A Component-Based Dual Decomposition Method for the OPF Problem

Abstract: This paper proposes a component-based dual decomposition of the nonconvex AC optimal power flow (OPF) problem, where the modified dual function is solved in a distributed fashion. The main contribution of this work is that is demonstrates that a distributed method with carefully tuned parameters can converge to globally optimal solutions despite the inherent nonconvexity of the problem and the absence of theoretical guarantees of convergence. This paper is the first to conduct extensive numerical analysis resulting in the identification and tabulation of the algorithmic parameter settings that are crucial for the convergence of the method on 72 AC OPF test instances. Moreover, this work provides a deeper insight into the geometry of the modified Lagrange dual function of the OPF problem and highlights the conditions that make this function differentiable. This numerical demonstration of convergence coupled with the scalability and the privacy preserving nature of the proposed method makes it well suited for smart grid applications such as multi-period OPF with demand response (DR) and security constrained unit commitment (SCUC) with contingency constraints and multiple transmission system operators (TSOs).