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GORESET
ThreePhaseTransformerBasics
Thusfarwehavelookedattheconstructionandoperationofthesingle-phase,twowindingvoltagetransformerwhich
canbeusedincreaseordecreaseitssecondaryvoltagewithrespecttotheprimarysupplyvoltage.Butvoltage
transformerscanalsobeconstructedforconnectiontonotonlyonesinglephase,butfortwo-phases,three-phases,six-
phasesandevenelaboratecombinationsupto24-phasesforsomeDCrectificationtransformers.Ifwetakethree
single-phasetransformersandconnecttheirprimarywindingstoeachotherandtheirsecondarywindingstoeachother
inafixedconfiguration,wecanusethetransformersonathree-phasesupply.
Three-phase,alsowrittenas3-phaseor3φsuppliesareusedforelectricalpowergeneration,transmission,and
distribution,aswellasforallindustrialuses.Three-phasesupplieshavemanyelectricaladvantagesoversingle-phase
powerandwhenconsideringthree-phasetransformerswehavetodealwiththreealternatingvoltagesandcurrents
differinginphase-timeby120degreesasshownbelow.
ThreePhaseVoltagesandCurrents
Atransformercannotactasaphasechangingdeviceandchangesingle-phaseintothree-phaseorthree-phaseinto
singlephase.Tomakethetransformerconnectionscompatiblewiththree-phasesuppliesweneedtoconnectthem
togetherinaparticularwaytoformaThreePhaseTransformerConfiguration.
Athreephasetransformeror3φtransformercanbeconstructedeitherbyconnectingtogetherthreesingle-phase
transformers,therebyformingaso-calledthreephasetransformerbank,orbyusingonepre-assembledandbalanced
threephasetransformerwhichconsistsofthreepairsofsinglephasewindingsmountedontoonesinglelaminated
core.
TheadvantagesofbuildingasinglethreephasetransformeristhatforthesamekVAratingitwillbesmaller,cheaper
andlighterthanthreeindividualsinglephasetransformersconnectedtogetherbecausethecopperandironcoreare
usedmoreeffectively.Themethodsofconnectingtheprimaryandsecondarywindingsarethesame,whetherusingjust
oneThreePhaseTransformerorthreeseparateSinglePhaseTransformers.Considerthecircuitbelow:
ThreePhaseTransformerConnections
Theprimaryandsecondarywindingsofatransformercanbeconnectedindifferentconfigurationasshowntomeet
practicallyanyrequirement.Inthecaseofthreephasetransformerwindings,threeformsofconnectionarepossible:
"star"(wye),"delta"(mesh)and"interconnected-star"(zig-zag).Thecombinationsofthethreewindingsmaybewiththe
primarydelta-connectedandthesecondarystar-connected,orstar-delta,star-starordelta-delta,dependingonthe
transformersuse.Whentransformersareusedtoprovidethreeormorephasestheyaregenerallyreferredtoas
aPolyphaseTransformer.
ThreePhaseTransformerStarandDeltaConfigurations
Butwhatdowemeanby"star"and"delta"three-phasetransformerconnection.Athreephasetransformerhasthree
setsofprimaryandsecondarywindings.Dependinguponhowthesesetsofwindingsareinterconnected,determines
whethertheconnectionisastarordeltaconfiguration.Theavailablevoltagewhichareeachdisplacedfromtheotherby
120electricaldegreesandflowofthetransformerscurrentsarealsodecidedbythetypeoftheelectricalconnection
usedonboththeprimaryandsecondarysides.
Withthreesingle-phasetransformersconnectedtogether,themagneticflux''sinthethreetransformersdifferinphaseby
120time-degrees.Withasinglethethree-phasetransformertherearethreemagneticflux''sinthecoredifferingintime-
phaseby120degrees.
Thestandardmethodformarkingthreephasetransformerwindingsistolabelthethreeprimarywindingswithcapital
(uppercase)lettersA,BandC,usedtorepresentthethree-phasesofRED,YELLOWandBLUE.Thesecondary
windingsarelabelledwithsmall(lowercase)lettersa,bandc.Eachwindinghastwoendsnormallylabelled1and2so
that,forexample,thesecondwindingoftheprimaryhasendswhichwillbelabelledB1andB2,whilethethirdwinding
ofthesecondarywillbelabelledc1andc2asshown.
