  A prominent challenge to the safe and optimal operation of the modern power
grid arises due to growing uncertainties in loads and renewables. Stochastic
optimal power flow (SOPF) formulations provide a mechanism to handle these
uncertainties by computing dispatch decisions and control policies that
maintain feasibility under uncertainty. Most SOPF formulations consider simple
control policies such as affine policies that are mathematically simple and
resemble many policies used in current practice. Motivated by the efficacy of
machine learning (ML) algorithms and the potential benefits of general control
policies for cost and constraint enforcement, we put forth a deep neural
network (DNN)-based policy that predicts the generator dispatch decisions in
real time in response to uncertainty. The weights of the DNN are learnt using
stochastic primal-dual updates that solve the SOPF without the need for prior
generation of training labels and can explicitly account for the feasibility
constraints in the SOPF. The advantages of the DNN policy over simpler policies
and their efficacy in enforcing safety limits and producing near optimal
solutions are demonstrated in the context of a chance constrained formulation
on a number of test cases.
