Distributed Generator Coordination for Initialization and Anytime Optimization in Economic Dispatch

This paper considers the economic dispatch problem for a group of generator units communicating over an arbitrary weight-balanced digraph. The objective of the individual units is to collectively generate power to satisfy a certain load while minimizing the total generation cost, which corresponds to the sum of individual arbitrary convex functions. We propose a class of distributed Laplacian-gradient dynamics that are guaranteed to asymptotically find the solution to the economic dispatch problem with and without generator constraints. The proposed coordination algorithms are anytime, meaning that its trajectories are feasible solutions at any time before convergence, and they become better solutions as time elapses. In addition, we design the provably correct DETERMINE FEASIBLE ALLOCATION strategy that handles generator initialization and the addition and deletion of units via a message passing routine over a spanning tree of the network. Our technical approach combines notions and tools from algebraic graph theory, distributed algorithms, nonsmooth analysis, set-valued dynamical systems, and penalty functions. Simulations illustrate our results.