Efficient Bound Tightening Techniques for Convex Relaxations of AC Optimal Power Flow

Convex relaxations of the ac optimal power flow problem in certain cases can recover a globally optimal point of the original problem. However, in general their solutions are not guaranteed to be physically meaningful. While the relaxation quality can be improved by enforcing tighter bounds on variables, existing bound tightening methods do not scale well with grid size. This paper presents three methods for tightening bounds on branch angle differences that complement each other and are highly parallelizable. The proposed methods are computationally efficient even for large-scale grids and thus can be used as a preprocessing step before solving the convex relaxation of the optimal power flow problem. Numerical experiments demonstrate that these methods can significantly tighten most of the bounds in a fraction of the time required to solve the convex relaxation. In addition, the experimental results show that tighter bounds improve the relaxation quality and reduce the optimality gap for large-scale instances.