  Coordinating inverters at scale under uncertainty is the desideratum for
integrating renewables in distribution grids. Unless load demands and solar
generation are telemetered frequently, controlling inverters given approximate
grid conditions or proxies thereof becomes a key specification. Although deep
neural networks (DNNs) can learn optimal inverter schedules, guaranteeing
feasibility is largely elusive. Rather than training DNNs to imitate already
computed optimal power flow (OPF) solutions, this work integrates DNN-based
inverter policies into the OPF. The proposed DNNs are trained through two OPF
alternatives that confine voltage deviations on the average and as a convex
restriction of chance constraints. The trained DNNs can be driven by partial,
noisy, or proxy descriptors of the current grid conditions. This is important
when OPF has to be solved for an unobservable feeder. DNN weights are trained
via back-propagation and upon differentiating the AC power flow equations
assuming the network model is known. Otherwise, a gradient-free variant is put
forth. The latter is relevant when inverters are controlled by an aggregator
having access only to a power flow solver or a digital twin of the feeder.
Numerical tests compare the DNN-based inverter control schemes with the optimal
inverter setpoints in terms of optimality and feasibility.
