  Convex relaxation methods have been studied and used extensively to obtain an
optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex
relaxed power flow equations are also prerequisites for efficiently solving a
wide range of problems in power systems including mixed-integer nonlinear
programming (MINLP) and distributed optimization. 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
optimization (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 (DC)
programming problem, then efficiently solved by a penalty convex concave
procedure (CCP). CCP iteratively linearizes the concave parts of the power flow
constraints and solves a convex approximation of the DCP problem. Numerical
tests show that the proposed method can find a global or near-global optimal
solution to the AC OPF problem, and outperforms those semidefinite programming
(SDP) based algorithms.
