Feasible Region of Optimal Power Flow: Characterization and Applications

The feasible region plays a fundamental role in solving optimal power flow (OPF) problems. In this paper, a mathematical characterization of the feasible region is presented. An equivalence is established between the feasible region of an OPF problem and the union of regular stable equilibrium manifolds of a quotient gradient system (QGS) that is derived from the set of equality and inequality constraints of the OPF problem. It is further shown that the QGS is completely stable and that each trajectory converges to an equilibrium manifold, making the QGS trajectories useful in locating feasible OPF solutions. The theoretical results developed in this paper have been numerically verified in several OPF problems. Finally, the notion of a local feasible region is proposed and discussed.