基于高保真建模的现代电力系统分析与稳定性

/Pubs/T2.每日分享：6+份行研精选、3个行业主题3.报告查找：群里直接咨询，免费协助查找4.严禁广告：仅限行业报告交流，禁止一切无关信息Copyright©2025,bytheauthor(s).AdissertationsubmittedinpartialsatisfactionoftheDoctorofPhilosophyinintheGraduateDivisionoftheUniversityofCalifornia,BerkeleyAbstractUniversityofCalifornia,Berkeleymakingtheirwayontothegrid.andarriveatthefirstgloballyasymptoticallystabilizingswitchingcontrollawforsinusoidaldifferentdegreesoffidelityshowingthatthestandardπtopoloframeworkwhichbuildsontheindustrystandardZIPloadtocapturethedynamicbehaviordq-framemodelingforpowersystems.Inparticular,duetoalackofclarityintheliterature,iAmifamiliaiiContentsContentsiiListofFiguresivListofTablesvi1Introduction1 1.3Motivationtostudypowersystemswithhighfidel 24682Analysis,stability,andcontrolofthehalf-bridgeinverterusingahybrid model102.1Introduction 2.2ProblemFormulatio 2.3GlobalAsymptotically- 2.4ControllerValidationThroughSimulation 3Analysisofmodernpowersystemswithhighfidelitytransmissionline dynamics263.1Introduction 4Analysisofmodernpowersystemswithhighfidelityloaddynamics: IntroducingZIP-Eloads474.1Introduction iii 5Analysisofrelationshipsbetweenabcanddqreferenceframesignals61 6Summaryandconclusions69Bibliography71ivListofFigures trackingerroratt=4sforavarietyofloadconditionswhen totesttheoreticallimitofthecontroller.22 v underavariationof(a)linelengths(withloadscale=1.0)and(b)loading(with generationconfigurations:SMGFLGFL,SMGFMGFL,S 4.5TransientsimulationofBus3invertercurrentmagnitudeaf viListofTables viiAcknowledgmentsbetter,andthat’sworthrecognizing.agedmetoensurethattheresearchIpursuedwasnotonlytheoreticallyimportant,butthat(CUBoulder)forparticipatinginmyqualifyingexamcommittee.Lastly,IwanttothankInadditiontoworkingwithprofessors,IhadthegreatopportunitytoworkcloselywithsupportandinterestinmyreseaChoi,JingqiLi,VictoriaTuck,LiyangWang,EliBrock,amongothersthatIsurelymissed(UPRM).NavigatingthePhDwasalsosignificantlyaidedbyimportantpeopleinthInparticular,IwanttorecogMeltemErol.TheybothhelpedoutwithmanyfundingandlogisticalsituationsthroughoutviiiSerenaWong,WhitneyNore.IalsowanttotothankmyCubanfamilyYanekRevilla,YiselrLastly,butofcoursenotleast,tomyfamilyArnaldo,Jossie,KamilafortheirunwaveringChapter1IntroductionTheUnitedStatesofAmerica’s(USA’s)CybersecurityandInfrastructureSecuriandwellnessofthenation”.Theyfurtherassertitsimportanceasacriticalinfrastructuresectorprovidingan“enablingfunction”acasagriculture,transportation,andhealthcarethereforeinsistielectricitygeneration,electricitytransmission,andelectricityconsumptionorloadsintoelectricity,transmissionlineinfrastructuretotransportthatelectricitytowhereitisthereforehasextremConsequently,notonlyisoperatingthegridreliablyacriticallyimportanttaskduetoInadditiontoanalreadydifficulttask,thegridhasexperiencedakingthewaythegridberrCHAPTER1.INTRODUCTION2thatwecanreliablyoperatethemostimportantcriticalinfrastructuretosociety.1.1DriversofchangeinthepowergridClimatechangePlanetEarth’sclimatehasbeensignificantlychangingsincethestationinthelatterhalfofthe18thcentury,anditisthecoredriverforthelargeandcontinutoconvertenergyfromtheiroriginalsourceintoelectricitywithoutemittinggreenhousegasDecreasingcostsofrenewablee1Levelizedcostofenergy,orLCOE,isanestimateofhowmuchitcoststogenerfromapowergenerationprojectoveritslifetime.CHAPTER1.INTRODUCTION3Developmentofnewtechnologiesrthisthesisisbeingwritten),andothermajormetropolitanareasaswell.arechargedwithdirectratherthanalternatingcurrentelectricity.Furthermore,trendsCHAPTER1.INTRODUCTION4materialswithwhichitiwayeachoftheminteractBasicgridoperationandproducingheattoboilwater.Whenwaterturnstohigh-pressuresteaaturbine,whichinturnspinstherotorofagenerator,andfinallyresultinginelectricityCHAPTER1.INTRODUCTION5tionaltothefrequencyatwhichtherotorspithisisreferredtoasalternatingcurrent(AC)electricity,contrarytodirectcurrent(DC)negligibleamountoftimetoburnfueltoheatalargNewdevicesonthegridfmuchfaster.Further,itinherentlyproducesDCelectricity,ratherthanACelectricity,soitneedstobeconvertedttaketheACgridelectricityandconvertittoDCtobeusable.sideisthattheyinterfacewiththeexistinggridthroughelectroniccircuitscalledpowerdevices.Inparticular,inveconvertittoACelectricity.Rectifiers,ontheotherhand,arepowerintheoppositewaybytakingACelectricityandconvertingittoDCelectricity.OftentimesCHAPTER1.INTRODUCTION61.3Motivationtostudypowersystemswithhighfidelitymodelsofinstructions,meaningthattheirmathematicalmodelingcanbedifficult.Consequently,MathematicalmodelingintroductionfIR(t)=VR(t)/RisanexamplewhichstatesthatthecurrentIRfisproportionaltothevoltageVRacrossit.AnotherdescripfunctionofthetimederivativeofthevoltageCHAPTER1.INTRODUCTION7problemistofindanequilibriumpointatwhichthesystemcanoperatestably:itisasteadystateproblem.Thereforeallvariablerelationshipsarealgeboperatingcondition.timeevolutionofthevariables.behavior,anymodelthattriestocapturethisbehaviorisanappffollowingform.ppn×m×pfCHAPTER1.INTRODUCTION8analyzabilityisneeded.Thatis,thehigherthefidelityamodelisdesired,themoredifficultitwillbetosolvethatproblemcomputationally.However,ifnotenoughfidelityisincludedModelingtoreplicateversusmodelingtogaininsightAnimportantdistinctiontobemadeisnotingadifferencebetweenmnexttoimpossibletomodelwithabsoluteprecision;infact,moreoftenthannot,substantialjustified,itisalwaysapossibilitythatimportantinformationisunintentionallymissed.1.4Thesiscontributionsandorganizationanalysisfromgeneration,totransempiricalandtheoreticalcontributions.•Chapter2presentsthefirstprovablygloballyasymptoticallystablecontrollawforcontrollawintheformofdroopcontrol.ThischapterincludescontributionsfromTLModels.jlintheJuliaprogramminglanguage.Thischapterincludescontribu-CHAPTER1.INTRODUCTION9•Chapter4presentstheZIP-Eload,newkindofloadmodelmodeling,ZIPEloads.jl,intheJuliaprogramminglanguage.ThischapterfeaturescontributionsfromReidDye,ClaireTomChapter2Analysis,stability,andcontrolofthehalf-bridgeinverterusingahybridmodelconverter-interfacedgeneration(ClaireTomlin.2.1IntroductionTheNeedforNewInverterControlsfparamountimportanceinthelow-point,in2016theEuropeanUnionfundedtheMIGRATE(MassiveIntegrationofPowerElectronicDevices)project[64]tostudyfuninstitutionsfromindustryandacademia.Furthermore,in2021,theUnitedStatesofAmer-ica’sDepartmentofEnergyfundedtheUNIFI(UniversalInteroperabilityforGrid-FormingCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL11inverter.Below,theproposedhybInverters)Consortium[18],consistingofexpertsfromover40participatinginstitutions,torinvertercontrolstrategieswillplayinthefuturegrid,webelieveitisimperativetoexploreOneapproachtoinvertercontrolisthegrid-forming(GFM)paradigm,inwhichtherandvalidatedthroughsimulationandhardwareexperimentation[31,3,2,50].Theirim-plementationsthusfarusuallyuseasinusoidalpulsed-widthmodulativertercontrols[50].Inthiscontext,aGFMcontrolstrategyinstructstheinvertertoachievelatingthemintoamodulationsignalforapulse-widthmodulator.Inthiswork,weproposereplacingtheinnerloopswithCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL12dynamicinteractions.Furthermore,someinitialresultspointtotheintheprimaryculpritsforinstabilityinsystem-widestudies[50].ofcontrollergains.WebelievethiscouldprovideawaytoHybridSystemsforPowerInthepowerelectronicsliterature,hybridsystemstanddesignahybridcontrollawtomaintainthesystemstatewithinthisset.Furtherworkstabilitytothedesiredoperatingpoint[8].ferrorcoordinatesandshowthatthesolutioSummaryofContributionsSpecifically,beyondpriorresultsin[1],thischapter’scontributionsincludei.)anclosed-formexpressionforaglobally-asymptoticallystabilizinghybridcontrhalf-bridgeinverterthatneedsnotuning,ii.)ananalyticalderivationforaglobalLyapunovCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL13functionthatprovesuniform,global,asymptoticstabilityoftheorigininerrorcoordinatesthusachievingthetrackingofthereferencesignalforahybriditionofthecontrollerinsimulation,andv.)ademonstrationinsimulationofthecontroller’soperationinconjunctionwithagrid-formingcontrolstrategy,suggestingthepotentialofhybridsystems-basedcontrolWefurtheraimtoaidunderstandingofthecontrolschemebyinterpretingthecontrollecontrolleritselfisaswitchingpolicy,wecallitahybrChapterOrganization2.2ProblemFormulationInthissection,wepresentNotationDotnotationindicatesthetimederivatiistheEuclideanvectornorm.Theoperatorsign(·)returns+1ifitsscalarargumentisfSwitchedModelWestudythehalf-bridgei[vCiL]T∈耽2,wherevCandiLarethecapacitorvoltageandinductorcurrent,respectively.CHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL14ApplyingKirchhoff’scurrentandvoltagelawstomodeltheu∈{+1,__1},characterizestheinverter’sterminalvoltagepolarityinKirchhoff(LTI)dynamicalsystemwithabinary-valued,discretecontrolinput.DesigningtheReferenceWedenotethereferencevectorxref=[vC,refiL,ref]T.WechooseasinusoidalvoltagereferencevC,ref(t)=Vmsin(ωt),withamplitudeVmandfrequencyω,bothbeingdesigniL,refintermsoftheseparametersasiL,ref(t)=ωCVmVmsin(ωt).NotethatΘisaskew-symmetricmatrixwitheigenvaluesλΘ∈{+jω,__jω}defininganoscillator.Therefore,weknowthat,foragiveninitialcondition,whichcanarbitralilybechosenasz(t=0s)=Vm[01],z(t)=[Vmsin(ωt)Vmcos(ωt)]T.CHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL15achievexrefbyref(2.4a)=ΠΘz(2.4b)=(AΠ+BΓ)z,(2.4c)Ax+Bu−(2.6a)=Ae+B(u−Γz).(2.6b)problemwearetryingtosolveistofindacontrollaw2.3GlobalAsymptotically-StableReferenceTrackingInthissection,wepresentourtheoreticalstabilityresultsincludingi.)thederivationofanexplicitcontrollawwithaproofthatthiscontroldrivesthereferenceerrortothezestate,ii.)ananalyticalparameters,andiii.)aproofshowingthatwecanappropriatelyadjustourcontrollawtobeGlobalAsymptoticStabilityResultA2×2matrixthatsatisfiestheLyapunovequation,ATP+PA=Q,foranegativedefiniteQ.u=−sign(BTPe)(2.7)CHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL16Proof.WeproposethecandidateLyapunovfunctionV(e)=eTPe,whichisgloballypositiveV.(e)=eT(ATP+PA)e+2(u−Γz)BTPe.(2.8)=Vm∥Γ∥sin(ωt+ψ),ψ=arctan(Γ1/Γ2),(2.9b)Therefore,theworstcasemagnitudeforu.−Γz,i.e.,max.z{u−Γz},isobtainedwhensin(ωt+ψ)=−1.So,wecanupperboundVyieldthefollowing.2)BTPe(2.10)2<,andu2willtakethesignofu.Bychoosingaswitchingpolicydefinedasu=−sign(BTPe)underV(e)≤0alwaysholds,implyingthatV(e)isavalid,globalLyapunovfunctionforthegivendynamics.Wecanthusconcludethattheorigininerrorcoor,asymptotically-stableequilibriumpoint.Thestateswilltrackthedesiredtrajectoriesintheoriginalcoordinates.Itisworthnotingthattheassumptionsrequiredforthistheoremarenotveryrestrictive.ItisalsoworthnotcaseupperboundfortheLyapunovfunction:itisonlyreachedwhensin(ωt+ψ)=−1.Thisimpliesthatitis,potentially,inherentlyrobusttosomedisturbances.Infact,itcanbeshownthatthiskindofformulationisactuallyrobustwithrespecttodisturbances[34].IntepretationofTheControlResultMaintheoremcondition2<1/Vm.ItturnsoutthatΓ2=1−ω2LC=0becauseitisthefilterdesignequationforitsCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL17voltageamplitude,Vm,tobestrictlylessthanascaInparticular,alargerω,smaller,R,andlargerLmaketheboundtighter,implyingitfwhichintuitivelymaketrackingthereferencesignalmoredifficult.AlargerVDCControlactionAnunderlyingswitchingsurfacehyperplane,thenthesign(·)functionwillreturna+1,anda__1otherwise.ThismeansthatExplicitLyapunovFunctioninTermsofR,L,andCIngeneral,findinganexplicitLyapunovfunctionthatguaranteesstabilityofahybriddy-calculatetheappropriatePmatrixthatsatisfiestheLyapunovequation,ATP+PA=Q,Inthissection,weshowthatintermsofarbitraryloadandinverterparameters,R,L,andC.CHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL18NotingthatPissymmetric,wehavethatwherep12=p21.SelectingQ=__I,thematrixequationATP+PA=__IevaluatestoanexplicitTherefore,afunctionV(e)=eTPe,withPgivenby(2.14),isguaranteedtobeaglobalRemark.WhileQisoftentαControllingforKnownChangesinLoadparameters.Notethatourcontroresistance,R,orfilterparameters,LorC,changeCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL19ParameterSymbolValueRInverterinductanceLCVDCfωVmload.Thiswillallowthecontroltostillasymptoticallydrivetheerrorstatetotheorigin[44].Weprovidevalidationthroughsimulationforthesethreetheoreticalresultsint2.4ControllerValidationThroughSimulationInthissection,wetestinsimulationtheperformanceofourswitrrAsymptoticStabilityUnderConstantLoadrCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL20CHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL21disturbancesforanon-updatedcontroller.StabilityUnderChangesinLoadthisresultinsimulationbychangingourinitialloadofR=14.4ΩtodifferentvaluesRdisturbed=10Ωand64.4Ωatt=1.0s.Updatingour10kHzconacontrollerupdatedthroughPwithbehavior.Rdisturbed=64.4Ωcthecontrollerisnotupdated.Theseresultssuggestthattheglobal,asymptoticstability.Moreover,empiricallywefindthatforsmalldisturbancesanunmodifiedcontrollermayalsoperformweStabilityUnderExtremeReferenceValues2<,and2rCHAPTER2.ANALYSIS,STABILITY,ANDCONTROLOFTHEHALF-BRIDGEINVERTERUSINGAHYBRIDMODEL22(2.11).πtheoreticallimitofthecontroller.LayeringaGrid-FormingControlStrategyamplitudeandfrequency.Inpractice,inverterswiregulation,orastabilitymetric.Examplesintheliteratureincludedroopcontrol,virtua