Distributed consensus-based algorithm for social welfare in smart grid with transmission losses

Abstract

In this paper, we present a distributed consensus-based algorithm to solve the social welfare maximization problem. This is one of typical problems of distributed energy management in smart grid. In this problem, we consider not only the generator and demand, but also the transmission losses which make the feasibility set of the formulated problem a non-convex set. In solving this issue, we find a noticeable result that the primal problem has the same solution with a new convex optimization problem by getting the utmost out of the implied term in practice. Considering the general communication topology among generators and demands, we first design a finite step algorithm to make each generator and demand know the information of parameters of others. Then, we design a distributed algorithm and also prove the optimality and convergence of the proposed algorithm. Finally, the convergence and optimality are examined through extensive simulations.