A Duality-Based Convex Optimization Method for Distributed Energy Management in Smart Grid Networks

Abstract

Structural shift of power grids to decentralized microgrids, rooftop solar, and elastic customer loads implies that centralized optimal power flow becomes numerically infeasible and the centralized scheduler is challenged by communication bottlenecks and privacy risks, which are only partly addressed by a simple sub gradient based distributed algorithm, since lack of further regularization implies slow convergence and oscillating multipliers. In this paper a dual-based convex optimization approach to decentralized energy dispatch by dualizing local generation prices and coupling network constraints into a Lagrangian relaxation formulation which decomposes the global problem into completely separate local subproblems solved by local balancing units in parallel, without any exchange of cost data. Strong duality is obtained via Slater's condition over a convex direct-current power flow formulation; an augmented Lagrangian is derived with proximal regularization that ensure convergence even for local objectives which are non-strictly convex. By rewriting the dual gradient iteration as a zero-finding for the sum of maximal monotone operators, derive a linear convergence rate for the distributed primal dual algorithm under a metric sub regularity assumption on the error bounds, and bounds on communication complexity that related the required number of consensus iterations to the network diameter. The study presents an inertial accelerated ADMM for large scale deployment. Finally, numerical experiment compare plain and inertial distributed algorithms and assess performance scalability as a function of the size of the system against centralized dispatch.