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2819Vol.28No.19200410PowerSystemTechnologyOct.20041000-3673200419-0024-05TM726A470·4051430074UNBALANCEISSUECAUSEDBYUN-TRANSPOSEDTRANSMISSIONLINESANDITSSOLUTIONDINGHong-faDUANXian-zhongSchoolofElectricalandElectronicEngineeringHuazhongUniversityofScienceandTechnologyWuhan430074HubeiProvinceChinaABSTRACTUnderlight-loadedconditionsorattheinitialphaseofpowersystemblackstart,thenegativesequencecurrentcausedbyunbalancedparametersoftheun-transposedlongdistanceEHVtransmissionlinesmayleadtocascadingtrippingofanumberofgeneratorsthenbringaboutlargeareablackoutsordamagesomeutilizationequipments.Thenegativevoltageandcurrent,causedbytheunbalancedparametersoftransmissionlineunderdifferenttransmittedpoweranddifferentlengthoftransmissionline,arecalculatedandanalyzedbymeansofthreephasepowerflowcalculationprogram.Thepossibilityofthemethodtoreducethenegativesequencecomponentbyrationallyconfiguringtheserialcompensationelementsandsettinguptheparametersofthepassivereactivepowercompensationelementsatbothendsoftransmissionlineisresearched.Theresultsfromcalculationandsimulationshowthattheproposedmethodcaneffectivelyrestrainthenegativesequencevoltageandcurrentcausedbyunbalancedparametersoftransmissionline.KEYWORDSHigh-voltagetransmissionlinesUnbalanceThree-phasepowerflowSeriescompensationShuntcompensationPowertransmissionanddistributionPowersystem1[1-3][4][5][6,7][8][9][10]2003034066SupportedbyChinaPostdoctoralScienceFoundation(CPSF)(2003034066)28192522.1[1]2.211zaazbbzccxabxbcxcaba0bb0bc0babbbcbcaijabcABCbbc2bab2bca2bab2bbc2bca2ba02ba02bb02bb02bc02bc02zaazbbzccxbcxabxcaij••1Fig.1Theequivalentcircuitofthree-phasetransmissionlines12ΠijYijYj0Yi0Uabc,jUabc,iIabc,jIabc,i2ΠFig.2TheΠequivalentcircuitofthree-phasetransmissionlines1aaabca1abbbbccabcccjjjjjjijijzxxxzxxxz−−==YZ(1)a0abcaabcab000abbcabbcc0cabcbcca1j(11jj222)1j(11jj222)1j(11jj222)ijbbbbbbbbbbbbbbb+−−++==−−++−−+YY(2)a,iU&b,iU&c,iU&a,jU&b,jU&c,jU&a,iI&b,iI&c,iI&a,jI&b,jI&c,jI&abc,iUabc,jUabc,iIabc,jITabc,a,b,c,[,,]iiiiUUU=U&&&Tabc,a,b,c,[,,]jjjjUUU=U&&&Tabc,a,b,c,[,,]iiiiIII=I&&&Tabc,a,b,c,[,,]jjjjIII=I&&&abc,abc,abc,abc,iiLjj=IUYIU(3)YL00ijiijLijijj+−=−+YYYYYYY(4)500kV1(1)(2)(4)3×LGJQ–400d=400mmD=11mLGJQ–400r=13.6mmH=40m[11]raa0=rbb0=rcc0=0.0263Ω/kmxaa0=xbb0=xcc0=0.564Ω/kmxab0=xbc0=0.283Ω/kmxca0=0.240Ω/kmba00=bc00=1.846×10−6S/kmbb00=1.568×10−6S/kmbab0=bbc0=0.831×10−6S/kmbca0=0.372×10−6S/km0zaa0=zbb0=zcc0=raa0+jxaa0=rbb0+jxbb0=26PowerSystemTechnologyVol.28No.19rcc0+jxcc01(4)2.3500kV1000MVA33USURISIR[1]0.95ΠΠΠΠURUSISIR12…3Fig.3Simplifiedmodelofpowersystemusedtocalculateunsymmetricalparametersofthetransmissionlines4500kVL100km200km300km500kmISISURURPL4(a)10%4(a)200km2000MVA4%4(b)200km1000MVA2%0.00.40.81.21.62.002468L=100kmL=200kmL=300kmL=500km(b)0.00.40.81.21.62.0024681012L=100kmL=200kmL=300kmL=500km(a)(IS_/IS+)/%(UR_/UR+)/%PL/puPL/pu281927TCSC(3)110,0,0110,0,0()()iiijiijjjijijj−−+−+−−−+−+−+−=−+IUSYYSSYSIUSYSSYYS(5)I+−0,i=[I+,i,I−,i,I0,i]TI+−0,j=[I+,j,I−,j,I0,j]TU+−0,i=[U+,i,U−,i,U0,i]TU+−0,j=[U+,j,U−,j,U0,j]TSS−1221113111αααα=S12211111αααα−=Sα=ej2π/3(5)SYijS−1S(Yij+Yi0)S−1S(Yij+Yj0)S−1SYijS−1SYi0S−1SYj0S−1A1=zaaA2=zbbA3=zccB=jxab=jxbcC=jxca2223321231312221121ijijAABBCABBACBCABAACBCABBACBCABAAB∆−−−−==−−−−−−YZ(6)222123132()2ijAAAAABBCAC∆==−++−ZTCSC(1)ZijA1A2A3TCSCYijYij+Yi0Yij+Yj0TCSCTCSCYijTCSC(6)YijA1A2A313223222313AABACBCABAABAAC=−=−−=−(7)(7)21322221214()2BBCBCAACABCBAAC−+++===+−==(8)(8)TCSC(8)5TCSCL200km300km500km0.00.40.81.21.62.0024681012L=200kmL=300kmL=500km0.00.40.81.21.62.00.00.10.20.30.40.50.6L=200kmL=300kmL=500km(b)(IS_/IS+)/%(a)(UR_/UR+)/%PL/puPL/pu5TCSCFig.5NegativesequencecurrentandvoltageaftercompensationbyTCSC5(a)4(a)Yi0Yj0Yi0Yj0Yi0Yj0YijYij28PowerSystemTechnologyVol.28No.195(b)4(b)YijYijTCSCTCSCTCSCYijYi0Yj06Yi0Yj0y1y3y2y4y5y6abc6Yi0Yj0Fig.6PrinciplediagramforapplyingpassiveelementstoregulatethematrixesYi0andYj0y1y2y3y4y5y613413C1125232326j()jjjj()jjjj()yyyyyyyyyyyyyyy++−−=−++−−−++Y(9)Yi0Yj0000C0Cijij′′==+=+YYYYYY(10)0i′Y0j′Yy1y2y3y4y5y610i−′SYS10j−′SYSy1=y2=y4=y6=0.0y3=(bab−bca)/2y5=(ba0−bb0)/27TCSC7(a)YijYij+Yi0Yij+Yj05(a)7(a)YijYij7(b)5(b)Yij0.00.40.81.21.62.00.00.10.20.30.40.50.6L=200kmL=300kmL=500km(a)0.00.40.81.21.62.00.00.10.20.30.40.50.6L=200kmL=300kmL=500km(b)(IS_/IS+)/%(UR_/UR+)/%PL/puPL/pu7TCSCFig.7NegativesequencecurrentandvoltageaftercompensationbyTCSCandshuntpassivedevices4123[1]AdibiMMMilaniczDPVolkmannTLAsymmetryissuesinpowersystemrestoration[J]IEEETransonPowerSystems199914(3)1085-109154continuedonpage5454PowerSystemTechnologyVol.28No.19EMSSCADAEMS4[1]8.14[J]200327(10)8-11YinYonghuaGuoJianboZhaoJianjunetalPreliminaryanalysisoflargescaleblackoutininterconnectednorthAmericapowergridonAugust14andlessonstobedrawn[J]PowerSystemTechnology200327(10)8-11[2][J]200327(9)T2-T6HuXuehaoRethinkingandenlightenmentoflargescopeblackoutininterconnectednorthAmericapowergrid[J]PowerSystemTechnology200327(9)T2-T6[3]8.14[A][C]2004[4][J]200428(4)58-62Fe