Transformer Losses and Efficiency

All transformers have copper and core losses. Copper loss is power lost in the primary and secondary windings of a transformer due to the ohmic resistance of the windings.

Copper loss, in watts, can be found using below Equation.

Copper Loss = I_P² R_P + I_S² R_S

where

I_P = primary current

I_S = secondary current

R_P = primary winding resistance

R_S = secondary winding resistance

Core losses are caused by two factors: hysteresis and eddy current losses. Hysteresis loss is that energy lost by reversing the magnetic field in the core as the magnetizing AC rises and falls and reverses direction.

Eddy current loss is a result of induced currents circulating in the core.

The efficiency of a transformer can be calculated using below Equations.

where

PF = power factor of the load

Example 1:

A 5:1 step-down transformer has a full-load secondary current of 20 amps. A short circuit test for copper loss at full load gives a wattmeter reading of 100 W. If R_P = 0.3Ω, find R_S and power loss in the secondary.

Solution :

Copper Loss = I_P² R_P + I_S² R_S   =  100 W

To find I_P

I_P = (N_S/N_P) I_S

I_P = (1/5) 20 = 4 amps

To find R_S

I_S² R_S   =  100 – I_P² R_P

R_S   =  (100 – I_P² R_P ) / I_S²

R_S   = (100 – 4²  x 0.3 ) / 20²

R_S   = 0.24

Power loss in secondary = I_S² R_S   = 20² x 0.24 = 96 W

Example 2:

An open circuit test for core losses in a 10 kVA transformer gives a reading of 70 W. If the PF of the load is 90%, find efficiency at full load.

Solution :