TransformerStarandDeltaConfigurations
Symbolsaregenerallyusedonathreephasetransformertoindicatethetypeortypesofconnectionsusedwithupper
caseYforstarconnected,DfordeltaconnectedandZforinterconnectedstarprimarywindings,withlower
casey,dandzfortheirrespectivesecondaries.Then,star-starwouldbelabelledYy,delta-deltawouldbe
labelledDdandinterconnectedstartointerconnectedstarwouldbeZzforthesametypesofconnectedtransformers.
TransformerWindingIdentification
ConnectionPrimaryWindingSecondaryWinding
DeltaDd
StarYy
InterconnectedZz
Wenowknowthattherearefourwaysinwhichthreesingle-phasetransformersmaybeconnectedtogetherbetween
primaryandsecondarythree-phasecircuits.Theconfigurationsaredelta-delta,star-star,star-delta,anddelta-star.
Transformersforhighvoltageoperationwiththestarconnectionshastheadvantageofreducingthevoltageonan
individualtransformer,reducingthenumberofturnsrequiredandanincreaseinthesizeoftheconductors,makingthe
coilwindingseasierandcheapertoinsulatethandeltatransformers.
Thedelta-deltaconnectionneverthelesshasonebigadvantageoverthestar-deltaconfiguration,inthatifone
transformerofagroupofthreeshouldbecomefaultyordisabled,thetworemainingoneswillcontinuetodeliverthree-
phasepowerwithacapacityequaltoapproximatelytwothirdsoftheoriginaloutputfromthetransformerunit.
TransformerDeltaandDeltaConnections
Inadeltaconnected(Dd)groupoftransformers,thelinevoltage,Visequaltothesupplyvoltage,V=V.Butthe
currentineachphasewindingisgivenas:1/√3×Iofthelinecurrent,whereIisthelinecurrent.
Onedisadvantageofdeltaconnectedthreephasetransformersisthateachtransformermustbewoundforthefull-line
voltage,(inourexampleabove100V)andfor57.7percent,linecurrent.Thegreaternumberofturnsinthewinding,
togetherwiththeinsulationbetweenturns,necessitatealargerandmoreexpensivecoilthanthestarconnection.
Anotherdisadvantagewithdeltaconnectedthreephasetransformersisthatthereisno"neutral"orcommonconnection.
Inthestar-stararrangement(Yy),(wye-wye),eachtransformerhasoneterminalconnectedtoacommonjunction,or
neutralpointwiththethreeremainingendsoftheprimarywindingsconnectedtothethree-phasemainssupply.The
numberofturnsinatransformerwindingforstarconnectionis57.7percent,ofthatrequiredfordeltaconnection.
Thestarconnectionrequirestheuseofthreetransformers,andifanyonetransformerbecomesfaultordisabled,the
wholegroupmightbecomedisabled.Nevertheless,thestarconnectedthreephasetransformerisespeciallyconvenient
andeconomicalinelectricalpowerdistributingsystems,inthatafourthwiremaybeconnectedasaneutralpoint,(n)of
thethreestarconnectedsecondariesasshown.
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TransformerStarandStarConnections
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Thevoltagebetweenanylineofthethree-phasetransformeriscalledthe"linevoltage",V,whilethevoltagebetween
anylineandtheneutralpointofastarconnectedtransformeriscalledthe"phasevoltage",V.Thisphasevoltage
betweentheneutralpointandanyoneofthelineconnectionsis1/√3×Vofthelinevoltage.Thenabove,theprimary
sidephasevoltage,Visgivenas.
Thesecondarycurrentineachphaseofastar-connectedgroupoftransformersisthesameasthatforthelinecurrentof
thesupply,thenI=I.
Thentherelationshipbetweenlineandphasevoltagesandcurrentsinathree-phasesystemcanbesummarisedas:
Three-phaseVoltageandCurrent
ConnectionPhaseVoltageLineVoltagePhaseCurrentLineCurrent
StarV=V÷√3V=√3×VI=II=I
DeltaV=VV=VI=I÷√3I=√3×I
Otherpossibleconnectionsforthreephasetransformersarestar-deltaYd,wheretheprimarywindingisstar-connected
andthesecondaryisdelta-connectedordelta-starDywithadelta-connectedprimaryandastar-connectedsecondary.
