Distributed algorithm for optimal power flow on an unbalanced radial network

The optimal power flow (OPF) problem is fundamental in power systems operation and planning. Large-scale renewable penetration calls for real-time feedback control, and hence the need for distributed solutions for the OPF problem. In this paper we propose a solution for an unbalanced radial distribution network. Our distributed algorithm is based on alternating direction method of multiplier (ADMM). The main idea is to exploit the tree topology of distribution networks and decompose the OPF problem in such a way that the subproblems in each ADMM macro-iteration either have closed-form solutions or reduce to eigenvalue problems whose size remains constant as the network size scales up. We present simulations on IEEE 13, 34, 37 and 123 bus unbalanced distribution network to illustrate the scalability and optimality of the proposed algorithm.