电力系统基频铁磁谐振谐波平衡分析

,,(,430072):,,,,,:;;;:TM864:A:100326520(2006)0120094203AnalysisofHarmonicBalanceBasedFundamentalResonanceoftheFerroresonanceCircuitinPowerSystemZHANGBo,LUTiecheng,DUXiaolei(SchoolofElectricalEngineering,WuhanUniversity,Wuhan430072,China)Abstract:Theovervoltageandovercurrentgeneratedbytheferroresonancewilllowerthepowerquality,andendan2gerthefacilitiesinthepowersystem.Choosingaproperparameterofthepowersystemisthekeytopreventandsuppresstheferroresonace.Inthispaper,anadaptedharmonicbalancealgorithmisappliedtoanalyzethefunda2mentalresonanceofatypicalferroresonancecircuit.Thefundamentalresonanceregionandsafetyregionofthecir2cuitcanbefoundbyusingthisalgorithm.Onthebaseoftheharmonicbalancetheory,theproperparameterofthepowersystemcanbechosenandtheferroresonancecanbeefficientlyavoided.Itishelpfulforthepowersystemdesign.Keywords:ferroresonance;fundamentalresonance;harmonicbalance;nonlinearcircuit0,:,,,,,,,,,,[14],,,,[79]1,,,11Fig11Typicalcircuitofferroresonance1L,C,RR,E=UL(I)+UCV2I,(2)2Fig12Graphicsolutionofaferroresonancecircuit2,13,1;23,23,31,,4932120061HighVoltageEngineeringVol.32No.1Jan.2006:i=f()=a+bn,(1)(1)nn911;n35,V2I,[10,11]1,e(t)=Esin(t),:d2/dt2+d/RCdt+i/C=Ecost(2)(2),2,,,d2x/dt2+f(dx/dt,x)=F(t)(3)F(t)tT,TT,:x(t)=a0+n=1(ancos(nt)+bnsin(nt))(4)(4)(3),n,,,1:(t)=1sin(t+1)+n=1(2n+1sin((2n+1)t+2n+1)+1/(2n+1)sin(t/(2n+1)+1/(2n+1))),:(t)=1sin(t+1)(5)(5)(1)(2)d21sin(t+1)/dt2+d1sin(t+1)/RCdt+(a1sin(t+1)+b(1sin(t+1))n)/C=Ecost(6)(6),;,(2),[7]31,3.1,V2I,V2I11V2ITab.1V2Icharacteristictestofthetesttransformer/kV4.2437.0718.1609.89912.72815.556/A0.0010.0020.0030.0050.0180.045,(1)n5i=f()=a+b51a=3.8510-5,b=1.4610-10,i=f()=3.8510-5+1.4610-105(7)3,,=22.5V.s,,1.84mA3.2n=5(6),25b210+80b(a-2C)6+64(2R-2+C24+a2-2aC2)2-64C22E2=0(8)1R=1M;C=1F;E=8.57kV;=314rad/s,(8)8.33210-910-17.9876+9.7141092-7.2461012=0(9)(10),,1=27.3Vs,2=173.7Vs,3=187.6Vs13;214,,,,4.11R,G=1/R,(8)G2=25b28-2/64+5b(2C-a-2)4/4+C2E2-2-(2C2-2Ca+a2-2)=-8.4510-268+1.8210-164+7.3510-5-2-9.8510-859200613213Fig.3Magnetizationcharacteris2ticcurveofthetesttransformer42GFig14Curveof2Grelation52EFig15Curveof2Erelation62CFig16Curveof2Crelation42G,=1=181.1VsdG/d=0,G=G1=4.710-5SGG13,,;GG1,,4.2(9)EE2=25b2C-2-210/64+5b(aC-2-2-C-1)6/4+(R2C2+2+a2C-2-2-2aC-1)2=8.4410-1410-1.8210-46+9.85104252E,=1=181.3Vs=2=121.2VsdE/d=0,E1=90.6VE2=30441.9VEE1,,;E1EE23,;EE2,,EE14.3(9)642(22-E2)C2-1622(5b4+8a)C+64a22+2510+80ab6+642R-22=0C=-2-4/2,=642(22-E2);=-1622(5b4+8a);=64a22+2510+80ab6+642R-22,2C(6)2=47.4Vs,dC/d=0,C2=5.6nFCC2,1=22.5Vs,C1=3.6nF,;CC2,,CC15,,,,[1],,.[J].,2003,29(11):15217.[2],,.MATLAB/SIMULINK[J].,2004,30(9):30232.[3],,.[J].,2002,20(4):49251.[4],.[J].,2002,21(4):58263.[5]LiYunge,ShiWei,QinRui.Asystematicalmethodforsuppressingfer2roresonanceatneutral2groundedsubstations[J].IEEETransonPowerDelivery,2003,18(3):100921014.[6]MorkBA.Five2leggedwound2coretransformermodel:Derivation,pa2rameters,implementation,andevaluation[C].IEEEPESWinterMeet2ing.Tampa,FL,Jan.1998,PE24142PWRD2021221997.[7].[M].:,1987.[8]KienyC.Applicationofthebifurcationtheoryinstudyingandunder2standingtheglobalbehaviorofferroresonantelectricpowercircuit[J].IEEETrans,1991,PWRD26,(2):8662872.[9]MartiJR,SoudackAC.Ferroresonanceinpowersystems:fundamentalsolutions[J].IEEProc.C,July1991,138(4):3212329.[10].V2I[J].,1997,23(4):61264.[11],.[J].,2003,23(10):94298.(2005206220)1979:[phone]E2mail:[e-mail]69Jan.2006HighVoltageEngineeringVol.32No.1