Recover feasible solutions for SOCP relaxation of optimal power flow problems in mesh networks

Abstract

The AC optimal power flow (OPF) problem is essential for the schedule and operation of power systems. Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the OPF problem. When the exactness of convex relaxations is not guaranteed, it is important to recover a feasible solution for the convex relaxation methods. This paper presents an alternative convex optimisation (ACP) approach that can efficiently recover a feasible solution from the result of second-order cone programming (SOCP) relaxed OPF in mesh networks. The OPF problem is first formulated as a difference-of-convex programming (DCP) problem, then efficiently solved by a penalty convex concave procedure (CCP). By using the solution of a tightened SOCP OPF as an initial point, the proposed algorithm is able to find a global or near-global optimal solution to the AC OPF problem. Numerical tests show that the proposed method outperforms those semi-definite programming (SDP) and quadratically constrained quadratic programming (QCQP)-based algorithms.