Module 3. Transformers

Lesson 13


13.1  Voltage Regulation

The electrical equipments are designed to be operated at a certain voltage. A tolerance limit is provided so that equipment may operate between this range. Transformers connect equipments and machines to the supply. If the terminal voltage drops too low below the rated value due to the load currents, it may affect the performance of the equipments. This is not desirable.    It is therefore important to specify and quantify that there is a voltage drop when certain load current is taken up from the transformer. Voltage regulation is quantified using two terms:

a.       Regulation down

b.      Regulation up

13.2  Regulation Down

Regulation down is the change in terminal voltage when a load current at any power factor is applied, expressed as a fraction of the no-load terminal voltage.


Vnl = no-load terminal voltage

Vl =  load terminal voltage

13.3  Regulation Up

Regulation up is the ratio of the change in the terminal voltage when a load at a given power factor is removed, and the load voltage.


Vnl = no-load terminal voltage.

Vl = load voltage.

13.4  Efficiency of Transformer

A practical transformer has following losses:

13.4.1  Iron losses

Since the iron core is subjected to alternating flux, the eddy current and hysteresis loss occurs in it. These two losses together are known as iron losses or core losses. The iron losses depend upon the supply frequency, maximum flux density in the core, volume of the core etc. It may be noted that magnitude of iron losses is quite small in a practical transformer.

13.4.2  Winding resistances

Since the windings consists of copper conductors, it immediately follows that both primary and secondary will have winding resistances. The primary resistance R1 and secondary resistance R2 act in series with the respective windings

13.4.3  Leakage reactances

Both primary and secondary currents produce flux. The flux which links both the winding is the useful flux and is called mutual flux. However, primary current would produce some flux 1 which would not link the secondary winding. Similarly, secondary current would produce some flux 2 that would not link the primary winding. The flux such as 1 or  2 which links only one winding is called leakage flux. The leakage flux paths are mainly through the air.

The dielectric losses take place in the insulation of the transformer due to the large electric stress. In the case of low voltage transformers this can be neglected. For constant voltage operation this can be assumed to be a constant.

The stray load losses arise out of the leakage fluxes of the transformer. These leakage fluxes link the metallic structural parts, tank etc. and produce eddy current losses in them. Thus they take place 'all round' the transformer instead of a definite place, hence the name 'stray'. Also the leakage flux is directly proportional to the load current unlike the mutual flux which is proportional to the applied voltage. Hence this loss is called 'stray load' loss. This can also be estimated experimentally. It can be modeled by another resistance in the series branch in the equivalent circuit. The stray load losses are very low in air-cored transformers due to the absence of the metallic tank.

Iron and copper losses are wasted as heat and temperature of the transformer rises. Therefore output power of the transformer will be always less than the input power drawn by the primary from the source and efficiency is defined as

Input power =

Output power =

13.4.4  Condition for maximum efficiency

Copper loss Pc =


Iron losses Pi = Pe + Ph


Pe = Eddy current loss

Ph = Hysteresis loss





Differentiating the above equation by


For maximum efficiency



Pi =


Condition for maximum efficiency of transformer lies when iron loss is equal to copper loss. i.e.

       Pi = Pc

13.5  All Day Efficiency

Heavy duty transformers are classified into power transformers and distribution transformers. Power transformers are used at the power generation stations and are operated as per need. In a power station there may be number of generators and transformers. Power transformers will be operated depending on the power generated. Thus, in a particular instant all the power transformers may not be put in use. Distribution transformers on the other hand are used in electrical network systems for power distribution. These have to be operated round the day (24 hours). There will be power loss due to operation of such transformers. The energy efficiency of these transformers is measured considering a 24 hour operation and is known as “All day efficiency”


1. Calculate regulation down value if the no load terminal voltage is 230 V and load voltage is 220 V

                                               = 4.3 %

1. Calculate regulation up value if the no load terminal voltage is 240 V and load voltage is 210 V


                                          = 14.2 %