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Convex relaxation for mixed-integer optimal power flow problems
C.-Y. Chang, S. Martínez, J. Cortés
Allerton Conference on Communications, Control, and Computing, Monticello, Illinois, 2017, pp. 307-314

Abstract

Recent years have witnessed the success of employing convex relaxations of the AC optimal power flow (OPF) problem to find global or near global optimal solutions. The majority of the focus has been on problem formulations where variables live in continuous spaces. Instead, general OPF problems may also involve discrete variables, such as control of capacitor banks or tap changers. Furthermore, those integer variables may introduce additional non-convex bilinear constraints, further complicating the solution of OPF problems. In this paper, we first rewrite the integer variables for topology design, control of tap changers, and capacitor banks as binary variables. We next incorporate those binary variables to a distributed semidefinite programming (SDP) convex formulation of the OPF problem. The proposed convex formulation incorporates the bilinear terms in a novel way that avoids the need for the commonly used McCormick approximation to deal with such terms. We compare the performance of our approach against existing nonlinear solvers for various classes of OPF problems.

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