the osilltory mode ς of the osilltory modes - 9. 86. 7 ± 4. 6i 4. 6 rd/se -. 4 -. 765 ±.47i. 866 rd / se.883
43 NATIONAL POWER SYSTEMS CONFERENCE, NPSC Tle 3. Prmeters of the UPFC sed ontrollers. Controller (m E ) Controller (δ E ) Controller (m B ) Controller (δ B ) K d T (seonds) T (seonds) 74.689. 3384. 76 7.53. 4. 468 96.7449. 36. 975 399.36. 9. 848 Tle 4. Eigenvlues of the system with UPFC ontrollers. Controller (m E ) Controller (δ E ) Controller (m B ) Controller (δ B ) Eigenvlues rtio Nturl frequeny of osilltion (ω n ) -.6 ± 3.46i.4 3.8 -.9 ± 3.3i.5 3.76 -.6 ± 3.37i. 49 3.74 -.7 ± 3.68i. 54 4.33 Tle 4 shows eigenvlues of the system t nominl operting ondition with the ove lterntive dmping ontrollers. Tle 4 lerly shows tht dmping rtios otined with ontrollers (δ E ) nd (δ B ) re higher thn those otined with ontrollers (m E ) nd (m B ). 3). Dynmi Performne of the system with Controllers Fig. 4 shows the dynmi responses for otined onsidering step lod perturtion T m =. p.u. with the four lterntive dmping ontrollers (Tle 3) Fig. 4 lerly shows tht the dynmi responses of the system otined with the four lterntive dmping ontrollers re virtully identil. At this stge it n e inferred tht ny of the UPFC sed dmping ontrollers provide stisftory dynmi performne t the nominl operting ondition..5.5 x - ontroller(δ B ) - ontroller(δ E ) - ontroller(m E ) d- ontroller(m B ) - 3 4 5 Fig. 4. Dynmi responses for with four lterntive ontrollers. Further investigtions re rried out to ssess the roustness of these four lterntive dmping ontrollers to d wide vrition in loding onditions nd line retne Xe. 4). Effet of Vrition of loding ondition nd system prmeters on the dynmi performne of the system In ny power system, the operting lod vries over wide rnge. It is extremely importnt to investigte the effet of vrition of the loding ondition on the dynmi performne of the system. In order to exmine the roustness of the dmping ontrollers to wide vrition in the loding ondition, loding of the system is vried over wide rnge (Pe =. to Pe =. p.u.) nd the dynmi responses re otined for eh of the loding ondition onsidering prmeters of the dmping ontrollers omputed t nominl operting ondition for the step lod perturtion in mehnil torque (i.e. T m =. p.u.) Figs. 5 nd 6 show the dynmi responses of with nominl optimum ontroller (m B ) nd ontroller (m E ) t different loding onditions. It is lerly seen tht the dynmi performne of the system is degrded signifintly s the system loding is redued from the nominl loding. Further it is seen tht system eomes unstle x.5.5.5 - -.5 - Pe =.p.u. Qe =. p.u. - Pe =.8p.u. Qe =.67p.u. - Pe =.p.u. Qe =.4 p.u. - 3 4 5 Fig. 5.Dynmi responses for with ontroller (m B ) for different loding onditions. x.5.5.5 - -.5 - Pe =.p.u. Qe =.p.u. - Pe =.8p.u. Qe =.67p.u. - Pe =.p.u. Qe =.4 p.u. - 3 4 5 Fig. 6. Dynmi responses for with dmping ontroller (m E ) for different loding onditions.
