外文翻译原文-电力系统检测与定位的约束优化设计

EventDetectionandLocationinElectricPowerSystemsusingConstrainedOptimizationMichaelJ.Smith,KevinWedewardStudentMember,IEEE,Albuquerque,NMDepartmentofElectricalEngineeringNewMexicoInstituteofMiningandTechnology,Socorro,NM87801AbstractOnlinemonitoringanddiagnosticsareimportantfunctionsintheoperationandmaintenanceofelectricpowersystems.Inthispreliminarypaperwepresenttwonewmethodsforelectricpowergridstateandparameterestimationwhenalimitedamountofgridinformationisavailable.Themethodsarebasedondevelopingaconstrainedoptimizationproblemwhosesolutionprovidesasetofdesiredgridinformation.Thefirstmethodattemptstoestimateanapproximatestateofthegridfromasetofmeasurementsatarelativelysmallnumberofsites.Constrainedtothepowerbalancemanifold,thismethodminimizesanobjectivefunctionbasedongenericgridbehavioraswellasanyavailableinformationabouttheparticularstateofthegridtoestimateaselectedsetofgridstatesandparameters.Thesecondapproachusestimedatafromasmallnumberofsitestotrytodetectandlocalizeaneventsuchasafaultedlineinthegrid.Thismethodminimizesanobjectivefunctiondefinedonthetime-varyingpowerbalancemanifoldthatisdesignedtobesensitivetoabruptlocalstateandparameterchanges.Thisdetectionandlocalizationtoolisintendedasanearlywarningsystemorasupplementalcheckwithinalargermulti-modaldetectionsystem.ThecapabilitiesoftheapproachesaredemonstratedthroughsimulationonaIEEEpowerflowtestgrid.I.INTRODUCTIONTheday-to-daydependenceofhomes,industry,commerce,etc.onelectricityrequiresasteadysupplyofelectricpower.TheinterconnectedgridusesSupervisoryControlandDataAcquisition(SCADA)systems,controlsystems,andprotectivedevicesystemstocopewithchangingloaddemandsandgridfailures.Sincethederegulationofelectricpowersystemsthegovernmenthasbeentryingtohelppowersystemcontrolareasunderstandtheirowngridbehaviorandstatustoensurereliablepowerdelivery.Acosteffectiveandeasywayformonitoringgridstatusistousealimitedsetofinstrumentationalreadyinplace.TheuseoflimitedSCADAmeasurementdatacanbeusedasabackupmonitoringtooltoquicklydetectandlocatedevicefailuressuchastransmissionlineoutages.Detectingandlocatingsuchfailuresinatimelyfashionwouldminimizedamagetoconnectingequipmentandreducethepossibilityofcascadingfailureswhileimprovingsituationalawarenessinelectricpowersystemoperations.Inordertoobservethestatusofthegridusinglimitedmeasurementsitesanewtechniquehasbeendeveloped.Thenewtechniqueiscastasanonlinear,constrained,optimiza-tionprobleminwhichthesystemstatesandparametersareforcedtothepower-balancemanifoldandimposedconstraints.BeyondusingSCADAinstrumentationforthepowersystemstateestimator,littleresearchhasbeendeployedinusinganoptimizationapproachwithlimitedmeasurementstoestimategridbehavioranddevicefailures,particularlyoutsideofthelocalareaofmeasurementsites.Theresearcharticlesthatcomeclosetothisapproacharefoundinreferences,1,2,3.Theworkpresentedin1isanewfaultlocationalgorithmbasedonbusvoltages.Anerrorfunctionisevaluatedbydif-ferencingthemeasuredbusvoltagemagnitudesandpredictedbusvoltagemagnitudes.Thepredictedbusvoltagemagnitudesarecalculatedthroughtheuseoftheimpedancematrixandmaximumavailablefaultcurrents.Inworkpresentedby2,existingphasormeasurementunits(PMUs)onthegridareusedtolocatetransmissionlinefaults.Followingasystemeventthebusvoltagephaseangledifferencesattheobservablebusesinthesystemwithrespecttotheirpre-eventvaluescanbedetermined.Afterchangesinvoltagephaseanglesaredeterminedanoptimizationproblemissolvedfordetectingeventoccurrences.Anotherfaultdetectionalgorithmistotrainneuralnetworkstolearnonsimulatedorrealdatafromanelectricpowersystemmodelorrealsystem,respectfully3.Afterthepowersystemathandistrainedmeasurementinputstothesystemarecomparedtotrainedneuralnetworksandclassifiedeitherasfaultsorsomeotheranomalyonthegrid.Theworkpresentedinthispaperdescribesanewalgorithmfordetectingandlocatinganomalouseventssuchasdevicefailuresorlineoutagesinlargeelectricpowersystemsgivenmultipletimemeasurementsfromalimitednumberofremotesites.Lineoutagesaredetectedandlocatedusinganopti-mizationbasedapproach,whereatime-differencingobjectivefunctionisbeingminimizedtoidentifyanygridchanges.Aseparateproblemofthisworkisestimatingstateandparametervaluesinanelectricpowersystemgivensingletimemeasurementinformationfromalimitednumberofremotesites.Toestimatestateandparametervaluesanoptimizationapproachisusedtominimizeanobjectivefunctionbasedupongridoperatingprinciples.II.ESTIMATINGPOWERSYSTEMSTATEThissectiondiscussessolvinganonlinearconstrainedop-timization(NLCO)problemtoprovideasetofdesiredgridinformation.Thismethodattemptstoestimateanapproximatestate(voltagesandpowers)ofthegridfromasetofmea-surementsatarelativelysmallnumberofsites.Constrainedtothepowerbalancemanifold,thismethodminimizesan978-1-4244-4241-6/09/$25.002009IEEEobjectivefunctionbasedongenericgridbehavioraswellasanyavailableinformationabouttheparticularstateofthegridtoestimateaselectedsetofgridstatesandparameters.IncontrasttoNLCOanoptimalpowerflow(OPF)approachhassufficientlymoreknowndata,thatincludesalltheloadrealandreactivepowersaswellasmeasureddatathroughoutthegrid.A.OptimalPowerFlowThemathematicalproblemformulationfortheOPFproblemisasfollows:Minimizef(x)subjecttog(x)=0h(x)0(1)xminxxmaxwherex,theadjustablevariables,arethebusvoltagemagni-tudes,andphaseangles,aswellasthefixedparametersofthesystem.Theobjectivefunction,f(x),isascalarthatrepresentstheminimizationofgeneratorcosts.Theequalityconstraintsg(x)=0representthepowerflowequations.Theinequalityconstraints,h(x)0,boundfunctionsofonvariablessuchaslinepowerflows.Inaddition,limits(xminxxmax)maybeplaceddirectlyonstatevariablesorcontrolvariables.ThisisatypicalOPFproblemformulation,whichcanbesolvedusingseveralmethodsasdiscussedin4.B.ObjectiveFunctionIntheNLCOproblemconsideredtheobjectivefunctionwasdesignedtocapturethecharacteristicsofnormalgridoperation.F=NBussummationdisplayk=1WV,k(Vk1)2+NLinesummationdisplayk=1W,k2k+WPparenleftbiggNGensummationdisplayk=1PGk+NLoadsummationdisplayk=1PLkparenrightbigg2+WQparenleftbiggNGensummationdisplayk=1QGk+NLoadsummationdisplayk=1QLkparenrightbigg2(2)whereWV,k,W,k,WP,WQareweightsgiventoeachtermtoemphasizedifferentlevelsofminimization.Largerweightsminimizespecifictermsmoreheavilythandosmallerweights.TheVkisthevoltagemagnitudeatbusk,NBusisnumberofbusespresent.kisthedifferenceofvoltagephaseanglesacrosslinek,whereNLineisnumberoflines.ThePGkandQGkaretherealandreactivegeneratorpowersatbusk,whereNGenisnumberofgenerators.ThePLkandQLkaretherealandreactiveloadpowersatbusk,whereNLoadisnumberofloads.Inthisproblemtheobjectivefunctionwasweightedasfollows:voltagemagnitudeandvoltagephaseangleswithWV,k=W,k=.01,realpowerlosseswithWP=.1,andreactivepowerlosseswithWQ=.001.Noteweightscouldbescaleduptogivethesameresults.Thefirstterm(Vk1)isthevoltageateachbusbeingdesignednear1p.u.