Distributed, anytime optimization in power-generator networks for economic dispatch

This paper considers the economic dispatch problem for a group of power generating units communicating over an arbitrary strongly connected, weight-balanced digraph. The goal of the group is to collectively meet a specified load while respecting individual generation bounds and minimizing the total generation cost, which corresponds to the sum of individual arbitrary convex functions. We introduce a distributed coordination algorithm, termed Laplacian-set-valued dynamics, and establish its asymptotic convergence to the solutions of the economic dispatch problem. In addition, we show that the algorithm is anytime, meaning that its executions are feasible solutions at all times and the total cost monotonically decreases as time elapses. The technical approach combines notions and tools from algebraic graph theory, nonsmooth analysis, set-valued dynamical systems, and penalty functions. Several simulations illustrate our results.