The iron loss in a 10 kVA transformer is 1 kW and the full load copper losses are 2 kW. The maximum efficiency occurs at a load of

Concept:

A transformer has mainly two types of losses

• core losses
• copper losses.

Core loss, which is also referred to 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 the secondary load of the transformer. In all loading conditions, 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 the 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 × \( \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)

Calculation:

Given that, full load kVA = 10 kVA

Iron losses (Wi) = 1 kW

Copper losses (Wcu) = 2 kW

Load kVA corresponds to maximum efficiency \(= 10 \times \sqrt {\frac{1}{2}} = 7.07\;kVA\)