Evaluation of line loss under load unbalance using the complex unbalance factor

The paper introduces simple criteria to evaluate the line loss under load unbalance by using the complex unbalance factor. The definitions of voltage and current unbalance factors have been extended from the conventional real values to the corresponding values. The complex-valued unbalance factor is composed of a magnitude and an argument portion. The magnitude portion is commonly used to evaluate the effects of load unbalance. In contrast, the argument portion is always neglected. The latter is considerable when the system configuration is asymmetrical or the phase load is unbalanced. The conventional approach which considers only the magnitude portion may therefore distort the explanation of the calculated results and lead to incorrect conclusions. The paper explores the effects of the argument portion as well as magnitude portion on line loss. Examples are given to demonstrate the effects of the phase load unbalance and the significance of the argument portion on the line loss