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Tight-and-cheap conic relaxation for the optimal reactive power dispatch problem

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

Abstract: The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modelled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of the ORPD problem and show that a round-off technique applied with this relaxation leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses.

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

Category 1: Linear, Cone and Semidefinite Programming

Citation: Christian Bingane, Miguel F. Anjos, and Sébastien Le Digabel. Tight-and-cheap conic relaxation for the optimal reactive power dispatch problem. IEEE Transactions on Power Systems, 2019.

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Entry Submitted: 10/06/2018
Entry Accepted: 10/08/2018
Entry Last Modified: 05/14/2019

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