Transformer on Load

8/14/2019 Transformer on Load

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Transformer on Load

V1

I0

I 2

Load

2

2

2

Fig. 4


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Phasor diagram for Transformer on Load

E2

V1

I2'

I2

I0

I1

Load I2 is

resistive

K=1

0

E2

V1

I2

'

I 2

I0

I1

Load I2

is

inductive

K=1

01

2

Fig. 5

1


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Actual transformer:

Winding resistance & magnetic leakage

R1

X1 I 1

E1

V1

R2

X2

I2

V2

E2

2

1

2

11XRZ +=

R1 & R2 : resistances of primary & secondary windings respectively.

X1 & X2 : leakage reactances of primary & secondary windings respectively.

2

2

2

22 XRZ +=


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Phasor diagram of actual transformer

a) I2 is resistive b) I2 is inductive c) I2 is capacitive


5/14

Transfer of resistances & reactances to any

side

The Cu loss by I2 in secondary = I22 R2. If is the

equivalent resistance in the primary which wouldhave caused the same loss as R2 in the secondary,

then

Similarly, equivalent primary resistance as referredto secondary is

2

2

2

2

1

2

2

22

122

2

k

R

I

I

RRor,

RIRI

=

=

=

1

2

1RkR =

2

R


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Leakage reactances can also be transferred

from one winding to other ;

Total resistance referred to primary is

Total reactance referred to primary is

Total impedance of transformer referred to

primary is

2

2

2kXX =

1

2

1 XkX =

+=2101

RRR

+= 2101 XXX

2

01

2

0101XRZ +=


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Similarly, total resistance referred to secondary is

Similarly, total reactance referred to secondary is

Similarly, total impedance of transformer

referred to secondary is

+=

1202

RRR

+= 1202 XXX

2

02

2

0202 XRZ +=


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R02

X02

Impedance referred to secondary

Z02


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Equivalent circuit of Transformer

I1

E1

V1

I2

V2

E2

R 1 X 1 I 1

I0

I2

'

V 1 E 1 E 2

R 2 X 2

R 0 X 0

I2

Z LV 2

A) Circuit

B) Equivalent circuit of transformer

Iw I


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Equivalent circuit of Transformer referred to

primaryR1 X1 I1

I0

I2'

V1 E2'= E1

R2' X2'

R0 X0 ZL'V2

'

I2'

I1

E2' = E2/K, R2' = R2/K

2, X2' = X2/K2, V2' =V2/K, ZL =ZL/K

2

E2/E1 = I1/I2 = K

R1 X1I1

I0

I2'

V1 E2'= E1

R2' X2'

ZL'

I2'

I1

R0 X0

V2'

D) Approximate equivalent circuit

Iw

Iw

I

I

C) Equivalent circuit with secondary impedances transferred to primary


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= R1 X01= X1I1

I0

I2'

V1

+R2' + X2'

ZL'

I2'

I1

R0 X0

V2'

R01

Approximate Equivalent circuit with secondary impedances

transferred to primary


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Transformer tests

The performance of a transformer can be calculated on the basis of its

equivalent circuit which contains the 4 main parameters:

1. Equivalent resistance R01(or R02)

2. Equivalent leakage reactance X01 (or X02)

3. Core loss resistance R0

4. Magnetizing reactance X0.

These parameters are determined from the following tests:

a) Open circuit test

b) Short circuit test


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Short Circuit test

This test is conducted to determine:1. Full-load copper loss

2. Equivalent resistance & reactance referred to metering side.

LV

supply

V

AW

Low Voltage windingHigh Voltage winding

A low voltage (5 -10% of normal primary voltage) at correct frequency is applied

to the primary winding & is continuously increased till full load currents flow both

in primary & secondary. Since applied voltage is small, flux linking with core is

very small & hence, iron loss can be neglected & reading of wattmeter givestotal copper losses at full load.

If Vsc is the voltage required to circulate rated load currents, then

2

01

2

010101

2

01 ; RZXRIWI

VZ

sc

sc

sc===

Transformer on Load

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