A distributed stochastic gradient algorithm for economic dispatch over directed network with communication delays

摘要

Economic dispatch problem (EDP) is one of the fundamental optimization problems in power systems, which involves a coupling linear constraint and several individual box constraints. In this paper, we propose a distributed stochastic gradient descent algorithm based on consensus theory to solve the EDP under directed network, where the convex cost function for each generator only needs to satisfy the condition that the function is strictly convex with Lipschitz continuous gradient. The proposed algorithm utilizes stochastic gradient descent to update values of generators for dealing with the noise which is incurred during the gradient estimation, and the step-sizes are heterogeneous. Under strictly convex assumption on objective functions, the algorithm can seek the exact optimal solution with probability one at the rate of (O(ln K/root K)), where K is the number of iteration. Furthermore, the algorithm is also suitable and effective to the network with communication delays if the communication delays are bounded. Simulation results illustrate the effectiveness of the algorithm.