  In this paper, we consider the scenario-based two-stage stochastic DC optimal
power flow (OPF) problem for optimal and reliable dispatch when the load is
facing uncertainty. Although this problem is a linear program, it remains
computationally challenging to solve due to the large number of scenarios
needed to accurately represent the uncertainties. To mitigate the computational
issues, many techniques have been proposed to approximate the second-stage
decisions so they can dealt more efficiently. The challenge of finding good
policies to approximate the second-stage decisions is that these solutions need
to be feasible, which has been difficult to achieve with existing policies.
  To address these challenges, this paper proposes a learning method to solve
the two-stage problem in a more efficient and optimal way. A technique called
the gauge map is incorporated into the learning architecture design to
guarantee the learned solutions' feasibility to the network constraints.
Namely, we can design policies that are feed forward functions that only output
feasible solutions. Simulation results on standard IEEE systems show that,
compared to iterative solvers and the widely used affine policy, our proposed
method not only learns solutions of good quality but also accelerates the
computation by orders of magnitude.
