n and Classification of Power System Stability

IEEETRANSACTIONSONPOWERSYSTEMS,VOL.19,NO.2,MAY20041387DefinitionandClassificationofPowerSystemStabilityIEEE/CIGREJointTaskForceonStabilityTermsandDefinitionsPrabhaKundur(Canada,Convener),JohnPaserba(USA,Secretary),VenkatAjjarapu(USA),GöranAndersson(Switzerland),AnjanBose(USA),ClaudioCanizares(Canada),NikosHatziargyriou(Greece),DavidHill(Australia),AlexStankovic(USA),CarsonTaylor(USA),ThierryVanCutsem(Belgium),andVijayVittal(USA)Abstract—TheproblemofdefiningandclassifyingpowersystemstabilityhasbeenaddressedbyseveralpreviousCIGREandIEEETaskForcereports.Theseearlierefforts,however,donotcompletelyreflectcurrentindustryneeds,experiencesandunderstanding.Inparticular,thedefinitionsarenotpreciseandtheclassificationsdonotencompassallpracticalinstabilityscenarios.ThisreportdevelopedbyaTaskForce,setupjointlybytheCIGREStudyCommittee38andtheIEEEPowerSystemDynamicPerformanceCommittee,addressestheissueofstabilitydefinitionandclassificationinpowersystemsfromafundamentalviewpointandcloselyexaminesthepracticalramifications.Thereportaimstodefinepowersystemstabilitymoreprecisely,provideasystem-aticbasisforitsclassification,anddiscusslinkagestorelatedissuessuchaspowersystemreliabilityandsecurity.IndexTerms—Frequencystability,Lyapunovstability,oscilla-torystability,powersystemstability,small-signalstability,termsanddefinitions,transientstability,voltagestability.I.INTRODUCTIONPOWERsystemstabilityhasbeenrecognizedasanimportantproblemforsecuresystemoperationsincethe1920s[1],[2].Manymajorblackoutscausedbypowersysteminstabilityhaveillustratedtheimportanceofthisphenomenon[3].Historically,transientinstabilityhasbeenthedominantstabilityproblemonmostsystems,andhasbeenthefocusofmuchoftheindustry’sattentionconcerningsystemstability.Aspowersystemshaveevolvedthroughcontinuinggrowthininterconnections,useofnewtechnologiesandcontrols,andtheincreasedoperationinhighlystressedconditions,differentformsofsysteminstabilityhaveemerged.Forexample,voltagestability,frequencystabilityandinterareaoscillationshavebecomegreaterconcernsthaninthepast.Thishascreatedaneedtoreviewthedefinitionandclassificationofpowersystemstability.Aclearunderstandingofdifferenttypesofinstabilityandhowtheyareinterrelatedisessentialforthesatisfactorydesignandoperationofpowersystems.Aswell,consistentuseofterminologyisrequiredfordevelopingsystemdesignandoperatingcriteria,standardanalyticaltools,andstudyprocedures.Theproblemofdefiningandclassifyingpowersystemsta-bilityisanoldone,andtherehavebeenseveralpreviousreportsManuscriptreceivedJuly8,2003.DigitalObjectIdentifier10.1109/TPWRS.2004.825981onthesubjectbyCIGREandIEEETaskForces[4]–[7].These,however,donotcompletelyreflectcurrentindustryneeds,ex-periences,andunderstanding.Inparticular,definitionsarenotpreciseandtheclassificationsdonotencompassallpracticalin-stabilityscenarios.ThisreportistheresultoflongdeliberationsoftheTaskForcesetupjointlybytheCIGREStudyCommittee38andtheIEEEPowerSystemDynamicPerformanceCommittee.Ourobjec-tivesareto:Definepowersystemstabilitymoreprecisely,inclusiveofallforms.Provideasystematicbasisforclassifyingpowersystemstability,identifyinganddefiningdifferentcategories,andprovidingabroadpictureofthephenomena.Discusslinkagestorelatedissuessuchaspowersystemreliabilityandsecurity.Powersystemstabilityissimilartothestabilityofanydynamicsystem,andhasfundamentalmathematicalunder-pinnings.Precisedefinitionsofstabilitycanbefoundintheliteraturedealingwiththerigorousmathematicaltheoryofstabilityofdynamicsystems.Ourintenthereistoprovideaphysicallymotivateddefinitionofpowersystemstabilitywhichinbroadtermsconformstoprecisemathematicaldefinitions.Thereportisorganizedasfollows.InSectionIIthedef-initionofPowerSystemStabilityisprovided.Adetaileddiscussionandelaborationofthedefinitionarepresented.Theconformanceofthisdefinitionwiththesystemtheoreticdefinitionsisestablished.SectionIIIprovidesadetailedclassi-ficationofpowersystemstability.InSectionIVofthereporttherelationshipbetweentheconceptsofpowersystemreliability,security,andstabilityisdiscussed.Adescriptionofhowthesetermshavebeendefinedandusedinpracticeisalsoprovided.Finally,inSectionVdefinitionsandconceptsofstabilityfrommathematicsandcontroltheoryarereviewedtoprovideback-groundinformationconcerningstabilityofdynamicsystemsingeneralandtoestablishtheoreticalconnections.TheanalyticaldefinitionspresentedinSectionVconstituteakeyaspectofthereport.Theyprovidethemathematicalun-derpinningsandbasesforthedefinitionsprovidedintheearliersections.Thesedetailsareprovidedattheendofthereportsothatinterestedreaderscanexaminethefinerpointsandassimi-latethemathematicalrigor.0885-8950/04$20.00©2004IEEE1388IEEETRANSACTIONSONPOWERSYSTEMS,VOL.19,NO.2,MAY2004II.DEFINITIONOFPOWERSYSTEMSTABILITYInthissection,weprovideaformaldefinitionofpowersystemstability.Theintentistoprovideaphysicallybaseddefinitionwhich,whileconformingtodefinitionsfromsystemtheory,iseasilyunderstoodandreadilyappliedbypowersystemengineeringpractitioners.A.ProposedDefinitionPowersystemstabilityistheabilityofanelectricpowersystem,for