  The AC Optimal Power Flow (AC-OPF) is a key building block in many power
system applications. It determines generator setpoints at minimal cost that
meet the power demands while satisfying the underlying physical and operational
constraints. It is non-convex and NP-hard, and computationally challenging for
large-scale power systems. Motivated by the increased stochasticity in
generation schedules and increasing penetration of renewable sources, this
paper explores a deep learning approach to deliver highly efficient and
accurate approximations to the AC-OPF. In particular, the paper proposes an
integration of deep neural networks and Lagrangian duality to capture the
physical and operational constraints. The resulting model, called OPF-DNN, is
evaluated on real case studies from the French transmission system, with up to
3,400 buses and 4,500 lines. Computational results show that OPF-DNN produces
highly accurate AC-OPF approximations whose costs are within 0.01% of
optimality. OPF-DNN generates, in milliseconds, solutions that capture the
problem constraints with high fidelity.
