  In electricity distribution networks, the increasing penetration of renewable
energy generation necessitates faster and more sophisticated voltage controls.
Unfortunately, recent research shows that local voltage control fails in
achieving the desired regulation, unless there is communication between the
controllers. However, the communication infrastructure for distribution systems
is less reliable and less ubiquitous as compared to that for the bulk
transmission system. In this paper, we design distributed voltage control that
uses limited communication. That is, only neighboring buses need to communicate
a few bits between each other for each control step. We investigate how these
controllers can achieve the desired asymptotic behavior of the voltage
regulation and we provide upper bounds on the number of bits that are needed to
ensure a predefined accuracy of the regulation. Finally, we illustrate the
results by numerical simulations.
