Certifying the Nonexistence of Feasible Path Between Power System Operating Points

By providing the optimal operating point that satisfies both the power flow equations and engineering limits, the optimal power flow (OPF) problem is central to power systems operations. While extensive research has focused on computing high-quality OPF solutions, assessing the feasibility of transitioning between operating points remains challenging since the feasible spaces of OPF problems may consist of multiple disconnected components. It is not possible to transition between operating points in different disconnected components without violating OPF constraints. To identify such situations, this paper introduces an algorithm for certifying the infeasibility of transitioning between two operating points within an OPF feasible space. As an indication of potential disconnectedness, the algorithm first seeks an infeasible point on the line connecting a pair of feasible points. The algorithm then certifies disconnectedness by using convex relaxation and bound tightening techniques to show that all points on the plane that is normal to this line are infeasible. Using this algorithm, we provide the first certifications of disconnected feasible spaces for a variety of OPF test cases.