The Efficiency of the transformer is defined as the ratio of useful power output to the input power, the two being measured in the same unit. Its unit is either in Watts (W) or KW. Transformer efficiency is denoted by Ƞ.
- V2 – Secondary terminal voltage
- I2 – Full load secondary current
- Cosϕ2 – power factor of the load
- Pi – Iron losses = hysteresis losses + eddy current losses
- Pc – Full load copper losses = I22Res
If x is the fraction of the full load, the transformer efficiency at this fraction is given by the relation shown below
Maximum Efficiency Condition of a Transformer
The transformer efficiency at a given load and power factor is given by the relation shown below
The value of the terminal voltage V2 is approximately constant. Thus, for a given power factor the Transformer efficiency depends upon the load current I2. In the equation (1) shown above the numerator is constant and the transformer efficiency will be maximum if the denominator with respect to the variable I2 is equated to zero.
Thus, the efficiency of a transformer will be maximum when the copper or variable losses are equal to iron or constant losses.
From equation (2) the value of output current I2 at which the transformer efficiency will be maximum is given as
If x is the fraction of full load KVA at which the efficiency of the transformer is maximum
Then, copper losses = x2Pc (where Pc is the full load copper losses)
Iron losses = Pi
For maximum efficiency x2 Pc = Pi
Putting the value of x from the above equation (3) in equation (4) we will get