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Chapter9Single-andTwo-PhaseMotors7/10/2024Single-PhaseInductionMachines1Qualitativeexaminationofsingle-phaseinductionmotorSquirrel-cagerotorbutonlyonephaseonthestatorStatorMMFwillpulsate,producingtwoequalforward-andbackward-rotatingMMFwavesNostartingtorque7/10/2024Single-PhaseInductionMachines2Oncethemotorisrunning,itwillproduceaveragetorquetosustaintherotationasshowninthetorque-speedcurvesbelow7/10/2024Single-PhaseInductionMachines3Startingandrunningperformanceofsingle-phasemotors1-phaseinductionmotorsclassifiedbystartingmethod:Split-phasemotorCapacitor-typemotorShaded-polemotor1-phasesynchronousmotors:Synchronous-reluctancemotorHysteresismotor7/10/2024Single-PhaseInductionMachines4Split-phaseinductionmotorMainwindingandauxiliarywindingAuxiliarywindinghasahigherresistancetoreactanceratiothanthemainwinding,switchedoutatspeedGivesasmallphaseshiftthatproducesmoderatestartingtorque7/10/2024Single-PhaseInductionMachines5Capacitor-startinductionmotorMainwindingandauxiliarywindingAuxiliarywindinghasaseriescapacitor,switchedoutatspeedGivesasignificantphaseshiftthatproduceshighstartingtorque7/10/2024Single-PhaseInductionMachines6Permanent-split-capacitorinductionmotorMainwindingandauxiliarywindingAuxiliarywindinghasaseriescapacitor,notswitchedout(essentiallyatwo-phasemotor)Givesasignificantphaseshiftthatproducesgoodrunningperformance7/10/20247Single-PhaseInductionMachinesCapacitor-start,capacitor-runinductionmotorMainwindingandauxiliarywindingAuxiliarywindinghastwoseriescapacitors,oneswitchedoutatspeedGivesasignificantphaseshiftthatproduceshighstartingtorqueandgoodrunningperformance7/10/2024Single-PhaseInductionMachines8Shaded-polemotorSmall,inexpensive,lowtorque,lowefficiencyShadingpolehasoneshortedturncausingaphaselag(byLenz’slaw)thatgivesasmallrotationalfluxforstarting7/10/2024Single-PhaseInductionMachines9Self-startingsynchronous-reluctancemotorStartsasaninductionmotorusingoneofthemethodsalreadydiscussed,thenrunsasasynchronousreluctancemotor7/10/2024Single-PhaseInductionMachines10HysteresismotorRotorissmoothcylinderofmagneticallyhardsteel:HysteresisinthesteelproducesaphaselagoftherotorfluxStatorneedsinusoidalwindingdistributionTwo-phasemotor:OperatessmoothlyasasynchronousmotorSingle-phasemotor:Statorisusuallypermanent-split-capacitorPracticalinsmallsizes7/10/2024Single-PhaseInductionMachines117/10/2024Single-PhaseInductionMachines12Hysteresismotorconfigurationandtorque-speedcharacteristicRevolving-fieldtheoryofsingle-phaseinductionmotorsThetworevolvingfields,oneforwardandtheotherbackwards,eachinducesitsownrotorcurrentsandproducesitsowninductionmotoractionWeconsiderthemachine’smainwinding,atfirstconsideringtherotorstationary,showingitsforwardandbackwardfieldeffects,thenconsidertherunningconditions7/10/2024Single-PhaseInductionMachines137/10/2024Single-PhaseInductionMachines14Single-phaseinductionmotor(a)rotorblocked,(b)rotorblockedshowingeffectofbothrotorfields,(c)runningconditions7/10/2024Single-PhaseInductionMachines15Subscriptfmeanstheforward-rotatingcomponentandbmeansthebackward-rotatingcomponent,andthesymbol||meansconnectedinparallelwith.Slipoftherotorwithrespecttotheforward-rotatingcomponentissandwithrespecttothebackward-rotatingcomponentis2-s.7/10/2024Single-PhaseInductionMachines16Two-phaseinductionmotorsSymmetricalcomponentscanbeusedtoanalyzeunbalancedtwo-phasemotors,wherethephasesareaandb:7/10/2024Single-PhaseInductionMachines177/10/2024Single-PhaseInductionMachines18Synthesisofanunbalancedtwo-phasesystemfromthesumoftwobalancedsystemsofoppositephasesequence7/10/2024Single-PhaseInductionMachines197/10/2024Single-PhaseInductionMachines20Resolutionofunbalancedtwo-phasevoltagesintosymmetricalcomponents.Seeexample9.3andpracticeproblem9.3inthetextforcomputationsusingMatlab.SummaryThesingle-phaseinductionmachineisdiscussedincluding:Methodsofproducingstartingtorquesuchassplit-phaseandcapacitor-typemotorsTheoryofdoublerevolvingfieldsforanalysisofinductionmotorrunningonitsmainfieldSingle-phasesynchronousmotorswerediscussedbrieflyaswastheuseofsymmetricalcomponentsforanalysisofunbalancedtwo-phasemotors7/10/2024Single-PhaseInductionMachines21Chapter10SpeedandTorqueControl7/10/2024SpeedandTorqueControl22ControlofDCmotorsSpeedcontrolisoftenperformedwithfield-currentcontrol(shunt,compoundorseparatelyexcited),armature-circuitresistancecontrol(series,shunt,compound,orpermanentmagnet),orarmature-terminalvoltagecontrol(shunt,separatelyexcited,orpermanentmagnet)Armature-circuitresistancecontrolismostoftenusedwithseriesmotors7/10/2024SpeedandTorqueControl23Field-currentcontrol:7/10/2024SpeedandTorqueControl24Field-currentcontrolincreasestheno-loadspeedbyweakeningthefield(reducingif)Armature-terminalvoltagecontroldirectlycontrolstheno-loadspeedbychangingVa7/10/2024SpeedandTorqueControl25Inaseparately-excitedmotor,thearmaturevoltagecontrolcanbeuseduptoratedvoltage,followedbyfieldweakeningtoobtainhigherspeeds7/10/2024SpeedandTorqueControl26wmTBasespeedFieldweakeningArmaturevoltagecontrolPowerlimitTorquelimit7/10/2024SpeedandTorqueControl27Torque(a)andpower(b)limitationsofcombinedarmature-voltageandfield-currentcontrol7/10/2024SpeedandTorqueControl28Armature-voltagecontrolimplementedwithafullH-bridgeinverter.Thedcvoltagemaybearectifieroutputfedbyanacinput.7/10/2024SpeedandTorqueControl29Blockdiagramforaspeed-controlsystemforaseparatelyexcitedorshuntdcmotorBlockdiagramofasimplespeedcontrollerOverallDCmotorspeedcontrolsystemwithdirectcontrolofmotortorque7/10/2024SpeedandTorqueControl30Controlofsynchronousmotors7/10/2024SpeedandTorqueControl31Three-phasevoltage-sourceinverterforvariable-frequencycontrolofanACmotorTomaintaintheair-gapfluxwhenthefrequencyischangedrequiresacorrespondingchangeinvoltage7/10/2024SpeedandTorqueControl32Ifthevoltagefixedatitsratingandthefrequencyisincreased,thefluxwilldrop:Constantvolts-per-hertzmodekeepsratedflux:7/10/2024SpeedandTorqueControl33Powerandtorqueinperunitofratingsplottedversusspeed.Aboveratedspeed,frequencyisincreasedwhilevoltageisatratedvalue.Belowratedspeed,constantvolts-per-hertzcontrolisused.TorquecontrolAppendixCshowsequationsind-qcoordinates:ld=Ldid+Laf
iflq=Lq
iqlf=(3/2)Laf
id+Lffif7/10/2024SpeedandTorqueControl347/10/2024SpeedandTorqueControl35Thisresult(whichisderivedinthetext)showsthatinanon-salientpolemachinetorqueisproducesbytheq-axiscurrentcomponentonlyTheimportanceofthisresultisduetotheabilitytolocatethed-qaxes,forexamplewithapositionsensorWiththeadventofrapidandinexpensivedigitalcomputation,thedqtransformationcanbecomputedinreal-timeforfield-orientedcontrolofACmotors,illustratedinthenextslidefortorqueandspeedcontrol7/10/2024SpeedandTorqueControl367/10/2024SpeedandTorqueControl377/10/2024SpeedandTorqueControl38Field-orientedcontrollerforapermanent-magnetsynchronousmotorControlofinductionmotors7/10/2024SpeedandTorqueControl39Pole-changingmotorsswitchbetweenseveralspeedsbychangingthenumberofpolesFigures(a)and(b)belowillustratechangingfrom4to2polesbyreversingconnectionofcoila’a’Variable-frequencycontrolChangingthefrequency,asintheconstantvolts-per-hertzcontroldiscussedearlierisaneffectivemethodforcontrollingthemotorspeedFiguresbelowshowtorque-speedcurvesforinductionmotorswith(a)neglectingR1and(b)includingR1Thistypeofcontroliswidelyusedforvariablespeedinductionmotordrives7/10/2024SpeedandTorqueControl407/10/2024SpeedandTorqueControl41Thewholetorque-speedcurveisshiftedtoalowerspeedasthefrequencyandvoltagearedecreasedAtlowfrequenciesR1becomessignificantandthepeaktorquedropsSimplyreducingvoltagemakesadrasticreductionintorquewhilereducingthespeedslightlyWound-rotormotorcanuseexternalresistorin
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