Distributed algorithm for economic dispatch with transmission losses under digraph

Abstract

By taking transmission losses and directed communication into considered, a more practical scenario of economic dispatch problem is studied in the paper. It is formulated as a non-convex optimization problem. Using convex relaxation, the non-convex optimization problem is transformed into convex optimization problem, and the conditions to ensure that they have the same solution are given. Then, a consensus-based distributed algorithm with time-varying feedback gains is presented, which can be used to the general directed communication networks. Especially, the convergence and optimality of the proposed algorithm are proved by using multi-parameter eigenvalue perturbation theory and graph theory. Finally, simulation results validate the theoretical results and illustrate the effectiveness and advantages of the proposed algorithm.