Computation of closest bifurcations in power systems.pdf

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1、918IEEETransactionsonPowerSystems,Vol.9,No.2,May1994COMPUTATIONOFCLOSESTBIFURCATIONSINPOWERSYSTEMSFernandoAlvaradoIanDobsonYiHuFellowMemberStudentMemberElectrical&ComputerEngineeringDepartmentTheUniversityofWisconsin-MadisonAbstractVoltagecollapseandblackoutcanocc

2、urinanelectricpowersystemwhenloadpowersvarysothatthesys-temlosesstabilityinasaddlenodebifurcation.Thispapercomputesloadpowersatwhichbifurcationoc-cursandwhicharelocallyclosesttogivenoperatingloadpowers.Thedistanceinloadpowerparameterspacetothislocallyclosestbifurc

3、ationisanindexofvoltagecollapseandaminimumloadpowermargin.Thecomputationsareillustratedforseveralpowersys-tems.Monte-Carlooptimizationtechniquesareappliedtoobtainmultipleminimumloadpowermargins.Theuseofloadpowermarginsensitivitiestoselectsystemcontrolsisdiscussed.

4、Keywords:voltagecollapse,sad-dlenodebifurcation,loadpowermargin,Monte-Carlooptimization.P21IntroductionP4Considertherepresentationofactiveandreactivede-Fig.1:Activeloadpowerparameterspaceforlloadmandsofanelectricpowersystemindependentlyvary-systemindicatinggivendi

5、rectionandclosestbifurcationinginahighdimensionalloadpowerparameterspace.loadincreasedirectionsfromagivenload.AgivensetofmdemandsisrepresentedbyapointA0inaparameterspaceofdimensionm.OfimportanceisthesetofcriticalloadingsCatwhichvoltagecollapsethisdistance.Thepoint

6、A,onCwhichislocallyclosestoccursbecausetheoperatingequilibriumofthepowertoA0inaEuclideansenseiscalledaclosestbifurcationsystemdisappearsinasaddlenodebifurcation[18,191.andisillustrated.ThelinejoiningA0toA*isnormaltoThesetofcriticalloadingsCiscomposedofhypersur-C.T

7、heloadincreasefromA0toA,isaworstcaseloadfacesintheparameterspace(hypersurfacesarecurvedincreaseandtheclosestdistance[A,-A01isapowersurfacesofdimensiononelessthanthenumberofdi-marginwhichmeasurestheproximityofA0tosaddlemensionsofthespace).Thedimensionofthecriticaln

8、odebifurcationandvoltagecollapse.loadhypersurfaceCisrn-1.Ifaloadforecastspecifyingthedirectionofloadin-The5busexamplepowersystemfrom[4]hasthreecreaseinl