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

Carleton Coffrin (Carleton.Coffrin***at***nicta.com.au)
Hassan Hijazi (hassan.hijazi***at***anu.edu.au)
Pascal Van Hentenryck (pvanhent***at***umich.edu)

Abstract: This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing semidefinite and quadratic programming relaxations and dominate existing cuts proposed in the litterature. Together with model intersections and bound tightening, the new linear cuts close 8 of the remaining 13 open test cases in the NESTA archive for the AC Optimal Power Flow problem.

Keywords: OPF, SDP, Convex relaxation, Cut generation

Category 1: Applications -- OR and Management Sciences

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: @article{Hijazi:15, year={2015}, month={Decembre}, journal={{ANU} Technical Report}, institution={{The Australian National University}}, title={Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Lifted Nonlinear Cuts}, author={Coffrin, Carleton and Hijazi, Hassan and Van Hentenryck, Pascal}, }

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Entry Submitted: 12/15/2015
Entry Accepted: 12/15/2015
Entry Last Modified: 01/04/2016

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