  Optimal power flow (OPF) is one of the most important optimization problems
in the energy industry. In its simplest form, OPF attempts to find the optimal
power that the generators within the grid have to produce to satisfy a given
demand. Optimality is measured with respect to the cost that each generator
incurs in producing this power. The OPF problem is non-convex due to the
sinusoidal nature of electrical generation and thus is difficult to solve.
Using small angle approximations leads to a convex problem known as DC OPF, but
this approximation is no longer valid when power grids are heavily loaded. Many
approximate solutions have been since put forward, but these do not scale to
large power networks. In this paper, we propose using graph neural networks
(which are localized, scalable parametrizations of network data) trained under
the imitation learning framework to approximate a given optimal solution. While
the optimal solution is costly, it is only required to be computed for network
states in the training set. During test time, the GNN adequately learns how to
compute the OPF solution. Numerical experiments are run on the IEEE-30 and
IEEE-118 test cases.

Systems and Control;Systems and Control