A Distributed Proximal Primal–Dual Algorithm for Energy Management With Transmission Losses in Smart Grid

This article aims to address the problem of distributed energy management for both the generation and demand sides in smart grid. Different from many existing works, we investigate the SWM problem with transmission losses. In addition, instead of transforming the local constraint into an approximate penalty function or the projection set, we consider it as a convex nonsmooth indicator function from a different viewpoint. For such a composite problem consisting of smooth and nonsmooth terms, we propose a distributed proximal primal–dual algorithm based on dual decomposition and operator splitting techniques. Each node performs the algorithm through only local computation and communication with limited information, especially not sharing the sensitive gradient directly. It is also proved that the proposed algorithm leads to the global optima at a convergence rate $O(\frac{1}{k})$ with a fixed stepsize. Several simulations verify the theoretical analysis and demonstrate the effectiveness of the proposed algorithm.