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ADVANCESINELECTRIC POWERANDENERGY IEEEPress
445HoesLane
Piscataway,NJ08854
IEEEPressEditorialBoard
EkramHossain, EditorinChief
JónAtliBenediktssonDavidAlanGrierElyaB.Joffe
XiaoouLi
PeterLian AndreasMolisch
SaeidNahavandiJeffreyReedDiomidisSpinellis
SarahSpurgeonAhmetMuratTekalp
ADVANCESIN ELECTRICPOWER ANDENERGY StaticStateEstimation EDITEDBY MOHAMEDE.EL-HAWARY
DalhousieUniversity
©2021byTheInstituteofElectricalandElectronicsEngineers,Inc.Allrightsreserved.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
PublishedsimultaneouslyinCanada.
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LibraryofCongressCataloging-in-PublicationData:
Names:El-Hawary,M.E.,editor.|JohnWiley&Sons,Inc.,publisher.
Title:Advancesinelectricpowerandenergy:staticstateestimation/ editedbyMohamedEEl-Hawary,DalhousieUniversity.
Description:Hoboken,NewJersey:JohnWiley&Sons,Inc.,[2021]| Series:IEEEPress|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2020028681(print)|LCCN2020028682(ebook)|ISBN 9781119480464(hardback)|ISBN9781119584506(hardback)|ISBN 9781119480365(adobepdf)|ISBN9781119480440(epub)
Subjects:LCSH:Electricpowersystems–Stateestimation.
Classification:LCCTK1005.A352020(print)|LCCTK1005(ebook)|DDC 621.319/1–dc23
LCrecordavailableathttps://lccn.loc.gov/2020028681
LCebookrecordavailableathttps://lccn.loc.gov/2020028682
CoverDesign:Wiley
CoverImages:(top)©SamRobinson/GettyImages,(middle)©SteveRamplin/EyeEm/GettyImages Setin10/12ptTimesbySPiGlobal,Pondicherry,India
10987654321
TOFREDC.SCHWEPPE,1933– 1988
Hebroughtstateestimationtoelectricpower,andlaterledthe developmentofthetheoreticalbasesofcompetitiveelectricpower markets.Ateacherandinnovatorofgreatunderstandingand creativity, “solvingtheproblem” wassecondarytobringingout thebestinthoseheworkedwith.
CHAPTER1 GENERALCONSIDERATIONS 1
1.1Prelude 1
1.2DefiningSSE 2
1.3TheNeedforStateEstimation 3
1.4StaticStateEstimationinPractice 4
1.5ApplicationsThatUseSESolution 10
1.6OverviewofChapters 13
CHAPTER2 STATEESTIMATIONINPOWERSYSTEMSBASED ONAMATHEMATICALPROGRAMMINGAPPROACH 23
2.1Introduction 23
2.2Formulation 24
2.3ClassicalStateEstimationProcedure 26
2.4MathematicalProgrammingSolution 31
2.5AlternativeStateEstimators 32
SYSTEMSTRESSANDCASCADINGBLACKOUTS
3.1Introduction 61
3.2CascadingBlackoutsandPreviousWork 62
3.3ProblemStatementandApproach 66
3.4DFAXes,Vulnerability,andCriticalityMetrics 70
3.5ValidityofMetrics 78
3.6StudieswithMetrics 82
3.7Summary 93
3.8ApplicationofStressMetrics 94
3.9Conclusions 94
CHAPTER4 MODEL-BASEDANOMALYDETECTIONFORPOWER SYSTEMSTATEESTIMATION 99
4.1Introduction 99
4.2CyberattacksonStateEstimation 100
4.3ATTACK-RESILIENTStateEstimation 103
4.4Model-BasedAnomalyDetection 106
4.5Conclusions 117
CHAPTER5 PROTECTION,CONTROL,ANDOPERATION OFMICROGRIDS 123
5.1Prelude 123
5.2Introduction 126
5.3StateoftheArtinMicrogridProtectionandControl 128
5.4EmergingTechnologies 146
5.5TestCaseforDDSE 154
5.6TestResults 159
5.7TestCaseforAdaptiveSetting-LessProtection 161
5.8Conclusions 167
PART2ROBUSTSTATEESTIMATION 171
CHAPTER6 PSSEREDUX:CONVEXRELAXATION,DECENTRALIZED, ROBUST,ANDDYNAMICSOLVERS 173
6.1Introduction 173
6.2PowerGridModeling 174
6.3ProblemStatement 176
6.4DistributedSolvers 186
6.5RobustEstimatorsandCyberattacks 193
6.6PowerSystemStateTracking 198
6.7Discussion 202
CHAPTER7 ROBUSTWIDE-AREAFAULTVISIBILITYANDSTRUCTURAL OBSERVABILITYINPOWERSYSTEMSWITHSYNCHRONIZED MEASUREMENTUNITS 209
7.1Introduction 209
7.2RobustFaultVisibilityUsingStrategicallyDeployedSynchronized Measurements 210
7.3OptimalPMUDeploymentforSystem-WideStructural Observability 221
7.4Conclusions 229
CHAPTER8 AROBUSTHYBRIDPOWERSYSTEMSTATEESTIMATOR WITHUNKNOWNMEASUREMENTNOISE
8.1Introduction 231
8.2ProblemStatement 233
8.3ProposedFrameworkforRobustHybridStateEstimation 234
8.4NumericalResults 245
8.5Conclusions 249
CHAPTER9 LEAST-TRIMMED-ABSOLUTE-VALUESTATEESTIMATOR
9.1BadDataDetectionandRobustEstimators 256
9.2ResultsandDiscussion 266
9.3Conclusions 287
10.1Introduction 297
10.2StateEstimationinDistributionNetworks 298
10.3ImprovingObservabilityinDistributionNetworks 309
10.4Conclusion 324
CHAPTER11 ADVANCEDDISTRIBUTIONSYSTEMSTATEESTIMATION INMULTI-AREAARCHITECTURES 329
11.1IssuesandChallengesofDistributionSystemStateEstimation 329
11.2DistributionSystemMulti-AreaStateEstimation(DS-MASE)Approach 342
11.3ApplicationoftheDS-MASEApproach 357
11.4ValidityandApplicabilityofDS-MASEApproach 369
CHAPTER12 HIERARCHICALMULTI-AREASTATEESTIMATION
12.1Introduction 377
12.2Preliminaries 381
12.3ModelingandProblemFormulation 385
12.4ABriefSurveyofSolutionTechniques 387
12.5HierarchicalStateEstimatorViaSensitivityFunctionExchanges 393
12.6Add-OnFunctionsinMulti-areaStateEstimation 399
12.7Properties 401
12.8Simulations 405
12.9Conclusions 409
CONTENTS
CHAPTER13 PARALLELDOMAIN-DECOMPOSITION-BASEDDISTRIBUTED STATEESTIMATIONFORLARGE-SCALEPOWERSYSTEMS 413
13.1Introduction 413
13.2FundamentalTheoryandFormulation 416
13.3ExperimentalResults 436
13.4Conclusion 449
CHAPTER14 DISHONESTGAUSS–NEWTONMETHOD-BASED POWERSYSTEMSTATEESTIMATIONONAGPU 455
14.1Introduction 455
14.2Background 456
14.3PerformanceofDishonestGauss–NewtonMethod 461
14.4GPUImplementation 463
14.5SimulationResults 467
14.6DiscussionsonScalability 468
14.7DistributedMethodofParallelization 470
14.8Conclusions 473 INDEX 475
ABOUTTHEEDITOR Mohamed “Mo” El-ArefEl-Hawary,age76, ofHalifaxpassedawayonFriday,26July 2019.BorninSohag,Egypt,hewaspredeceasedbyhisparentsMahmoodandAmina El-HawaryofAlexandria,Egypt.Heissurvivedbyhiswife,Ferial(El-Bibany) El-Hawary,Halifax;daughter,Elizabeth “Bette” El-Hawary,Halifax;sons,Robert “Bob” El-Hawary,London,UK,andRany “Ron” (TriciaLane)El-Hawary,Halifax;sisters,MervatEl-Hawary,MonaEl-Hawary, andMawaheb(Heba)El-Hawary(alllocated inAlexandria,Egypt);andgrandchildren, Alexa,Ben,Grace,Ryan,Eoin,Kegan,Duncan,andLiam.
