简介:Thispaperusesthegeometricsingularperturbationtheorytoinvestigatedynamicalbehaviorsandsingularitiesinafundamentalpowersystempresentedinasingle-machineinfinite-busformulation.ThepowersystemcanbeapproximatedbytwosimplifiedsystemsSandF,whichcorrespondrespectivelytoslowandfastsubsystems.Thesingularities,includingHopfbifurcation(HB),saddle-nodebifurcation(SNB)andsingularityinducedbifurcation(SIB),arecharacterized.WeshowthatSNBoccursatPTc=3.4382,SIBatPTO=2.8653andHBatPTh=2.802forthesingularperturbationsystem.ItmeansthatthepowersystemwillcollapsenearSIBwhichprecedesSNBandthatthepowersystemwilloscillatenearHBwhichprecedesSIB.Inotherwords,thepowersystemwillloseitsstabilitybymeansofoscillationneartheHBwhichprecedesSIBandSNBasPTisincreasingtoacriticalvalue.Theboundaryofthestabilityregionofthesystemcanbedescribedapproximatelybyacombinationofboundariesofthestabilityregionsofthefastsubsystemandslowsubsystem.
简介:Thisworkdealswiththecoolingofhigh-speedelectricmachines,suchasmotorsandgenerators,throughanairgap.Itconsistsofnumericalandexperimentalmodelingofgasflowandheattransferinanannularchannel.Velocityandtemperatureprofilesaremodeledintheairgapofahigh-speedtestmachine.Frictionandheattransfercoefficientsarepresentedinalargevelocityrange.Thegoalsarereachedacceptablyusingnumericalandexperimentalresearch.Thevelocityfieldbythenumericalmethoddoesnotmatchineveryrespecttheestimatedflowmode.TheabsenceofsecondaryTaylorvorticesisevidentwhenusingtimeaveragednumericalsimulation.
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