Analysis of consensus-based economic dispatch algorithm under uniform time delays

In smart grid, the consensus-based economic dispatch algorithm is to allocate multiple generation units to meet expected demand, while minimizing the total generation cost in a distributed manner. Since the network-induced time delays ubiquitously exist in smart grid, the investigation of the effect of time delays on the dispatch performance is of both theoretical merit and practical value. In this paper, under a well-developed consensus-based economic dispatch protocol, we consider that the optimal generation power of each unit does not reach its upper or lower bounds. We firstly exploit that no matter how large the uniform finite delay could be, there always exists a small enough learning gain parameter such that the convergence of the dispatch algorithm can be ensured. Further, we establish an upper bound for the learning gain parameter which explicitly depends on the time delay and the generation cost parameters. Finally, we present the update method for initial iterations when no neighboring information is received due to time delays, and show the achieved optimality. Simulation studies validate the theoretical results.