Optimal Power Flow in Distribution Networks

The optimal power flow (OPF) problem seeks to control the generation/consumption of generators/loads to optimize certain objectives such as to minimize the generation cost or power loss in the network. It is becoming increasingly important for distribution networks due to the emerging distributed generation and controllable loads. In this paper, we study the OPF problem in distribution networks. In particular, OPF is nonconvex and we study solving it through convex relaxations. We prove that after a “small” modification to the OPF problem, the solution to its second-order-cone programming (SOCP) relaxation is the global optimum of OPF, under a “mild” condition that can be checked prior to solving the relaxation. Empirical studies justify that the modification to OPF is “small” and that the “mild” condition holds for all test distribution networks, including the IEEE 13-bus test distribution network and practical distribution networks with high penetration of distributed generation.