  Voltage control plays an important role in the operation of electricity
distribution networks, especially with high penetration of distributed energy
resources. These resources introduce significant and fast varying
uncertainties. In this paper, we focus on reactive power compensation to
control voltage in the presence of uncertainties. We adopt a chance constraint
approach that accounts for arbitrary correlations between renewable resources
at each of the buses. We show how the problem can be solved efficiently using
historical samples via a stochastic quasi gradient method. We also show that
this optimization problem is convex for a wide variety of probabilistic
distributions. Compared to conventional per-bus chance constraints, our
formulation is more robust to uncertainty and more computationally tractable.
We illustrate the results using standard IEEE distribution test feeders.
