Accelerated Algorithms for Distributed Economic Dispatch

Abstract

AbstractIn this chapter, we focus on introducing accelerated distributed optimization algorithms in the application scenario of the economic dispatch problem (EDP) for smart grids. This application scenario focuses on researching how to allocate the generation power among generators to match the load demand with the minimum total generation cost while observing all constraints on the local generation capacity. Each generator possesses its own local generation cost, and the total generation cost is the sum of all local generation costs. For the EDP question, most existing methods, such as push-sum-based strategies, overcome the unbalancedness induced by directed networks by employing column-stochastic weights, which may be infeasible in distributed implementations. In contrast, to apply to directed networks with row-stochastic weights, we develop a new directed distributed Lagrangian momentum algorithm, D-DLM, which integrates a distributed gradient tracking method with two momentum terms and non-uniform step-sizes in the update of the Lagrangian multipliers. Next, we give proof that if the maximum step-size and the maximum momentum coefficient are positive and sufficiently small, the D-DLM can be optimally dispatched with a linear assignment under smooth and strongly convex generation costs. Finally, various studies of EDP in smart grids are simulated.KeywordsDistributed economic dispatchSmart gridsDirected networkDistributed Lagrangian momentum algorithmLinear convergence