  This paper introduces, for the first time to our knowledge, physics-informed
neural networks to accurately estimate the AC-OPF result and delivers rigorous
guarantees about their performance. Power system operators, along with several
other actors, are increasingly using Optimal Power Flow (OPF) algorithms for a
wide number of applications, including planning and real-time operations.
However, in its original form, the AC Optimal Power Flow problem is often
challenging to solve as it is non-linear and non-convex. Besides the large
number of approximations and relaxations, recent efforts have also been
focusing on Machine Learning approaches, especially neural networks. So far,
however, these approaches have only partially considered the wide number of
physical models available during training. And, more importantly, they have
offered no guarantees about potential constraint violations of their output.
Our approach (i) introduces the AC power flow equations inside neural network
training and (ii) integrates methods that rigorously determine and reduce the
worst-case constraint violations across the entire input domain, while
maintaining the optimality of the prediction. We demonstrate how
physics-informed neural networks achieve higher accuracy and lower constraint
violations than standard neural networks, and show how we can further reduce
the worst-case violations for all neural networks.
