Question

A transformer rated 200 V/500 V, 10 KVA has a core loss of 100 watts, what is the maximum efficiency of transformer at 0.8 lagging power factor. If full load copper loss is 200 Watt.
1. 94.5%
2. 96.6%
3. 97.3%
4. None of these

Answer 1

Correct Answer - Option 2 : 96.6%

Concept:

A transformer has mainly two types of losses

1. Core losses

2. 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.

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

Where,

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

W_cufl is the copper losses at the full load.

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

The fraction of Loading which occurs at maximum efficiency is given by

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

Where W_i = iron losses

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

η_max = \(\frac{P_0}{P_0+losses}=\frac{(KVA_{max})\ cosϕ}{(KVA_{max})\ cosϕ\ +\ 2W_i}\)

APPLICATION:

Given: W_i = 100 W, W_{cu fl} = 200 W, Rated KVA = 10 kVA, cos ϕ = 0.8

\(x = \sqrt {\frac{{{W_i}}}{{{W_{cu\ fl}}}}}\) = \(\sqrt{\frac{100}{{200}}}\) = 0.707

(KVA)_max = x (KVA)_rated = 0.707 × 10 = 7.07 kVA

η_max = \(\frac{7.07\times0.8\times10^3}{7.07\times0.8\times10^3+2(100)}\)

= 0.965

≈ 96.5 %