Capacity of transformer; efficiency at 25% overload

Capacity of a transformer is its rated apparent power output (in kVA) at rated voltage and frequency. It is given in kVA, not kW, because the copper loss depends on the current and the core loss on the voltage, both independent of the power factor of the load.

Given: 150 kVA, $P_i = 700$ W, $P_{cu,fl} = 1800$ W, pf $= 0.8$ lagging, load $= 125\%$ of full load, so $x = 1.25$.

Copper loss at 25% overload

$$P_{cu} = x^2P_{cu,fl} = 1.25^2\times1800 = 2812.5\ \text{W}$$

Iron loss is independent of load: $P_i = 700$ W.

Output power

$$P_{out} = x\times S\times\cos\phi = 1.25\times150\times0.8 = 150\ \text{kW}$$

Efficiency

$$\begin{aligned} \text{Total loss} &= 2812.5 + 700 = 3512.5\ \text{W} \\ \eta &= \frac{150\,000}{150\,000 + 3512.5} \times100 = 97.71\% \end{aligned}$$

Answer: copper loss = 2812.5 W; iron loss = 700 W; output = 150 kW; efficiency = 97.71%