Dr.El-HawarywasaProfessorofElectricalandComputerEngineeringatDalhousieUniversityinHalifax,NovaScotia, Canada.HehadaBScinElectricalEngineering,DistinctionandFirst-Class Honors,UniversityofAlexandria,Egypt,1965,andaPhDinElectricalEngineering,UniversityofAlberta,Edmonton,1972,wherehewasanIzaakWaltonKillam MemorialFellowfrom1970to1972.HewasAssociateProfessorofElectrical EngineeringattheFederalUniversityofRiodeJaneirofortwoyearsandsubsequentlyservedforeightyearsonfacultyatMemorialUniversityofNewfoundland since1974.HewasappointedChairmanofElectricalEngineeringProgramin 1976.In1981,hejoinedtheTechnicalUniversityofNovaScotia(TUNS)asProfessorofElectricalEngineering.In1997,TUNSwasamalgamatedwithDalhousie University.Dr.El-HawaryhasbeenAssociateDeanofEngineeringatDalhousie between1995and2007,DirectorofInternationalandExternalRelationsforthe FacultyofEngineeringin2008–2009,andChairoftheSenateofDalhousieUniversityin2001–2007.Hecherishedhavinghadtheopportunitytobepartofeducating,mentoring,andtouchingthelivesandcareersofcountlessstudentsinthe fieldofElectricalEngineeringoverhislonganddistinguishedcareer.
Throughouthiscareer,Moauthoredover10textbooksandalmost200full journalpapers.HewastheInstituteofElectricalandElectronicsEngineering (IEEE)PressPowerEngineeringSeriesEditorandFoundingEditorinChiefof theIEEESystems,ManandCyberneticsMagazine,andPowerLettersofPES.
HewasAssociateEditorforthethreemajorElectricMachinesandPowerSystems’ JournalsandEditorofElectricalPowerEngineering,McGraw-HillEncyclopedia ofScienceandTechnology.HewasaFellowofIEEE,CanadianAcademyofEngineering,EngineersCanada,andtheEngineeringInstituteofCanada.HewasaDistinguishedLectureroftheIEEEPowerandEnergySociety.
HeservedasamemberoftheBoardofDirectorsandSecretaryofIEEEand asPresidentofIEEECanada.HeservedontheIEEEPublicationServicesandProductsBoard,FellowsCommittee,IEEEPressBoardChairman,PowerEngineering Society(PES):SystemOperationsCommitteeChairand,memberofHKNBoard, andVicePresident,Development,IEEECanadaFoundation.Hehasbeenrecipient ofIEEECanada,W.S.ReadServiceAward,2010.In1999IEEEawardedhimthe EABMeritoriousAchievement,PowerEngineeringEducatoroftheYear,and IEEECanadaGeneralA.G.L.McNaughtonGoldMedal.
ABOUTTHECONTRIBUTORS VenkataramanaAjjarapu currentlyholdstheDavidNicholasProfessorof ElectricalandComputerEngineeringatIowaStateUniversity.Hisareaof expertiseincludespowersystemstability,reactivepowercontrol,andoptimization.HeisaFellowoftheIE.
AdityaAshok isaseniorresearchengineerintheElectricityInfrastructureand BuildingsdivisionatthePacificNorthwestNationalLaboratory(PNNL)and hasbeenwithPNNLsinceFebruary2016.Adityareceivedhisdoctoraldegree inElectricalEngineeringfromIowaStateUniversityinMay2017.Aditya’s researchinterestsincludeanalyzingcybervulnerabilitiesinenergydelivery systems,assessingpotentialimpactstosystemoperations,reliability,andeconomics,anddevelopingnovelalgorithmstomitigatecybervulnerabilitiesandhelp enhancetheoverallsecurityandresilienceofenergydeliverysystems.
BerndBrinkmann receivedhisBachelor’sdegreeinElectricalEngineeringfrom theUniversityofAppliedSciencesBielefeld,Germany,in2011.Aftergaining experienceasadesignengineerandsoftwaredeveloper,heiscurrentlypursuing thePhDdegreeinElectricalPowerEngineeringattheUniversityofTasmania, Australia.Hisresearchinterestsincludestateestimationuncertainty,distribution networkobservability,andoptimalmeterplacement.
EduardoCaro receivedtheElectricalEngineeringdegreefromtheTechnicalUniversityofCatalonia,Barcelona,Spain,2007,andthePhDdegreeintheUniversity ofCastilla-LaMancha,Spain,2011.HeiscurrentlyanAssistantProfessoratthe UniversidadPolitécnicadeMadrid,Madrid,Spain.Hisresearchinterestsinclude powersystemestimation,optimization,andelectricityloadforecasting.
SungyunChoi receivedtheBEdegreeinElectricalEngineeringfromKoreaUniversity,Seoul,SouthKorea,in2002andtheMSandPhDdegreesinElectricaland ComputerEngineeringfromGeorgiaInstituteofTechnology,Atlanta,GA,USA, in2009and2013,respectively.From2002to2005,hewasaNetworkandSystem Engineer,andfrom2007to2013,hewasaResearchAssistantwiththePowerSystemControlandAutomationLaboratory,Atlanta,GA,USA.Since2014,hehas beenaSeniorResearcherwithSmartPowerGridResearchCenter,KoreaElectrotechnologyResearchInstitute,Uiwang,SouthKorea.Hisresearchinterests includesmartgridtechnology,autonomousoperationofmicrogrids,powersystem protection,distributeddynamicstateestimation,andcommunicationnetworksand systemsinpowerindustries.
GeorgeJ.Cokkinides wasborninAthens,Greece,in1955.HereceivedtheBS, MS,andPhDdegreesfromtheGeorgiaInstituteofTechnology,Atlanta,GA, USA,in1978,1980,and1985,respectively.From1983to1985,hewasa ResearchEngineerattheGeorgiaTechResearchInstitute.Since1985,hehasbeen withtheUniversityofSouthCarolina,Columbia,SC,USA,whereheiscurrently anAssociateProfessorofElectricalEngineering.Hisresearchinterestsinclude powersystemmodelingandsimulation,powerelectronicsapplications,power systemharmonics,andmeasurementinstrumentation.ProfessorCokkinidesisa memberoftheIEEEPowerandEnergySociety.
VenkataDinavahi receivedtheBEng.degreeinelectricalengineeringfromthe VisveswarayaNationalInstituteofTechnology(VNIT),Nagpur,India,in1993, theMTech.degreeinElectricalEngineeringfromtheIndianInstituteofTechnology(IIT)Kanpur,India,in1996,andthePhDdegreeinElectricalandComputer engineeringfromtheUniversityofToronto,Ontario,Canada,in2000.Presentlyhe isaProfessorwiththeDepartmentofElectricalandComputerEngineering, UniversityofAlberta,Edmonton,Alberta,Canada.Hisresearchinterestsinclude real-timesimulationofpowersystemsandpowerelectronicsystems,electromagnetictransients,device-levelmodeling,large-scalesystems,andparalleland distributedcomputing.HeisaFellowofIEEE.
JamesW.Feltes receivedhisBSdegreewithhonorsinElectricalEngineering fromIowaStateUniversityandhisMSdegreeinElectricalEngineeringfrom UnionCollege.
HejoinedPowerTechnologies,Inc.(PTI),nowpartofSiemensPowerTransmissionandDistributionInc.,in1979andiscurrentlyaseniormanager.AtPTI,he hasparticipatedinmanystudiesinvolvingplanning,analysis,anddesignoftransmissionanddistributionsystems.Hehasalsobeeninvolvedinmanyprojectsinvolvingthedevelopmentofmodelsforstudiesofpowersystemdynamics,testingto recordequipmentresponse,andmodelparameterderivation.
HeisaregisteredprofessionalengineerinthestateofNewYorkandaFellow oftheIEEE.HeisamemberoftheIEEEPowerEngineeringSocietyandIndustry ApplicationsSocietyandisactiveonseveralIEEEcommitteesandtaskforces.
GeorgiosB.Giannakis (Fellow’97)receivedhisDiplomainElectricalEngineering fromtheNationalTechnicalUniversityofAthens,Greece,1981.From1982to1986 hewaswiththeUniversityofSouthernCalifornia(USC),wherehereceivedhis MScinElectricalEngineering,1983,MScinMathematics,1986,andPhDin ElectricalEngineering,1986.HewasafacultymemberwiththeUniversityof Virginiafrom1987to1998,andsince1999hehasbeenaprofessorwiththe UniversityofMinnesota,whereheholdsanADCEndowedChair,aUniversity ofMinnesotaMcKnightPresidentialChairinECE,andservesasdirectorofthe DigitalTechnologyCenter.
