An Initialization-Free Distributed Algorithm for Economic Dispatch Problem

Abstract

This paper investigates the conventional distributed economic dispatch problem in the smart grid, in which the objective function is the sum of all local cost functions with equality demand constraints and inequality generating capacity constraints of each generator. Furthermore, the local cost function is known only by each generator itself. To handle the inequality constraints, a nonsmooth exact penalty function is introduced. Based on the above transformation, an initialization-free distributed algorithm with fixed step-size is proposed for solving the economic dispatch problem over the undirected network. Moreover, it is prove that the optimal solution can be achieved at an exponential convergence speed. Furthermore, to deal with the dispatch problem over the directed network, the algorithm is modified by using the row stochastic matrix. Finally, we provide several simulations to illustrate the effectiveness of the proposed algorithms.