E283C5.docx

E283C5.docx

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E283C5

CHAPTER5–SYNCHRONOUSGENERATOR

Summary:

1.SynchronousGeneratorConstruction

2.TheSpeedofRotationofaSynchronousGenerator

3.TheInternalGeneratedVoltageofaSynchronousGenerator

4.TheEquivalentCircuitofaSynchronousGenerator

5.ThePhasorDiagramofaSynchronousGenerator

6.PowerandTorqueinSynchronousGenerator

7.MeasuringSynchronousGeneratorModelParameters

8.TheSynchronousGeneratorOperatingAlone

-TheEffectofLoadChangesonaSynchronousGeneratorOperatingAlone.

9.ParalleloperationofACGenerators

-Theconditionsrequiredforparalleling

-Thegeneralprocedureforparallelinggenerators

-Frequency-powerandVoltage-ReactivePowercharacteristicsofasynchronousgenerator.

-Operationofgeneratorsinparallelwithlargepowersystems

-Operationofgeneratorsinparallelwithothergeneratorsofthesamesize.

10.SynchronousGeneratorRatings

-TheVoltage,SpeedandFrequencyRatings

-ApparentPowerandPower-FactorRatings

-SynchronousGeneratorCapabilityCurve

1.SynchronousGeneratorConstruction

ADCcurrentisappliedtotherotorwinding,whichthenproducesarotormagneticfield.Therotoristhenturnedbyaprimemover（eg.Steam,wateretc.）producingarotatingmagneticfield.Thisrotatingmagneticfieldinducesa3-phasesetofvoltageswithinthestatorwindingsofthegenerator.

“Fieldwindings”appliestothewindingsthatproducethemainmagneticfieldinamachine,and“armaturewindings”appliestothewindingswherethemainvoltageisinduced.Forsynchronousmachines,thefieldwindingsareontherotor,sotheterms“rotorwindings”and“fieldwindings”areusedinterchangeably.

Generallyasynchronousgeneratormusthaveatleast2components:

a）RotorWindingsorFieldWindings

a.SalientPole

b.NonSalientPole

b）StatorWindingsorArmatureWindings

Therotorofasynchronousgeneratorisalargeelectromagnetandthemagneticpolesontherotorcaneitherbesalientornonsalientconstruction.Non-salientpolerotorsarenormallyusedforrotorswith2or4polesrotor,whilesalientpolerotorsareusedfor4ormorepolesrotor.

Non-salientrotorforasynchronousmachine

Salientrotor

Adccurrentmustbesuppliedtothefieldcircuitontherotor.Sincetherotorisrotating,aspecialarrangementisrequiredtogetthedcpowertoitsfieldwindings.Thecommonwaysare:

a）supplythedcpowerfromanexternaldcsourcetotherotorbymeansofslipringsandbrushes.

b）Supplythedcpowerfromaspecialdcpowersourcemounteddirectlyontheshaftofthesynchronousgenerator.

Slipringsaremetalringscompletelyencirclingtheshaftofamachinebutinsulatedfromit.Oneendofthedcrotorwindingistiedtoeachofthe2slipringsontheshaftofthesynchronousmachine,andastationarybrushridesoneachslipring.

A“brush”isablockofgraphitelikecarboncompoundthatconductselectricityfreelybuthasverylowfriction,henceitdoesn’tweardowntheslipring.Ifthepositiveendofadcvoltagesourceisconnectedtoonebrushandthenegativeendisconnectedtotheother,thenthesamedcvoltagewillbeappliedtothefieldwindingatalltimesregardlessoftheangularpositionorspeedoftherotor.

Someproblemswithslipringsandbrushes:

-Theyincreasetheamountofmaintenancerequiredonthemachine,sincethebrushesmustbecheckedforwearregularly.

-Brushvoltagedropcanbethecauseofsignificantpowerlossesonmachineswithlargerfieldcurrents.

Smallsynchronousmachines–useslipringsandbrushes.

Largermachines–brushlessexcitersareusedtosupplythedcfieldcurrent.

Abrushlessexciterisasmallacgeneratorwithitsfieldcircuitmountedonthestatoranditsarmaturecircuitmountedontherotorshaft.The3-phaseoutputoftheexcitergeneratorisrectifiedtodirectcurrentbya3-phaserectifiercircuitalsomountedontheshaftofthegenerator,andisthenfedtothemaindcfieldcircuit.Bycontrollingthesmalldcfieldcurrentoftheexcitergenerator（locatedonthestator）,wecanadjustthefieldcurrentonthemainmachinewithoutslipringsandbrushes.Sincenomechanicalcontactsoccurbetweentherotorandstator,abrushlessexciterrequireslessmaintenance.

Abrushlessexcitercircuit:

Asmall3-phasecurrentisrectifiedandusedtosupplythefieldcircuitoftheexciter,whichislocatedonthestator.Theoutputofthearmaturecircuitoftheexciter（ontherotor）isthenrectifiedandusedtosupplythefieldcurrentofthemainmachine.

Tomaketheexcitationofageneratorcompletelyindependentofanyexternalpowersources,asmallpilotexcitercanbeused.

