Distributed Learning Algorithms and Lossless Convex Relaxation for Economic Dispatch with Transmission Losses and Capacity Limits

This paper considers problems of economic dispatch in power networks that contain independent power generation units and loads. For efficient distributed economic dispatch, we present a mechanism of multiagent learning in which each agent corresponding to a generation unit updates the power generation based on the received information from the neighborhood. The convergence of the proposed distributed learning algorithm to the global optimal solution is analyzed. Another method of distributed economic dispatch we propose is a decentralized iterative linear projection method in which the necessary optimality conditions are solved without considering the generation capacities and the obtained solutions are iteratively projected onto the convex set corresponding to the generation capacities. A centralized method based on semidefinite programming for economic dispatch with a loss coefficient matrix is also presented for comparisons. For demonstration, the proposed methods of distributed economic dispatch are applied to a 6-generator test case and the three different methods of economic dispatch give the same solutions. We also analyze parametric dependence of the optimal power generation profiles on varying power demands in economic dispatch.