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Tight-and-cheap conic relaxation for the AC optimal power flow problem

Christian Bingane (christian.bingane***at***polymtl.ca)
Miguel Anjos (anjos***at***stanfordalumni.org)
Sébastien Le Digabel (sebastien.le-digabel***at***polymtl.ca)

Abstract: The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. We propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks.

Keywords: Conic optimization, optimal power flow, power systems, semidefinite programming.

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering (Other )

Category 3: Nonlinear Optimization (Other )

Citation: Christian Bingane, Miguel F. Anjos, and Sébastien Le Digabel. Tight-and-cheap conic relaxation for the AC optimal power flow problem. IEEE Transactions on Power Systems, 33(6):7181–7188, 2018.

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Entry Submitted: 01/16/2018
Entry Accepted: 01/16/2018
Entry Last Modified: 05/14/2019

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