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Dr.Prabodh Bajpai

AssociateProfessor

IndianInstituteofTechnologyKharagpur

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M2Transformer

U2Practicalsinglephasetransformer

Taking

finite

permeability

of

core

into

account

Takingcorelossintoaccount

Takingwindingresistancesandleakagefluxinto

account

Equivalentcircuitofanpracticaltransformer

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U2Practicalsinglephasetransformer

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PracticalTransformer

Thecorematerialwillhavefinitepermeability,

Therewillbeeddycurrentandhysteresislosses

a ngp ace n ecore,

There will be leaka e fluxes and

Finitewindingresistances.

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Finitepermeability

Afinitemagnetizingcurrentforestablishingflux

Fluxlevelincoreisdecidedbyvoltage,frequency

andnumberofturnsofprimaryanddoesnot

depend

upon

the

nature

of

the

core

material

1

1max

2 fN

V

Amount

o

magnet z ng

current

rawn

w

e

differentfordifferentcorematerial

2

, maxmax1

max

m

m

mI

l

H

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Finitepermeability

Magnetizing mmfImN1

mustexistinthetransformer

core allthetime,independentofthedegreeofloading.

Underloaded

condition,

net

mmf

,acting

in

the

magneticcircuitisonceagainImN1 asmmfsI2N1

and

I2N2 cance eac ot er.

Transformerhaving

afinite

magnetizing

current

can

be

modeledbyanidealtransformerwithafixed

magnetizingreactanceXm acrosstheprimary.

mm

mm

Nf

V

NNIvalueRMS

N

ti1

1

111 222

,sin

m

m

XN

I 12

1

1

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Phasor diagramwithmagnetizing

currentta en

into

account

a

II 2

'

2

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Magnetising reactancetotakeImintoaccount

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Core

loss

effect Magnitudeofthecorelossispracticallyindependent

fromthe

supply

ee ec o core oss sman es e y ea ngo e

coreandisarealpower(orenergy)loss.

Totakethisintoaccount,afixedresistanceRcl

is

connectedinparallelwiththemagnetizingreactance

ThenoloadcurrentdrawnfromthesupplyIo,(sumofIclandIm isabout2to5%oftheratedcurrent

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Phasor Diagramofatransformerhavingcore

loss and ma netisin current.

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Takingcorelossintoaccount

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Effectofwindingresistancesandleakageflux

Mutualflux

alone

takes

part

in

the

energy

transfer

fromtheprimarytothesecondary,theeffectofthe

.

Thisdropcanberepresentedbyasmallreactance

ropca e t e ea agereactance rop.

Theeffect

of

winding

resistances

are

taken

into

accountbywayofsmalllumpedresistances.

Resistance and leaka e reactance dro s will be resent

onboth

the

sides

leakageimpedance

of

both

the

sides

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Takingwindingresistancesandleakage

fluxintoaccount

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ExactEquivalentcircuitreferredto

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E uivalent

CircuitR1 X1 R2 X2

'

2I

I Io

2

Ro Xo

V12

V2E1 E2 load

2121

N

Vor

N

V

N

E

N

E 111'

222 NININI

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Referredimpedance

R1 X1 R2 X2'

2IN1 N2

VI1 Io I2E

o Xo

2222

2

1

2

2

1

1 VjXRIN

NE

N

NE

222

1'

2

1

2

1

1 VjXRN

IN

EN

E

16

222

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1'11 NNN

222 NNN2

Define: 21221'21 VNjXRNIE

2

21'

2 R

N

R

21' N Then:

'

2

N

N ''''

VjXRIE 2

2

2

N

17

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'

2

'

2

'

2

'

21 VjXRIE

'

EquivalentCircuitReferredto

SourceSide

R1 1 R2 X22 N1 N2

R XV1 I

1

o

I2E1 E2 V2

X ' '1

Io '

2

Ro XoV1

1 2E1

'2V

18

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' '

Io '

1 2

Ro XoV1

1 2E1

'2V

'o21

'2o1 RRR '

1o22o1

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Approximateequivalentcircuit

R1X1 '2R

'2X

V1 I1

Ro Xo

o '

2I '2V

'' 'X

Io

21 2

V1I1

Ro Xo

'2V

20

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Approximateequivalentcircuit

R1X1 '

2R

'2X

'21 II '

V

Define: '

'XXX

eq eqR X

21

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eX

'21 II V1

'2V

Z

eqeq221 jXRIVV

22

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eqR eqX

'21 II V ' Z

eq'2eq

'2

'21 XIjRIVV

1

V

eq'2 XI

eq'2 ZI

'

eq'2 RI

'

2V

2

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Exam leAtransformerhasthefollowingparameters:

101 N

o.Z 3050 2

50001000101 '' XRXXXRRR

The rated voltage of the primary winding (V1) is 1000V.

Compute the load voltage.

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Solution eqR eqX

2

1

N'

'21 II V ' Z

2

NLL

A..

V

I o

o'

'

3138717

01000 0

1

2

Leqeq

oo''' 0 ...L22

V.N

VV ' 5881

885222 1

25

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TerminologiesTerminologies2V LoadVoltageLoadVoltage

21'

2 VNV

Loa Vo tagere erre toSources eLoa Vo tagere erre toSources e

2

2

2

2

2 RN

R

2I

oa urrenoa urren

2

2

1'

2 X

NNX

Load

current

referred

to

Source

sideLoad

current

referred

to

Source

side

2

1

2'

2 I

N

I

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Ratin s

of

Actual

3

hase

Transformer

100MVA, 13.8/138KV

lin t lin

V2linetoline

2V

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