A Distributed Approach for the Optimal Power-Flow Problem Based on ADMM and Sequential Convex Approximations

The optimal power-flow (OPF) problem, which plays a central role in operating electrical networks, is considered. The problem is nonconvex and is, in fact, NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semidefinite programming relaxation-based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on an alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated with each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically substantiated. Finally, the proposed algorithm is evaluated on a number of test examples, where the convergence properties of the proposed algorithm are numerically substantiated, and the performance is compared with a global optimal method.