Monthly energy loss of 50 kVA transformer

A transformer has two losses: the core (no-load) loss, present all 720 h of the month, and the copper loss, which varies with the square of the load and is averaged using the loss load factor (LLF). Month taken as 30 days = 720 h.

Step 1: Core loss energy

$$E_{core} = 120\times720 = 86\,400\ \text{Wh} = 86.4\ \text{kWh}$$

Step 2: Copper loss at peak

Copper loss varies as $(S/S_{rated})^2$:

$$P_{cu,peak} = 200\times\left(\frac{30}{50}\right)^2 = 200\times0.36 = 72\ \text{W}$$

Step 3: Loss load factor

$$LLF = 0.3(0.3) + 0.7(0.3)^2 = 0.09 + 0.063 = 0.153$$

Step 4: Copper loss energy

$$E_{cu} = 72\times0.153\times720 = 7931.5\ \text{Wh} = 7.93\ \text{kWh}$$

Step 5: Energy delivered in the month

Peak demand in kW $= 30\times0.9 = 27$ kW.

$$E_{out} = 27\times0.3\times720 = 5832\ \text{kWh}$$

Step 6: Percentage loss

$$\begin{aligned} E_{loss} &= 86.4 + 7.93 = 94.33\ \text{kWh}\\ \%\,\text{loss} &= \frac{94.33}{5832}\times100 = 1.62\ \% \end{aligned}$$

(If expressed on input energy, $94.33/(5832+94.33) = 1.59\ \%$.)

Observation: at low load factor the core loss dominates (over 90 % of the loss), so for rural transformers with low LF, low no-load-loss (e.g. amorphous core) designs are preferred.

Answer: Monthly loss ≈ 94.3 kWh, i.e. about 1.62 % of the energy delivered.