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Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-0PowerPointSlidestoaccompanyElectricMachineryFourthEditionStephenJ.ChapmanChapter2TransformersCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-1Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-2LaminatedironcorePrimarywindingNPSecondarywindingNSLoadSupplyN1N2BasiccomponentsofsinglephasetransformerCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-3PrimaryWindingSecondaryWindingMulti-layerLaminatedIronCoreX1X2H1H2WindingTerminalsSinglephasetransformerarrangementCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-4051015201000100Vpt()Vst()tmillis051015201000100Vpt()Vst()tmillisH1H2X2X1VpVsH1H2X2X1VpVs(a)(b)PolarityfortransformerCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-5IroncoreTerminalsSecondarywindingInsulationSmalltransformerconstructiona)Lamination,b)IroncorewithwindingCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-6A)CoretypeB)ShelltypeSinglephasetransformerconstructionCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-7HolderPrimaryWindingSecondaryWindingWiresInsulationWindingConstructionCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-8WindingIroncorebehindthesteelbarRadiatorSteeltankInsulationBushingOilInsulatedandcooledtransformerCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-9MetalbarExteriorporcelaintubeInteriorporcelaintubeFlangePorcelaintransformerbushingParametersPNINUNfNCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-10Transformerwithopensecondary.Figure2.4Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-11OperationofunloadedtransformerTheprimarywindingsisconnectedtosupplyandthesecondwindingsisunloaded.Theprimarycurrentiscalledasunloadedcurrent.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-12Ф1σLeakagefluxintherealtransformerCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-13TheinductiveEMFofunloadedtransformerdtdNRieRiu1101101KNNeeUU212121TurnratioExcitationcurrentarIII000UnloadedcurrentCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-14Leakageresistance,Leakageflux,LeakagereactanceLeakageresistance–TheresistanceprimarywindingsThevoltageequationofprimary:11101EErIUImagingareactancewhichproducetheleakageEMF01112INL01011IXJILJEThatis:Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-15No-loadphasordiagram.Figure2.5Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-16ThephasediagramofanunloadedtransformerTheequationofanunloadedtransformer2111101)(EEEjxrIUCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-17TheequivalentcircuitofanunloadedtransformerCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-18Idealtransformerandload.Figure2.6Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-19Primary-SupplySecond-LoadCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-20physicalreasoningThereiscurrentinsecondarywindingswhenthesecondaryisloaded.Consequently,theEMFisproduced.Therefore,thenewMMFisconstructedbybothprimarycurrentandsecondarycurrent.Thatis:21FFFmCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-21Thereisstillfluxleakageinprimarywindings.Whilethefluxleakageinsecondarywindingsisavailablenowbecauseoftheloading.111IjxE222IjxECopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-22EquivalentofvoltageAccordingKirchhoff’svoltagelaw,theequationsofprimaryandsecondarycanbeshown:1111111111111)(EZIUEjxRIERIEU2222222222222)(ZIEUEjxRIERIEUCopyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-23Thetotalequationsoftransformer:1111ZIEU2222ZIEUKEE21012211INININmmZIE0LZIU22Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-24WindingsconvertItisdifficulttogetthephasediagramandanalysisbyusingthetotalequationsoftransformer.Thealgorithmofwindingconvertisadoptedinthissection.Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-25Currentconverting:MMFispreservedConvertingofEMF,voltageandresistance2222ININ221222221IKINNINNIKNNNNEE212222Copyright©TheMcGraw-HillCompanies,Inc.Permissionrequiredforreproductionordisplay.2-26TheconvertedequationsoftransformerThepowerandlossofsecondarywindingsarepreserved1111EZIU2222ZIEU021IIImZIEE021''2'2LZIUCopyright©TheM