Delta-starconnectedtransformersarewidelyusedinlowpowerdistributionwiththeprimarywindingsprovidingathree-
wirebalancedloadtotheutilitycompanywhilethesecondarywindingsprovidetherequired4th-wireneutralorearth
connection.
Whentheprimaryandsecondaryhavedifferenttypesofwindingconnections,starordelta,theoverallturnsratioofthe
transformerbecomesmorecomplicated.Ifathree-phasetransformerisconnectedasdelta-delta(Dd)orstar-star
(Yy)thenthetransformercouldpotentiallyhavea1:1turnsratio.Thatistheinputandoutputvoltagesforthewindings
arethesame.
However,ifthe3-phasetransformerisconnectedinstar–delta,(Yd)eachstar-connectedprimarywindingwillreceive
thephasevoltage,Vofthesupply,whichisequalto1/√3×V.Theneachcorrespondingsecondarywindingwillthen
havethissamevoltageinducedinit,andsincethesewindingsaredelta-connected,thevoltage1/√3×Vwillbecome
thesecondarylinevoltage.Thenwitha1:1turnsratio,astar–deltaconnectedtransformerwillprovidea√3:1step-down
line-voltageratio.
Thenforastar–delta(Yd)connectedtransformertheturnsratiobecomes:
Star-DeltaTurnsRatio
Likewise,foradelta–star(Dy)connectedtransformer,witha1:1turnsratio,thetransformerwillprovidea1:√3step-up
line-voltageratio.Thenforadelta-starconnectedtransformertheturnsratiobecomes:
Delta-StarTurnsRatio
L
P
L
P
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Thenforthefourbasicconfigurationsofathree-phasetransformer,wecanlistthetransformerssecondaryvoltagesand
currentswithrespecttotheprimarylinevoltage,VanditsprimarylinecurrentIasshowninthefollowingtable.
Three-phaseTransformerLineVoltageandCurrent
Primary-SecondaryConfigurationLineVoltageLineCurrent
Delta–Delta
Delta–Star
Star–Delta
Star–Star
Where:nequalsthetransformers"turnsratio"(T.R.)ofthenumberofsecondarywindingsN,dividedbythenumberof
primarywindingsN.(N/N)
Soforexample,theprimarywindingofadelta-star(Dy)connected50VAtransformerissuppliedwitha100volt,50Hz
three-phasesupply.Ifthetransformerhas500turnsontheprimaryand100turnsonthesecondarywinding,calculate
thesecondaryvoltagesandcurrents.
GivenData:transformerrating,50VA,supplyvoltage,100v,primaryturns500,secondaryturns,100.
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ThreePhaseTransformerConstruction
Wehavesaidpreviouslythatthethree-phasetransformeriseffectivelythreeinterconnectedsingle-phasetransformers
onasinglelaminatedcoreandconsiderablesavingsincost,sizeandweightcanbeachievedbycombiningthethree
windingsontoasinglemagneticcircuitasshown.
Athree-phasetransformergenerallyhasthethreemagneticcircuitsthatareinterlacedtogiveauniformdistributionof
thedielectricfluxbetweenthehighandlowvoltagewindings.Theexceptiontothisruleisathree-phaseshelltype
transformer.Intheshelltypeofconstruction,eventhoughthethreecoresaretogether,theyarenon-interlaced.
ThreePhaseTransformerConstruction
Thethree-limbcore-typethree-phasetransformeristhemostcommonmethodofthree-phasetransformerconstruction
allowingthephasestobemagneticallylinked.Fluxofeachlimbusestheothertwolimbsforitsreturnpathwiththethree
magneticflux''sinthecoregeneratedbythelinevoltagesdifferingintime-phaseby120degrees.Thusthefluxinthecore
remainsnearlysinusoidal,producingasinusoidalsecondarysupplyvoltage.
Theshell-typefive-limbtypethree-phasetransformerconstructionisheavierandmoreexpensivetobuildthanthecore-
type.Five-limbcoresaregenerallyusedforverylargepowertransformersastheycanbemadewithreducedheight.A
shell-typetransformerscorematerials,electricalwindings,steelenclosureandcoolingaremuchthesameasforthe
largersingle-phasetypes.
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