Stochastic gradient-push for economic dispatch on time-varying directed networks with delays

Abstract Economic dispatch problem (EDP) is an elementary optimization problem of power systems whose purpose is to minimize the total generation cost while meeting total demands and complying with individual generator output constraints. This paper proposes a distributed optimization algorithm with noisy gradient based on stochastic gradient-push approach to solve the EDP on time-varying directed communication networks potentially with time delays. It shows that the proposed algorithm can be ensured to solve the EDP when the time-varying directed communication networks are uniformly jointly strongly connected. The algorithm with asynchronous step-sizes can deal with the finite time-varying delays on communication links as well. The generation cost functions are considered as strictly convex and strongly convex functions respectively with convergence rate of O l n k / k and O ln k / k . Simulation results are provided to validate the availability of the algorithm.