  We develop DeepOPF as a Deep Neural Network (DNN) approach for solving
security-constrained direct current optimal power flow (SC-DCOPF) problems,
which are critical for reliable and cost-effective power system
operation.DeepOPF is inspired by the observation that solving SC-DCOPF problems
for a given power network is equivalent to depicting a high-dimensional mapping
from the load inputs to the generation and phase angle outputs. We first train
a DNN to learn the mapping and predict the generations from the load inputs. We
then directly reconstruct the phase angles from the generations and loads by
using the power flow equations. Such a predict-and-reconstruct approach reduces
the dimension of the mapping to learn, subsequently cutting down the size of
the DNN and the amount of training data needed. We further derive a condition
for tuning the size of the DNN according to the desired approximation accuracy
of the load-generation mapping. We develop a post-processing procedure based on
$\ell_1$-projection to ensure the feasibility of the obtained solution, which
can be of independent interest. Simulation results for IEEE test cases show
that DeepOPF generates feasible solutions with less than 0.2% optimality loss,
while speeding up the computation time by up to two orders of magnitude as
compared to a state-of-the-art solver.
