Distributed Equilibrium-Learning for Power Network Voltage Control with a Locally Connected Communication Network

We address the problem of voltage control in power distribution networks by coordinating the distributed energy resources (DERs) at different buses. This problem has been investigated actively via either distributed optimization-based or local feedback control-based approaches. The former one requires a strongly-connected communication network among all DERs for implementing the optimization algorithms, which is not yet realistic in existing distribution systems with under-deployed communication infrastructure. The latter one, on the other hand, has been proven to suffer from loss of network-wide operational optimality. In this paper, we propose a game-theoretic characterization for semi-local voltage control with only a locally connected communication network. We analyze the existence and uniqueness of the generalized Nash equilibrium (GNE) for this characterization, and develop a fully distributed equilibrium-learning algorithm that hinges on only neighbor-to-neighbor information exchange of DERs. Provable convergence results are provided along with numerical tests, to illustrate the robust convergence property of our algorithm.