(thenominalbusvoltagemagnitude),thesecondtermkisthedifferenceofljateachtransmissionlinekbetweenbuseslandjusedtokeepksmallforstabilitypurposes,andthethirdandfourthtermswereputintheobjectivefunctiontominimizethetotaltransmissionlinelossesforrealandreactivepower.Forfurtherinformationonnominaloperationoflargeelectricpowersystemssee5.Inthisobjectivefunctioneachtermissquaredtoyieldapositiveobjectivefunction.Ingeneral,thedesignoftheobjectivefunctionisanengineeringlookathowanelectricpowersystemshouldoperateinnormalconditions.C.EqualityConstraints(powerflowconstraints)Thepowerbalanceequationsarethenonlinearequalitycon-straints.Theseequationsdefinethepowerbalancemanifoldtowhichallfeasiblesolutionsareconstrained.GkV2k+Nsummationdisplayj=1,jnegationslash=kVkVj(GjkcoskjBjksinkj)PGkPLk=0(3)BkV2k+Nsummationdisplayj=1,jnegationslash=kVkVj(Gjksinkj+Bjkcoskj)QGkQLk=0(4)GkandBkarethetotallinesshuntconductanceandsusceptanceforalllinesconnectedtobusk,respectively.GjkandBjkarethelinesseriesconductanceandsusceptancefrombusjtok.kjisthedifferenceofphaseangles,jkfrombusjtok.D.InequalityConstraintsTheinequalityconstraintsusedinthisproblemaretherealloadpowersrankedaccordingtosize.Forexampleiftherealloadpoweratbusk,PLk,islargerthanthatofbusj,PLj,i.e.,PLkPLj,thenthisinequalityconstraintcanbewrittenas:PLjPLk=11bracketleftbiggPLjPLkbracketrightbigg0.Ingeneralforrankingofallloads,matrixAcanbeconstructedwith1inthecolumnofthelargerrealpowerand1inthecolumnofthesmallerrealpower.Allotherelementsintheroware0.Thisleadstothegeneralformintheequationbelow.APL1.PLNLoad0(5)PL1throughPLNLoadareallrealloadpowersinthesystem.E.SideConstraintsThesideconstraintsimposelimitsonvariablesateachbusinthesystem.PGkminPGkPGkmaxk=1,.,NGenQGkminQGkQGkmaxk=1,.,NGenVkminVkVkmaxk=1,.,NBuskminkkmaxk=1,.,NBus(6)(7)Whereminandmaxdenotetheminimumandmaximumvaluesintheaboveterms.ThesolverusedforthisnonlinearprogrammingproblemistheMATLABfunctionfmincon,whichisbasedontheSQP(successivequadraticprogramming)method6.ThesoftwarewasdevelopedusingMATLAB7.ForanalysisusingtheNLCOsetup,itisassumedthatalltransmissionlineparameters,Gjks,Bjks,andBksareknownthroughoutthegrid,andGksarepracticallyzeroandareignored.ThecapabilitytoperturbtheseparametersispossibleintheNLCOcode.Intheupcomingtestcase,systemvariablesPGkandVkareknownatbuseswithgeneratorsthroughoutthegrid.Thegeneratorbusvariableswerechosenasknownsbecausetheyaretheheartofapowersystemandthereforeheavilyinstrumented.Itisimportantthatourinitialstartingpointbewithinafea-siblesolutionregion,hencetheimportanceofgridknowledge.AninitialconditionforallunknownVksandksis1p.u.and0rad,respectively.TheloadPLkswerecalculatedbytakingthesumoftheknowngeneratorPGksanddividingbythenumberofloadsinthegrid.LoadQLksandgeneratorQGkswereinitializedusinganassumedpowerfactor(PF).BecauseweknowmeasurementsofrealpoweratallgeneratorswecancalculatethegeneratorreactivepowerassumingaPFat.95.F.ResultsIntheseresultstheIEEE118-bustestsytem(see8fordetails),isusedforsimulationandanalysiswhere15%ofknownmeasurementsaretakenfromthegrid.Thereareatotalof472variablesinthissystem.Thissystemhas118buses,34generators,91loads,and186lines.Thereare34knowngeneratorrealpowersand34knownvoltagemagnitudesatgeneratorbuses.Unknownvariblesinclude:118voltagephaseangle,84voltagemagnitudes,34reactivegeneratorpowersand91realandreactiveloadpowers.Anarbitraryloadflowsolutionofthissystemwasavailablewiththatdataandisusedonlyforcomparison.NLCOsolutionscanbevariedbytuningtheobjectivefunctionweightsoneachterm.Thereareatotaloffourvariablestypesplottedforthissystem:voltagemagnitudes,voltagephaseangles,andloadrealpowersandreactivepowers.Recallrealpowersandmagnitudesofvoltagesatgeneratorbusesareassumedknown(measured),whereforeveryred“*”thatmatchesablack“o”isaknownmeasurement.Ared“*”markerthatdoesnotmatchablack“