A Necessary and Sufficient Condition for Computed OPF Solutions to be Locally Optimal

Although a significant amount of research has been directed to developing necessary and sufficient conditions for the optimal solutions of several engineering problems, there is little work on the development of a necessary and sufficient condition for optimal power flow (OPF) solutions. This paper seeks to develop the following: (1) a necessary and sufficient condition for a local OPF solution, and (2) a necessary and sufficient condition for an OPF Karush-Kuhn-Tucker (KKT) solution. The derived necessary and sufficient conditions were numerically verified on IEEE 30-, 57- and 118-bus systems. Computationally, the derived necessary and sufficient condition is also useful in assisting existing OPF methods to obtain OPF solutions instead of KKT solutions (i.e., KKT saddle points).