  We consider the problem of controlling the voltage of a distribution feeder
using the reactive power capabilities of inverters. On a real distribution
grid, we compare the local Volt/VAr droop control recommended in recent grid
codes, a centralized dispatch based on optimal power flow (OPF) programming,
and a feedback optimization (FO) controller that we propose. The local droop
control yields suboptimal regulation, as predicted analytically. The OPF-based
dispatch strategy requires an accurate grid model and measurement of all loads
on the feeder in order to achieve proper voltage regulation. However, in the
experiment, the OPF-based strategy violates voltage constraints due to
inevitable model mismatch and uncertainties. Our proposed FO controller, on the
other hand, satisfies the constraints and does not require load measurements or
any grid state estimation. The only needed model knowledge is the sensitivity
of the voltages with respect to reactive power, which can be obtained from
data. As we show, an approximation of these sensitivities is also sufficient,
which makes the approach essentially model-free, easy to tune, compatible with
the current sensing and control infrastructure, and remarkably robust to
measurement noise. We expect these properties to be fundamental features of FO
for power systems and not specific to Volt/VAr regulation or to distribution
grids.