Apilotexciterisasmallacgeneratorwithpermanentmagnetsmountedontherotorshaftanda3-phasewindingonthestator.Itproducesthepowerforthefieldcircuitoftheexciter,whichinturncontrolsthefieldcircuitofthemainmachine.Ifapilotexciterisincludedonthegeneratorshaft,thennoexternalelectricpowerisrequired.

Abrushlessexcitationschemethatincludesapilotexciter.Thepermanentmagnetsofthepilotexciterproducethefieldcurrentoftheexciter,whichinturnproducesthefieldcurrentofthemainmachine.

Eventhoughmachineswithbrushlessexcitersdonotneedslipringsandbrushes,theystillincludetheslipringsandbrushessothatanauxiliarysourceofdcfieldcurrentisavailableinemergencies.

2.TheSpeedofRotationofaSynchronousGenerator

Synchronousgeneratorsarebydefinitionsynchronous,meaningthattheelectricalfrequencyproducedislockedinorsynchronizedwiththemechanicalrateofrotationofthegenerator.Asynchronousgenerator’srotorconsistsofanelectromagnettowhichdirectcurrentissupplied.Therotor’smagneticfieldpointsinthedirectiontherotoristurned.Hence,therateofrotationofthemagneticfieldinthemachineisrelatedtothestatorelectricalfrequencyby:

3.TheInternalGeneratedVoltageofaSynchronousGenerator

Voltageinducedisdependentuponfluxandspeedofrotation,hencefromwhatwehavelearntsofar,theinducedvoltagecanbefoundasfollows:

Forsimplicity,itmaybesimplifiedtoasfollows:

4.TheEquivalentCircuitofaSynchronousGenerator

ThevoltageEAistheinternalgeneratedvoltageproducedinonephaseofasynchronousgenerator.Ifthemachineisnotconnectedtoaload（noarmaturecurrentflowing）,theterminalvoltagewillbeequivalenttothevoltageinducedatthestatorcoils.Thisisduetothefactthattherearenocurrentflowinthestatorcoilshencenolosses.Whenthereisaloadconnectedtothegenerator,therewillbedifferencesbetweenEAandVφ.Thesedifferencesaredueto:

a）Distortionoftheairgapmagneticfieldbythecurrentflowinginthestatorcalledarmaturereaction.

b）Selfinductanceofthearmaturecoil

c）Resistanceofthearmaturecoils

d）Theeffectofsalientpolerotorshapes.

Wewillexplorefactorsa,b,andcandderiveamachinemodelfromthem.Theeffectofsalientpolerotorshapewillbeignored,andallmachinesinthischapterareassumedtohavenonsalientorcylindricalrotors.

ArmatureReaction

Whentherotorisspun,avoltageEAisinducedinthestatorwindings.Ifaloadisattachedtotheterminalsofthegenerator,acurrentflows.Buta3-phasestatorcurrentflowwillproduceamagneticfieldofitsown.Thisstatormagneticfieldwilldistortstheoriginalrotormagneticfield,changingtheresultingphasevoltage.Thiseffectiscalledarmaturereactionbecausethearmature（stator）currentaffectsthemagneticfield,whichproduceditinthefirstplace.

Refertothediagramsbelow,showingatwo-polerotorspinninginsidea3-phasestator.

（a）ArotatingmagneticfieldproducestheinternalgeneratedvoltageEA.

（b）Theresultingvoltageproducesalaggingcurrentflowwhenconnectedtoalaggingload.

（c）ThestatorcurrentproducesitsownmagneticfieldBSwhichproducesitsownEstatinthestatorwindings.

（d）ThefieldBSaddstoBRdistortingitintoBnet.ThevoltageEstataddstoEA,producingVφattheoutputofthephase.

（a）Thereisnoloadconnectedtothestator.TherotormagneticfieldBRproducesaninternalgeneratedvoltageEAwhosepeakcoincideswithdirectionofBR.Withnoload,thereisnoarmaturecurrentandEAwillbeequaltothephasevoltageVφ.

（b）Whenalaggingloadisconnected,thepeakcurrentwilloccuratananglebehindthepeakvoltage.

（c）Thecurrentflowinginthestatorwindingsproducesamagneticfieldofitsown.ThisstatormagneticfieldBSanditsdirectionaregivenbytheright-handrule.ThestatorfieldproducesavoltageofitsowncalledEstat.

（d）With2voltagesand2magneticfieldspresentinthestatorwindings,thetotalvoltageandthenetmagneticfieldare:

Howcantheeffectsofarmaturereactiononthephasevoltagebemodeled?

-ThevoltageEstatliesatanangleof90°behindtheplaneofIA.

-ThevoltageEstatisdirectlyproportionaltothecurrentIA.

IfXisaconstantofproportionality,thenthearmaturereactionvoltagecanbeexpressedas:

Therefore:

Thus,thearmaturereactionvoltagecanbemodeledasaninductorinserieswiththeinternalgeneratedvoltage.

Self-inductanceandResistanceoftheArmatureCoils

Ifthestatorself-inductanceiscalledLA（reactanceisXA）whilethestatorresistanceiscalledRA,thenthetotaldifferencebetweenEAandVφis:

WhereXS=X+XA

Thefullequivalentcircuitisshownbelow:

Adcpowersourceissupplyingtherotorfieldcircuit,whisismodeledbythecoil’sinductanceandresistanceinseries.InserieswithRFisanadjustableresistorRadjwhi