Voltage stability analysis in unbalanced power systems by optimal power flow

The deregulated market requires a great deal of attention to satisfy reliability, security and optimisation objectives. As is well known, the voltage stability problem may become more and more frequent in this new scenario. Various techniques have been proposed in order to incorporate voltage stability aspects into the classical analysis methods of power systems. However, some technical problems, such as unbalances typical of distribution or transmission systems, require suitable formulations in order to derive critical conditions and their dependence on interest parameters. Hence, a three-phase formulation arises in order to characterise properly the inability of unbalanced power systems to meet heavy load demand. More specifically, a three-phase constrained optimal power flow is proposed in which the load demand at the assigned bus is maximised, simultaneously satisfying power balance equations and various technical constraints. An application is presented with reference to the IEEE 13-bus test system, which highlights the feasibility and the goodness of the proposed technique. Sensitivity analyses are performed in order to capture the dependence of voltage stability on the level of unbalance.