Hisgeneralinterestsspantheareasofstatisticallearning,communications, andnetworking – subjectsonwhichhehaspublishedmorethan470journal papers,770conferencepapers,25bookchapters,twoeditedbooks,andtwo
researchmonographs.HiscurrentresearchfocusesonDataScience,andNetwork SciencewithapplicationstotheInternetofThings,andpowernetworkswith renewables.Heisthe(co-)inventorof34issuedpatents,andthe(co-)recipient of9bestjournalpaperawardsfromtheIEEESignalProcessing(SP)andCommunicationsSocieties,includingtheG.MarconiPrizePaperAwardinWireless Communications.HealsoreceivedtheIEEE-SPSNorbertWienerSocietyAward (2019);EURASIP’sA.PapoulisSocietyAward(2020);TechnicalAchievement AwardsfromtheIEEE-SPS(2000)andfromEURASIP(2005);theIEEEComSoc EducationAward(2019);theG.W.TaylorAwardforDistinguishedResearch fromtheUniversityofMinnesota,andtheIEEEFourierTechnicalFieldAward (2015).HeisaforeignmemberoftheAcademiaEuropaea,andFellowofthe NationalAcademyofInventors,theEuropeanAcademyofSciences,IEEEand EURASIP.HehasservedtheIEEEinanumberofposts,includingthatofa DistinguishedLecturerfortheIEEE-SPS.
ManimaranGovindarasu currentlyholdstheMehlProfessorofComputer EngineeringatIowaStateUniversity.HisareaofexpertiseincludesCPSforthe smartgrid,cybersecurity,andreal-timesystemsandnetworks.HeisaFellow oftheIEEE.
YeGuo isanAssistantProfessoratTsinghua-BerkeleyShenzhenInstitute, TsinghuaUniversity.Hereceivedhisbachelordegreein2008anddoctoraldegree in2013,bothfromtheDepartmentofElectricalEngineering,TsinghuaUniversity. HewasaPostdoctoralAssociateatCornellUniversitybetween2014and2018.His researchinterestsincludedistributedoptimization,gameandmarkettheory,state estimation,andtheirapplicationsinpowerandenergysystems.Hehasreceived theBest-of-the-BestpaperawardandanotherBestPaperAwardatIEEEPESGeneralMeeting,2019,andanotherBestPaperAwardatIEEEPESGeneralMeeting 2020.HealsoreceivedtheBestPosterAwardatPSERCIABMeeting2018.
IbrahimOmarHabiballah isanAssociateProfessorofEEDepartmentatKing FahdUniversityofPetroleumandMinerals,SaudiArabia.Inhisareahetaught severalundergraduateandgraduatecoursesinelectrical,powersystems,power transmission,andelectricalmachines.Hisresearchinterestsincludepowersystems ingeneral,powersystemstateestimation,powersystemoptimization,HVinsulators,andenergyconservation.
AraceliHernández receivedthePhDdegreeinElectricalEngineeringfromthe UniversidadPolitécnicadeMadrid(UPM),Madrid,Spain,in2000.Currently, sheworksattheDepartmentofControl,ElectricalandElectronicEngineering andComputingatUPM,wheresheisanAssociateProfessor.Herfieldsofinterest includepowersystemanalysisandpowerqualityestimationandmeasurement.
HadisKarimipour receivedthePhDdegreefromtheUniversityofAlbertain 2016.SheiscurrentlyaPostdoctoralFellowattheDepartmentofElectricaland ComputerEngineeringattheUniversityofCalgary.Herresearchinterestsinclude large-scalepowersystemstateestimation,cyber-physicalmodeling,cybersecurity ofthesmartgrids,andparallelanddistributedcomputing.
VassilisKekatos isanAssistantProfessorattheBradleyDepartmentofECEat VirginiaTech.HeobtainedhisDiploma,MSc,andPhDinComputerScience andEngineeringfromtheUniversityofPatras,Greece,in2001,2003,and 2007,respectively.HewasarecipientofaMarieCurieFellowshipduring 2009–2012andaresearchassociatewiththeECEDepartmentattheUniversity ofMinnesota,wherehereceivedthepostdoctoralcareerdevelopmentaward(honorablemention).During2014,hestayedwiththeUniversityofTexasatAustinand theOhioStateUniversityasavisitingresearcher.Hisresearchfocusisonoptimizationandlearningforfutureenergysystems.HeiscurrentlyservingintheeditorialboardoftheIEEETrans.onSmartGrid.
MertKorkali receivedhisMSandPhDdegreesinElectricalEngineeringfrom NortheasternUniversity,Boston,MA,USA,in2010and2013,respectively.He iscurrentlyaResearchStaffMemberattheComputationalEngineeringDivision atLawrenceLivermoreNationalLaboratory,Livermore,CA,USA.Previously,he wasaPostdoctoralResearchAssociateattheUniversityofVermont,Burlington, VT,USA.Hiscurrentresearchinterestslieatthebroadinterfaceofrobuststate estimationandfaultlocationinpowersystems,extremeeventmodeling,cascading failures,uncertaintyquantification,andprobabilisticgridplanning.Heisthe Co-chairoftheIEEETaskForceonStandardTestCasesforPowerSystemState Estimation.HeiscurrentlyservingasanEditorofthe IEEEOpenAccessJournal ofPowerandEnergy andofthe IEEEPowerEngineeringLetters,andanAssociateEditorof JournalofModernPowerSystemsandCleanEnergy.Dr.Korkaliis aSeniorMemberofIEEE.
MassimoLaScala isProfessorofElectricalEnergySystemsatPolitecnicodiBari andIEEEFellow.HehasbeenPrincipalInvestigatorofnumerousresearchprojects insmartgridsandsmartcitiesandscientificconsultantoftheMinistryoftheEconomicDevelopmentinItalyandofAEEGSItheItalianRegulatoryAuthorityof Electricity,GasandWater.Heisthedirectorofthe “Laboratoryforthedevelopmentofrenewablesandenergyefficiency:LabZERO” atPolitecnicodiBari.
YuLiu wasborninHefei,China,in1990.HereceivedtheBSandMSdegreesin ElectricPowerEngineeringfromShanghaiJiaoTongUniversity,Shanghai,China, in2011and2013,respectively,andtheMSdegreeinelectricalandcomputerengineeringin2013fromGeorgiaInstituteofTechnology,Atlanta,GA,USA,where heiscurrentlyworkingtowardthePhDdegreeinelectricalandcomputerengineering.Hisresearchinterestsincludepowersystemprotection,parameterestimation, andcircuitfaultlocating.
A.P.SakisMeliopoulos wasborninKaterini,Greece,in1949.Hereceivedthe MEandEEDiplomainElectricalEngineeringfromtheNationalTechnicalUniversityofAthens,Athens,Greece,in1972andtheMSEEandPhDdegreesinelectricalengineeringfromtheGeorgiaInstituteofTechnology,Atlanta,GA,USA,in 1974and1976,respectively.HeispresentlyaGeorgiaPowerDistinguishedProfessor.Hehaspublishedthreebooks,holdsthreepatents,andhaspublishedmore than300technicalpapers.ProfessorMeliopoulosreceivedtheIEEERichardKaufmanAwardin2005,andin2010,hereceivedtheGeorgeMontefioreAwardfrom
theMontefioreInstitute,Belgium.HeistheChairmanoftheGeorgiaTechProtectiveRelayingConferenceandamemberofSigmaXi.
HydeM.Merrill receivedtheBAdegreeinMathematicsandMSdegreeinElectricalEngineeringfromtheUniversityofUtahandthePhDdegreeinElectrical EngineeringfromtheMassachusettsInstituteofTechnology.Heisaregistered professionalengineerinNewYorkandaFellowoftheIEEE.
HehasworkedfortheAmericanElectricPowerServiceCorp,theMIT EnergyLab,PowerTechnologies,Inc.,theRensselaerPolytechnicInstitute,and MerrillEnergyLLC.In2015,hejoinedtheUniversityofUtahasAdjunctProfessor.Heteachespowersystemsandleadsresearchonblackouts.
