Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment

This paper considers the economic dispatch problem for a network of power generating units communicating over a strongly connected, weight-balanced digraph. The collective aim is to meet a power demand while respecting individual generator constraints and minimizing the total generation cost. In power networks, this problem is also referred to as tertiary control. We design a distributed coordination algorithm consisting of two interconnected dynamical systems. One block uses dynamic average consensus to estimate the evolving mismatch in load satisfaction given the generation levels of the units. The other block adjusts the generation levels based on the optimization objective and the estimate of the load mismatch. Our convergence analysis shows that the resulting strategy provably converges to the solution of the dispatch problem starting from any initial power allocation, and therefore does not require any specific procedure for initialization. We also characterize the algorithm robustness properties against the addition and deletion of units (capturing scenarios with intermittent power generation) and its ability to track time-varying loads. Our technical approach employs a novel refinement of the LaSalle Invariance Principle for differential inclusions, that we also establish and is of independent interest. Several simulations illustrate our results.