o”markerrepresentsavariablesolvedforatitsbuslocation.Allotherfigurescanbesimilarlyinterpreted.InFigure1NLCOsoutputforvoltagemagnitudesisrepresentedbyaredlinewitha“*”.Theblackdashedlinewitha“o”isagivenloadflowsolutionforbothsystems.Allreactiveloadpowersareunknownsinthesystem.ThescalingintheFigures3and4maygoupto120onthehorizontalaxisbutkeepinmindthereareonly91loadbusesforthissystem,meaningthereisnota“*”or“o”foreverybusnumber.UsingNLCOinthisworkisusefulforsolvingforunknownvariablesinahighlyunderdeterminedsystemforpurposesofestimatinggridconditions.Toimprovethesolutionmoreinformationaboutthegridisneededintheformofmeasurements,objectivefunction,andconstraints.0204060801001200.920.940.960.9811.021.041.06VoltageMagnitudeBusNumberVoltageMagnitude(V)NLCOLoadFlowFig.1.VoltagemagnitudeforIEEE118-bussystem02040608010010.5BusNumberVoltagePhaseAnlge()VoltagePhaseAngleNLCOLoadFlowFig.2.VoltagephaseangleforIEEE118-bussystem02040608010012032.521.510.500.5BusNumberRealPower(P)OutputLoadPowerPNLCOLoadFlowFig.3.RealloadpowerforIEEE118-bussystem0204060801001BusNumberReactivePower(Q)OutputLoadPowerQNLCOLoadFlowFig.4.ReactiveloadpowerforIEEE118-bussystemIII.NLCOANOMALYDETECTIONAPPROACHTheworkpresentedinthissectionismainfocusofpaperanddescribesanewalgorithmfordetectingandlocatinganomalouseventssuchaslineoutagesinlargeelectricpowersystemsgivenmultipletimemeasurementsfromalimitednumberofremotesites.Lineoutagesaredetectedandlo-catedusinganoptimizationbasedapproach,whereatime-differencingobjectivefunctionisminimizedtobesensitivetoabruptstateandparameterchangesinthegrid.Thesys-temsnonlinearconstraints,inequalityconstraints,andsideconstraints,usedintheprevioussectionareidentical.Thedifferencesaretheobjectivefunction,measurementstaken,andremotesitelocation.Overtimefminconminimizestheobjectivefunctionbaseduponatime-seriesofmeasurements.TheoutputoftheNLCOcodeisavectorfilledstatevaluesfortimesatwhichmeasurementsweretaken.Forlargeelectricpowersystemsitisdifficulttolookatvariousplotsofthetime-seriesdatafordetectionandlocationofthelineoutage.Toovercomethisproblemitwascrucialtounderstandgridbehaviorduringalineoutage.AMATLAB-basedsimulationandanalysiscodeforelectricpower(EP)systems,alsoknownastheEPcode9,wasusedtosimulatelineoutagesandstudyhowthegridreacted.Itwasobservedthatthemostcommontrendduringalineoutagewasvoltagemagnitudeandvoltagephaseanglewoulddivergeacrosslines.Obtainingthisgridknowledgewasimportantforthedevelopmentofpost-processingtool-setsnecessarytoanalyzetheoutputoftheNLCOcode.Thetoolsusedarebasedoffthebusvoltagemagnitudesandbusvoltagephaseangles.Lackingdatafromarealpowersystem,themultipletimemeasurementsusedintheNLCOcodearesyntheticmea-surementstakenfromtheEPsimulationandanalysiscode.Themethodusedforchoosingmeasurementsistofindandrankthesteady-statesensitivitiesofthemeasuredquantitieswithrespecttothelineparameters.Figure5isabigpicturelookattheNLCOfordetectionandlocationoflineoutagesonthegrid.TheprocessstartsbytakingmeasurementsfromGeneratedMultipleTimeMeasurementsBusVoltageMagnitude,GeneratorRealPower,LoadRealPowerOptimizationProcessOptimizationOutputBusVoltageMagnitudesBusVoltagePhaseAngles*NormalOperatingProcedures&ConstraintBasedGridKnowledgeTime(sec)*Time(sec)*Time(sec)*Fig.5.NLCOProcessfor118-bustestsystem.limitedsitesonthegrid,inthisdiagramthegeneratedmultipletimemeasurementsaretakenfromthetransformerwiththegreenoutline.Thebusvoltagemagnitude,generatorrealpowerandloadrealpowerarethensenttotheoptimizationblockforprocessing.Genericgridknowledgeisalsosenttotheoptimizationprocessintheformofconstraints.TheoutputofNLCOistime-seriesdatanotonlyforbusvoltagemagnitudeandvoltagephaseangleasshowninthefigure,butalsoforallotherunknownvariables(suchasloadpowers)beingsolved.A.Time-DifferencingObjectiveFunctionAmathematicaldescriptionofthetime-differencingobjec-tivefunctionisshowninequation8.Allsummationtermsaresimpletime-differencesbetweenthecurrentsetofunknownsatiterationitandtheirvaluesatpreviousiterationit1.F=Nbussummationdisplayk=1WV,k(Vk(it)Vk(it1)2+Nbussummationdisplayk=1W,k(k(it)k(it1)2+NGensummationdisplayk=1WPG,k(PG,k(it)PG,k(it1)2+NLoadsummationdisplayk=1WPL,k(PL,k(it)PL,k(it1)2+NGensummationdisplayk=1WQG,k(QG,k(it)QG,k(it1)2+NLoadsummationdisplayk=1WQL,k(QL,k(it)QL,k(it1)2(8)Lookingattermsinequation8,allothervariablesattheit1iterationneedtobefilledwithafeasiblestartingpointtogetthetime-differencingobjectivefunctionstarted.Thisfirstsolutionisfilledinwithabestinitialconditionthatsatisfiespowerbalanceequations3and4aswellasconstraintsjustlikewasdoneinwiththeobjectivefunctioninsectionII.Thestartingpointforoptimizationisthesolutionatthepreviousiterationwithnewmeasurementstakenasknowns.Theinitialstartingpointfromstarttofinishofthisalgorithmchangesateveryiterationduetothenewsetofchangingmeasurementsinjectedintoequations3and4.Lookingatequation8itmustbeunderstoodthatthegoalistominimizeanychange,meaningfromstarttofinishtheinitialconditionwillnotchange,butwhathasbeenfoundandwillbeshowninthefollowingresults,isthereisenoughofachangetobeabletodetectandcloselyapproximatewherethelineoutageoccurred.B.ResultsTheresultspresentedallcomefromtestsrunontheIEEE118-bussystem.Themeasurementsusedwere15generatorrealpowers(PGks),10realandreactiveloadpowers(PLks,QLks),and15voltagemagnitudes(Vks).Figure6isaMATLABgenerateddiagramoftheIEEE118-bustestsystemusedforvisualizationandinterpretationofresults.Thesmallerblacksquaresarethebusesinthesystem,theredboxesindicatewheremeasurementsweretaken,theblueandyellowboxesspecifytheresultoflineoutagedetectiontoolsusedinalltestcases,andthethickredlinesignifiesthelineoutage.ThearrowspointingfromthedVnanddn,arewherethelineoutagedetectiontoolspickedoutthebiggestchangeonthegrid.ThedVnanddntoolsarethedifferenceofvoltagemagnitudesandvoltagephaseanglestakenacrosstransmissionlinesandthentime.ThemetricusedtocomputehowfarthetoolswereawayfromtheactuallineoutagewasDijkstrashortestpathcode10.Thiscodefindstheshortestpathfromaselectedsourcebustoallotherbusesinthegrid.InthefirsttestcaseshowninFigure6thedntoolfoundamaximumchangeinvoltagephaseangleat2and3busesawayfromthebusesconnectingthefaultedline.ThedVntoolfoundalargestchangeinvoltagemagnitudeat2and3busesawayfromthebusesconnectingthefaultedline.Thereisahoppairawayfromthefaultedlinebecausethesetwospecifictoolsfindchangesacrosslines.123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118dnLineOutagedVnMeasurementsdVndnFig.6.MATLABgenerateddiagramoflineoutagelocationandlocationestimatedbyoutagedetectors.Lineoutagewasbetweenbuses34and36,and50measurementswereused.InTableI,8testcaseswererunonrandomlyselectedtransmissionlinesinthegrid.Thefirstcolumnisthebusnumbersoneitherendofthetransmissionlinethatwastakenoutofservice.Thesecondcolumnisthetool-setthatwasusedtofindthelineoutage.Thethirdcolumnisthedistanceinbusesawayfromthelineoutagetothebusesselectedbythetool-sets.Thefourthcolumnistheaveragedistanceinbusesawayfromthelineoutagetoallmeasurementbusesinthegrid.Inthesamesetoftestcasesanormalprobabilitydistributionfunctionwasusedtoperturballthelineparametersindepen-dentlybyastandard