Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities

This work revisits the semidefine programming (SDP) relaxation of the ac power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the convex quadratic relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% of the open cases considered, leaving only eight for future investigation.