Convergence Guarantees of a Distributed Network Equivalence Algorithm for Distribution-OPF

The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power flow (OPF) problem have generally been managed by approximated or relaxed models; however, they may lead to infeasible or inaccurate solutions. Decomposition-based methods have also been used to solve the OPF problems. But the existing methods require several message passing rounds for relatively small systems, causing significant delays in decision making; related feedback-based methods also suffer from slow tracking of the optimal solutions. In this paper, we propose a provably convergent distributed algorithm to solve the nonlinear OPF problem for power distribution systems. Our method is based on a previously developed decomposition-based optimization method that employs the network equivalence method. We present a thorough mathematical analysis that includes sufficient conditions that guarantee convergence of the method. We also present simulation results using the IEEE-123 bus test system to demonstrate the algorithm's effectiveness and provide additional insights into theoretical results.