Voltage stability in unbalanced power systems: a new complementarity constraints-based approach

Voltage stability has become a fundamental issue in the new, liberalized markets due to the fact that the new power systems are approaching more and more the stability limits. Then, several approaches were proposed in the relevant literature to find the critical conditions and recently the problem was faced also with reference to unbalanced three phase power systems. The unbalances, in fact, can be responsible of more critical stability conditions than in balanced power systems. Continuation power flow and optimal power flows were applied to analyze such conditions. This paper deals with voltage stability analysis in unbalanced power systems and proposes a new optimization model to determine the critical point based on the use of complementarity constraints. Different formulations, with increasing complexity, of the optimization model are proposed and tested. In particular, the maximum stability margin is calculated by a single-stage or a multi-stage procedure that accounts for the relationship between the actual operating point and the maximum loading point. In addition, the multi-stage maximum stability margin problem is formulated also in a probabilistic framework to account for the uncertainties affecting the input data (e.g., load powers). An application is presented on a test system highlighting the feasibility and the goodness of the proposed technique. Both load and line unbalances are taken into account to capture the dependence of voltage stability on the level of unbalances.