LamineMili isaProfessorofElectricalandComputerEngineeringatVirginia Tech.HeisanIEEEFellowandamemberofInstituteofMathematicalStatistics andtheAmericanStatisticalAssociation.Hisresearchinterestsincludepowersystemanalysisandcontrol,powersystemdynamicsandstability,androbuststatistics asappliedtoengineeringproblems.
MichaelNegnevitsky receivedhisBE(Hons.)andPhDdegreesfromtheByelorussianUniversityofTechnology,Belarus,in1978and1983,respectively.Currently,heisaProfessorinPowerEngineeringandComputationalIntelligence andDirectoroftheCentreforRenewableEnergyandPowerSystems,University ofTasmania,Australia.HeisaCharteredProfessionalEngineer,FellowofEngineersAustralia,andMemberoftheNationalITEECollegeBoard.Hisresearch interestsincludepowersystemsecurity,renewableenergy,andstateestimation.
MarcoPau receivedtheMSdegree(cumlaude)inElectricalEngineeringandthe PhDdegreeinElectronicEngineeringandComputerSciencefromtheUniversityof Cagliari,Italy,in2011and2015,respectively.Currently,heisresearchassociateat theInstituteforAutomationofComplexPowerSystemsattheE.ONEnergy ResearchCenter,RWTHAachenUniversity,Germany,whereheleadstheteam forDistributionGridMonitoringandAutomation.Hisresearchactivitiesmainly concernthedesignofsolutionsforthemonitoringandautomationofdistribution systemsaswellastechniquesforthesmartmanagementofactivedistributiongrids.
PaoloAttilioPegoraro receivedtheMS(summacumlaude)degreeinTelecommunicationsengineeringandthePhDdegreeinElectronicandTelecommunication EngineeringfromtheUniversityofPadova,Padua,Italy,in2001and2005, respectively.From2015to2018hewasanAssistantProfessorwiththeDepartmentofElectricalandElectronicEngineering,UniversityofCagliari,Cagliari, Italy,whereheiscurrentlyAssociateProfessor.Hehasauthoredorcoauthored over110scientificpapers.Hiscurrentresearchinterestsincludethedevelopment ofnewmeasurementtechniquesformodernpowernetworks,withattentiontosynchronizedmeasurementsandstateestimation.
Dr.Pegoraro isaSeniorMemberofIEEEInstrumentationandMeasurement Society,memberofTC39(MeasurementsinPowerSystems)andofIECTC 38/WG47.HeisanAssociateEditoroftheIEEETransactionsonInstrumentation andMeasurement.
FerdinandaPonci graduatedwithPhDinElectricalEngineeringfromthePolitecnicodiMilano,in2002.ShejoinedtheDepartmentofElectricalEngineering,UniversityofSouthCarolina,asanAssistantProfessorin2003andbecameAssociate Professorin2008.In2009,shejoinedtheInstituteforAutomationofComplex PowerSystems,RWTHAachenUniversity,wheresheiscurrentlyProfessorfor “Monitoringanddistributedcontrolforpowersystems.”
SheisSeniorMemberofIEEEandoftheAdComoftheIEEEInstrumentationandMeasurementSociety.
Md.AshfaqurRahman isaPhDcandidateintheDepartmentofElectricaland ComputerEngineeringinClemsonUniversity,Clemson,SC,USA.Hereceived hisBSfromBangladeshUniversityofEngineeringandTechnologyin2009 andMSfromTexasTechUniversityin2012.Hehasatotalof7technicalpapers with98citationswithh-indexandi-indexbe3.Hiscurrentresearchinterests includethedevelopmentofadistributeddynamicstateestimator.Healsoworked onfalsedatainjectionattack,parallelanddistributedcomputation,stateprediction, contingencyanalysis,optimalpowerflow,etc.HehasservedasareviewerofIEEE journalsandconferencepapers.
SaraSulis receivedtheMSdegreeinElectricalEngineeringandthePhDdegreein IndustrialEngineeringfromtheUniversityofCagliari,Cagliari,Italy,in2002and 2006,respectively.SheiscurrentlyAssociateProfessorofInstrumentationandMeasurementswiththeUniversityofCagliari.Dr.SulisisaSeniorMemberoftheIEEE, memberoftheInstrumentationandMeasurementSociety,oftheIEEETC39 “MeasurementsinPowerSystems,” andoftheCENELECTC38 “InstrumentTransformers.” Shehasauthoredorcoauthoredmorethan100scientificpapers.Her currentresearchinterestsincludedistributedmeasurementsystemsdesignedtoperformstateestimationandharmonicsourcesestimationofdistributionnetworks.
HongbinSun isaProfessorintheDepartmentofElectricalEngineering,Tsinghua University,Beijing,China,theChangjiangChairProfessorofEducationMinistry ofChina,andanIEEEFellow.HereceiveddoubleBSdegreesin1992andPhDin 1997,respectively,bothfromElectricalEngineering,TsinghuaUniversity.His researchinterestsincludeautomaticvoltagecontrol(AVC),smartgrid,renewable energyandelectricalvehicleintegration,andpowersystemoperationandcontrol.
LangTong istheIrwinandJoanJacobsProfessorofEngineeringatCornellUniversityandtheCornellsiteDirectorofPowerSystemsEngineeringResearchCenter(PSERC).HereceivedaBEdegreefromTsinghuaUniversityandaPhDdegree inElectricalEngineeringfromtheUniversityofNotreDame.HeheldvisitingpositionsatStanfordUniversity,theUniversityofCaliforniaatBerkeley,theDelft UniversityofTechnology,andtheChalmersUniversityofTechnologyinSweden.
LangTong’s currentresearchfocusesondataanalytics,optimization,and economicproblemsinenergyandpowersystems.AFellowofIEEEandthe 2018FulbrightDistinguishedChairinAlternativeEnergy,hereceivedpaper awardsfromtheIEEECircuitandSystems,SignalProcessing,Communications, andPowerandEnergySystemssocieties.
GaneshKumarVenayagamoorthy istheDukeEnergyDistinguishedProfessor ofPowerEngineeringandProfessorofElectricalandComputerEngineeringat ClemsonUniversity.Dr.VenayagamoorthyistheFounder(2004)andDirector oftheReal-TimePowerandIntelligentSystemsLaboratory(http://rtpis.org). HeholdsanHonoraryProfessorpositionintheSchoolofEngineeringattheUniversityofKwazulu-Natal,Durban,SouthAfrica.Dr.Venayagamoorthyreceived hisPhDandMSc(Eng.)degreesinElectricalEngineeringfromtheUniversityof Natal,Durban,SouthAfrica,inFebruary2002andApril1999,respectively.He receivedhisB.Eng.(Honors)degreewithaFirstClassfromAbubakarTafawa BalewaUniversity,Bauchi,Nigeria,inMarch1994.HeholdsaMBAdegreein EntrepreneurshipandInnovationfromClemsonUniversity,SC(2016).Dr. Venayagamoorthy’sinterestsareintheresearch,development,andinnovation ofsmartgridtechnologiesandoperations,includingcomputationalintelligence, intelligentsensingandmonitoring,intelligentsystems,integrationofrenewable energysources,powersystemoptimization,stabilityandcontrol,andsignalprocessing.Heisaninventoroftechnologiesforscalablecomputationalintelligence forcomplexsystemsanddynamicstochasticoptimalpowerflow.Heledthe brain2gridprojectfundedbyUSNSF.Hehaspublishedover500refereedtechnicalarticles.Hispublicationsarecited>18,000timeswithah-indexof64.Dr. Venayagamoorthyhasbeeninvolvedinover75sponsoredprojectsinexcessof US$12million.Dr.Venayagamoorthyhasgivenover500invitedkeynotes,plenaries,presentations,tutorials,andlecturesinover40countriestodate.Hehasseveralinternationaleducationalandresearchcollaborations.Dr.Venayagamoorthyis aSeniorMemberoftheIEEE,andaFellowoftheIET,UK,andtheSAIEE.
