Voltage Stability Analysis in Unbalanced Three-phase Power Systems with Complementarity Constraints

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 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. In this paper a new three-phase optimal power flow is proposed that makes use of complementarity constraints to take into account the effect of reactive generation limits on voltage stability in unbalanced power systems. 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.