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Power Transformers

Prof Peter Crossley

Ferranti Building, C14

School of Electrical and Electronic Engineering

p.crossley@manchester.ac.uk

01613064803(office)

EEEN60301 Power System Modelling

Power Transformers

Monday 23rd October 2013

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Transformers in Power Systems

400 kV Power transformer, *from ALSTOM Grid

2

400 kV transformer core and winding,

*from Electrical Engineering Portal

400 kV transformer end insulation, *from

CIGRE brochure 323

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Outline

• Concept (‘Ideal’ Transformer)

• Equivalent Circuit (‘Real’ Transformer)

– No load condition, load condition

• Determination of Circuit Parameters

– Open circuit test, short circuit test

• Transformer Operation Performance

– Voltage regulation, efficiency

• Transformer Design and Construction

– Turns, three phase, auto transformer 3

Basic Electromagnetism

André-Marie Ampère (1775-1836) Michael Faraday 1791-1867

* from Wikipedia

dt

dNe

iNdlH

Ampère’s law

Faraday’s law

4

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Concept of Transformer

• ‘Transform’ voltage

(and current);

• ‘Transform’ ac

voltage (not dc

voltage);

• Sine wave

‘transforms’ to sine

wave

Secondary Primary

Right-hand grip rule 5

dt

dNe

‘Ideal’ Transformer

• Voltage ratio

2

1

2

1

N

N

E

E

• No resistance

• No leakage flux

• No core loss

• Permeability μr =∞

1 1

2 2

V N

V N

6

dt

dNe

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‘Ideal’ Transformer

• Ampère’s law

• μr ∞

• Magnetic field intensity (H)

• Current ratio

02211 ININ

0r

BH

iNdlH

1

2

2

1

N

N

I

I

AB

HB

r

0

Flux density

Magnetic flux

7

0

‘Ideal’ Transformer

• Power, Var flow

1 1

2 2

V N

V N

1

2

2

1

N

N

I

I

8

21

21

2211

2211

QQ

PP

jQPjQP

IVIV

IVjQPS

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Transfer of Impedance

• Assumed an impedance ZL connected at

secondary side, refer this impedance into

the primary side as ZL’

• Derive the equation:

1 1

2 2

V N

V N 1 2

2 1

I N

I N

9

LZIV 22

LL ZN

NZ 2

2

1 )('

‘Real’ Transformer

• Coil resistance: R1, R2

• Coil leakage flux: ΦL1(X1), ΦL2(X2)

• Permeability μ is limited, so magnetising current

is required to establish Φm: Xm

• Core losses, the effect of eddy current and

hysteresis loss: Rm

10

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‘Real’ Transformer

• No load condition

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Equivalent Circuit

tN

E

cos

2

dt

dNtE

sin2

2

1

2

1

22

11011 )(

N

N

E

E

EV

jXRIEV

‘Real’ Transformer

• Load condition

12 2

1

2

1

22222

11111

)(

)(

N

N

E

E

jXRIEV

jXRIEV

Equivalent Circuit

m

L

Z

EI

ZIV

IN

NII

10

22

0

1

221

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‘Real’ Transformer

• Load condition

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Equivalent Circuit (referred to primary side)

Simplified Equivalent Circuit (referred to primary side)

(Neglect magnetising current and core losses)

2

21

2

21

2121

)'()'(

)'()'(

XXRRZ

XXjRRZ

w

w

Transformer impedance

Determination of Circuit Parameters

• Open-circuit test: – Apply rated voltage V1N

– Keep secondary side open

– Measure Voltage Voc, Current Ioc, Power Poc

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I2=0, I1=0;

Ignore R1,X1 (<< Rm,Xm)

22

2

)(m

ococ

ocm

oc

ocm

R

VI

VX

P

VR

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Determination of Circuit Parameters

• Short-circuit test: – Apply rated current I1N

– Shot circuit secondary side

– Measure Voltage Vsc, Current Isc, Power Psc

15

2

21

2

21

221

)'()()'(

)'(

RRI

VXX

I

PRR

sc

sc

sc

sc

V2=0, V1 small;

Ignore Rm,Xm

Transformer Operation Performance

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• Voltage Regulation:

Difference between voltage magnitude at no-load

and load conditions expressed as a percentage

of load value.

Voltage regulation is due to the voltage drop on

transformer impedance at load condition.

