LAUSR

Under consensus-based economic dispatch (ED) algorithm, multiple agents, which control local generation units, cooperatively minimize the total generation cost subject to the balance of the generation and expected demand in smart grids. As ubiquitous time delays on communication links exist in communication networks, studying the effect of delays on the dispatch performance is of both theoretical merit and practical value for the efficient and stable operation of smart grids. In this paper, we consider a well-developed consensus-based ED protocol under constant time delays. We find that there always exists a sufficiently small learning gain parameter under finite constant delays such that the convergence of the consensus-based algorithm is guaranteed. Further, an analytical expression of the upper bound is established for the learning gain parameter, which is determined by the largest delay, the weight matrix and the parameters of generation cost functions. In order to guarantee the optimality of the final solution, we propose the updating rule for iterations when initial states are not received by their neighbors due to time delays. The optimality of the final solution under the proposed updating rule is analyzed. We validate our theoretical results through extensive simulation studies.