# Efficiency Of A Transformer

Due to the losses in a transformer, its output power is less than the input power.

∴ Power output = Power input – Total losses

∴ Power input = Power output + Total losses = Power output + *P _{i}* +

*P*

_{Cu}The ratio of power output to power input of any device is called its *efficiency* (*η*).

Output power of a transformer at full-load = *V*_{2}*I*_{2ft}cos*θ*, where cos*θ* is the power factor of the load, *I*_{2ft}is the secondary current at full load and *V*_{2} is the rated secondary voltage of the transformer.

Full-load copper loss of the transformer = *I*_{2ft}*R*_{02}.

∴ Efficiency of the transformer at full load is given by

Now *V*_{2}*I*_{2ft} = *VA* rating of the transformer.

∴

i.e.,

Efficiency of the transformer at any load *m* is given by

where *m*= and *P _{Cuft}* is the Cu loss of the transformer at full load.

## 1.34 CONDITION FOR MAXIMUM EFFICIENCY

During working of a transformer at constant voltage and frequency, its efficiency varies with the load. Its efficiency increases as the load increases. At a certain load, its efficiency becomes maximum. If the transformer is further loaded, its efficiency starts decreasing. Figure 1.43 shows the plot of efficiency versus load current.

**Figure 1.43** Comparison Efficiency and Current

To determine the condition of maximum efficiency, let us assume that the power factor of the load remains constant and the secondary terminal voltage (*V*_{2}) is constant. Therefore, efficiency becomes only a function of load current (*I*_{2}).

For maximum efficiency

Now,

∴

i.e.,

i.e., *V*_{2}*I*_{2}cos*θ*+*P _{i}*+

*I*

_{2}

^{2}

*R*

_{02}–

*V*

_{2}

*I*

_{2}cos

*θ*–2

*I*

_{2}

^{2}

*R*

_{02}=0

i.e.,

*P*=

_{i}*I*

_{2}

^{2}

*R*

_{02}(1.66)

To achieve maximum efficiency,

*Iron loss*=

*Cu loss*

i.e.,

*Constant loss*=

*Variable loss*

### 1.34.1 Load Current at Maximum Efficiency

Let *I*_{2M} be the load current at maximum efficiency.

∴ *I*_{2M}^{2}*R*_{02}=*P _{i}*

i.e.,

Let

*I*

_{2ft}be the full-load current.

∴

i.e.,

Equation (1.67) shows the load current in terms of full-load current at maximum efficiency.

### 1.34.2 kVA Supplied at Maximum Efficiency

*For constant V*_{2} the kVA supplied is the function of load current only.

∴

In general,

where