GangWang receivedtheBEng.degreeinAutomaticControlfromtheBeijing InstituteofTechnology,Beijing,China,in2011,andthePhDdegreeinElectrical EngineeringfromtheUniversityofMinnesota,Minneapolis,USA,in2018,where hestayedasapostdoctoralresearcheruntil2020.SinceAugust2020,hehasbeena professorwiththeSchoolofAutomation,BeijingInstituteofTechnology.His researchinterestsfocusontheareasofsignalprocessing,deeplearning,andreinforcementlearningwithapplicationstocyber-physicalsystemsanddatascience. HewastherecipientoftheExcellentDoctoralDissertationAwardfromthe ChineseAssociationofAutomationin2019,theBestStudentPaperAwardfrom the2017EuropeanSignalProcessingConference,andtheBestConferencePaper atthe2019IEEEPower&EnergySocietyGeneralMeeting.
WenchuanWu isaProfessorintheDepartmentofElectricalEngineering,TsinghuaUniversity,Beijing,China.HereceivedhisBSin1996,MSin1999,andPhD degreesin2003allfromtheElectricalEngineeringDepartment,TsinghuaUniversity.HisresearchinterestsincludeEnergyManagementSystem,activedistribution systemoperationandcontrol,andEMTP-TSAhybridreal-timesimulation.Heis anAssociateEditorof IEEProceedings – Generation,Transmissionand DistributionandJournalofElectricPowerComponentsandSystems
YuanhaiXia isanElectricalEngineerwithChinaStateConstructionEngineering Corporation(MiddleEast).Hehasoneandhalfyears’ experienceinbuildingelectricandhalfyearinhighvoltagepowertransmission.HegothisMScfrom
KFUPM,SaudiArabia,inelectricalandpowersystemin2014.Heisfamiliarwith internationalanddomesticcodes/standards,AutoCADdrawing,masterexcelskills withVBprogramming,andotherprogramminglanguagesuchasMatlab,python, andLinuxshell.
BomingZhang isaProfessorintheDepartmentofElectricalEngineering,TsinghuaUniversity,Beijing,China.HereceivedMEng.fromHarbinInstituteof Technologyin1982andPhDfromTsinghuaUniversityin1985,bothinElectrical Engineering.HehasbeenservingforTsinghuaUniversitysince1985.Hisresearch areaincludespowersystemanalysis,computerapplicationinpowersystemcontrol center,etc.HewonIEEEPES/CSEEYu-HsiuKuElectricalEngineeringAward in2015.
JunboZhao (SM’19)receivedthePhDdegreefromtheBradleyDepartmentof ElectricalandComputerEngineering,VirginiaTech,Blacksburg,VA,USA,in 2018.HewasanAssistantProfessor(Research)withVirginiaTechfromMay 2018toAugust2019.HedidthesummerinternshipatthePacificNorthwest NationalLaboratoryfromMay2017toAugust2017.HeiscurrentlyanAssistant ProfessorwithMississippiStateUniversity,Starkville,MS,USA.Hehaswritten threebookchaptersandpublishedmorethan70peer-reviewedjournalandconferencepapers,amongwhichtherearethreeESIpapers.Hisresearchinterestsare powersystemmodeling,stateestimation,dynamicsandcybersecurity,synchrophasorapplications,renewableenergyintegrationandcontrol,androbuststatisticalsignalprocessingandmachinelearning.
Dr.Zhaoisaco-recipientofthebestpaperawardof2019IEEEPESISGT Asia,andthebestrevieweroftheIEEETRANSACTIONSONPOWERSYSTEMS2018andtheIEEETRANSACTIONSONSMARTGRID2019.HeiscurrentlytheChairoftheIEEETaskForceonPowerSystemDynamicStateand ParameterEstimation,andtheSecretaryoftheIEEEWorkingGrouponStateEstimationAlgorithmsandtheIEEETaskForceonSynchrophasorApplicationsin PowerSystemOperationandControl.HeservesastheAssociateEditorofthe IEEETRANSACTIONSONPOWERSYSTEMS,theIEEETRANSACTIONS ONSMARTGRID,and InternationalJournalofElectricalPowerandEnergy Systems,andtheSubjectEditorof IETGeneration,TransmissionandDistribution.
HaoZhu isanAssistantProfessorofECEatUniversityofTexasatAustin.She receivedaBEdegreefromTsinghuaUniversityin2006andMScandPhDdegrees fromtheUniversityofMinnesotain2009and2012,allinElectricalEngineering. Hercurrentresearchinterestsincludepowergridmonitoring,distributionsystem operationsandcontrol,andenergydataanalytics.ShereceivedtheNSFCAREER Awardin2017,theSiebelEnergyInstituteSeedGrantAwardandtheUSAFRL SummerFacultyFellowshipin2016.
GENERALCONSIDERATIONS MohamedE.El-Hawary
DalhousieUniversityinHalifax,NovaScotia,Canada
Inthisintroductorychapter,weintroducetheconceptofstateestimation(SE)in electricpowersystemandtraceitsevolutionfromahistoricalperspective.SE emergedasanindispensablereal-timetoolthatispartofasuiteofapplications designedtosupportandenableelectricpoweroperators’“situationalawareness.” Theterm “situationalawareness” inthecontextofpowergridoperationis “understandingthepresentenvironmentandbeingabletoaccuratelyanticipatefuture problemstoenableeffectiveactions.”
ThischapteroffersadetaileddiscussionoftheroleofSEinpractice.Aguide tothechaptersincludedinthisvolumeisofferedtoconcludethechapter.
1.1PRELUDE AttheIEEEPowerIndustryComputerApplications(PICA)conferenceheldon 18–21May1969inDenver,Colorado,ProfessorFredC.Schweppeandhisassociates presentedathree-partpaperonstaticstateestimationandrelateddetectionandidentificationproblemsinelectricpowersystems.Thepapersweresubsequentlypublishedinthe IEEETransactionsonPowerApparatusandSystems [1–3].Thefirst paper[1]introducedtheoverallproblemstatement,mathematicalmodeling,andgeneralalgorithmsforstateestimation,detection,andidentification(SEDI)using weightedleastsquares(WLS)approximations.Thesecondpaper[2]discussedan approximatemathematicalmodelandtheresultingsimplificationsinSEDI.Thethird paper[3]dealtwithimplementationproblems,considerationsofdimensionality,executionspeedandstorage,andthetime-varyingnatureofactualpowersystems.
Ayearlater,MerrillandSchweppe[4]introducedabaddatasuppression (BDS)estimator,whichiscomputationallyverysimilartoWLSapproximation.
AdvancesinElectricPowerandEnergy:StaticStateEstimation,FirstEdition. EditedbyMohamedE.El-Hawary.
©2021byTheInstituteofElectricalandElectronicsEngineers,Inc. Published2021byJohnWiley&Sons,Inc.
Theconceptisnomorecomplex,andbaddatadetectionandidentificationcanbe performed “forfree,” sinceBDSrequiresnomorecomputertimeorcomplexity thandoesWLS,andintheabsenceofbaddata,BDSreducestoWLS.
1.2DEFININGSSE In1974,SchweppeandHandschin[5]describedstateestimation(SE)usingthe followingmetaphor: “Thelifebloodofthecontrolsystemisabaseofcleanpure datadefiningthesystemstateandstatus(voltages,networkconfiguration).Thislife bloodisobtainedfromthenourishmentprovidedbythemeasurementsgathered fromaroundthesystem(dataacquisition).Astaticstateestimatoristhedigestive systemwhichremovestheimpuritiesfromthemeasurementsandconvertstheminto aformwhichthebrain(manorcomputer)ofthecentralcontrolsystemcanreadily usetomake ‘action’ decisionsonsystemeconomy,quality,andsecurity.”
Reference[1]formallydefinesthestaticstateofanelectricpowersystemasthe vectorofvoltagemagnitudesandanglesatallnetworkbuses.Thestaticstateestimator (SSE)isadataprocessingalgorithmforconvertingimperfectredundantmeter readingsandotheravailableinformationtoanestimateofthestaticstate.
Item603-02-09oftheInternationalElectrotechnicalCommission(IEC) Electropedia[6]offersthefollowingdefinitionof “stateestimation” as “thecomputationofthemostprobablecurrentsandvoltageswithinthenetworkatagiven instantbysolvingasystemofmostlynonlinearequationswhoseparametersare obtainedbymeansofredundantmeasurements.”
