The value of communication in the voltage regulation problem

We consider the problem of controlling the reactive power injection of microgenerators to regulate the voltage profile in a power distribution network. We consider a large class of purely local controllers including most of the solutions proposed in the literature, and we show that these strategies do not guarantee the desired regulation; namely, that for each of them there are equilibria that are not feasible with respect to the desired voltage constraints. We then show that, by adding short range communication between microgenerators, it is possible to design control strategies that provably converge to the feasible set, and we propose one possible strategy. This fundamental performance gap between local and networked strategies is finally illustrated via simulations.