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Achieving Acceleration for Distributed Economic Dispatch in Smart Grids Over Directed Networks

In this paper, the economic dispatch problem (EDP) in smart grids is investigated over a directed network, which concentrates on allocating the generation power among the generators to satisfy the load demands with minimal total generation cost while complying with all constraints of local generation capacity. Each generator possesses its own local generation cost, and the total generation cost is the sum of all local generation costs. To deal with EDP, most of the existing methods, such as strategy based on push-sum, surmount the unbalancedness induced by the directed network via employing column-stochastic weights, which might be infeasible in distributed implementation. In contrast, in order to be suitable for the directed network with row-stochastic weights, we develop a novel directed distributed Lagrangian momentum algorithm, named as D-DLM, which integrates distributed gradient tracking method with two types of momentum terms and utilizes non-uniform step-sizes with respect to the updates of Lagrangian multipliers. If the largest step-size and the maximum momentum coefficient are positive and sufficiently small, D-DLM can linearly allocate the optimal dispatch on condition that the generation costs are smooth and strongly convex. Finally, a variety of studies on EDP in smart grids are simulated.