TheNorthAmericanElectricReliabilityCorporation(NERC)Real-Time ToolsBestPracticesTaskForce(RTBPTF)2008finalreport[7]offersthefollowingdefinition: “Astateestimatorisanapplicationthatperformsstatisticalanalysis usingasetofimperfect,redundant,telemeteredpower-systemdatatodetermine thesystem’scurrentcondition.Thesystemconditionorstateisafunctionofseveralvariables:busvoltages,relativephaseangles,andtapchangingtransformer positions.Astateestimatorcantypicallyidentifybadanalogtelemetry,estimate non-telemeteredflowsandvoltages,anddetermineactualvoltageandthermalviolationsinobservableareas.”
Accordingto[5],SSEhasevolvedrapidlytoonlineimplementationsbeginningwiththeNorwegianTokkeinstallation[8]followedbythelargerAEPinstallation[9]soonafter.Notlonglater,T.E.DyLiacco[10]stated: “Althoughthe numberofcontrolcenterswithStateEstimationisstillrathersmall,thenumber isincreasingatarapidrate.TherequirementforStateEstimationatamoderncontrolcenterhasbecometherule,ratherthantheexception.”
Thefundamentalproblemofstateestimationcanbedefinedasanoverdeterminedsystemofnonlinearequationssolvedasanunconstrainedweightedleast squares(WLS)minimizationproblem.TheWLSestimatorminimizesthe weightedsumofthesquaresoftheresiduals.Residualsaretheerrorordifference betweentheestimatedandtheactualvalues[11].Manypapersandbookstreatthe broadgenericareaof “stateestimation” insystemtheory[12–14].Stateestimation conceptscanbeappliedinotherpowersystemsareas[15–20].
1.3THENEEDFORSTATEESTIMATION Securitycontrolisthemainstrategyusedintheoperationofelectricpowersystems,whereactionsaretakentopreventanimpendingemergency,tocorrectan existingemergency,ortorecoverfromanemergency.Knowingthestateofthe systemundersteady-stateconditionsisthekeytosecuritycontrol.
Controlcentersmaybeclassifiedintotwotypes,accordingtotheinformationbaseavailable.Inonetypeofcontrolcenter,therawpowersystemdataas obtainedinrealtimeisanadequateinformationbaseforoperation.Theothertype ofcontrolcentergoesbeyondthemereacquisitionofdata.Byapplyingstateestimation,afarbetterandamorecomprehensiveinformationbasethanrawdatais obtained.
Theimportanceofthereal-timeloadflowfedbystateestimationliesinits useasbasisforsecurityanalysis.Withtheloadflowasabase,referenceallows analyzingtheeffectsonthesystemofanycontingencyevent.Incontrast,without stateestimation,thereisnotmuchtobedonewithrawdataexcepttocheckitfor abnormalvalues.
Afurtherimportantfeatureofstateestimationistheabilitytodetectthepresenceofbaddata(outliers)andtoidentifywhichdataisinerror.Correctionscan thenbeexpeditedinthefieldonthefaultyinstrumentation.Withoutstateestimation,thereisnoeffective,systematicwayoffindingmeasurementerrors.Somesort ofdatavalidationhasbeenattemptedwhereinpowermeasurementsaroundabus aresummedupandflowsatbothendsofabranchcheckedagainsteachother,but thesechecksapartfrombeinginconclusiveendupbeingtoocomplicatedasithas totakeintoaccountthetopologyofthenetwork.Nownetworktopologyishandled systematicallyandcorrectlybystateestimation.Henceforallthecheckingdoneby so-calleddatavalidationprograms,itisbesttogodirectlytostateestimation.
Inthemodelingofpowersystemsforsecuritycontrolfunctions,thereare usuallyexternalnetworks,i.e.networksorsubnetworks,whicharenotbeingtelemeteredbythecontrolcenterandwhicharenotobservable.Therearetwo approachesforestimatingthestateoftheseexternalnetworks.Oneapproachis tousepseudo-measurements,basedonstatisticsandforecasts,oftheinjections atthenodesoftheexternalnetwork.Thepseudo-measurementsarethenassigned relativelylowweightsandincludedaspartofthemeasurementsetinthestateestimationroutine.Thesecondapproachistoperformthestateestimationonlyonthe observablepart.Thestateoftheexternalnetworkisthenobtainedbyfindingaload flowsolutionusingthepseudo-measurementsasinputswiththeboundarynodevoltagesheldatthevaluesdeterminedbythestateestimationoftheobservablepart.
Forbaddataidentification,earlystateestimatorssingledoutmeasurements withthehighestvaluesoftheweightedresidual.Newerbaddataidentification techniquesuseboththeweightedresidualandthenormalizedresidual.Either thevaluesofthenormalizedresidualortheratiosofthenormalizedonesfrom theweightedresidualareusedtoidentifybaddata.Baddatarejectionisatimeconsumingprocedureatcontrolcentersespeciallyiftherearemorethanonemeasurementinerror.
Theconceptofsecuritycontrolcannotbefullyrealizedwithoutacomplete informationbasethatisderivedfromthevoltagemagnitudesandphaseanglesof allbusesinapowersystemobtainedviastateestimation[1–3].
1.4STATICSTATEESTIMATIONINPRACTICE ThematerialinthissectionisbasedonaNERCTaskForcereport[7].To quotetheTaskForce:
ThisreportpresentsthefindingsandrecommendationsoftheNorth AmericanElectricReliabilityCorporation(NERC)Real-TimeToolsBest PracticesTaskForce(RTBPTF)concerningminimumacceptablecapabilitiesandbestpracticesforreal-timetoolsnecessarytoensurereliableelectric systemoperationandreliabilitycoordination.RTBPTF’sundertakingis basedontheU.S.-CanadaPowerSystemOutageTaskForcefindingsthat keycausesoftheAugust14,2003northeastblackoutincludedabsenceof situationalawarenessandinadequatereliabilitytools.Thatreportalsonotes theneedforvisualizationdisplaysystemstomonitorsystemreliability.
RTBPTF’srecommendationsresultfromanextensive,three-yearprocessof fact-findingandanalysissupportedbytheresultsoftheReal-TimeTools Survey,themostcomprehensivesurveyeverconductedofcurrentelectric industrypractices.
RTBPTF’sfindingsandrecommendationsarefirmlygroundedintheresults oftheReal-TimeToolsSurvey,amorethan300-page,web-baseddocument withnearly2,000questionsonabroadscopeofcurrentindustrypractices andplansforusingreal-timetools.
While[21]referredtoRTUsastheeyesandearsandhandsofthemaster station,thephrasecametobecommonlyusedtorefertothestateestimatoras theeyesandearsofthereal-timeoperator.Indeed,incurrentpracticethestateestimatorprevailsasan “essential ” toolforpowersystemoperators’“situational awareness.” ExistingNERCreliabilitystandardsassumetheuseofstateestimators toaidRCsandTOPsinmaintainingsituationalawarenessforthebulkelectric system.Thestateestimatormustbeavailableandabletoproduceanaccuratesolutionbecausemanyapplicationsrelyonthestateestimatorsolutionasbasecase.
StateestimatorsarecommerciallyavailableallowingSCADA/EMSvendors toprovideviablestateestimatorsofftheshelfwithsomecustomizationandfully integratedwithusers’ productionSCADA/EMSsystems.Stateestimatorsareused asinputtomonitorMVA/ampereloadingsandlowandhighbusvoltages,voltage drop,voltagenodeangleseparation,SCADA,andvisualization.Therefore,itis importantthatitbeavailableandproduceanaccuratesolution.
Single-passmethodsexecuteoneestimationthatsimultaneouslyincludes internalandexternalnetworks,observable/internalnetwork,andnonobservable/
externalnetworksolvedtogether.Thetwo-passmethoddealswithtwostate estimates,onefortheinternalsystemandanotherfortheexternalsystemorfor theentiresystem(observable/internalnetworkandnonobservable/externalnetworksolvedseparately).Manyinthepowerindustrypreferusingasingle-pass overatwo-passsolution.
Accordingto[22],thesingle-passmethodsuffersfromnumericalinstability. Anenhancementtotheone-passmethodusesasetofcriticalexternalpseudomeasurements.Somealternativetwo-pa ssstateestimatorsrequirealoadflow studyfortheexternalsystem.Bothtwo-passmethodsreducetheeffectsof boundaryerrorsintheinternalsystemsolutionbyproperlyweighingtheexternal pseudo-measurements,buttheymayresultinveryhighornegativeloadsand generationsintheexternalsystem.Zero -injectionbusesaremorecommonlytreatedashigh-confidencebusinjectionmeasurementsthanashardconstraints.
