The condition of maximum efficiency of the transformer is-

Concept:

A transformer has mainly two types of losses

• core losses
• copper losses.

Core loss, which is also referred as iron loss, consists of hysteresis loss and eddy current loss.

These two losses are constant when the transformer is charged. That means the amount of these losses does not depend upon the condition of secondary load of the transformer. In all loading condition, these are fixed.

Copper losses are directly proportional to the square of the load on the transformer.

\({W_{cu}} = {x^2}{W_{cufl}}\)

Here, x is the percentage of a full load of the transformer.

Wcufl­ is the copper losses at the full load.

The maximum efficiency in a transformer that occurs at copper losses is equal to iron losses.

Efficiency is maximum at some fraction x of full load.

\(x = \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)

Where Wi = iron losses

Wcu = copper losses

kVA at maximum efficiency is given by,

kVA at ηmax = full load kVA × \( \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)