  In this paper, we develop a data-driven voltage regulation framework for
distributed energy resources (DERs) in a balanced radial power distribution
system. The objective is to determine optimal DER power injections that
minimize the voltage deviations from a desirable voltage range without knowing
a complete power distribution system model a priori. The nonlinear relationship
between the voltage magnitudes and the power injections in the power
distribution system is approximated by a linear model, the parameters of
which---referred to as the voltage sensitivities---can be computed directly
using information on the topology and the line parameters. Assuming the
knowledge of feasible topology configurations and distribution line
resistance-to-reactance ratios, the true topology configuration and
corresponding line parameters can be estimated effectively using a few sets of
measurements on voltage magnitudes and power injections. Using the estimated
voltage sensitivities, the optimal DER power injections can be readily
determined by solving a convex optimization problem. The proposed framework is
intrinsically adaptive to changes in system conditions such as unknown topology
reconfiguration due to its data-driven nature. The effectiveness and efficiency
of the proposed framework is validated via numerical simulations on the IEEE
123-bus distribution test feeder.
