A scheduled-asynchronous distributed optimization algorithm for the optimal power flow problem

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems. Finding an optimal solution for the OPF problem in real time is challenging and important in various applications. Recent studies show that a wide class of OPF problems have an exact semidefinite programming (SDP) convex relaxation. However, only few works have considered distributed algorithms to solve these. In this paper, we propose a scheduled-asynchronous algorithm with this objective. The proposed algorithm follows an ADMM-like iteration for every edge in the electrical network and is asynchronous in the sense that the agents do not simultaneously update their local variables, but only do so when they have received fresh information from all of their neighbors. In addition, if the electrical network topology is bipartite, the proposed algorithm has a convergence rate of O(1/n), where n is the iteration per agent. The asynchronous property and fast convergence rate make the proposed algorithm suitable for the OPF problem. Simulation studies demonstrate that the proposed algorithm is scalable with the number of buses and robust to network effects including delays and packet drops.