Foranoverwhelmingmajorityofusers,thestateestimatorsolutionisusedas abasecaseforreliability-analysisapplicationssuchascontingencyanalysis(CA), powerflow(PF),andasinputtosystemanalysistoolssuchas:
1. Online/operatorPF
2. OfflinePF
3. Locationalmarginalpricing(LMP)
4. Voltagestabilityanalysis
5. Security-constrainedeconomicdispatch
Insomecases,thestateestimatorisusedprimarilyasthebasisforinformationcommunicatedtooperatorsregardingpowersystemstatus;e.g.thestateestimatordrivesthealarmapplicationthatalertsoperatorstoimpendingpowersystem events.
1.4.1SEPerformanceIssues Itiscommonpracticetorelyonperiodictriggerstorunstateestimatorseverytwo minutes.ManualandSCADAeventssuchasbreakertripsandanalogratesof changearealsoused.Moreover,theaveragestateestimatorexecutiontimeranges fromonesecondtotwominutes(withanaverageofabout20seconds).
Itisdifficulttorecommendspecificstateestimatorvoltageandangleconvergencetolerancesbecauseofthedifferentalgorithmsemployedbydifferentstate estimatorsandthewayspecificconvergenceparametersareusedinthesealgorithms.Forexample,somestateestimatorscheckconvergencebasedonchanges oftheabsolutevaluesofvoltagemagnitudesandvoltagephaseangles(relativeto ground)betweensuccessiveiterations.
Commonindustrypracticeforthevoltage-magnitudeconvergence-tolerance criteria(perunit)isamaximumof0.1(0.01kVperunit)forbothinternal/observableandexternal/unobservablesystems.Fortheangledifferenceinradians,the toleranceis0.0100.
1.4.2WeightsAssignedtoMeasurements Thestateestimatorrequiresmeasurementweights(confidences)thataffectitssolution.Theweightsfortelemeteredandnon-telemeteredmeasurementsareselected accordingtothefollowing:
1. Useindividuallydefinedweightsforatleastsomeofthetelemeteredmeasurementsusedbythestateestimators.
2. Usegloballydefinedweightsforatleastsomeofthetelemeteredmeasurementsusedbythestateestimators.
Thebasisforweightsappliedtoatleastsomeanalogvaluesusedbythestate estimatoriseitheragenericpercentagemeteringerrororspecificmeteraccuracies.
1.4.3SEAvailabilityConsiderations Thestateestimatormustbehighlyavailableandmustalsobeabletoprovidea reasonable,accurate,androbustsolutionthatmeetsthepurposesforwhichitis intended.Practitionersreportthattheaveragetimeduringwhichstateestimator solutionsareunavailableis15minutesorlessperoutageforalmostallusers. Inaddition,unavailabilityofthestateestimatorforupto30minutesisconsidered ashavingnosignificantimpactonsystemoperations.
Havingstateestimatorfailureslessthan30minutesapartisperceivedashavinga “significant” impactonsystemoperations.Thishowevervariesaccordingto internalpoliciesandmarketconsiderations.
1.4.4SESolutionQuality(Accuracy) Stateestimatoravailabilityrequirementsarecomplementedbysolution-quality requirementstoensurethatoperatorsaregivenaccurateinformationallowingthem tobefullyawareofthesystemsituationinatimelymanner.
Operatorsreportthattheycandetectandidentifybadanalogmeasurements andremovethemfromthestateestimatormeasurementset.Usersquantifiedthe real/reactivepowermismatchtolerancecriteriafortheirinternal/observable systemsisinthe0.05MW(perunit) – 170MWrealpowermismatchtolerance rangeanda0.001Mvar(perunit) – 500Mvarreactivepowermismatchtolerance range.Theaveragerealandreactivemismatchtolerancecriteriareportedwere 35MWand69.5Mvar,respectively.
Macedo[23]statesthatstateestimatorMVAmismatchshouldbelessthan 10MVA.Hedoesnotdistinguishbetweeninternalandexternalsystems.
1.4.4.1MetricstoEvaluateSESolutionQuality
Morethanonemetricisusedtoevaluatetheaccuracyoftheresultsofthestate estimatorsolution:
• Costindexisalsoreferredtoas “performanceindex” or “quadraticcost.” In general,itmeasuresthesumofthesquaresofthenormalizedestimateerrors (residuals).Increasingcostindexvaluescouldindicatedeterioratingstate estimatorsolutionquality.Thisisthemostcommonlyusedindicator,whose valuesrangebetween45and58%.
• Chi-squaredcriterionisthesecondmostused,anditsvaluerangesbetween 36and42%.
• Measurementerror/biasanalysisisusedasaperformanceindicator.
• Averageresidualvalueisusedasaperformanceindicator.
Thereliabilityentityshouldtracktheselectedmetricovertimetoestablish thepatternanddeterminewhatindicatesaproblemwithstateestimatorsolution quality.Deviationfromthe “normalrange” ofthesemetricsshouldtriggerstate estimatormaintenanceandsupport.Thesemetricsareimportantbecausethey couldaffecttheCAsolution.
ManyfactorsaffectSEsolution-qualitymetricssuchas:
1. Electricaldevicemodeling,connectivity,andtelemetrydatamapping.Ifthe topologyisincorrect,thestateestimatormaynotconvergeormayyield grosslyincorrectresults.Atopologyerrormaybecausedbyeitherinaccurate statusofbreakersandswitchingdevicesorerrorsinthenetworkmodel.
2. Availabilityandqualityoftelemetrydata.Telemetrydataareessentialcomponentsofthestateestimationprocess.
3. Inadequateobservability.Stateestimationisextendedtotheunobservable partsofthenetworkthroughtheadditionofpseudo-measurementsthat arecomputedbasedonloadpredictionusingloaddistributionfactors,orthey canrepresentnon-telemeteredgenerationassumedtooperateatabase-case outputlevel.Thequalityofpseudo-measurementsmaybebadiftheyarenot updatedregularlytoreflectcurrentconditions.
4. Measurementredundancyofthenetworkisdefinedastheratioofthenumberofmeasurementstothenumberofstatevariablesintheobservablearea ofthenetwork.
1.4.4.2MethodsforEvaluatingSESolutionQuality(Accuracy)
Thefollowingmethodsareusedtoevaluatetheaccuracyofthestateestimator results:
• Continuallymonitorandminimizetheamountofbaddatadetectedby correctingmodel,telemetry,andbadstatus.
• Comparecriticaltelemetrywiththestateestimatorsolution(ties,majorlines, largeunits,etc.).
• Usemeasurementerror/biasanalysistodetectandresolvetelemetryand modelproblems.
• Periodicallyreviewallstationstocorrecthighresidualsandminimizeall residualsasmuchasreasonablypossible.
• CompareCAresultstoactualsystem.
• Comparepowerflowresultswithactualsystem.
• Comparestateestimatoractualviolationstoseeiftheycloselymatchactual SCADAviolations.
• Comparestateestimatortotalcompanyload/generation/interchangeintegratedovertimetoseeifitcloselymatchesbillingmetering.
1.4.5UsingSEtoMonitorExternalFacilities Thestateestimatorsolutionqualitywhenitisusedtomonitorexternalfacilities dependsontheaccuracyoftheirmodels.Theexternalnetworkmodelscouldaffect thequalityofstateestimatorsolutionsby:
1. Propagationoferrorsintotheinternalmodelsolutionfromtheexternal modelsolution.Thisappliestoone-passstateestimatorsiftheexternalnetworkmodelsolutionismainlybasedonforecastedand/orpseudomeasurementsratherthantelemetereddata.Theexternalnetworkmodel equivalencingmethodscouldalsocauseerrorstopropagate.Fortwo-pass stateestimator,therecouldbeboundaryproblems(betweentheinternal/ observablesolutionandtheexternal/unobservablesolution)thatcouldcause thetotalnetworksolutiontonotconverge.
2. Measurementdensityintheexternalsystem.Manybusesinexternalmodels aremeasurementunobservable.Thelowvaluesfortheexternal-status-pointto-external-busratiosformanyrespondents(i.e.lessthanonestatuspointper bus)indicatethatmanyexternalbusesdonothavetelemeteredbreaker/ switchinformation,whichimpliesabus-branch-typeexternalmodel(i.e. aplanningmodel)formanybuses.