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 73, DECEMBER 7-9, 43 x.5 x.5.5 - Pe =.8p.u. Qe = -.p.u. - Pe =.8p.u. Qe =.67p.u. - Pe =.p.u. Qe =.4 p.u..5 - Xe =.3 p.u. - Xe =.5 p.u. - Xe =.65 p.u..5.5 - - -.5 3 4 5 Fig. 7. Dynmi responses for with dmping ontroller (δ B ) for different loding onditions..5.5 x - d - Pe =.8p.u. Qe = -.p.u. - Pe =.8p.u. Qe =.67p.u. - Pe =.p.u. Qe =.4 p.u. d - Pe =.p.u. Qe =. p.u. -.5 3 4 5 Fig. 8. Dynmi responses for with dmping ontroller(δ E ) for different loding onditions. for typil leding power ftor ondition (i.e. Pe =.8 p.u., Qe = -. p.u.). Figs. 7 nd 8 show the dynmi responses of with nominl optimum ontroller (δ B ) nd ontroller (δ E ) respetively. It is lerly seen tht the responses re hrdly ffeted in terms of settling time following wide vritions in loding ondition. Both the ontrollers perform well for the leding power ftor loding ondition lso. From the ove studies, it n e onluded tht the Controller (δ B ) nd ontroller (δ E ) exhiit roust dynmi performne s ompred to tht otined with ontroller (m B ) or ontroller (m E ). In view of the ove, the performne of dmping Controller (δ B ) nd ontroller (δ E ) re further studied with vrition in equivlent retne, Xe of the system. Figs. 9 nd show the dynmi performne of the system with ontroller (δ B ) nd ontroller (δ E ) respetively for wide vrition in Xe. -.5 3 4 5 Fig. 9. Dynmi responses for with ontroller (δ B ) for different vlues of Xe..5.5 x - - Xe =.65 p.u. - Xe =.5 p.u. - Xe =.3 p.u. -.5 3 4 5 Fig.. Dynmi responses for with dmping ontroller (δ E ) for different vlues of Xe. Exmining Figs. nd, it n e inferred tht ontroller (δ B ) nd ontroller (δ E ) re quite roust to vritions in Xe lso. It my thus e onluded tht ontroller (δ B ) nd ontroller (δ E ) re quite roust to wide vrition in loding ondition nd system prmeters.the reson for the superior performne of ontroller (δ B ) nd ontroller (δ E ) my e ttriuted to the ft tht modultion of δ B nd δ E results in exhnge of rel power. VI. CONCLUSIONS The signifint ontriutions of the reserh work presented in this pper re s follows:. A systemti pproh for designing UPFC sed ontrollers for dmping power system osilltions hs een presented.. The performne of the four lterntive dmping ontrollers, (i.e. ontroller (m E ), ontroller (δ E ), ontroller (m B ), nd ontroller (δ B ) ) hs een exmined onsidering wide vrition in the loding onditions nd line retne Xe.
43 NATIONAL POWER SYSTEMS CONFERENCE, NPSC 3. Investigtions revel tht the ontroller (δ E ) nd ontroller (δ B ) provide roust performne to wide vrition in loding onditions nd line retne Xe. It my thus e reommended tht the dmping ontrollers sed on UPFC ontrol prmeters δ E nd δ B my e preferred over the dmping ontrollers sed on ontrol prmeters m B or m E. APPENDIX The nominl prmeters nd the operting ondition of the system re given elow. Genertor : M = H = 8.MJ / MVA D =. Tdo = 5.44 se. X d =. p.u. X q =.6 p.u. X d =.3 p.u. Exittion system : K =. T =. se. Trnsformer : X te =. p.u. X E = X B =. p.u. Trnsmission line : X Bv =.3 p.u. Xe =.5 p.u. Operting ondition : Pe =.8 p.u. V t =. p.u. V =. p.u. f = 6 Hz UPFC Prmeters : m E =.43 m B =.789 δ E = -85.3478 δ B = -78.74 DC Link Prmeters : V d = p.u. C d = p.u. REFERENCES [] A Edris, K. Gyugyi et l., Proposed terms nd Definitions for Flexile AC Trnsmission Systems (FACTS), IEEE Trns. on Power Delivery, Vol., pp. 848-853, Otoer 997. [] L. Gyugyi, Unified power flow ontrol onept for flexile AC trnsmission systems, IEE Proeedings-C, Vol. 39, No. 4, pp. 33-33, July 99. [3] L Gyugyi, C.D. Shuder et l., The unified power flow ontroller: A new pproh to power trnsmission ontrol, IEEE Trns. on Power Delivery, Vol., N., pp. 85-93, April 995. [4] A Nvi-Niki nd M.R. Irvni, Stedy-stte nd dynmi models of Unified power flow ontroller (UPFC) for power system studies, IEEE Trns. on Power Systems, Vol., No. 4, pp. 937-943, Novemer 996. [5] K.S. Smith, L.Rn, J. Penmn, Dynmi modeling of Unified power flow ontroller, IEE Proeedings-C, Vol. 44, No., pp. 7-, Jnury 997. [6] T. Mkome nd N. Jenkins, Investigtion of Unified power flow ontroller, IEE Proeedings-C, Vol. 46, No. 4, pp. 48, July 999. [7] Ppi, P. Zunko et l., Bsi ontrol of Unified Power Flow ontroller, IEEE Trns. on Power Systems, Vol., No. 4, pp. 734-739, Novemer 997. [8] H.F. Wng, funtion of unified power flow ontroller, IEE Proeedings-C, Vol. 46, No., pp. 8-87, Jnury 999. [9] H.F. Wng, A unified model for the nlysis of FACTS devies in dmping power system osilltions Prt III: Unified power flow ontroller, IEEE Trns. on Power Delivery, Vol. 5, No. 3, pp. 978-983, July. [] H.F. Wng, Applitions of modeling UPFC into multi-mhine power systems, IEE Proeedings-C, Vol. 46, No. 3, pp. 36-3, My 999. [] Yo-Nn Yu, Eletri Power System dynmis, Ademi Press, In., London, 983.