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PSCADCasesSR_case_01.pscandSSR_case_02.pscHarmonicImpedancenearmachinebus(LVbus)Figure1Harmonicimpedancemeasuredatthemachinebus.Themachinewasdisconnectedfromthecircuitduringthismeasurement.Thenetworkresonancepointisaround15Hzapproximately.Thenetworkresonancepointshiftatdifferentseriescompensationlevelsismarginal.Thisisbecausethetransformerreactanceaswellastheequivalentsystem(voltagesource)reactanceiscomparabletothelinereactance.Theinductionmachinedatausedintheexampleare:Rating-100MVARatedvoltage-26kVStatorresistance-.0.01pu(or0.015pu)Woundrotorresistance-0.0507[pu]SSRcase01.psc:Runthesimulationunderthefollowingconditionsandobservethesystemresponse.Youwillnotethat,at45%compensation,iftherotorresistanceofthemachineis0.015pu,IGdoesnothappen.?SeriescompensationLevel(whenfn<30hz,C-,fn+,s-,Rr/s+,negativeresistance+):?114uF-Approx.45%compensations?90uF-Approx.55%compensations?80uF-Approx.60%compensations?65uF-Approx.75%compensations?Statorresistance:?0.015puand0.01pu?At65uFandRs=0.015pu=>notetheimpactofnetworkequivalencemodel(changethenetworkequivalencesourcetoincludelosses)?Increasethecapacitanceto120uFandRs=0.01pu.Notetheresults.?Increasethecapacitanceto125uFandRs=0.01pu.Notetheresults.SSRcase02.psc:Runthesimulationunderthefollowingconditionsandobservethesystemresponse.?Statorresistance:0.01pu?Seriescompensation:114uF-Approx.45%compensationsSimulationscenarios:OpenthefaultedcircuitbutkeepthesecondcircuitconnectedKeeponlyonecircuitconnectedinitially.Openthecircuitfollowingthefault.Keeponlyonecircuitconnectedinitially.Openthecircuitfollowingthefaultandre-close.Bypassthecapacitorsandrunthesimulations.SimplemathematicalanalysisoftheIGsituationfortheparametersusedinthesimulationmodel:TheinductionmachnedatausedintheSSR-IGexampleare:Rating-100MVARatedvoltage-26kVStatorresistance-0.01pu(or0.015pu)Woundrotorresistance-0.0507[pu]Rotorspeedisapproximatelythevaluecorrespondingto60Hz.ThusdefineWras:Wr60Wsisthesubsynchronousresonancepointofthenetwork,lookingfromthemachinebus.Itisafunctionofthelevelofseriescompensation.DefineWsasavariabletorepresentthesubsynchronousresonancepoint.Ws52055WsWrS(Ws)The'slip',definedforthesubsynchronousresonancecurrentsis(asafunctionofWs)WsWrS(Ws)WsThevalue(slip)isnegative.S(15)3S(20)2Machinewindingresistancereferedtothestator:Statorresistance(Ohms)-Rs-0.01pu226Rs0.01——Rs0.068Ohms100Rotorresistance(Ohms)-Rr-0.0507pu262Rr0.0507—Rr0.343yschronouscurrents)100yschronouscurrents)Effectiverotorresistancefordifferentslipvalues(forsubsRr

S(10)0.069RrS(15)Rr

S(10)0.069RrS(15)0.114Rr

S(55)3.77Thustheabsulutevalueofthe'effective'negativerotorresistanceincreaseswhenthesubsyschronanceresonancefrequencyincreases.Thatis,whenthelevelofseriescompennsationincereases,theefectivenegativeresistancealsoincrease.=>Atlargerlevelsofcompensation,therisknegativeresistance'experiences'at15Hzsthestatorresistance.However,theresistanceofIGeffectincreases.Notethattheubsyschrnousecurrentsislargerthanofthelines,transformersandtherest=>Atlargerlevelsofcompensation,therisknegativeresistance'experiences'at15Hzsthestatorresistance.However,theresistanceofIGeffectincreases.Notethattheubsyschrnousecurrentsislargerthanofthelines,transformersandtherestofthesystemwillcontributetothetotalresistanceofthesystemLineresistance0.001723454.047100Onthe345kVside(fromPSCADlineconstantcalculations,theresistanceofonehalfofthe345kVline(oneithersideoftheseriescapacitor)in0.0017pu)Referedto26kVside:26R_264.047——一ofthesystemwillcontributetothetotalresistanceofthesystemLineresistance0.001723454.047100Onthe345kVside(fromPSCADlineconstantcalculations,theresistanceofonehalfofthe345kVline(oneithersideoftheseriescapacitor)in0.0017pu)Referedto26kVside:26R_264.047——一345R_260.023TwoparallellinesR_effR_262R_eff0.011Totalresistanceas'seen'fromthemachineairgap-Rt:RtRsR_effRt0.079OhmsRtRsR_effRt0.079OhmsNote:Ifthesubsynchronousresonancepointiscloserto10Hz,theriskofIGshouldvanish.InthePSCADsimulation,114uF(45%compensation)res

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