Lecture 6

Inductive Load

• In the case of inductive load, the secondary voltage I2 leads V2 by an angle 2.

• The angle 1 between V1 and I1 gives the power factor angle of the transformer.

Equivalent Resistance, Reactance and ImpedanceThe resistances and reactance of the two windings of a transformer can be transferred to any one of the tow windings.

The advantage of concentrating both resistances and reactances in one winding is that it makes calculations very simple and easy because one has then to work in one winding only.

It will be provided that the resistance R2, X2, in secondary is equivalent to R2/K2, X2/K2 in primary.

The value R2/K2, X2/K2 will be denoted by R2’, X2

’ the equivalent secondary resistance as referred to primary.

The power loss of resistance R2 in secondary is= I22R2.

The power loss of resistance R2’ when R2 is referred to in secondary is= I1

2R2’.

Equating the above two power, we obtain2

22

'2

21

RIRI 22

2

2

1

2'2

orK

RR

I

IR

Similarly, equivalent primary resistance as referred to secondary is 21

'1

KRR

Similarly, the leakage reactances can also be transferred from one winding to the other in the same way as resistance. Thus

21

'1

and2/2

'2

KXXKXX

Total or effective resistance and reactance of the transformer as referred to primary is

2/21

'2101

Similarly,

2/21

'2101

primary toreferredasresistancesecondaryequivalentresistanceprimary01

KXXXXX

KRRRRR

R

Similarly total or effective resistance of the transformer as referred to secondary is

212

'1202

Similarly,

212

'1202

primarytoreferredasresistanceprimaryequivalentresistancesecondary02

KXXXXX

KRRRRR

R

Total or effective impedance of the transformer as referred to primary is

Similarly total or effective impedance of the transformer as referred to secondary is

01

011tan201

201010101 R

XXRjXRZ

02

021tan202

202020202 R

XXRjXRZ

As shown in Fig. 32.30(a)

As shown in Fig. 32.30(b)

Equivalent Circuit The transformer shown in Fig. 30.37(a) can be resolved into an equivalent circuit in as shown in Fig. 30.37 (b).

To make transformer calculation simpler, it is preferable to transfer voltage, current and impedance either to the primary or to the secondary.

The primary equivalent of the secondary induced voltage is E2

’=E2/K=E1.

Similarly, primary equivalent of the secondary terminal or output voltage is V2

’=V2/K.

Primary equivalent of the secondary current is I2

’=I2K.

For transferring secondary impedance to primary, K2 is used.

The secondary circuit is shown in Fig. 30.38(a) and its equivalent primary values are shown in Fig. 30.38(b).

R2’= R2/K2; X2

’= X2/K2 ; ZL’= ZL/K2 ; E2

’=E2/K=E1.

The total equivalent circuit of the transformer is obtained by adding in the primary impedance as shown in Fig. 32.39.

This is known as the exact equivalent circuit but it presents a somewhat harder circuit problem to solve.

A simplification can be made by transferring the exciting circuit across the terminal as in Fig. 32.40 or in Fig. 32.41 (a).

Further simplification may be achieved by omitting I0 altogether as shown in Fig. 32.41(b).

From Fig. 32.39, it is found that total impedance between the input terminal is

''2

)''2

(1

)''2

(1

LZZmZLZZmZZ

LZZmZZZ

.'2

'2

'2

;111

;00

where, jXRZjXRZjXRmZ

Zm is called impedance of the exciting circuit.

''2

)''2

(111

LZZmZLZZmZZIVThe input voltage can be given by