# 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 = IP2 RP + IS2 RS

where

IP = primary current

IS = secondary current

RP = primary winding resistance

RS = 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 RP = 0.3Ω, find RS and power loss in the secondary.

Solution :

Copper Loss = IP2 RP + IS2 RS   =  100 W

To find IP I= (NS/NP) IS

I= (1/5) 20 = 4 amps

To find RS

IS2 RS   =  100 – IP2 RP

RS   =  (100 – IP2 RP ) / IS2

RS   = (100 – 4 x 0.3 ) / 202

RS   = 0.24

Power loss in secondary = IS2 RS   = 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.

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