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NegativeSide:DirectMethodIntroductionsClassificationsAnAnalogyOfRollingBallModelApplicationtopowersysytem:ThebasisfortheapplicationoftheTEF(TransientEnergyFunction)methodtotheanalysisofpowersystemstabilityisconceptuallysimilartothatforaballrollinginabowl.Initiallythesystemisoperatingatastableequilibriumpoint.Ifafaultoccurs,theequilibriumisdisturbedandthesynchronousmachinesaccelerate.Thepowersystemgainskineticandpotentialenergyduringfault-onperiodandthesystemmovesawayfromtheSEP.ThestepsforLyapunovfunctionmethod:1)Defineenergyfunction;2)Determinecriticalenergy;3)Comparingtheenergyatfaultclearingandcriticalenergytojudgethesystemisstableornot.DefinitionOfTheTransientEnergyFunctionStabilityRegionAndPhasePlaneDiagramIntheabovefigure,eachlotus（1~5）isanequalenergycurve.Thetotalenergyincreasesfrominsidertooutsider,untilthecorrespondingmaximumsealedcurvetounstableequilibriumpointandreachescriticalenergy.Thiscurveiscalledpolarcircle,theinsideisstableregion.Thus,wegetcriticalenergyTheProcedureOfLyapunovFunctionMethodPotentialEnergyBoundarySurface(PEBS)ApproachPrincipleStepsAssessIndividualMachineEnergyFunction(单机能量法)ReferenceFirstPresentedByMichelInHisThesis:powersystemtransientstabilityusingindividualmachineenergyfunction,IEEETrans.Oncircuitsandsystems,Vol.3,No.5,May1983,pp266~276TwoProblems:Situationsareoftenencounteredinpowersystemswherecomplex“modes”ofinstabilityarise,makingitdifficulttodetermine(withconfidence)therelevantu.e.pSignificantportionsofthesystemtransientenergydonotcontributetosystemseparation;henceitshouldbecorrectedforintransientstabilityassessment.CriticalGroupOfMachinesOverallsystemenergyfunctionConclusionsAccuratelypredicts:a)whichmachineslosesynchronism,b)criticalclearingtimeAgoodestimateofisobtainedfromthesustainedfaulttrajectory.Provideslessconservativestabilityresults.ExtendedEqual-areaCriterionTimeDomainSimulationMethodAllYourWorksAreBasedOnMyTheory!!!SEEACTomapthetwo-machinesystemintotheOMIBsystem,wefurthermoredotheRMtransform:Applica
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