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1、http://www.paper.edu.cnComputationofEllipticFunctionsforSubharmonicBifurcationinaPower1TransmissionSystemXingwuChen,WeinianZhangDepartmentofMathematics,SichuanUniversityChengdu,SichuanP.R.China610064matzwn@tom.comAbstractInordertocontroloscillationwithlargedeviation,anonlinearnonautonom
2、ouspowertransmissionsystemisdiscussed.Inthispaperweshowthetechniquesincomputationofellipticfunctions,whichareemployedindeterminingsubharmonicbifurcationofthesystem.Keywords:Powertransmissionsystem,nonlinearoscillation,subharmonicbifurcation,ellipticfunctions1.IntroductionPowertransmissi
3、onsystemsoscillateperiodicallywhentheyrunnormally.However,sometimestheyperformirregularly(see[1,2,3]),oscillatingpersistentlywithnodefiniteamplitudeandnodefinitefrequency,oroscillatingsuddenly,randomlyandchaotically.Disintegrationcouldbecausedinsomeseriouscases.Asreportedin[4],in1966whe
4、nUSNorthwestSystemandSouthwestSystemwereconnectedtogetherastrangeoscillation,which"theoperatorhadneverobserved",occurredsixtimesaminuteanditfinallyresultedindisintegration.SimilarphenomenaalsooccurredinChina[2].Sincesuchmorbidoscillationsareveryharmfultosecurityofpowertransmissionsystem
5、s,recentlygreateffortsaremadetoresearchcomplicatedoscillationsofpowertransmissionsystemsbothintheoryandinpractice.Thepeoplewanttounderstandthemechanismdeeply,findmoreeffectivemethodstocontroloscillations,anddesignnewcontroldevicesforpowertransmissionsystems.Actually,apowertransmissionsy
6、stemdisplaysacomplicatedmechanismandismatchedwithnonlinearmathematicalmodels.In[2]thefollowingnonlinearsimplepowertransmissionsystemisconsideredδ”=-(Ps/H)sinδ-(D/H)δ’+Pm/H+(Pe/H)cos(βt),(1)whereδistherelativeanglebetweenvoltageofgeneratorofsystem1andvoltageofgeneratorofsystem2attimet,H,
7、Dareequivalentrotationalinertiaandequivalentdampcoefficientrespectively,Psisthemaximumofelectricpowertransmittingfromsystem1tosystem2,Pmismachinerypowerofgenerator1,Peisamplitudeofperturbationpowerandβisfrequencyofperturbation.Asusualweconsidertransmissionoflargepowerinsystemsa
