  At the heart of power system operations, alternating current optimal power
flow (ACOPF) studies the generation of electric power in the most economical
way under network-wide load requirement, and can be formulated as a highly
structured non-convex quadratically constrained quadratic program (QCQP).
Optimization-based solutions to ACOPF (such as ADMM or interior-point method),
as the classic approach, require large amount of computation and cannot meet
the need to repeatedly solve the problem as load requirement frequently
changes. On the other hand, learning-based methods that directly predict the
ACOPF solution given the load input incur little computational cost but often
generates infeasible solutions (i.e. violate the constraints of ACOPF). In this
work, we combine the best of both worlds -- we propose an innovated framework
for learning ACOPF, where the input load is mapped to the ACOPF solution
through a neural network in a computationally efficient and reliable manner.
Key to our innovation is a specific-purpose "activation function" defined
implicitly by a QCQP and a novel loss, which enforce constraint satisfaction.
We show through numerical simulations that our proposed method achieves
superior feasibility rate and generation cost in situations where the existing
learning-based approaches fail.
