1、TheTransformeronloadIntroductiontoDCMachinesTheTransformeronloadIthasbeenshownthataprimaryinputvoltage1Vcanbetransformedtoanydesiredopen-circuitsecondaryvoltage2Ebyasuitablechoiceofturnsratio/2Eisavailableforcirculatingaloadcurrentimpedance/Forthemoment/alaggingpowerfactorwillbeconsidered/Theseconda
2、rycurrentandtheresultingampere-turns22NIwillchangetheflux/tendingtodemagnetizethecore/reducemandwithit1E/Becausetheprimaryleakageimpedancedropissolow/asmallalterationto1Ewillcauseanappreciableincreaseofprimarycurrentfrom0Itoanewvalueof1IequaltoijXREV111//Theextraprimarycurrentandampere-turnsnearlyca
3、ncelthewholeofthesecondaryampere-turns/Thisbeingso/themutualfluxsuffersonlyaslightmodificationandrequirespracticallythesamenetampere-turns10NIasonnoload/Thetotalprimaryampere-turnsareincreasedbyanamount22NInecessarytoneutralizethesameamountofsecondaryampere-turns/Inthevectorequation/102211NININI；alt
4、ernatively/221011NININI/Atfullload/thecurrent0Iisonlyabout5%ofthefull-loadcurrentandso1Iisnearlyequalto122/NNI/Becauseinmindthat2121/NNEE/theinputkVAwhichisapproximately11IEisalsoapproximatelyequaltotheoutputkVA/22IE/Thephysicalcurrenthasincreased/andwithintheprimaryleakagefluxtowhichitisproportiona
5、l/Thetotalfluxlinkingtheprimary/111mp/isshownunchangedbecausethetotalbacke/m/f//（dtdNE/111）isstillequalandoppositeto1V/However/therehasbeenaredistributionoffluxandthemutualcomponenthasfallenduetotheincreaseof1with1I/Althoughthechangeissmall/thesecondarydemandcouldnotbemetwithoutamutualfluxande/m/f/a
6、lterationtopermitprimarycurrenttochange/Thenetfluxslinkingthesecondarywindinghasbeenfurtherreducedbytheestablishmentofsecondaryleakagefluxdueto2I/andthisopposesm/Althoughmand2areindicatedseparately/theycombinetooneresultantinthecorewhichwillbedownwardsattheinstantshown/Thusthesecondaryterminalvoltag
7、eisreducedtodtdNVS/22whichcanbeconsideredintwocomponents/i/e/dtdNdtdNVm/2222orvectorially2222IjXEV/Asfortheprimary/2isresponsibleforasubstantiallyconstantsecondaryleakageinductance222222/NiN/Itwillbenoticedthattheprimaryleakagefluxisresponsibleforpartofthechangeinthesecondaryterminalvoltageduetoitse
8、ffectsonthemutualflux/Thetwoleakagefluxesarecloselyrelated；2/forexample/byitsdemagnetizingactiononmhascausedthechangesontheprimarysidewhichledtotheestablishmentofprimaryleakageflux/Ifalowenoughleadingpowerfactorisconsidered/thetotalsecondaryfluxandthemutualfluxareincreasedcausingthesecondaryterminal
9、voltagetorisewithload/pisunchangedinmagnitudefromthenoloadconditionsince/neglectingresistance/itstillhastoprovideatotalbacke/m/f/equalto1V/Itisvirtuallythesameas11/thoughnowproducedbythecombinedeffectofprimaryandsecondaryampere-turns/Themutualfluxmuststillchangewithloadtogiveachangeof1Eandpermitmore
10、primarycurrenttoflow/1Ehasincreasedthistimebutduetothevectorcombinationwith1Vthereisstillanincreaseofprimarycurrent/Twomorepointsshouldbemadeaboutthefigures/Firstly/aunityturnsratiohasbeenassumedforconveniencesothat21EE/Secondly/thephysicalpictureisdrawnforadifferentinstantoftimefromthevectordiagram
11、swhichshow0m/ifthehorizontalaxisistakenasusual/tobethezerotimereference/Thereareinstantsinthecyclewhenprimaryleakagefluxiszero/whenthesecondaryleakagefluxiszero/andwhenprimaryandsecondaryleakagefluxiszero/andwhenprimaryandsecondaryleakagefluxesareinthesamesense/Theequivalentcircuitalreadyderivedfort
12、hetransformerwiththesecondaryterminalsopen/caneasilybeextendedtocovertheloadedsecondarybytheadditionofthesecondaryresistanceandleakagereactance/Practicallyalltransformershaveaturnsratiodifferentfromunityalthoughsuchanarrangementissometimesemployedforthepurposesofelectricallyisolatingonecircuitfroman
