Monthly energy loss in four secondary lines

Assumptions: the 80 kVA peak is shared equally by the four lines, load on each line is uniformly distributed, lines are 3-phase at 400 V, and a month = 30 days = 720 h.

Step 1: Current per line

Peak load per line $= 80/4 = 20$ kVA.

$$I = \frac{20\,000}{\sqrt3\times400} = 28.87\ \text{A}$$

Step 2: Peak power loss per line (UDL)

For a uniformly distributed load, 3-phase loss $= 3\cdot\frac13 I^2 R = I^2 R$, where $R = 1\times1.5 = 1.5\ \Omega$ per phase.

$$P_{L,line} = 28.87^2\times1.5 = 1250\ \text{W}$$

Total peak loss in 4 lines:

$$P_{L,peak} = 4\times1250 = 5000\ \text{W} = 5\ \text{kW}$$

Step 3: Loss load factor

$$\begin{aligned} LLF &= 0.3LF + 0.7LF^2\\ &= 0.3(0.4) + 0.7(0.4)^2 = 0.12 + 0.112 = 0.232 \end{aligned}$$

Step 4: Monthly energy loss

$$\begin{aligned} E_{loss} &= P_{L,peak}\times LLF\times720\\ &= 5\times0.232\times720 = 835.2\ \text{kWh} \end{aligned}$$

Summary

Note: if the whole line load were assumed lumped at the far end, the loss would be three times larger (2505.6 kWh); the uniform-load assumption is the usual one for LT distribution lines serving houses along the route.

Answer: Monthly energy loss in the lines ≈ 835 kWh.