Optimal operation and design of power transmission systems involves the solution of a non-convex optimization problem. In particular, the non-convexity in the optimal power flow problem arises due to bilinear terms in the constraints of the problem. Global optimization methods typically rely on convex relaxations of non-convex constraints.
While off-the-shelf convex relaxations have performed poorly for this problem, in this work we build a tight convex relaxation that is inspired and informed by the physics of the problem. Further, we use this convex relaxation in a novel, parallelized bound tightening procedure. The algorithm developed in this work is tested on two benchmarking libraries. The algorithm successfully solves all but one problem across the two libraries, demonstrating the efficacy of the proposed approach.