13、otheroperatingatthesamevoltage/Toexplainthecasewhere21NNthereactionofthesecondarywillbeviewedfromtheprimarywinding/Thereactionisexperiencedonlyintermsofthemagnetizingforceduetothesecondaryampere-turns/Thereisnowayofdetectingfromtheprimarysidewhether2Iislargeand2Nsmallorviceversa/itistheproductofcurr
14、entandturnswhichcausesthereaction/Consequently/asecondarywindingcanbereplacedbyanynumberofdifferentequivalentwindingsandloadcircuitswhichwillgiverisetoanidenticalreactionontheprimary/Itisclearlyconvenienttochangethesecondarywindingtoanequivalentwindinghavingthesamenumberofturns1Nastheprimary/With2Nc
15、hangesto1N/sincethee/m/f/sareproportionaltoturns/2212)/(ENNEwhichisthesameas1E/Forcurrent/sincethereactionampereturnsmustbeunchanged1222NINImustbeequalto22NI/i/e/2122)/(INNI/Forimpedance/sinceanysecondaryvoltageVbecomesVNN)/(21/andsecondarycurrentIbecomesINN)/(12/thenanysecondaryimpedance/includingl
16、oadimpedance/mustbecomeIVNNIV/)/(/221/Consequently/22212)/(RNNRand22212)/(XNNX/Iftheprimaryturnsaretakenasreferenceturns/theprocessiscalledreferringtotheprimaryside/Thereareafewcheckswhichcanbemadetoseeiftheprocedureoutlinedisvalid/Forexample/thecopperlossinthereferredsecondarywindingmustbethesameas
17、intheoriginalsecondaryotherwisetheprimarywouldhavetosupplyadifferentlosspower/222RImustbeequalto222RI/）222122122/()/(NNRNNIdoesinfactreduceto222RI/Similarlythestoredmagneticenergyintheleakagefield)2/1(2LIwhichisproportionalto22XIwillbefoundtocheckas22XI/Thereferredsecondary2212221222)/()/(IENNINNEIE
18、kVA/Theargumentissound/thoughatfirstitmayhaveseemedsuspect/Infact/iftheactualsecondarywindingwasremovedphysicallyfromthecoreandreplacedbytheequivalentwindingandloadcircuitdesignedtogivetheparameters1N/2R/2Xand2I/measurementsfromtheprimaryterminalswouldbeunabletodetectanydifferenceinsecondaryampere-t
19、urns/kVAdemandorcopperloss/undernormalpowerfrequencyoperation/Thereisnopointinchoosinganybasisotherthanequalturnsonprimaryandreferredsecondary/butitissometimesconvenienttorefertheprimarytothesecondarywinding/Inthiscase/ifallthesubscript1sareinterchangedforthesubscript2s/thenecessaryreferringconstant
20、sareeasilyfound；e/g/21RR/21XX；similarly12RRand12XX/Theequivalentcircuitforthegeneralcasewhere21NNexceptthatmrhasbeenaddedtoallowforironlossandanideallosslesstransformationhasbeenincludedbeforethesecondaryterminalstoreturn2Vto2V/Allcalculationsofinternalvoltageandpowerlossesaremadebeforethisidealtran
21、sformationisapplied/Thebehaviourofatransformerasdetectedatbothsetsofterminalsisthesameasthebehaviourdetectedatthecorrespondingterminalsofthiscircuitwhentheappropriateparametersareinserted/Theslightlydifferentrepresentationshowingthecoils1Nand2Nsidebysidewithacoreinbetweenisonlyusedforconvenience/Ont
22、hetransformeritself/thecoilsare/ofcourse/woundroundthesamecore/Verylittleerrorisintroducedifthemagnetisingbranchistransferredtotheprimaryterminals/butafewanomalieswillarise/Forexample/thecurrentshownflowingthroughtheprimaryimpedanceisnolongerthewholeoftheprimarycurrent/Theerrorisquitesmallsince0Iisu
23、suallysuchasmallfractionof1I/Slightlydifferentanswersmaybeobtainedtoaparticularproblemdependingonwhetherornotallowanceismadeforthiserror/Withthissimplifiedcircuit/theprimaryandreferredsecondaryimpedancescanbeaddedtogive/221211)/(ReNNRRand221211)/(NNXXXeItshouldbepointedoutthattheequivalentcircuitasderivedhereisonlyvalidfornormaloperationatpowerfrequencies；capacitanceeffectsmustbetakenintoaccountwhenevertherateofchangeofvoltagewouldgiverisetoappreciablecapacitancecurrents/dtCdVIc//Theyareimportantathighvoltagesandatfrequenciesmuchbeyond100cycles/sec/Afurtherpointisnotthe
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