100(%)Re2

22

load

loadloadno

V

VVg

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Transformer Operation Performance

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• Voltage Regulation:

Simplified Equivalent Circuit

(referred to secondary side)

100sincos

(%)

100sin)'(cos)'(

(%)

2

2222Re

2

22122212Re

load

wwg

loadg

V

XIRIV

V

XXIRRIV

ABVVV loadloadno

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Transformer Operation Performance

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• Transformer impedance (resistance,

leakage reactance) can also be

expressed as a percentage voltage drop:

100(%)2

V

ZIV wFL

z

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Transformer Operation Performance

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Lossespower Output

power Output

power Input

power OutputEfficiency

• Efficiency:

– Efficiency is defined in terms of power transfer:

– Core loss is combination of eddy current and

hysteresis losses, constant at constant voltage

– I2R or copper loss varies with the load

loss Coreloss RIpower Output

power Output2

Transformer Design and Construction

• Volts per turn and flux density

For a given core, the cross-sectional area (A) of

the limb is a constant, the relationship between

volts per turn (E/N) in the winding and the flux

density (B) remains constant at a given

frequency (f).

mBAfN

E

fN

E

44.4

44.4

20

tN

E

cos

2

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Transformer Design and Construction

• Exercise:

The maximum flux density within the magnetic

core of a 50 Hz, 400 kV/132 kV transformer is

restricted to 1.55 Tesla as the core has a circular

cross section with a diameter of 1 m. Calculate

the volts per turn for the winding and the number

of turns for HV and LV windings.

(This transformer is connected as Yyn*)

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Transformer Design and Construction

kVE

2303

400

3

1

kVE

763

132

3

2

The phase voltage for HV winding is

The phase voltage for LV winding is

Volt per turn is calculated as

)(2705.055.15044.444.4 2 VAfBN

Em

The HV winding has N1=230000/270=851 turns

The LV winding has N2=76000/270=281.5 turns

• Solution:

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Transformer Design and Construction

• Transformer construction

• Auto Transformer – single winding per phase, low voltage terminal

is made from a tap part way down the winding

– more economical than two-winding

transformer for voltage ratio up to 3:1

– auto-transformers are usually star connected

and share the same neutral, often undesirable

except in transmission system where solid

earthing at all voltage level

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Transformer Design and Construction

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N1: series winding

N2: common winding

V1/(N1+N2)=V2/N2

I1N1=(I2-I1)N2

V1

V2

I1

I2

I2-I1

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Transformer Design and Construction

• Auto Transformer

N1

N2

+

-

+

-

• Three phase winding connection

– Star/ Y connection

B

A

C

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Transformer Design and Construction

Advantages

– more economical for a high voltage winding

– neutral point available for earthing

– permits reduced insulation level of the neutral

– permits taps and tap changer to be located near

neutral

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• Three phase winding connection

– Delta/ D connection

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Transformer Design and Construction

Advantages

– more economical for a high current, low voltage

winding

– in combination with a start connected winding, it

reduces the zero-sequence impedance current

in that winding

A

C B

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Transformer Design and Construction

• Phase relationship

A conventional notation indicating the connections

of the high-voltage and low-voltage windings and

their relative phase displacement expressed as a

combination of letters and clock-hour figure.

First symbol: HV side (minute hand, 12 o’clock)

Second symbol: LV side (hour hand)

Third symbol: phase displacement expressed as

the clock hour number

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Transformer Design and Construction

• Phase relationship

HV delta D

star Y

interconnected star Z

LV delta d

star y

interconnected star z

Group number Phase displacement Clock hour number

I 0o 0

II 180o 6

III -30o 1

IV 30o 11

Example:

Group I connection Yy0

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Transformer Design and Construction

Group I Yy0

Group IV Yd11

Group IV Dy11

Group IV Yz11

• Phase relationship

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Summary

1. Transformer Equivalent Circuit

31

2

2

2

12 )(' Z

N

NZ

Summary

2. Determination of Circuit Parameters

32

22

2

)(m

ococ

ocm

oc

ocm

R

VI

VX

P

VR

2

21

2

21

221

)'()()'(

)'(

RRI

VXX

I

PRR

sc

sc

sc

sc

Open-circuit test Short-circuit test

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Summary

3. Voltage Regulation

4. Efficiency

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100(%)Re2

22

load

loadloadno

V

VVg

loss Coreloss RIpower Output

power Output2

Summary

5. Volts per Turn

6. Phase Relationship

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mBAfN

E

fN

E

44.4

44.4

Group I Yy0

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Reading…

• Power System Analysis

– John J. Grainger, William D. Stevenson.

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