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This paper considers state-of-the-art convex relaxations for the AC powerflow equations and introduces new valid cuts based on convex envelopes andlifted nonlinear constraints. These valid linear inequalities strengthenexisting semidefinite and quadratic programming relaxations and dominateexisting cuts proposed in the litterature. Together with model intersectionsand bound tightening, the new linear cuts close 8 of the remaining 16 open testcases in the NESTA archive for the AC Optimal Power Flow problem.

Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Lifted Nonlinear Cuts