外文翻译原文-利用稳态测量跟踪电力系统等效电路参数

TrackingPowerSystemEquivalentCircuitParametersUsingSteadyStateMeasurementsS.A.Arefifar,StudentMember,IEEE,andW.Xu,Fellow,IEEEAbstract-Thispaperdealswiththeproblemofcalculatingthepowersystemequivalentcircuitparametersusinglocalmeasurementsatthepointofcommoncoupling(PCC).Forthispurpose,anewalgorithmbasedonthreesetsofmeasurementsisproposed.Theproposedalgorithmismorepracticalandhassomeadvantagesoverthepreviousmethods.Thenecessarymeasureddataforthisapproacharemagnitudeofvoltageandcurrentandthepowerfactor.Verificationstudies,includingsimulationandexperimentalresults,areprovidedtoverifythealgorithm.Moreover,somepracticalsituationssuchasnoiseconditionandslowvariationsofsystemparametersareinvestigated.IndexTermsEquivalentcircuit,Impedance,Measurementdata,Powersystem.I.INTRODUCTIONHEneedforsupplysystemimpedancedatahasbeenamatterofgreatconcernforbothsupplyauthoritiesandindustrialcustomers1.Duringrecentyears,theconstantincreaseofthepowerdemandedbyloadshasnotbeenfollowedbyanadequatedevelopmentoftheelectricalnetwork.Thereforethesupplysystemwilllikelybesubjectedtoincreasingdisturbancesinjectedbydirectlyconnectedloadssuchasarcfurnacesandpowerelectronicdevices.Insuchascenario,theutilityimpedancewillplayanimportantroleinthedisturbancepropagationandtheaccuratemodelingofthesupplysystemisthentheprerequisitefortheoptimizationofpowerquality.Today,powerelectronicdevicesarewidelyusedinpowersystems.Inordertofullyexploittheircapabilitiesandtoreducetheeffectsoftheirdrawbacks,particularlytolimitvoltagewaveformdistortions,theinteractionbetweenthepowerelectronicdevicesandthepowersystemtheyareconnectedtohastobemodeledindetails.TheTheveninequivalentcircuitsatfundamentalandharmonicfrequenciesusuallyprovideenoughinformationregardingtheeffectsofthechangesofthepowerelectronicdeviceoperatingconditionsonthesupplyvoltagewaveform2.Moreover,withtheknowledgeofTheveninequivalentparameters,seenattheloadbus,thevoltagestabilitymarginandmaximumloadabilityofthesystemcouldbeeasilyThisworkhasbeenfullysupportedbytheAlbertaIngenuityFundandiCORE.TheauthorsarewithElectricalandComputerEngineeringDepartmentofUniversityofAlberta,Canada(e-mail:arefifarece.ualberta.ca).estimated3.Severalmethodshavebeenproposedsofartotrackandestimatethepowersystemimpedance,whichhavetheirownadvantagesanddisadvantages.Someofthemarebasedonsynchronizedmeasurementsofwaveformsandsomerequirenonlinearloadtoestimatepowersystemequivalentcircuit.Thesemethodsbasicallyrefertotwodifferentapproaches.Thenon-invasiveapproachusestheexistingloadcurrentandvoltagevariationstoidentifythenetworkequivalentimpedance2-6,andtheinvasiveapproach,usestheswitchingtransientscausedbynetworkequipmentsuchascapacitorbanksorforcedsystemcurrentexcitationbyaharmonicgeneratingdevice7-12.Thenon-invasivemethodsareusuallysimplerandmoreapplicablesincetheydonotimposeanydisturbanceorwaveformdistortiontothesystem.Inthispaper,anewalgorithmbasedonthreesetsoflocalmeasurements,voltage,currentandpowerfactor,isproposedtocalculatethepowersystemequivalentcircuitparameters.Theadvantagesofthismethodoverpreviousonesare:1)Themethodisnon-invasiveanddoesnotimposeanydisturbancetothesystem2)Thereisnorestrictionontheloadmodel3)Thereisnorequirementtohavesynchronizedmeasurements.4)Theonlyrequiredinformation,fortheproposedalgorithmtoestimatepowersystemequivalentcircuitparametersarethesteady-stateRMSvaluesofvoltageandcurrentandthepowerfactorattheloadpoint.ThisinformationisalreadyavailableatthePCC.Themethodhasbeentheoreticallyvalidatedandsomecasestudiesandexperimentalresultsarepresentedtocheckthevalidityofthealgorithm.II.THEPROPOSEDALGORITHMThepowersystemasseenatthePCCcanbemodeledasanequivalentcircuitshowninFig.1.GsEsRsjXMV0IFig.1.PowersystemmodelseenatthepointofcommoncouplingThegoalistocalculatetheTheveninequivalentT108978-1-4244-1726-1/07/$25.00c2007IEEEparameters,and,whiletheonlyinformationavailablefromthesystemisourlocalmeasurementdata,whichare,andthepowerfactor(sEsRsXiViIiM).Theproposedmethodusesthreedifferentsetofmeasurementsatthreedifferentinstantsandisapplicableforeachphaseofathreephasesystem.Forabetterunderstandingofthealgorithm,weassumethatthesystemside,(,and),areconstantandloadsidehassomevariations,therefore,applyingKVL,thesystemequationsforasetofmeasurementdataattime,areasfollows:sEsRsX1t11110)(MGuVIjXREsss(1)Usingtheassumptionthat,andareconstantduringthemeasurements,forthesecondandthirdsetofV,IandsEsRsXMforthesamephaseandattimesand,wewillhavethesameequation.2t3tIfweseparatetherealandimaginarypartofequation(1),andrewritethemwewillhave:uuuuu)sin()cos(000)sin()cos(iiiiissisisVVIXREEMMGGi=1,2,3(2)Equations(2)canbewrittenforeachphaseofthethreephasesystemandrepresentsixequationsandsixunknowns.Theunknownparameters,foronephaseofthesystem,inthissetofequationsare:,sEsRsX1G,2G,3GAsexplainedbefore,forthisalgorithmthemeasurementsarenotnecessarilysynchronized,therefore,thevaluesofiGdependontheinstantofswitchingandcanhaveanyvalue.Sincethenumberofequationsandunknownsareequal,wecanproceedandsolvethesetofnonlinearequations.Thereareseveralmethodstosolvethissetofequations.InthispapertheNewtongradientmethodhasbeenusedtogetthesolutions.Usuallyatthepointofcommoncouplingtherearemeterstomeasurevoltage,active(P),andreactivepower(Q).UsingP,Qandvoltageateachmeasurement,wecancalculatethemagnitudeofcurrent,andthepowerfactor.ThereforetherequiredinformationforestimatingthesystemequivalentcircuitparametersisalreadyavailableandthereisnoneedtoinstallanyadditionaldataacquisitionsystematthePCC.Sincethevoltage,PandQrepresenttimeseries,thevaluesofsystemimpedanceandequivalentsystemsourcearealsoestimatedastimeseriesandcouldbedisplayedonthemeters(newgenerationofmeters).Theestimationprocedureisnotdependentontheloadmodelandisapplicablefordifferentkindofloads.TheproposedmodelforsomeoftheloadsinpowersystemisThevenin(Norton)equivalentcircuitthatmeanstheycanbemodeledasavoltage(current)sourceandaseries(parallel)impedance.ForTheveninequivalentcircuitloadmodels,suchasmotorsorharmonicgeneratingloads,thealgorithmcanbeusedtotracktheloadimpedanceaswell.Forthiskindofloadswecanwriteasimilarsetofequationsfortheloadsidetoestimateandasfollows:LVLZiiiLLiLVIjXRVMGu0)(i=1,2,3(3)Inequation(3),istheTheveninequivalentvoltagesourceoftheloadandistheTheveninequivalentimpedanceoftheloadseenatthepointofcommoncoupling.V,IandLVLLjXRMarethesamesetofmeasurementsusedforcalculationofsystemsideparameters.Theonlydifferenceisthedirectionofthecurrentthataddsanegativesigntotheequations.Usingthesamemeasurementdatatosolveequations(3),wecancalculatetheloadsideparameters.Inthefollowingsectionssomecasestudieshavebeendoneandsimulationandexperimentalresultsarepresentedtoshowthevalidityoftheproposedalgorithm.III.VERIFICATIONSTUDIESA.SimulationResultsTwodifferentloadmodels,impedanceandTheveninequivalentloadmodel,aresimulatedinthissectionandtheresultsarepresentedtoshowthevalidityoftheproposedalgorithm.1)ImpedanceLoadModelSomeoftheloadsinpowersystemarepassiveandcanbemodeledasanimpedance.Forsimulationofthiskindofloads,theloadhasbeenmodeledasavariableimpedance(1215jZLohms)andthesystemismodeledasshowninFig.1,(43jZsohmsand120sEVolts).Thesystemandloadsidehavechangedrandomlywithmaximumvariationof5%,andtheproposedalgorithm,usingequations(2),havebeenusedtoestimatethesystemequivalentcircuitparameters.Thesystemequivalentcircuitparametersseenfromaspecificbus(PCC)areusuallyconstant;howevertheymaychangeduetothevariationofsystemconfiguration,availabilityofgeneratingunitsorothersystemloadsthatarebehindthePCC.TheestimationofsystemparametersandtheiractualvaluesareplottedinFig.2.200739thNorthAmericanPowerSymposium(NAPS2007)1090501001502002503001234Rs(Ohms)050100150200250300246Xs(Ohms)05010015020025030050100150200Es(Volts)TimestepActualCalculatedFig.2.ActualandcalculatedsystemparametersAscanbeseen,theiterativealgorithmhasconvergedtotheexactvaluesofsystemimpedanceandequivalentvoltagesourcevalues.2)TheveninEquivalentCircuitLoadModelTheequivalentcircuitofsomeoftheloadsinpowersystemisTheveninorNortonloadmodel.Forsimulationofthiscase,thesystemandloadhavebeenmodeledasTheveninequivalentcircuitandtheparametersare:1215jZLohms,ohms,VoltsandVolts.Thesystemandloadsidehavechangedrandomlywithmaximumvariationof5%andtheproposedalgorithmhavebeenusedtoestimatethesystemandloadsideequivalentcircuitparameters.43jZs120sE110LVTheestimatedandactualvaluesofsystemandloadparametersareplottedintheFig.3andFig.4.0501001502002503001234Rs(Ohms)050100150200250300246Xs(Ohms)05010015020025030050100150Es(Volts)TimestepActualCalculatedFig.3.ActualandcalculatedsystemparametersAsexplainedbefore,theproposedalgorithmcanbeusedtocalculateloadsideequivalentcircuitparameters.Usingequations(3)forthesamesetofdata,wecancalculatetheloadsideparameters,asshowninFig.4.0501001502002503005101520RL(Ohms)0501001502002503005101520XL(Ohms)05010015020025030050100150VL(Volts)TimestepActualCalculatedFig.4.ActualandcalculatedloadparametersSimulationresultsshowthatforthiskindofloadstheproposedalgorithmprovidestheexactresultsforestimationofsystemandloadsideparameters.Usingtheleastsquareestimationwillhelpustoimprovetheresultsandcanceltheeffectofmeasurementnoise.B.PracticalIssuesOneoftheadvantagesofthismethodisthepossibilityofsolvingequation(2)forevensmalldisturbancesatthePCC.Ifthereisnonoiseortransientinthemeasuredvoltageandcurrent,andthesystemparametersdonotchangefortheperiodofmeasurement,theaccuracyofthismethodis100%.Inthefollowing,somepracticalissuessuchasnoiseconditionandslowvariationofsystemparametersareexplained.Forthispurpose,tocalculateeachplottedvalueinthefigures,300caseshavebeenrunandtheestimationerrorshavebeencalculatedforeachcaseandthentheaveragehasbeenplotted.Theerroriscalculatedasfollows:Error(%)=100)(30013001uiActualCalculatedActualiiiDataDataData(4)Thesameprocedurehasbeenfollowedforcalculationofaccuracyoftheresults.1)NoiseconditionsUsuallymeasurementsinpowersystemscontainnoise.Thisnoisecanhavedifferentsourcesbutthemostcommonsourceofit,isthemeasurementdevicesandswitchingtransients.InFig.5theaccuracyofcalculated,andisplottedasafunctionofmeasurementnoise.Themeasurementnoiseisthemaximumrandomnoiseaddedtothemeasuredvoltageandcurrentwaveforms.sEsRsX110200739thNorthAmericanPowerSymposium(NAPS2007)00.020.040.060.080.10.12708090100Rs(%)00.020.040.060.080.10.12708090100Xs(%)00.020.040.060.080.10.129095100105Es(%)MeasurementNoise(%)Fig.5.AccuracyofthemethodinnoiseconditionAscanbeseen,theaccuracyoftheproposedmethodisacceptablewhenthenoiselevelislow.Sincethemagnitudeofisusuallylargerthanand,theaccuracyofcalculatedismuchhigherthantheaccuracyofcalculatedand.Inthiscasethevariationofloadisrandomwiththemaximumof5%andtheaverageofandsEsRsXsEsRsXVIare0.8713%and2.7169%respectively.Ingeneraltheaccuracyofthealgorithminnoiseconditiondependsonthevariationofloadparameters.Themorechangesintheloadsideparameters,themoreaccuratearethecalculatedvaluesforsystemequivalentcircuitparameters.InFig.6foracertainlevelofnoise,theaccuracyofcalculated,andisplottedwhenthemaximumvariationofloadsideparameterschangesfrom0%to2%.sEsRsXFig.6showsthattheproposedalgorithmisnotabletodetectsystemparameterswhenthereisnovariationintheloadsideparameters;however,theaccuracyofthecalculatedresultsincreasesasthevariationofloadparametersrises.00.81.82050100Rs(%)00.81.82050100Xs(%)00.81.82050100Es(%)MaximumVariationofLoadParameters(%)Fig.6.AccuracyofthemethodinnoiseconditionForthiscasetheaverageofandVIchangesfrom0%to0.3455%andfrom0%to1.0888%respectively.Simulationsshowthattheproposedalgorithmworksundernoiseconditionifthemaximumnoiselevelislessthanthevariationofloadparameters.Moreoverusingleastsquareestimationmethodcansignificantlyreducethecalculationerror,causedbymeasurementnoises.2)SlowvariationconditionsInthissection,theaccuracyoftheproposedmethodisinvestigatedforthecasesthatthesystemsidehasslopevariation.Forthispurpose,thesystemequivalentimpedanceandvoltagesourcechangesimultaneouslywithdifferentvariationslopes.Tocalculatetheaccuracyforeachslope,300differentcaseshavebeensimulatedandFig.7showstheaverageoftheaccuracyofthosecases.051015708090100Rs(%)051015708090100Xs(%)0510159999.5100Es(%)SlopeofEs&Zs(%)Fig.7.AccuracyofthemethodinslopeconditionsAsanexamplethecalculationresultsforthecasethatthesystemparameterschangecontinuouslywith5%slopeareplottedinFig.8.05010015020025030051015Rs(Ohms)050100150200250300246810Xs(Ohms)05010015020025030050100150200Es(Volts)TimestepActualCalculatedFig.8.ActualandcalculatedsystemparametersinslopeconditionsThesimulationresultsshowthattheaccuracyofthemethodisacceptableintherangeofpowersystemvariations(lessthan10%)Therefore,thismethodcanalsobeusedforthecasesthatthesystemsideiscontinuouslyvarying.200739thNorthAmericanPowerSymposium(NAPS2007)111C.ExperimentalresultsInthissectionthepowersystemhasbeenmodeledasaresistanceinserieswithareactanceandthevoltagesourceisthesupplyvoltagesourceatthelabfacilitiesinUniversityofAlberta.Sincethemagnitudeofresistanceandreactanceofthemodeledsystemarehigherthanthesystembehindthem,thesupplysourceisconsideredasaninfinitebus.Every30secondsasnapshotofvoltageandcurrentcontaining12cyclesarecapturedandtheRMSvaluesneededforthecalculationsaretheaveragevaluesofthese12cyclesaccordingtoIECstandard13.Forthisexperimenttheload,whichisaninductiveandpassiveloadhasbeenchangedrandomlyfortheperiodofmeasurementsandthesystemside,whichareresistanceandinductancehaschangedonceafter15minutes.ThecalculatedandactualvaluesofsystemparametersareplottedinFig.9.010203040506001020Rs(Ohms)010203040506002040Xs(Ohms)01020304050600100200Es(Volts)TimestepCalculatedActualFig.9.ActualandcalculatedexperimentalsystemparametersThetimestepinFig.9is30seconds.Theresultsshowthattheproposedalgorithmworksproperlyforexperimentalresultsanditcanalsofollowanddetectthevariationofsystemparametersautomatically.Theleastsquareestimationcanbeappliedtoimprovetheaccuracyofcalculatedresults.IV.ACKNOWLEDGMENTTheauthorsgratefullyacknowledgetheAlbertaIngenuityFund,iCOREandNSERCforthesupportprovidedduringthiswork.V.CONCLUSIONInthispapertheproblemofestimatingthepowersystemequivalentcircuitparameters,usinglocalmeasurementsatthepointofcommoncoupling(PCC),hasbeensolved.Forthispurposeanewiterative-basedalgorithmbasedonthreesetsofmeasurementsisproposedtoestimatethesystemparameters.Theadvantageoftheproposedalgorithmcomparingtotheonesavailableinliterature,isthatthismethoddoesnotdependontheloadmodelandalsothereisnoneedtohavesynchronizedmeasurements.TheonlyrequiredinformationforthismethodistheRMSvaluesofvoltage,current,andthepowerfactor.ThisinformationcaneasilybeobtainedfromthemetersthatarealreadyinstalledatthePCCandthereisnoneedtoinstallanyadditionaldataacquisitionsystemsthatareusuallycostly.SimulationresultsshowthatinnoiseconditiontheaccuracyofthemethodincreaseswhenthevariationofvoltageandcurrentatPCCincreases.Theproposedmethodalsoworksunderslopevariationsofsystemparameters.Experimentalresultsareprovidedforfurtherverificationofthealgorithm,whichshowthatthismethodcanbeusedinpracticalsituationsandtheresultsmatchtheactualvalues.Theproposedalgorithmcanalsobeusedforcalculationofharmonicimpedancesaswell.Inthiscasewecandeterminetheharmoniccontributionofutilitiesandcustomersforthetotalharmonicdistortionatthepointofcommoncouplingandalsotheharmonicimpedancesofloadandsystem,thatnoappropriateapproachhasbeenproposedsofar.VI.REFERENCES123456789101112A.DeOliveira,J.C.DeOliveira,J.W.andM.S.“ResendeMiskulin,PracticalapproachesforACsystemharmonicimpedancemeasurements”,IEEETrans.PowerDelivery,vol.6,issue4,pp.1721-1726,Oct.1991.G.Fusco,A.Losi,andM.Russo,“ConstrainedLeastSquaresMethodsforParameterTrackingofPowerSystemSteady-StateEquivalentCircuits”,IEEETrans.PowerDelivery,vol.15,issue3,pp.1073-1080,2000.K.Vu,M.M.Begovic,D.Novosel,andM.M.Saha,“Useoflocalmeasurementstoestimatevoltage-stabilitymargin”,IEEETrans.PowerSystems,vol.14,issue3,pp.1029-1035,Aug.1999.M.BahadornejadandG.Ledwich,“SystemTheveninImpedanceEstimationUsingSignalProcessingonLoadBusData,”Proceedingsof6thInternationalConferenceonAdvancesinPowerSystemControl,OperationandManagement,APSCOM,pp.274279,Nov.2003.T.andW.“Tayjasanant,ChunLiXu,Aresistancesign-basedmethodforvoltagesagsourcedetection”,IEEETrans.PowerDelivery,vol.20,no.4,Oct.2005.K.Vu,andD.Novosel,“Voltageinstabilitypredictor(VIP)-methodandsystemforperformingadaptivecontroltoimprovevoltagestabilityinpowersystems”,U.S.Patent6219591,May15,1998.M.Sumner,B.Palethorpe,andD.W.P.Thomas,“ImpedanceMeasurementforImprovedPowerQualityPart1:TheMeasurementTechnique”IEEETrans.PowerDelivery,vol.19,n