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

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , ,

    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 … Read more

    Polynomial SDP Cuts for Optimal Power Flow

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) prob- lem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack … Read more