电路基础chapter9

Chapter9BalancedThree-PhaseCircuitsAbasicthree-phasecircuitThree-phasevoltagesourceThree-phaseloadThree-phaselineFig.10.1Athree-phasegeneratorFig.10.2Thegeneratedvoltagesare120oapartfromeachotherChapter9BalancedThree-PhaseCircuits9.1Basicconceptsofthree-phasecircuit9.2AnalysisoftheWye-Wye(Y-Y)Circuit9.3AnalysisoftheWye-Delta(Y-△)Circuit9.4BalanceDelta-deltaConnection9.5BalanceDelta-WyeConnection9.6SummaryofBalanceConnection9.7PowerinBalanceSystem9.8UnBalancethree-phaseSystemChapterObjectiveChapterContents1.Basicconceptsofthree-phasecircuit2.AnalysisoftheWye-Wye(Y-Y)circuit3.AnalysisoftheWye-Delta(Y-△)circuitLearningthedistinctionbetweensingle-phaseandpolyphasesystemsBecomingfamiliarwithworkingwithbothY-and△-connectedthree-phasesourcesBecomingfamiliarwithworkingwithbothY-and△-connectednetworksMasteringthetechniqueofper-phaseanalysisofthree-phasesystems9.1Basicconceptsofthree-phasecircuit1.Balancedthree-phasevoltagesaUcUbUaUbUcUHaveequalamplitudesandfrequenciesEachofthethreevoltagesis120°outofphasewitheachoftheothertwo.a-phasevoltagec-phasevoltageb-phasevoltagePhasesequenceChoosea-phaseasthereferencephase.VUUoaa0abc(orpositive)phasesequence(正序):theb-phasevoltagelagsthea-phasevoltageby120o,andthec-phasevoltagelagstheb-phasevoltageby120o.VUUoab120VUUoac120acb(ornegative)phasesequence(反序):theb-phasevoltageleadsthea-phasevoltageby120o,andthec-phasevoltageleadstheb-phasevoltageby120o.VUUoab120VUUoac120120°120°0cbaUUU0cbauuu2.Three-phasevoltagesourcesTwobasicconnectionofanidealthree-phasesource+-aU+-+-bUcUabcY-connectedsource-++aU-bUcUabc+-△-connectedsourceNeutralterminal(中点)Lineterminal(端线)3.Three-phaseloadsTwobasicconnectionofthree-phaseloadsY-connectedsource△-connectedsourceNeutralterminal(中点)Lineterminal(端线)abcaZbZcZabcaZbZcZo4.Three-phasecircuitSourceLoadYYY△△Y△△BalancedThree-PhaseCircuits：balancedthree-phasevoltages,balancedthree-phaseloads+-aU+-+-bUcUabcabcaZcZbZY-YconnectionLinevoltage（线电压）:thevoltageacrossanypairoflines（端线）.ABUBCUCAU+-ABU-+BCU+-CAUPhasorvoltage(相电压):voltageacrossasinglephase每相元件两端电压。bUcUaULinecurrent（线电流）:thecurrentinasingleline(端线）.AIAIBICICIBIPhasorcurrent（相电流）:thecurrentinasinglephase。aIaIbIcIbIcIbalancedthree-phasecircuitsthree-phasecircuits三相电路平衡三相电路three-phasesource三相电源three-phaseload三相负载abc(orpositive)phasesequence正序acb(ornegative)phasesequence反序theb-phasevoltagelagsthea-phasevoltageby120o,andthec-phasevoltagelagstheb-phasevoltageby120oaUbU120°120°cUtheb-phasevoltageleadsthea-phasevoltageby120o,andthec-phasevoltageleadstheb-phasevoltageby120oaUbU120°120°cUSometermsThephrasesequenceisthetimeorderinwhichthevoltagespassthroughtheirrespectivemaximumvalues+-aU+-+-bUcUabcabcaZbZcZY-△connectionAIBICIaIbIcIaIbIcIPhasecurrentLinecurrentAIBICIPhasevoltage+-ABU+-bULinevoltage+--+cUaU-+BCU+-CAUABUBCUCAUbUcUaU-++aU-bUcUabc+-abcaZcZbZ△-Yconnection-++aU-bUcUabc+-abcaZbZcZ△-△connection9.2AnalysisoftheWye-Wye(Y-Y)CircuitY-Yconnection(three-phasorthree-wirecircuit)+-aU+-+-bUcUabN+-aU+-+-bUcUabcabcZZZN’AbalancedY-Ysystemisathree-phasesystemwithabalancedY-connectedsourceandabalancedY-connectedload.+-aU+-+-bUcUabN+-aU+-+-bUcUabcabcZZZN’ApplythenodalanalysisandselectthenodeN’asreferencenode,wehave0)(31/1/1/1///cbacbaNNUUUZZZZUZUZUUThuswecanalsogetthefollowingequivalentcircuit+-aU+-+-bUcUabN+-aU+-+-bUcUabcabcZZZN’ThuswecangetthefollowingequivalentcircuitY-Yconnection(three-phasorfour-wirecircuit)Supposeareknownandintheabcsequences,trytocalculatebUcUaUaIbIcI(1)PhasorcurrentsAIBICI(2)LinecurrentsABUBCUCAU(4)Linevoltage+-aU+-cUabN++-+-bUabcabcZZZN’Z0+-CAU+-ABU-+BCUAICIaIbIcIBI-AU++-BUCU+-(3)PhasorvoltageAUBUCU+-aU+-cUabN++-+-bUabcabcZZZN’Z0+-CAU+-ABU-+BCUAICIaIbIcIBI-AU++-CUBU+-Applythenodalanalysis,wehave0/1/1/1/1///ZZZZZUZUZUUcbaNN0/111ZZUUUcba0cbaUUU0NNUSinceThuswecangetthefollowingequivalentcircuitThuswecangetthefollowingequivalentcircuitItiseasytofindphasecurrentsandphasevoltage.AI+-aU+-cUabN++-+-bUabcabcZZZN’+-CAU+-ABU-+BCUCIaIbIcIBI-AU++-CUBU+-Z0Athree-phasecircuitchangesintothreesinglephasecircuitsnow.(一个三相电路——三个单相电路)→+-cU+-ccZCIcI+-CUAI-aUN+aZN’aI-AU+NN’+-bUbZbIBIBU+-NN’AI+-aU+-cUabN++-+-bUabcabcZZZN’+-CAU+-ABU-+BCUCIaIbIcIBI-AU++-BUCU+-phasevoltages：aAUU00120120AabBUUUU00120120AacCUUUUphasecurrents：ZUIAa00120120aABbIZUZUI00120120aACcIZUZUITogetphasorvoltageandphasorcurrents:justcalculateonephasevoltageandphasecurrent,thenwecanwriteotherphasorvoltagesandphasorcurrentsdirectly.AI+-aU+-cUabN++-+-bUabcabcZZZN’+-CAU+-ABU-+BCUCIaIbIcIBI-AU++-BUCU+-linecurrents：aAII0120AbBIII0120AcCIIITogetlinecurrents:justcalculateonephasecurrent,thenwecanwriteallofthelinecurrentsdirectly.linevoltages：+-aU+-cUabN++-+-bUabcabcZZZN’+-CAU+-ABU-+BCU-AU++-BUCU+-ABbabaABUUUUUU