Define loss of load factor

Loss of load factor (LLF), also called loss factor, is the ratio of the average power loss in a system element over a period to the power loss at peak load during that period:

$$LLF = \frac{\text{Average power loss}}{\text{Power loss at peak load}} = \frac{\text{Energy loss in time } T}{P_{loss,peak} \times T}$$

Since copper loss varies as the square of the current, $LLF = \frac{1}{T}\int_0^T \left(\frac{P}{P_{max}}\right)^2 dt$. It always lies between $LF^2$ and $LF$, and an empirical relation is used in practice:

$$LLF = 0.3\,LF + 0.7\,LF^2$$

Significance in distribution design:

• Energy loss in feeders and transformer windings is found simply as $E_{loss} = P_{loss,peak} \times LLF \times 8760$ kWh/year, without a full hourly load curve.
• It is used to cost the losses over the life of the system, which decides the economic conductor size and transformer rating.
• Because LLF < LF, the % energy loss is lower than the % peak power loss ($\%E_{loss} = \%P_{loss,peak} \times LLF/LF$); designers use this to set acceptable peak loss limits.
• It shows the benefit of improving load factor (flatter load means lower loss per kWh sold).