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THETRANSFORMERONLOADINTRODUCTIONTODCMACHINESTHETRANSFORMERONLOADITHASBEENSHOWNTHATAPRIMARYINPUTVOLTAGECANBETRANSFORMEDTOANYDESIREDOPENCIRCUIT1VSECONDARYVOLTAGEBYASUITABLECHOICEOFTURNSRATIOISAVAILABLEFORCIRCULATINGALOADCURRENT2E2EIMPEDANCEFORTHEMOMENT,ALAGGINGPOWERFACTORWILLBECONSIDEREDTHESECONDARYCURRENTANDTHERESULTINGAMPERETURNSWILLCHANGETHEFLUX,TENDINGTODEMAGNETIZETHECORE,REDUCEAND2NIMWITHITBECAUSETHEPRIMARYLEAKAGEIMPEDANCEDROPISSOLOW,ASMALLALTERATIONTOWILLCAUSE1E1EANAPPRECIABLEINCREASEOFPRIMARYCURRENTFROMTOANEWVALUEOFEQUALTO0IITHEEXTRAPRIMARYCURRENTANDAMPERETURNSNEARLYCANCELTHEWHOLEOFTHEIJXRV11/SECONDARYAMPERETURNSTHISBEINGSO,THEMUTUALFLUXSUFFERSONLYASLIGHTMODIFICATIONANDREQUIRESPRACTICALLYTHESAMENETAMPERETURNSASONNOLOADTHETOTALPRIMARYAMPERETURNSAREINCREASED10NIBYANAMOUNTNECESSARYTONEUTRALIZETHESAMEAMOUNTOFSECONDARYAMPERETURNSINTHEVECTOR2NIEQUATION,ALTERNATIVELY,ATFULLLOAD,THECURRENTIS101I2101NII0IONLYABOUT5OFTHEFULLLOADCURRENTANDSOISNEARLYEQUALTOBECAUSEINMINDTHAT1/,THEINPUTKVAWHICHISAPPROXIMATELYISALSOAPPROXIMATELYEQUALTOTHE211/NE1IEOUTPUTKVA,ITHEPHYSICALCURRENTHASINCREASED,ANDWITHINTHEPRIMARYLEAKAGEFLUXTOWHICHITISPROPORTIONALTHETOTALFLUXLINKINGTHEPRIMARY,ISSHOWNUNCHANGEDBECAUSETHETOTALBACK1MPEMF,()ISSTILLEQUALANDOPPOSITETOHOWEVER,THEREHASBEENAREDISTRIBUTIONDTNE/11VOFFLUXANDTHEMUTUALCOMPONENTHASFALLENDUETOTHEINCREASEOFWITHALTHOUGHTHECHANGEIS1ISMALL,THESECONDARYDEMANDCOULDNOTBEMETWITHOUTAMUTUALFLUXANDEMFALTERATIONTOPERMITPRIMARYCURRENTTOCHANGETHENETFLUXLINKINGTHESECONDARYWINDINGHASBEENFURTHERREDUCEDBYSTHEESTABLISHMENTOFSECONDARYLEAKAGEFLUXDUETO,ANDTHISOPPOSESALTHOUGHAND2IMM2AREINDICATEDSEPARATELY,THEYCOMBINETOONERESULTANTINTHECOREWHICHWILLBEDOWNWARDSATTHEINSTANTSHOWNTHUSTHESECONDARYTERMINALVOLTAGEISREDUCEDTOWHICHCANBEDTNVS/2CONSIDEREDINTWOCOMPONENTS,IEORVECTORIALLYDTM/2ASFORTHEPRIMARY,ISRESPONSIBLEFORASUBSTANTIALLYCONSTANTSECONDARY22IJXEV2LEAKAGEINDUCTANCEITWILLBENOTICEDTHATTHEPRIMARYLEAKAGEFLUXISRESPONSIBLE2/NIFORPARTOFTHECHANGEINTHESECONDARYTERMINALVOLTAGEDUETOITSEFFECTSONTHEMUTUALFLUXTHETWOLEAKAGEFLUXESARECLOSELYRELATED,FOREXAMPLE,BYITSDEMAGNETIZINGACTIONONHASCAUSEDTHE2MCHANGESONTHEPRIMARYSIDEWHICHLEDTOTHEESTABLISHMENTOFPRIMARYLEAKAGEFLUXIFALOWENOUGHLEADINGPOWERFACTORISCONSIDERED,THETOTALSECONDARYFLUXANDTHEMUTUALFLUXAREINCREASEDCAUSINGTHESECONDARYTERMINALVOLTAGETORISEWITHLOADISUNCHANGEDINMAGNITUDEPFROMTHENOLOADCONDITIONSINCE,NEGLECTINGRESISTANCE,ITSTILLHASTOPROVIDEATOTALBACKEMFEQUALTOITISVIRTUALLYTHESAMEAS,THOUGHNOWPRODUCEDBYTHECOMBINEDEFFECTOFPRIMARYAND1V1SECONDARYAMPERETURNSTHEMUTUALFLUXMUSTSTILLCHANGEWITHLOADTOGIVEACHANGEOFANDPERMIT1EMOREPRIMARYCURRENTTOFLOWHASINCREASEDTHISTIMEBUTDUETOTHEVECTORCOMBINATIONWITH1E1VTHEREISSTILLANINCREASEOFPRIMARYCURRENTTWOMOREPOINTSSHOULDBEMADEABOUTTHEFIGURESFIRSTLY,AUNITYTURNSRATIOHASBEENASSUMEDFORCONVENIENCESOTHATSECONDLY,THEPHYSICALPICTUREISDRAWNFORADIFFERENTINSTANTOFTIME21FROMTHEVECTORDIAGRAMSWHICHSHOW,IFTHEHORIZONTALAXISISTAKENASUSUAL,TOBETHEZERO0MTIMEREFERENCETHEREAREINSTANTSINTHECYCLEWHENPRIMARYLEAKAGEFLUXISZERO,WHENTHESECONDARYLEAKAGEFLUXISZERO,ANDWHENPRIMARYANDSECONDARYLEAKAGEFLUXISZERO,ANDWHENPRIMARYANDSECONDARYLEAKAGEFLUXESAREINTHESAMESENSETHEEQUIVALENTCIRCUITALREADYDERIVEDFORTHETRANSFORMERWITHTHESECONDARYTERMINALSOPEN,CANEASILYBEEXTENDEDTOCOVERTHELOADEDSECONDARYBYTHEADDITIONOFTHESECONDARYRESISTANCEANDLEAKAGEREACTANCEPRACTICALLYALLTRANSFORMERSHAVEATURNSRATIODIFFERENTFROMUNITYALTHOUGHSUCHANARRANGEMENTISSOMETIMESEMPLOYEDFORTHEPURPOSESOFELECTRICALLYISOLATINGONECIRCUITFROMANOTHEROPERATINGATTHESAMEVOLTAGETOEXPLAINTHECASEWHERETHEREACTIONOFTHESECONDARYWILLBEVIEWEDFROM21NTHEPRIMARYWINDINGTHEREACTIONISEXPERIENCEDONLYINTERMSOFTHEMAGNETIZINGFORCEDUETOTHESECONDARYAMPERETURNSTHEREISNOWAYOFDETECTINGFROMTHEPRIMARYSIDEWHETHERISLARGEAND2ISMALLORVICEVERSA,ITISTHEPRODUCTOFCURRENTANDTURNSWHICHCAUSESTHEREACTIONCONSEQUENTLY,A2NSECONDARYWINDINGCANBEREPLACEDBYANYNUMBEROFDIFFERENTEQUIVALENTWINDINGSANDLOADCIRCUITSWHICHWILLGIVERISETOANIDENTICALREACTIONONTHEPRIMARYITISCLEARLYCONVENIENTTOCHANGETHESECONDARYWINDINGTOANEQUIVALENTWINDINGHAVINGTHESAMENUMBEROFTURNSASTHEPRIMARY1NWITHCHANGESTO,SINCETHEEMFSAREPROPORTIONALTOTURNS,WHICHIS2N122/ETHESAMEAS1EFORCURRENT,SINCETHEREACTIONAMPERETURNSMUSTBEUNCHANGEDMUSTBEEQUALTO122NIIE2NI21/IIFORIMPEDANCE,SINCEANYSECONDARYVOLTAGEBECOMES,ANDSECONDARYCURRENTVV/21BECOMES,THENANYSECONDARYIMPEDANCE,INCLUDINGLOADIMPEDANCE,MUSTBECOMEII/12CONSEQUENTLY,ANDVNV/1212/RN21/XNXIFTHEPRIMARYTURNSARETAKENASREFERENCETURNS,THEPROCESSISCALLEDREFERRINGTOTHEPRIMARYSIDETHEREAREAFEWCHECKSWHICHCANBEMADETOSEEIFTHEPROCEDUREOUTLINEDISVALIDFOREXAMPLE,THECOPPERLOSSINTHEREFERREDSECONDARYWINDINGMUSTBETHESAMEASINTHEORIGINALSECONDARYOTHERWISETHEPRIMARYWOULDHAVETOSUPPLYADIFFERENTLOSSPOWERMUSTBEEQUAL2RITODOESINFACTREDUCETO2RI)21212/NRN2ISIMILARLYTHESTOREDMAGNETICENERGYINTHELEAKAGEFIELDWHICHISPROPORTIONALTO/1LWILLBEFOUNDTOCHECKASTHEREFERREDSECONDARY2XI2XI212212/ENINEIKVATHEARGUMENTISSOUND,THOUGHATFIRSTITMAYHAVESEEMEDSUSPECTINFACT,IFTHEACTUALSECONDARYWINDINGWASREMOVEDPHYSICALLYFROMTHECOREANDREPLACEDBYTHEEQUIVALENTWINDINGANDLOADCIRCUITDESIGNEDTOGIVETHEPARAMETERS,AND,MEASUREMENTSFROMTHEPRIMARYTERMINALS12RX2IWOULDBEUNABLETODETECTANYDIFFERENCEINSECONDARYAMPERETURNS,DEMANDORCOPPERLOSS,KVAUNDERNORMALPOWERFREQUENCYOPERATIONTHEREISNOPOINTINCHOOSINGANYBASISOTHERTHANEQUALTURNSONPRIMARYANDREFERREDSECONDARY,BUTITISSOMETIMESCONVENIENTTOREFERTHEPRIMARYTOTHESECONDARYWINDINGINTHISCASE,IFALLTHESUBSCRIPT1SAREINTERCHANGEDFORTHESUBSCRIPT2S,THENECESSARYREFERRINGCONSTANTSAREEASILYFOUNDEG,SIMILARLYAND21R21X12R12XTHEEQUIVALENTCIRCUITFORTHEGENERALCASEWHEREEXCEPTTHATHASBEENADDEDTO2NMRALLOWFORIRONLOSSANDANIDEALLOSSLESSTRANSFORMATIONHASBEENINCLUDEDBEFORETHESECONDARYTERMINALSTORETURNTOALLCALCULATIONSOFINTERNALVOLTAGEANDPOWERLOSSESAREMADEBEFORETHISIDEAL2VTRANSFORMATIONISAPPLIEDTHEBEHAVIOUROFATRANSFORMERASDETECTEDATBOTHSETSOFTERMINALSISTHESAMEASTHEBEHAVIOURDETECTEDATTHECORRESPONDINGTERMINALSOFTHISCIRCUITWHENTHEAPPROPRIATEPARAMETERSAREINSERTEDTHESLIGHTLYDIFFERENTREPRESENTATIONSHOWINGTHECOILSANDSIDEBYSIDE1N2WITHACOREINBETWEENISONLYUSEDFORCONVENIENCEONTHETRANSFORMERITSELF,THECOILSARE,OFCOURSE,WOUNDROUNDTHESAMECOREVERYLITTLEERRORISINTRODUCEDIFTHEMAGNETISINGBRANCHISTRANSFERREDTOTHEPRIMARYTERMINALS,BUTAFEWANOMALIESWILLARISEFOREXAMPLE,THECURRENTSHOWNFLOWINGTHROUGHTHEPRIMARYIMPEDANCEISNOLONGERTHEWHOLEOFTHEPRIMARYCURRENTTHEERRORISQUITESMALLSINCEISUSUALLYSUCHASMALL0IFRACTIONOFSLIGHTLYDIFFERENTANSWERSMAYBEOBTAINEDTOAPARTICULARPROBLEMDEPENDINGONWHETHER1IORNOTALLOWANCEISMADEFORTHISERRORWITHTHISSIMPLIFIEDCIRCUIT,THEPRIMARYANDREFERREDSECONDARYIMPEDANCESCANBEADDEDTOGIVEAND2121/REN2121/NXEITSHOULDBEPOINTEDOUTTHATTHEEQUIVALENTCIRCUITASDERIVEDHEREISONLYVALIDFORNORMALOPERATIONATPOWERFREQUENCIESCAPACITANCEEFFECTSMUSTBETAKENINTOACCOUNTWHENEVERTHERATEOFCHANGEOFVOLTAGEWOULDGIVERISETOAPPRECIABLECAPACITANCECURRENTS,THEYAREDTCVIC/IMPORTANTATHIGHVOLTAGESANDATFREQUENCIESMUCHBEYOND100CYCLES/SECAFURTHERPOINTISNOTTHEONLYPOSSIBLEEQUIVALENTCIRCUITEVENFORPOWERFREQUENCIESANALTERNATIVE,TREATINGTHETRANSFORMERASATHREEORFOURTERMINALNETWORK,GIVESRISETOAREPRESENTATIONWHICHISJUSTASACCURATEANDHASSOMEADVANTAGESFORTHECIRCUITENGINEERWHOTREATSALLDEVICESASCIRCUITELEMENTSWITHCERTAINTRANSFERPROPERTIESTHECIRCUITONTHISBASISWOULDHAVEATURNSRATIOHAVINGAPHASESHIFTASWELLASAMAGNITUDECHANGE,ANDTHEIMPEDANCESWOULDNOTBETHESAMEASTHOSEOFTHEWINDINGSTHECIRCUITWOULDNOTEXPLAINTHEPHENOMENAWITHINTHEDEVICELIKETHEEFFECTSOFSATURATION,SOFORANUNDERSTANDINGOFINTERNALBEHAVIOURTHEREARETWOWAYSOFLOOKINGATTHEEQUIVALENTCIRCUITAVIEWEDFROMTHEPRIMARYASASINKBUTTHEREFERREDLOADIMPEDANCECONNECTEDACROSS,OR2VBVIEWEDFROMTHESECONDARYASASOURCEOFCONSTANTVOLTAGEWITHINTERNALDROPSDUETO1V1REANDTHEMAGNETIZINGBRANCHISSOMETIMESOMITTEDINTHISREPRESENTATIONANDSOTHECIRCUITREDUCES1XETOAGENERATORPRODUCINGACONSTANTVOLTAGEACTUALLYEQUALTOANDHAVINGANINTERNALIMPEDANCE1E1ACTUALLYEQUALTOJR1REJXINEITHERCASE,THEPARAMETERSCOULDBEREFERREDTOTHESECONDARYWINDINGANDTHISMAYSAVECALCULATIONTIMETHERESISTANCESANDREACTANCESCANBEOBTAINEDFROMTWOSIMPLELIGHTLOADTESTSINTRODUCTIONTODCMACHINESDCMACHINESARECHARACTERIZEDBYTHEIRVERSATILITYBYMEANSOFVARIOUSCOMBINATIONOFSHUNT,SERIES,ANDSEPARATELYEXCITEDFIELDWINDINGSTHEYCANBEDESIGNEDTODISPLAYAWIDEVARIETYOFVOLTAMPEREORSPEEDTORQUECHARACTERISTICSFORBOTHDYNAMICANDSTEADYSTATEOPERATIONBECAUSEOFTHEEASEWITHWHICHTHEYCANBECONTROLLED,SYSTEMSOFDCMACHINESAREOFTENUSEDINAPPLICATIONSREQUIRINGAWIDERANGEOFMOTORSPEEDSORPRECISECONTROLOFMOTOROUTPUTTHEESSENTIALFEATURESOFADCMACHINEARESHOWNSCHEMATICALLYTHESTATORHASSALIENTPOLESANDISEXCITEDBYONEORMOREFIELDCOILSTHEAIRGAPFLUXDISTRIBUTIONCREATEDBYTHEFIELDWINDINGISSYMMETRICALABOUTTHECENTERLINEOFTHEFIELDPOLESTHISAXISISCALLEDTHEFIELDAXISORDIRECTAXISASWEKNOW,THEACVOLTAGEGENERATEDINEACHROTATINGARMATURECOILISCONVERTEDTODCINTHEEXTERNALARMATURETERMINALSBYMEANSOFAROTATINGCOMMUTATORANDSTATIONARYBRUSHESTOWHICHTHEARMATURELEADSARECONNECTEDTHECOMMUTATORBRUSHCOMBINATIONFORMSAMECHANICALRECTIFIER,RESULTINGINADCARMATUREVOLTAGEASWELLASANARMATUREMMFWAVEWHICHISFIXEDINSPACETHEBRUSHESARELOCATEDSOTHATCOMMUTATIONOCCURSWHENTHECOILSIDESAREINTHENEUTRALZONE,MIDWAYBETWEENTHEFIELDPOLESTHEAXISOFTHEARMATUREMMFWAVETHENIN90ELECTRICALDEGREESFROMTHEAXISOFTHEFIELDPOLES,IE,INTHEQUADRATUREAXISINTHESCHEMATICREPRESENTATIONTHEBRUSHESARESHOWNINQUARATUREAXISBECAUSETHISISTHEPOSITIONOFTHECOILSTOWHICHTHEYARECONNECTEDTHEARMATUREMMFWAVETHENISALONGTHEBRUSHAXISASSHOWNTHEGEOMETRICALPOSITIONOFTHEBRUSHESINANACTUALMACHINEISAPPROXIMATELY90ELECTRICALDEGREESFROMTHEIRPOSITIONINTHESCHEMATICDIAGRAMBECAUSEOFTHESHAPEOFTHEENDCONNECTIONSTOTHECOMMUTATORTHEMAGNETICTORQUEANDTHESPEEDVOLTAGEAPPEARINGATTHEBRUSHESAREINDEPENDENTOFTHESPATIALWAVEFORMOFTHEFLUXDISTRIBUTIONFORCONVENIENCEWESHALLCONTINUETOASSUMEASINUSOIDALFLUXDENSITYWAVEINTHEAIRGAPTHETORQUECANTHENBEFOUNDFROMTHEMAGNETICFIELDVIEWPOINTTHETORQUECANBEEXPRESSEDINTERMSOFTHEINTERACTIONOFTHEDIRECTAXISAIRGAPFLUXPERPOLEDANDTHESPACEFUNDAMENTALCOMPONENTOFTHEARMATUREMMFWAVEWITHTHE1AFBRUSHESINTHEQUADRATUREAXIS,THEANGLEBETWEENTHESEFIELDSIS90ELECTRICALDEGREES,ANDITSSINEEQUALSUNITYFORAPPOLEMACHINE12DFTINWHICHTHEMINUSSIGNHASBEENDROPPEDBECAUSETHEPOSITIVEDIRECTIONOFTHETORQUECANBEDETERMINEDFROMPHYSICALREASONINGTHESPACEFUNDAMENTALOFTHE1AFSAWTOOTHARMATUREMMFWAVEIS8/TIMESITSPEAKSUBSTITUTIONINABOVE2EQUATIONTHENGIVESADADIKIMPCT2WHERECURRENTINEXTERNALARMATURECIRCUITAITOTALNUMBEROFCONDUCTORSINARMATUREWINDINGCNUMBEROFPARALLELPATHSTHROUGHWINDINGMANDMPCKA2ISACONSTANTFIXEDBYTHEDESIGNOFTHEWINDINGTHERECTIFIEDVOLTAGEGENERATEDINTHEARMATUREHASALREADYBEENDISCUSSEDBEFOREFORANELEMENTARYSINGLECOILARMATURETHEEFFECTOFDISTRIBUTINGTHEWINDINGINSEVERALSLOTSISSHOWNINFIGURE,INWHICHEACHOFTHERECTIFIEDSINEWAVESISTHEVOLTAGEGENERATEDINONEOFTHECOILS,COMMUTATIONTAKINGPLACEATTHEMOMENTWHENTHECOILSIDESAREINTHENEUTRALZONETHEGENERATEDVOLTAGEASOBSERVEDFROMTHEBRUSHESISTHESUMOFTHERECTIFIEDVOLTAGESOFALLTHECOILSINSERIESBETWEENBRUSHESANDISSHOWNBYTHERIPPLINGLINELABELEDINFIGUREWITHAEADOZENORSOCOMMUTATORSEGMENTSPERPOLE,THERIPPLEBECOMESVERYSMALLANDTHEAVERAGEGENERATEDVOLTAGEOBSERVEDFROMTHEBRUSHESEQUALSTHESUMOFTHEAVERAGEVALUESOFTHERECTIFIEDCOILVOLTAGESTHERECTIFIEDVOLTAGEBETWEENBRUSHES,AEKNOWNALSOASTHESPEEDVOLTAGE,ISMDAMDAWKPCE2WHEREISTHEDESIGNCONSTANTTHERECTIFIEDVOLTAGEOFADISTRIBUTEDAKWINDINGHASTHESAMEAVERAGEVALUEASTHATOFACONCENTRATEDCOILTHEDIFFERENCEISTHATTHERIPPLEISGREATLYREDUCEDFROMTHEABOVEEQUATIONS,WITHALLVARIABLEEXPRESSEDINSIUNITSMATWIETHISEQUATIONSIMPLYSAYSTHATTHEINSTANTANEOUSELECTRICPOWERASSOCIATEDWITHTHESPEEDVOLTAGEEQUALSTHEINSTANTANEOUSMECHANICALPOWERASSOCIATEDWITHTHEMAGNETICTORQUE,THEDIRECTIONOFPOWERFLOWBEINGDETERMINEDBYWHETHERTHEMACHINEISACTINGASAMOTORORGENERATORTHEDIRECTAXISAIRGAPFLUXISPRODUCEDBYTHECOMBINEDMMFOFTHEFINFIELDWINDINGS,THEFLUXMMFCHARACTERISTICBEINGTHEMAGNETIZATIONCURVEFORTHEPARTICULARIRONGEOMETRYOFTHEMACHINEINTHEMAGNETIZATIONCURVE,ITISASSUMEDTHATTHEARMATUREMMFWAVEISPERPENDICULARTOTHEFIELDAXISITWILLBENECESSARYTOREEXAMINETHISASSUMPTIONLATERINTHISCHAPTER,WHERETHEEFFECTSOFSATURATIONAREINVESTIGATEDMORETHOROUGHLYBECAUSETHEARMATUREEMFISPROPORTIONALTOFLUXTIMESSPEED,ITISUSUALLYMORECONVENIENTTOEXPRESSTHEMAGNETIZATIONCURVEINTERMSOFTHEARMATUREEMFATACONSTANTSPEED0E0MWTHEVOLTAGEFORAGIVENFLUXATANYOTHERSPEEDISPROPORTIONALTOTHEEMWSPEED,IE0AMAEWFIGURESHOWSTHEMAGNETIZATIONCURVEWITHONLYONEFIELDWINDINGEXCITEDTHISCURVECANEASILYBEOBTAINEDBYTESTMETHODS,NOKNOWLEDGEOFANYDESIGNDETAILSBEINGREQUIREDOVERAFAIRLYWIDERANGEOFEXCITATIONTHERELUCTANCEOFTHEIRONISNEGLIGIBLECOMPAREDWITHTHATOFTHEAIRGAPINTHISREGIONTHEFLUXISLINEARLYPROPORTIONALTOTHETOTALMMFOFTHEFIELDWINDINGS,THECONSTANTOFPROPORTIONALITYBEINGTHEDIRECTAXISAIRGAPPERMEANCETHEOUTSTANDINGADVANTAGESOFDCMACHINESARISEFROMTHEWIDEVARIETYOFOPERATINGCHARACTERISTICSWHICHCANBEOBTAINEDBYSELECTIONOFTHEMETHODOFEXCITATIONOFTHEFIELDWINDINGSTHEFIELDWINDINGSMAYBESEPARATELYEXCITEDFROMANEXTERNALDCSOURCE,ORTHEYMAYBESELFEXCITEDIE,THEMACHINEMAYSUPPLYITSOWNEXCITATIONTHEMETHODOFEXCITATIONPROFOUNDLYINFLUENCESNOTONLYTHESTEADYSTATECHARACTERISTICS,BUTALSOTHEDYNAMICBEHAVIOROFTHEMACHINEINCONTROLSYSTEMSTHECONNECTIONDIAGRAMOFASEPARATELYEXCITEDGENERATORISGIVENTHEREQUIREDFIELDCURRENTISAVERYSMALLFRACTIONOFTHERATEDARMATURECURRENTASMALLAMOUNTOFPOWERINTHEFIELDCIRCUITMAYCONTROLARELATIVELYLARGEAMOUNTOFPOWERINTHEARMATURECIRCUITIE,THEGENERATORISAPOWERAMPLIFIERSEPARATELYEXCITEDGENERATORSAREOFTENUSEDINFEEDBACKCONTROLSYSTEMSWHENCONTROLOFTHEARMATUREVOLTAGEOVERAWIDERANGEISREQUIREDTHEFIELDWINDINGSOFSELFEXCITEDGENERATORSMAYBESUPPLIEDINTHREEDIFFERENTWAYSTHEFIELDMAYBECONNECTEDINSERIESWITHTHEARMATURE,RESULTINGINASHUNTGENERATOR,ORTHEFIELDMAYBEINTWOSECTIONS,ONEOFWHICHISCONNECTEDINSERIESANDTHEOTHERINSHUNTWITHTHEARMATURE,RESULTINGINACOMPOUNDGENERATORWITHSELFEXCITEDGENERATORSRESIDUALMAGNETISMMUSTBEPRESENTINTHEMACHINEIRONTOGETTHESELFEXCITATIONPROCESSSTARTEDINTHETYPICALSTEADYSTATEVOLTAMPERECHARACTERISTICS,CONSTANTSPEEDPRIMEMOVERSBEINGASSUMEDTHERELATIONBETWEENTHESTEADYSTATEGENERATEDEMFAEANDTHETERMINALVOLTAGEISTVATRIEWHEREISTHEARMATURECURRENTOUTPUTANDISTHEARMATURECIRCUITAIARRESISTANCEINAGENERATOR,ISLARGETHANANDTHEELECTROMAGNETICTORQUETATVISACOUNTERTORQUEOPPOSINGROTATIONTHETERMINALVOLTAGEOFASEPARATELYEXCITEDGENERATORDECREASESSLIGHTLYWITHINCREASEINTHELOADCURRENT,PRINCIPALLYBECAUSEOFTHEVOLTAGEDROPINTHEARMATURERESISTANCETHEFIELDCURRENTOFASERIESGENERATORISTHESAMEASTHELOADCURRENT,SOTHATTHEAIRGAPFLUXANDHENCETHEVOLTAGEVARYWIDELYWITHLOADASACONSEQUENCE,SERIESGENERATORSARENOTOFTENUSEDTHEVOLTAGEOFSHUNTGENERATORSDROPSOFFSOMEWHATWITHLOADCOMPOUNDGENERATORSARENORMALLYCONNECTEDSOTHATTHEMMFOFTHESERIESWINDINGAIDSTHATOFTHESHUNTWINDINGTHEADVANTAGEISTHATTHROUGHTHEACTIONOFTHESERIESWINDINGTHEFLUXPERPOLECANINCREASEWITHLOAD,RESULTINGINAVOLTAGEOUTPUTWHICHISNEARLYCONSTANTUSUALLY,SHUNTWINDINGCONTAINSMANYTURNSOFCOMPARATIVELYHEAVYCONDUCTORBECAUSEITMUSTCARRYTHEFULLARMATURECURRENTOFTHEMACHINETHEVOLTAGEOFBOTHSHUNTANDCOMPOUNDGENERATORSCANBECONTROLLEDOVERREASONABLELIMITSBYMEANSOFRHEOSTATSINTHESHUNTFIELDANYOFTHEMETHODSOFEXCITATIONUSEDFORGENERATORSCANALSOBEUSEDFORMOTORSINTHETYPICALSTEADYSTATESPEEDTORQUECHARACTERISTICS,ITISASSUMEDTHATTHEMOTORTERMINALSARESUPPLIEDFROMACONSTANTVOLTAGESOURCEINAMOTORTHERELATIONBETWEENTHEEMFGENERATEDINTHEARMATUREANDTHEAETERMINALVOLTAGEISTVATRIEVWHEREISNOWTHEARMATURECURRENTINPUTTHEGENERATEDEMFISNOWAIAESMALLERTHANTHETERMINALVOLTAGE,THEARMATURECURRENTISINTHEOPPOSITETDIRECTIONTOTHATINAMOTOR,ANDTHEELECTROMAGNETICTORQUEISINTHEDIRECTIONTOSUSTAINROTATIONOFTHEARMATUREINSHUNTANDSEPARATELYEXCITEDMOTORSTHEFIELDFLUXISNEARLYCONSTANTCONSEQUENTLY,INCREASEDTORQUEMUSTBEACCOMPANIEDBYAVERYNEARLYPROPORTIONALINCREASEINARMATURECURRENTANDHENCEBYASMALLDECREASEINCOUNTEREMFTOALLOWTHISINCREASEDCURRENTTHROUGHTHESMALLARMATURERESISTANCESINCECOUNTEREMFISDETERMINEDBYFLUXANDSPEED,THESPEEDMUSTDROPSLIGHTLYLIKETHESQUIRRELCAGEINDUCTIONMOTOR,THESHUNTMOTORISSUBSTANTIALLYACONSTANTSPEEDMOTORHAVINGABOUT5PERCENTDROPINSPEEDFROMNOLOADTOFULLLOADSTARTINGTORQUEANDMAXIMUMTORQUEARELIMITEDBYTHEARMATURECURRENTTHATCANBECOMMUTATEDSUCCESSFULLYANOUTSTANDINGADVANTAGEOFTHESHUNTMOTORISEASEOFSPEEDCONTROLWITHARHEOSTATINTHESHUNTFIELDCIRCUIT,THEFIELDCURRENTANDFLUXPERPOLECANBEVARIEDATWILL,ANDVARIATIONOFFLUXCAUSESTHEINVERSEVARIATIONOFSPEEDTOMAINTAINCOUNTEREMFAPPROXIMATELYEQUALTOTHEIMPRESSEDTERMINALVOLTAGEAMAXIMUMSPEEDRANGEOFABOUT4OR5TO1CANBEOBTAINEDBYTHISMETHOD,THELIMITATIONAGAINBEINGCOMMUTATINGCONDITIONSBYVARIATIONOFTHEIMPRESSEDARMATUREVOLTAGE,VERYWIDESPEEDRANGESCANBEOBTAINEDINTHESERIESMOTOR,INCREASEINLOADISACCOMPANIEDBYINCREASEINTHEARMATURECURRENTANDMMFANDTHESTATORFIELDFLUXPROVIDEDTHEIRONISNOTCOMPLETELYSATURATEDBECAUSEFLUXINCREASESWITHLOAD,SPEEDMUSTDROPINORDERTOMAINTAINTHEBALANCEBETWEENIMPRESSEDVOLTAGEANDCOUNTEREMFMOREOVER,THEINCREASEINARMATURECURRENTCAUSEDBYINCREASEDTORQUEISSMALLERTHANINTHESHUNTMOTORBECAUSEOFTHEINCREASEDFLUXTHESERIESMOTORISTHEREFOREAVARYINGSPEEDMOTORWITHAMARKEDLYDROOPINGSPEEDLOADCHARACTERISTICFORAPPLICATIONSREQUIRINGHEAVYTORQUEOVERLOADS,THISCHARACTERISTICISPARTICULARLYADVANTAGEOUSBECAUSETHECORRESPONDINGPOWEROVERLOADSAREHELDTOMOREREASONABLEVALUESBYTHEASSOCIATEDSPEEDDROPSVERYFAVORABLESTARTINGCHARACTERISTICSALSORESULTFROMTHEINCREASEINFLUXWITHINCREASEDARMATURECURRENTINTHECOMPOUNDMOTORTHESERIESFIELDMAYBECONNECTEDEITHERCUMULATIVELY,SOTHATITSMMFADDSTOTHATOFTHESHUNTFIELD,ORDIFFERENTIALLY,SOTHATITOPPOSESTHEDIFFERENTIALCONNECTIONISVERYRARELYUSEDACUMULATIVELYCOMPOUNDEDMOTORHASSPEEDLOADCHARACTERISTICINTERMEDIATEBETWEENTHOSEOFASHUNTANDASERIESMOTOR,THEDROPOFSPEEDWITHLOADDEPENDINGONTHERELATIVENUMBEROFAMPERETURNSINTHESHUNTANDSERIESFIELDSITDOESNOTHAVETHEDISADVANTAGEOFVERYHIGHLIGHTLOADSPEEDASSOCIATEDWITHASERIESMOTOR,BUTITRETAINSTOACONSIDERABLEDEGREETHEADVANTAGESOFSERIESEXCITATIONTHEAPPLICATIONADVANTAGESOFDCMACHINESLIEINTHEVARIETYOFPERFORMANCECHARACTERISTICSOFFEREDBYTHEPOSSIBILITIESOFSHUNT,SERIES,ANDCOMPOUNDEXCITATIONSOMEOFTHESECHARACTERISTICSHAVEBEENTOUCHEDUPONBRIEFLYINTHISARTICLESTILLGREATERPOSSIBILITIESEXISTIFADDITIONALSETSOFBRUSHESAREADDEDSOTHATOTHERVOLTAGESCANBEOBTAINEDFROMTHECOMMUTATORTHUSTHEVERSATILITYOFDCMACHINESYSTEMSANDTHEIRADAPTABILITYTOCONTROL,BOTHMANUALANDAUTO
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