text: abstract— in current power distribution systems, one of the
  most challenging operation tasks is to coordinate the networkwide distributed energy resources (ders) to maintain the
  stability of voltage magnitude of the system. this voltage control
  task has been investigated actively under either distributed
  optimization-based or local feedback control-based characterizations. the former architecture requires a strongly-connected
  communication network among all ders for implementing
  the optimization algorithms, a scenario not yet realistic in
  most of the 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 relies on only neighbor-toneighbor information exchange. provable convergence results
  are provided along with numerical tests which corroborate the
  robust convergence property of the proposed algorithm.