Resistive network optimal power flow: uniqueness and algorithms

Abstract—The optimal power flow (OPF) problem minimizes the power loss in an electrical network by optimizing the voltage and power delivered at the network buses, and is a nonconvex problem that is generally hard to solve. By leveraging a recent development on the zero duality gap of OPF, we propose a second-order cone programming convex relaxation of the resistive network OPF, and study the uniqueness of the optimal solution using differential topology especially the Poincare–Hopf Index Theorem. We characterize the global uniqueness for different network topologies, e.g., line, radial and mesh networks. This serves as a starting point to design distributed local algorithms with global behaviors that have low complexity, computationally fast and can run under synchronous and asynchronous settings in practical power grids. I