  Modern distribution grids are currently being challenged by frequent and
sizable voltage fluctuations, due mainly to the increasing deployment of
electric vehicles and renewable generators. Existing approaches to maintaining
bus voltage magnitudes within the desired region can cope with either
traditional utility-owned devices (e.g., shunt capacitors), or contemporary
smart inverters that come with distributed generation units (e.g., photovoltaic
plants). The discrete on-off commitment of capacitor units is often configured
on an hourly or daily basis, yet smart inverters can be controlled within
milliseconds, thus challenging joint control of these two types of assets. In
this context, a novel two-timescale voltage regulation scheme is developed for
distribution grids by judiciously coupling data-driven with physicsbased
optimization. On a faster timescale, say every second, the optimal setpoints of
smart inverters are obtained by minimizing instantaneous bus voltage deviations
from their nominal values, based on either the exact alternating current power
flow model or a linear approximant of it; whereas, on the slower timescale
(e.g., every hour), shunt capacitors are configured to minimize the longterm
discounted voltage deviations using a deep reinforcement learning algorithm.
Extensive numerical tests on a real-world 47- bus distribution network as well
as the IEEE 123-bus test feeder using real data corroborate the effectiveness
of the novel scheme.
