  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. 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.

Optimization and Control