3. Convergenceissuesrelatedtoexternalmodelsand/ortelemetrydatafor externalmodel.Measurementsfortheexternalnetworkmodelusuallyoriginatefromdatalinks.Asaresult,dataavailabilitydependsondatalink availability.
4. Theimpactofinterchangetransactions,especiallyfortheexternalportionof themodel,couldinfluencethestateestimatorsolution.
5. Addingdetailorexpandingtheexternalnetworkmodelcouldaffectthe throughput(executiontime)ofthestateestimatorapplication.
Externalnetworkmodelimprovementsareexpectedtoenhancetheaccuracy oftheresults.
• Addingbreaker/switchdetailtotheexternalandinternalmodels
• Addingextensivetelemetrytotheexternalandinternalmodels
• Addinglower-voltagedetailtotheexternalandinternalmodels
• Addingoneormorecontrolareastotheexternalmodel
• Creatinganewexternalmodel
1.4.6SEMaintenance/TroubleshootingandSupport Practices Manyusershavestateestimatorsupportpersonnelavailablecontinuously.Most usersmonitorstateestimatorstatusonacontinuousbasis(24×7×365)andmaintaintheirstateestimatorswithin-housestaff,andsomeusevendorstaffinaddition toin-housestaffforsupport.
Mostusersnotifyoperatorsandcontrolroomstaffofastateestimatorfailure. Stateestimatorstatusispresentedprimarilyviaalarmtoolsandphysicaldisplays. Someuserspageandsendemailnotifyingofastateestimatorfailure.
Operatorsattempttoresolvestateestimatorproblemspriortonotifyingsupportpersonnel.
Manyusershaveaprocesstoinvestigateanddebugunsolved/nonconvergedandbad/inaccuratestateestimatorsolutions.
Theoperatorreceivesanalarmnotificationofstateestimatorproblemsand thencallsforsupportpersonnelasneededtosolvetheproblem.Alternativelysupportpersonnelareoncallandconnectremotelyafterbusinesshourstofixreported problems.Supportpersonnelmaybepagedautomaticallybytheapplication(s)to troubleshoottheproblem.
Forexample,theElectricReliabilityCouncilofTexas(ERCOT)requiresthe followingstateestimatorperformancemeasures[24]:
1. StateEstimatortoconverge97%ofrunsduringaone-monthperiod.
2. Ontransmissionelementsidentifiedascausing80%ofcongestioncostinthe latestyearforwhichdataisavailable,theresidualdifferencebetweenState EstimatorresultsandPowerFlowresultsforcriticallymonitoredtransmissionelementMWflowsarerequiredtobelessthan3%oftheassociated elementemergencyratingonatleast95%ofsamplesmeasuredinaonemonthperiod.
3. Ontransmissionelementsidentifiedascausing80%ofcongestioncostinthe latestyearforwhichdataisavailable,thedifferencebetweentheMWtelemetryvalueandtheMWStateEstimatorvalueshallbelessthan3%ofthe associatedelementemergencyratingonatleast95%ofsamplesmeasured inaone-monthperiod.
4. On20mostimportantstationvoltagesdesignatedbyERCOTandapproved byROS;thetelemeteredvoltageminusStateEstimatorvoltageshallbe within2%ofthetelemeteredvoltagemeasurementinvolvedforatleast 95%ofsamplesmeasuredduringaone-monthperiod.
5. Onalltransmissionelementsgreaterthan100kV;thedifferencebetween StateEstimatorMWsolutionandtheSCADAmeasurementwillbelessthan
10MWor10%oftheassociatedemergencyrating(whicheverisgreater)on 99.5%ofallsamplesduringaone-monthperiod.Allequipmentfailingthis testwillbereportedtotheassociatedTSPforrepairwithin10daysof detection.
1.5APPLICATIONSTHATUSESESOLUTION ThestateestimatorsolutionisabasecaseforCAandPFforalmostallusers.Some usersemploythestateestimatorsolutioninsecurity-constrainedeconomicdispatchandLMPandofflinepowerflowapplications[25].Insummary,thefollowingapplicationsusethestateestimatorsolutionasabasecase:
Contingencyanalysis
Online/operatorPF
Locationalmarginalpricing
Security-constrainedeconomicdispatch
Voltagestabilityanalysis
Dynamicstabilityanalysis
Abriefdiscussionofsomeofthesefunctionsisgivennext.
1.5.1ContingencyAnalysis Asareal-timeapplication,CAusescurrentSEsystemconditionstodeterminethe effectsofspecific,simulatedoutages(lines,generators,orotherequipment)on powersystemsecurityorhigherload,flow,orgenerationlevels.Inaddition, CAconsidersunexpectedfailureoroutageofasystemcomponent(transmission lines,generators,circuitbreaker,switch,oranyotherelectricalequipment)and naturallylineoverloadsorvoltageviolationsorhigherload,flow,orgeneration level[26–27].
FailedornonfunctionalCAapplicationhasbeenidentifiedasakeycauseof manysignificantblackouts.Therefore,itmustbehighlyavailableandredundant. TheinformationproducedbyCAallowstheoperatortoimplementmitigation actionsaheadofacontingencyandmaintainthereliabilityoftheelectricpower system.
1.5.2PowerFlow(Online/Operator) PFcalculatesthestateoftheelectricpowersystemintheformofflows,voltages, andanglesbasedonload,generation,netinterchange,andfacilitystatusdata.PF determinessystemstate.PFareavailableinbothonlineandofflineversions.
Onlineloadflowprogramsareastandardpartofallenergymanagementsystem specification[28].
OnlinePFiswidelyusedtoassesssystemconditionsorperformlook-ahead analysis.Itisalsousedin “ n 1” CAandtoidentifypotentialfuturevoltagecollapseorreliabilityproblems.
Real-timereliabilitytoolscanonlyprovideresultsthataccuratelyrepresent currentandpotentialreliabilityproblemsifthesetoolshavereal-timePFandvoltagevaluesandstatusdataforotherelementsincludedintheirmodels.Theaccuracyoftheinformationthatreal-timereliabilitytoolsprovidedependsonthe accuracyofthedatasuppliedtothetools.
1.5.3LocationalMarginalPricing Theequalincrementalcost(systemlambda)rulearisesinconventionaleconomic dispatchofasystemoffossilfuelthermalgeneratingunitsservinganactivepower load(demand)neglectingtransmissionlosses.Thiscaseusesoneactivepowerbalanceequation(APBE)tomodeltheelectricnetworkphysicalconstraints.AccountingfortransmissionlossesintheAPBEleadstothewell-knownlosspenalty factorsthatareusedtopenalizetheincrementalcostofgenerationforeachunit. Losspenaltyfactorswhosevaluesaregreaterthanonecorrespondtounitswhose lossesincreasewiththeloaddemandandarefurtherawayfromtheloadcenter.In optimalPF,theelectricnetworkismodeledusingthePFequationsandresultsin twolambdas(onefortheactivepowerequationandthesecondforthereactive equation)foreachnodeinthesystem.ThisisthebasisofLMP.
LMPreflectsthewholesalevalueofelectricenergyatdifferentpricingnodes (locations)consideringtheoperatingcharacteristics,physicalconstraints,and lossescausedbythephysicalconstraintsandlimitsofthetransmissionsystem andpatternsofloadgeneration.Pricingnodesincludeindividualpointsonthe transmissionsystem,loadzones(i.e.aggregationsofpricingnodes),external nodes,andnodeswheretheindependentsystemoperatorinterconnectswitha neighboringregionandtheHub.TheHubisacollectionoflocationsthatrepresent anuncongestedpriceforelectricenergy,facilitateelectricenergytrading,and enhancetransparencyandliquidityinthemarketplace[29–32].
DifferentlocationsinthesystemhavedifferentLMPssincetransmissionand reservedconstraintspreventthenextleastexpensivemegawatt(MW)ofelectric energyfromreachingalllocationsofthegrid.Evenduringperiodswhentheleast expensivemegawattcanreachalllocations,themarginalcostofphysicallosses willresultindifferentLMPsatdifferentlocations.
Typically,theLMPsarecalculatedeveryfiveminutes.TheLMPataload zoneisusedto:
1. Establishthepriceforelectricenergypurchasesandsalesatspecificlocationsthroughoutthewholesaleelectricitymarketforcompensatinggeneratorsandchargingloads.
2. Collecttransmissioncongestioncharges.
