T/F: % power loss affected by load factor

FALSE (for percentage power loss); load factor affects the percentage energy loss.

Reasons:

• Power loss at any instant is $P_{loss} = 3I^2R$. The percentage power loss at peak is

$$\%P_{loss} = \frac{3 I_{max}^2 R}{P_{max}} \times 100 = \frac{P_{max} R}{V^2 \cos^2\phi} \times 100$$

It depends only on the peak demand, voltage, power factor and resistance (conductor size and length). Load factor does not appear, so two load centres with the same peak but different load factors have the same % power loss.

• Load factor describes how the load varies with time. It therefore affects energy quantities:

$$\%E_{loss} = \%P_{loss} \times \frac{LLF}{LF}, \quad LLF = 0.3LF + 0.7LF^2$$

so $\%E_{loss} = \%P_{loss}(0.3 + 0.7LF)$.

Example: % peak power loss = 8%.

The % power loss stays 8% for both, while the % energy loss changes with LF.

• Indirectly, if the energy consumption is fixed, a higher LF lowers the peak demand and hence the peak power loss. In that sense the planner sees load factor influencing losses, but for a load centre of given peak demand the percentage power loss is independent of load factor.