A distributed consensus based algorithm for economic dispatch over time-varying digraphs

In this paper, a consensus based fully distributed optimization algorithm is proposed for solving economic dispatch problem (EDP) in smart grid. Since the incremental cost of all buses reach consensus when the optimal solution is achieved, it is selected as a consensus variable. An additional variable at each bus, called "surplus" is added to record the local power mismatch, which is used as a feedback variable to purse the balance between power supply and demand. Different from most of the existing distributed methods which require the communication network to be balanced, the algorithm uses a row random matrix and a column random matrix to precisely steer all the agents to asymptotically converge to a global optimal solution over a time-varying directed communication network. Due to the use of a fixed step size, the proposed algorithm also outperforms other algorithms in terms of convergence speed. The graph and eigenvalue perturbation theories are employed for the algorithm convergence analysis, and the upper bound of the parameters required for convergence is given theoretically. Finally, the performance and scalability of the proposed distributed algorithm are verified by several case studies conducted on the IEEE 14-bus power system and a 200-node test system.