电机学（第七版）（修订版）课件 Chapter-3-Electromechanical-Energy-Conversion-Principles、Chapter-4-Introduction-to-Rotating-Machines

Chapter3

Electromechanical-Energy-ConversionPrinciples7/10/2024ElectromechanicalEnergyConversion1IntroductionConversionofenergyfromelectricaltomechanicalformorfrommechanicaltoelectricalformthroughthemediumofelectricormagneticfieldsDevicesincludeTransducers(sensorsandspeakersForce-producingdevices(actuators)Continuousenergyconverters(motorsandgenerators)7/10/2024ElectromechanicalEnergyConversion23.1Forceandtorque

inmagnetic-fieldsystemsLorentzforcelawgivestheforceF[N]onachargeq[C]movingwithvelocityv[m/s]throughanelectricfieldE[V/m]andamagneticfluxdensityB[T]F=q(E+v×B)7/10/2024ElectromechanicalEnergyConversion3Right-handrulefordirectionofforceduetomagneticfield3.2EnergybalancemethodThismethodusesasimplerphysicalpicturebasedonenergyconservationDoesnotrequireddetailedfielddistributionsFocusesonthemostimportantforcesortorquesCanbeappliedeasilytopracticaldevicesEnergybalanceforamagnetic-fielddevice7/10/2024ElectromechanicalEnergyConversion4Signconventionisfor:electricalenergyinputandmechanicalenergyoutputInamotor,signswillbepositiveInagenerator,signswillbenegative7/10/2024ElectromechanicalEnergyConversion5SimpleenergyconversiondeviceEnergybalanceforadevice7/10/2024ElectromechanicalEnergyConversion63.3Energyinsinglyexcitedmagnetic-fieldsystemsAmagneticcircuitwithacoil,anairgap,andamovablesectionofthecoreThedeviceisanelectromagneticrelay7/10/2024ElectromechanicalEnergyConversion77/10/2024ElectromechanicalEnergyConversion8IntegrationpathsforWfldConservativesystemhasenergythatdoesnotdependontheparticularpathWeusepath2forevaluatingWfld7/10/2024ElectromechanicalEnergyConversion97/10/2024ElectromechanicalEnergyConversion103.4Determinationofmagneticforceandtorquefromenergy7/10/2024ElectromechanicalEnergyConversion11Forceortorque?Inatranslationalsystem,useforcefandpositionxInananalogousrotatingsystem,useTandangularpositionqTorqueisforcetimeradiusarm,tendingturnarotoraboutanaxis7/10/2024ElectromechanicalEnergyConversion123.5DeterminationofmagneticforcefromcoenergyAstatefunctionrelatedtoenergyiscalledcoenergyW’7/10/2024ElectromechanicalEnergyConversion13RemarksCoenergyisoftenconvenientsincecurrentisamoreeasilymeasuredthanfluxlinkageEitherformulation(energyorcoenergy)willgivethecorrectresults,ifusedcorrectlySeefigures3.10and3.11inthetexttoverifythattheygiveidenticalresults7/10/2024ElectromechanicalEnergyConversion143.6Multiplyexcitedmagnetic-fieldsystemsSystemswithmorethanonecoilarecalledmultiplyexcitedConsideradoublyexcitedrotatingsystem(twocoilsandtwoelectricalsources)butonerotatingshaft7/10/2024ElectromechanicalEnergyConversion157/10/2024ElectromechanicalEnergyConversion16Rememberthatpartialderivativesaretakenwithrespecttoonevariableasifallothervariableswereconstant7/10/2024ElectromechanicalEnergyConversion17IntegrationpathtoobtainfieldenergyforadoublyexcitedmagneticfieldsystemLinearmagneticcoreSpecialcaseoflinearmagnetics7/10/2024ElectromechanicalEnergyConversion18SystemswithpermanentmagnetsPermanent-magnetsystemswillneedspecialconsideration,sincetheenergyinthemagneticfieldwillbezeroonlyifthemagnetisdemagnetizedWemodelthisbyafictitiouswindingthathasacurrenttocounteractthefluxofmagnetforthepurposeoffindinganenergyexpression7/10/2024ElectromechanicalEnergyConversion197/10/2024ElectromechanicalEnergyConversion20Thefictitiouscurrentif=0atnormalconditions,butanonzerovalueonpath1atogivenomagneticforceonthatpath(theintegraliszeroonpath1a)Forsystemswithbothpermanentmagnetsandwindings:Useafictitiouscoiltoreplacethemagnet:(Ni)equiv=-H’cd7/10/2024ElectromechanicalEnergyConversion21Analysisnowproceedsasifthemagneticcircuithadtwocoils.Seeexample3.9fordetailsDynamicequations7/10/2024ElectromechanicalEnergyConversion22TheelectromagneticforceffldandtheinductanceL(x)arecalculatedbythemethodsdevelopedearlierTheequationsarenon-linearanddifficulttosolveSection3.9.1discussessimulationwithMATLAB/SimulinkSection3.9.2discusseslinearization(whichisequivalenttosmall-signalanalysis7/10/2024ElectromechanicalEnergyConversion23SummaryEnergyinanelectromechanicalsystemreliesoncouplingmagneticorelectricfieldWehavelookedatsingly-anddoubly-excitedmagneticfieldsystems,withtranslationalmotionorrotationinonedimensionEnergy-basedmethodssimplifytheanalysisandallowcalculationofforceortorquebydifferentiatingenergyorcoenergywithrespecttothedisplacement7/10/2024ElectromechanicalEnergyConversion24Chapter4IntroductiontoRotatingMachines7/10/2024IntroductiontoRotatingMachines254.1ElementaryConceptsRotatingmachines:voltagesareinducedinwindingsorgroupsofcoilsbyrotationofamagneticfieldpastawindingorrotationofawindingthroughthefield,orbydesigningthemagneticcircuitsothatthereluctancevarieswithrotationoftherotorSincethefluxlinkingacoilchangescyclically,atime-varyingvoltageisinducede=dl/dtAgroupsuchcoilscarryingACcurrentsisoftencalledanarmaturewinding7/10/2024IntroductiontoRotatingMachines267/10/2024IntroductiontoRotatingMachines27Statorofa100-MVAthree-phasesynchronousgeneratorunderconstruction.(GeneralElectricCompany.)Armatureofadcmotor.(BaldorElectric/ABB)InanACsynchronousmachine,thearmatureistypicallyonthestatorInaDCmachine,thearmatureislocatedontherotorDCandsynchronousmachinestypicallyhavefieldwindingscarryingDCtosetupthemainoperatingflux,usuallylocatedonthestatorforDCmachinestherotorofACsynchronousmachinesSomemachines,especiallymotors,usemagnetsinsteadoffieldwindingsInductionmachinesdonothavefields,butproducefluxsimilarlytotransformersManytypesofmachinesexist,butverysimilarphysicalprinciplesgoverntheirperformance7/10/2024IntroductiontoRotatingMachines284.2IntroductiontoACandDCmachinesTraditionalacmachinesareclassifiedassynchronousorinductionmachinesSynchronousmachines:rotorcurrentsaresupplieddirectlyfromthestationaryframe,througharotatingcontactforexampleInductionmachines:rotorcurrentsareinducedintherotorwindingsbymagneticinductionfromthestatorwindings7/10/2024IntroductiontoRotatingMachines29Fieldhasasinglepairofpoles,soitisatwo-polemachineArmatureherehasasinglecoilofNturnsFieldisexcitedthroughbrushescontactingsliprings,orbybrushlessexcitationsystemIftheair-gapfluxissinusoidalinspace,theinducedvoltageinthearmatureissinusoidalintime,asthemachinerotatesatconstantspeed7/10/2024IntroductiontoRotatingMachines30Schematicviewofasimple,two-pole,single-phasesynchronousgeneratorManymachineshavemorethantwopoles.Afour-polesynchronousmachine,whichwillrotateathalfthespeedofatwo-polemachineifthefrequencyisthesame7/10/2024IntroductiontoRotatingMachines31IdealizedfluxdistributionandwaveformofgeneratedvoltageFour-polesingle-phasesynchronousgeneratorForconvenienceinanalyzingmachineswithmorethantwopoles,defineelectricalangleandelectricalspeed,asfollows:7/10/2024IntroductiontoRotatingMachines32SubscripteindicateselectricalunitswhilemindicatesmechanicaloractualunitsThisisusefulsincetherearepoles/2completewavelengthsorcyclesinone(mechanical)revolutionInductionMachinesStatorwindingsareessentiallythesameasasynchronousmachineRotorwindingiselectricallyshort-circuitedandoftenhasnoexternalconnections,derivingitsexcitationbymagneticinductionAlsocalledasynchronousmachinesCommonconstructionforaninductionmotorusesthesquirrel-cagerotorwithnoexternalconnectionSquirrel-cageinductionmotorsarethemostcommontypeofmotorusedtoday7/10/2024IntroductiontoRotatingMachines33CagerotorhasbarsthatareshortedbyendringsInexpensivetoconstructandyetveryruggedRotorcurrentsareinducedastherotorslipspastthestatorfluxwave,whichrotatesatsynchronousspeedFluxwavesetupbytherotorcurrentsrotatesatsynchronousspeed,andinteractswiththestatorfluxtoproducetorqueThismachineisverysimilartoatransformer,butwithrotationofwindings7/10/2024IntroductiontoRotatingMachines34Cutawayviewofa460-V,7.5hpsquirrel-cageinductionmotor.DCMachinesAsimplifieddcgeneratorarmaturewinding(asinglecoilofNturns)isshownThecommutatorisacylindricalstructurewithtwosegmentsattachedtotherotor,servingasamechanicalrectifiertoconverttheacinthearmaturecoiltodcatthestationarybrushes7/10/2024IntroductiontoRotatingMachines35ElementarydcmachineDCinthefieldsetsupastationaryfluxThecommutatorcausesarmaturefluxtobefixedinspacebetweenthefieldpolesInteractionoffluxessetsuptorque7/10/2024IntroductiontoRotatingMachines36Air-gapfluxdistributionandvoltagewaveform4.3MMFofDistributedWindingsPracticalarmaturewindingsareusuallydistributed,orspreadoveranumberofslotsConsideronephaseofanacthree-phasetwo-polewinding(calledafull-pitchwindingsinceeachcoilspanspradians)FourieranalysisgivesthespacefundamentalcomponentoftheMMF,developedinAppendixB7/10/2024IntroductiontoRotatingMachines377/10/2024IntroductiontoRotatingMachines38Themmfofonephaseofadistributedtwo-pole,three-phasewindingwithfull-pitchcoils.7/10/2024IntroductiontoRotatingMachines39Thepeakvalueofthespacefundamentalisgiveninthefollowingequation,wherekwisthewindingfactorthataccountsforthedistributionofthewinding(seeAppendixBfordetails)ThefactorkwNphistheeffectivenumberofseriesturnsperphaseTypicalvaluesforkware0.85to0.90ConsiderthedcmachinewithanarmaturewindingdistributedovermanyslotsAnapproximationtothemmfisasawtoothwave7/10/2024IntroductiontoRotatingMachines40Crosssectionofatwo-poledcmachine7/10/2024IntroductiontoRotatingMachines41Currentandmmfwaveofidealizeddcmachine4.4MagneticFieldsinRotatingMachineryMachinewithauniformairgapandasinglefull-pitchN-turncoilonahighlypermeableironcore7/10/2024IntroductiontoRotatingMachines42Diagramofmachine7/10/2024IntroductiontoRotatingMachines43MMFandfielddistributionsSpacefundamentalfieldpeakvalue:4.5RotatingMMFWavesSingle-phasewindingproducesapulsatingMMFthatcanberesolvedintotwoequalrotatingwaves,rotatinginoppositedirectionsPolyphasewindingproducesarotatingMMFthathasconstantamplitudeandconstantspeedinsteadystateThefigureonthenextslideshowsagraphicalexplanationwhilethetextgivesamathematicalderivationforthethree-phasecase7/10/2024IntroductiontoRotatingMachines447/10/2024IntroductiontoRotatingMachines45