The existence of multiple power flow solutions in unbalanced three-phase circuits

This paper presents a new phenomenon found for unbalanced power flow solutions-the existence of two voltage solutions at the neutral points of unbalanced three-phase circuits. The phenomenon is different from that found in traditional single-phase balanced power flow solutions. It is dependent on the degree of system or load unbalance. If the unbalance is reduced to zero, the two solutions will merge into one. This paper presents our observations and analysis on the problem. A test system is used to illustrate the practical significance of the phenomenon. We hope this work will stimulate further research on this challenging and interesting problem.