# Copper Loss In Transformer

The copper loss in the transformer is equal to the I2R loss. The copper loss is very important for the calculation of the transformer efficiency. The efficiency of the transformer can be improved by minimizing the copper loss and core loss.

In the transformer, the copper loss in the primary winding is Ip2Rp, and the copper loss in the secondary winding is Is2Rs loss, where Ip and Is are the primary and secondary current of the transformer and Rp and Rs are resistances of primary and secondary winding respectively.

The copper loss is the wastage of power due to I2R loss in the transformer winding, and the energy is wasted as heat. As both primary and secondary currents depend upon the percentage loading of the transformer, the current increases as the load on the transformer is increased. With an increase in the primary and the secondary current, the copper loss in the transformer increases with the load.

The copper loss value is not constant, and it varies as the load on the transformer is increased. That is why the copper loss is also called a variable loss.

The total copper loss (I2R) in the transformer is load-dependent. The copper losses are proportional to the square of the RMS current flowing in the winding and also proportional to the resistance of the winding. The resistance of the conductor varies with the rise in temperature.

The copper loss in the transformer is proportional to the square of the current flowing through the winding. When the load on the transformer is increased, the copper loss varies because of the increased current and increased resistance caused by temperature rise.

The resistance value of the copper or aluminum must be corrected for the maximum permissible rise of the transformer winding at the rated capacity of the transformer. For example, the resistance of the winding measured at 30° C must be corrected for 75° C for an oil-cooled transformer.

For copper winding, the increased value of resistance with temperature can be calculated using the following formula.

Where,

RL = Resistance at TL temperature
R0 = Resistance at ambient temperature
RL = Operating temperature
T0 = Ambient temperature

For aluminum winding, the increased value of resistance with temperature can be calculated using the following formula.

#### Example of increase of resistance with temperature

Let the resistance of three HV winding of the transformer be 0.967 Ω,0.968 Ω, and 0.967 Ω at 23.8° C. The average HV winding resistance per phase at 23.8°C is;

=(0.967+0.968+0.967)/3 =0.967 Ω

The average HV winding resistance per phase at 75°C is;
RL = R0 *  [(TL+235)/(To+235)]
R75  = 0.967 *  [(75+235)/(23.8+235)]
= 0.967 *  [(75+235)/(23.8+235)
R75  = 1.159 Ω

Percentage increase in resistance
=(1.159-0.967)/0.967 *100
= 19.85%

From the above calculation, it is clear that the resistance increases with an increase in temperature caused by the flow of current in a conductor.

### Example of Copper Loss

The full load copper loss of a transformer is 1000 watts, and the copper loss at half load(50% Load) will be;

Pcu  =  ( % Load/100)2 x P
=  ( 50/100)2 x 1000
=  ( 1/2)2 x 1000
= 1/4 x 1000
Pcu  =  250 Watts

Thus, the transformer’s copper loss at 50 % load is equal to 1/4 th of the full load copper loss.

The copper loss at 3/4 th load is equal to

Pcu = (3/4) x 1000 = 562.5 Watts

The copper loss at 1/4 th load is equal to

Pcu = (1/4) x 1000 = 62.5 Watts

The total transformer loss, Ptotal, at any load level can then be calculated from;

Where,