Transformer On Load

Transformer on Load Φ2

Φ

Φ

Φ2 Φ2’ I0 V

Φ

Φ I2

1

Load

Fig. 4

Phasor diagram for Transformer on Load V1

V

1

I1 I2 '

θ1 θ0

I1

I2 ' θ1 θ0

I0

I0

Φ

I2

Φ θ2

Load I2 is resistive

Load I inductive

I2

K=1

K=1

E

E2 Fig. 5

2

2

is

Actual transformer: Winding resistance & magnetic leakage R V

X

1

I1

1

X E

1

2

Z1 = R 1 + X 1

2

1

E

R

2

I2

2

V

2

2

Z2 = R 2 + X 2

2

2

R1 & R2 : resistances of primary & secondary windings respectively. X1 & X2 : leakage reactances of primary & secondary windings respectively.

Phasor diagram of actual transformer

a) I2 is resistive

b) I2 is inductive

c) I2 is capacitive

Transfer of resistances & reactances to any side •

The Cu loss by I2 in secondary = I22 R2. If R 2 ′is the equivalent resistance in the primary which would have caused the same loss as R2 in the secondary, then 2

2

I 2 R 2 = I1 R 2

′

R2 R2 ′ or, R 2 = = 2 k2  I1     I2 

•

Similarly, equivalent primary resistance as referred to secondary is ′ R1 = k 2R1

• Leakage reactances can also be transferred from one winding to other ; X2

′

X2 = 2 k

′ X1 = k 2 X1

Total resistance referred to primary is Total reactance referred to primary is

R 01 = R 1 + R 2

X 01 = X 1 + X 2

• Total impedance of transformer referred to primary is 2 2

Z 01 = R 01 + X 01

′

′

Similarly, total resistance referred to secondary is

′

R 02 = R 2 + R 1

Similarly, total reactance referred to secondary is

′

X 02 = X 2 + X 1

Similarly, total impedance of transformer referred to secondary is 2

Z 02 = R 02 + X 02

2

Z R

Impedance referred to secondary

02

02

X

02

Equivalent circuit of Transformer Φ

I1 V

E

1

E

1

I2 V

2

A) Circuit R

1

X

Iw V

1

R

0

I2 '

I1

1

I0

R

2

X

I2

2

Iμ X

0

E

1

E

2

B) Equivalent circuit of transformer

V

2

Z

L

2

Equivalent circuit of Transformer referred to primary R1

I0

Iw V1

I2'

I1

X1

R0

X2'

R 2'

Iμ

X0

V2' ZL'

E2'= E1

E2/E1 = I1/I2 = K

I2'

I1

E2' = E2/K, R2' = R2/K2, X2' = X2/K2, V2' =V2/K, Z′L =ZL/K2

C) Equivalent circuit with secondary impedances transferred to primary I1

R1

I2'

X1

R2'

X2 '

I0

Iw V1

Iμ R0

I1

E2' = E1

X0

I2'

D) Approximate equivalent circuit

ZL '

V2'

Approximate Equivalent circuit with secondary impedances transferred to primary I1

R01 = R1+R 2'

X01= X1 + X2'

I 2'

I0 V1

R0

ZL

X0

V2' I1

I2'

'

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

Open circuit test W V1

A

V

V2=E2

Low Voltage winding

High Voltage winding

Open Circuit Test

• As the primary no-load current I0 is small, Copper loss is negligibly small in primary & nil in secondary. Hence, wattmeter reading represents the core loss under no load condition. • Core loss = W = input power on no-load = V1I0cosΦ0 => cosΦ0 = W/(V1I0) Hence, Iw = I0 cos Φ0 & Iμ=I0sin Φ0 Also, X0 = V1/ Iμ & R0 = V1/ Iw

Short Circuit test •

This test is conducted to determine: 1. Full-load copper loss 2. Equivalent resistance & reactance referred to metering side. W LV supply

A

V

High Voltage winding

•

•

Low 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 gives total copper losses at full load. If Vsc is the voltage required to circulate rated load currents, then

Z 01 =

Vsc 2 2 2 ;W = I sc R01 ⇒ X 01 = Z 01 − R01 I sc