Energy loss of 100 kVA transformer in third year

Energy loss = core loss for all hours + copper loss at peak × loss of load factor × hours.

Assumptions: "additional 10 kVA for subsequent two years" means the load is 85 kVA in year 2 and 95 kVA in year 3. The given copper loss (1100 W) is at rated load (100 kVA). The year has 8760 h.

Step 1: Third-year peak load

$$S_3 = 75 + 10 + 10 = 95 \text{ kVA}$$

Step 2: Loss of load factor

$$\begin{aligned} LLF &= 0.3\,LF + 0.7\,LF^2 = 0.3(0.8) + 0.7(0.8)^2 \\ &= 0.24 + 0.448 = 0.688 \end{aligned}$$

Step 3: Copper loss at 95 kVA

$$P_{cu} = 1100 \times \left(\frac{95}{100}\right)^2 = 1100 \times 0.9025 = 992.75 \text{ W}$$

Step 4: Annual energy losses

$$\begin{aligned} E_{cu} &= 0.99275 \times 0.688 \times 8760 = 5983.19 \text{ kWh} \\ E_{core} &= 0.200 \times 8760 = 1752.00 \text{ kWh} \\ E_{total} &= 5983.19 + 1752.00 = 7735.19 \text{ kWh} \end{aligned}$$

Answer: Energy loss in the third year ≈ 7735 kWh (copper 5983 kWh + core 1752 kWh).

Because the load factor is high (0.8) and the transformer is loaded at 95%, copper loss is the dominant part of the energy loss.