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1、1PowerSystemApplicationsofTrajectorySensitivitiesIanA.Hiskens,SeniorMemberM.A.Pai,LifeFellowDepartmentofElectricalandComputerEngineeringUniversityofIllinoisatUrbana-ChampaignUrbanaIL61801USAAbstract—Trajectorysensitivitiescomplementtimedo-effectsofparameters[
2、3].Thisanalysisisbasedonlineariz-mainsimulationintheanalysisoflargedisturbancedynamicingthesystemaroundatrajectory,ratherthanaroundanbehaviourofpowersystems.Theyareformedbylineariza-equilibriumpoint[4],[5].Thereforeitispossibletodeter-tionaroundanonlinear,an
3、dpossiblynon-smooth,trajec-tory.Theinfluenceofparametervariationsonlargedis-minedirectlythechangeinthetrajectoryduetoa(small)turbancebehaviourcanbeestimated(tofirstorder)fromchangeinparameters.Theideasextendnaturallythroughthesesensitivities.Large(small)sensit
4、ivitiesindicatethatdiscontinuities,providedafewtechnicalconditionsaresat-aparameterhasasignificant(negligible)effectonbehav-iour.Theseinsightsarehelpfulinanalysingtheunderlyingisfied[3].influencesonsystemdynamics,andforassessingthesignif-Thepaperisstructuredasfo
5、llows.Anoverviewoftrajec-icanceofparameteruncertainty.Further,trajectorysensi-torysensitivityconceptsisprovidedinSectionII.Numer-tivitiesprovidegradientinformationforapplicationssuchousapplicationareoutlinedinSectionIII,andconclusionsasparameterestimation,bo
6、undaryvalueproblems,border-collisionbifurcations,andoptimalcontrol.arepresentedinSectionIV.Keywords:Powersystemdynamics,trajectorysensitivities,parameterestimation,inverseproblems.II.TrajectorySensitivityConceptsPowersystemdynamicbehaviouroftenexhibitsinter-
7、I.Introductionplaybetweencontinuousdynamicsandstate-drivendis-creteevents.SuchbehaviourcanbecapturedbyaOOLSforsystematicallyexploringlargedisturbancedifferential-algebraicmodelthatincorporatesimpulsiveac-Tbehaviourofpowersystemsarequitelimited.Gener-tionandsw
8、itching(DAISmodel).Thatmodelisfullyde-allysuchanalysisreliesontimedomainsimulationandin-scribedin[3],[6].Howevertofacilitateaclearerpresenta-tuition.Whilstsimulationprovidesavastamountofinfor-ti
