TheTransformeronloadIntroductiontoDCMachinesTheTransformeronloadIthasbeenshownthataprimaryinputvoltage1Vcanbetransformedtoanydesiredopen-circuitsecondaryvoltage2Ebyasuitablechoiceofturnsratio.2Eisavailableforcirculatingaloadcurrentimpedance.Forthemoment,alaggingpowerfactorwillbeconsidered.Thesecondarycurrentandtheresultingampere-turns22NIwillchangetheflux,tendingtodemagnetizethecore,reducemandwithit1E.Becausetheprimaryleakageimpedancedropissolow,asmallalterationto1Ewillcauseanappreciableincreaseofprimarycurrentfrom0Itoanewvalueof1IequaltoijXREV111/.Theextraprimarycurrentandampere-turnsnearlycancelthewholeofthesecondaryampere-turns.Thisbeingso,themutualfluxsuffersonlyaslightmodificationandrequirespracticallythesamenetampere-turns10NIasonnoload.Thetotalprimaryampere-turnsareincreasedbyanamount22NInecessarytoneutralizethesameamountofsecondaryampere-turns.Inthevectorequation,102211NININI；alternatively,221011NININI.Atfullload,thecurrent0Iisonlyabout5%ofthefull-loadcurrentandso1Iisnearlyequalto122/NNI.Becauseinmindthat2121/NNEE,theinputkVAwhichisapproximately11IEisalsoapproximatelyequaltotheoutputkVA,22IE.Thephysicalcurrenthasincreased,andwithintheprimaryleakagefluxtowhichitisproportional.Thetotalfluxlinkingtheprimary,111mp,isshownunchangedbecausethetotalbacke.m.f.,（dtdNE/111）isstillequalandoppositeto1V.However,therehasbeenaredistributionoffluxandthemutualcomponenthasfallenduetotheincreaseof1with1I.Althoughthechangeissmall,thesecondarydemandcouldnotbemetwithoutamutualfluxande.m.f.alterationtopermitprimarycurrenttochange.Thenetfluxslinkingthesecondarywindinghasbeenfurtherreducedbytheestablishmentofsecondaryleakagefluxdueto2I,andthisopposesm.Althoughmand2areindicatedseparately,theycombinetooneresultantinthecorewhichwillbedownwardsattheinstantshown.ThusthesecondaryterminalvoltageisreducedtodtdNVS/22whichcanbeconsideredintwocomponents,i.e.dtdNdtdNVm/2222orvectorially2222IjXEV.Asfortheprimary,2isresponsibleforasubstantiallyconstantsecondaryleakageinductance222222/NiN.Itwillbenoticedthattheprimaryleakagefluxisresponsibleforpartofthechangeinthesecondaryterminalvoltageduetoitseffectsonthemutualflux.Thetwoleakagefluxesarecloselyrelated；2,forexample,byitsdemagnetizingactiononmhascausedthechangesontheprimarysidewhichledtotheestablishmentofprimaryleakageflux.Ifalowenoughleadingpowerfactorisconsidered,thetotalsecondaryfluxandthemutualfluxareincreasedcausingthesecondaryterminalvoltagetorisewithload.pisunchangedinmagnitudefromthenoloadconditionsince,neglectingresistance,itstillhastoprovideatotalbacke.m.f.equalto1V.Itisvirtuallythesameas11,thoughnowproducedbythecombinedeffectofprimaryandsecondaryampere-turns.Themutualfluxmuststillchangewithloadtogiveachangeof1Eandpermitmoreprimarycurrenttoflow.1Ehasincreasedthistimebutduetothevectorcombinationwith1Vthereisstillanincreaseofprimarycurrent.Twomorepointsshouldbemadeaboutthefigures.Firstly,aunityturnsratiohasbeenassumedforconveniencesothat21EE.Secondly,thephysicalpictureisdrawnforadifferentinstantoftimefromthevectordiagramswhichshow0m,ifthehorizontalaxisistakenasusual,tobethezerotimereference.Thereareinstantsinthecyclewhenprimaryleakagefluxiszero,whenthesecondaryleakagefluxiszero,andwhenprimaryandsecondaryleakagefluxiszero,andwhenprimaryandsecondaryleakagefluxesareinthesamesense.Theequivalentcircuitalreadyderivedforthetransformerwiththesecondaryterminalsopen,caneasilybeextendedtocovertheloadedsecondarybytheadditionofthesecondaryresistanceandleakagereactance.Practicallyalltransformershaveaturnsratiodifferentfromunityalthoughsuchanarrangementissometimesemployedforthepurposesofelectricallyisolatingonecircuitfromanotheroperatingatthesamevoltage.Toexplainthecasewhere21NNthereactionofthesecondarywillbeviewedfromtheprimarywinding.Thereactionisexperiencedonlyintermsofthemagnetizingforceduetothesecondaryampere-turns.Thereisnowayofdetectingfromtheprimarysidewhether2Iislargeand2Nsmallorviceversa,itistheproductofcurrentandturnswhichcausesthereaction.Consequently,asecondarywindingcanbereplacedbyanynumberofdifferentequivalentwindingsandloadcircuitswhichwillgiverisetoanidenticalreactionontheprimary.Itisclearlyconvenienttochangethesecondarywindingtoanequivalentwindinghavingthesamenumberofturns1Nastheprimary.With2Nchangesto1N,sincethee.m.f.sareproportionaltoturns,2212)/(ENNEwhichisthesameas1E.Forcurrent,sincethereactionampereturnsmustbeunchanged1222NINImustbeequalto22NI.i.e.2122)/(INNI.Forimpedance,sinceanysecondaryvoltageVbecomesVNN)/(21,andsecondarycurrentIbecomesINN)/(12,thenanysecondaryimpedance,includingloadimpedance,mustbecomeIVNNIV/)/(/221.Consequently,22212)/(RNNRand22212)/(XNNX.Iftheprimaryturnsaretakenasreferenceturns,theprocessiscalledreferringtotheprimaryside.Thereareafewcheckswhichcanbemadetoseeiftheprocedureoutlinedisvalid.Forexample,thecopperlossinthereferredsecondarywindingmustbethesameasintheoriginalsecondaryotherwisetheprimarywouldhavetosupplyadifferentlosspower.222RImustbeequalto222RI.）222122122/()/(NNRNNIdoesinfactreduceto222RI.Similarlythestoredmagneticenergyintheleakagefield)2/1(2LIwhichisproportionalto22XIwillbefoundtocheckas22XI.Thereferredsecondary2212221222)/()/(IENNINNEIEkVA.Theargumentissound,thoughatfirstitmayhaveseemedsuspect.Infact,iftheactualsecondarywindingwasremovedphysicallyfromthecoreandreplacedbytheequivalentwindingandloadcircuitdesignedtogivetheparameters1N,2R,2Xand2I,measurementsfromtheprimaryterminalswouldbeunabletodetectanydifferenceinsecondaryampere-turns,kVAdemandorcopperloss,undernormalpowerfrequencyoperation.Thereisnopointinchoosinganybasisotherthanequalturnsonprimaryandreferredsecondary,butitissometimesconvenienttorefertheprimarytothesecondarywinding.Inthiscase,ifallthesubscript1sareinterchangedforthesubscript2s,thenecessaryreferringconstantsareeasilyfound；e.g.21RR,21XX；similarly12RRand12XX.Theequivalentcircuitforthegeneralcasewhere21NNexceptthatmrhasbeenaddedtoallowforironlossandanideallosslesstransformationhasbeenincludedbeforethesecondaryterminalstoreturn2Vto2V.Allcalculationsofinternalvoltageandpowerlossesaremadebeforethisidealtransformationisapplied.Thebehaviourofatransformerasdetectedatbothsetsofterminalsisthesameasthebehaviourdetectedatthecorrespondingterminalsofthiscircuitwhentheappropriateparametersareinserted.Theslightlydifferentrepresentationshowingthecoils1Nand2Nsidebysidewithacoreinbetweenisonlyusedforconvenience.Onthetransformeritself,thecoilsare,ofcourse,woundroundthesamecore.Verylittleerrorisintroducedifthemagnetisingbranchistransferredtotheprimaryterminals,butafewanoma