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Optimal power flow is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. This is a non-convex problem shown to be NP-hard. We use a graph neural network to learn a nonlinear function between the power demanded and the corresponding allocation. We learn the solution in an unsupervised manner, minimizing the cost directly. To consider the power system constraints, we propose a novel barrier method that is differentiable and works on initially infeasible points.

In this paper, we focus on the problem of joint load scheduling and generation management to better match supply and demand. We formulate an optimization problem to jointly minimize the generation cost and discomfort cost of the users subject to the voltage and power balance equations for the equivalent circuit of the power system. The optimal power flow (OPF) equations are solved using semidefinite programming (SDP) relaxation technique. In our system model, we assume that users can exploit renewable energy resources (RERs).