Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this work, we propose to leverage graph signal processing and machine learning. More specifically, we use a graph neural network to learn a nonlinear parametrization between the power demanded and the corresponding allocation. We learn the solution in an unsupervised manner, minimizing the cost directly. In order to take into account the electrical constraints of the grid, we propose a novel barrier method that is differentiable and works on initially infeasible points. We show through simulations that the use of GNNs in this unsupervised learning context leads to solutions comparable to standard solvers while being computationally efficient and avoiding constraint violations most of the time.

翻译：最佳电流( OPF) 是一个至关重要的优化问题, 向发电机分配电力, 以便以最低的成本满足需求。 解决这个问题在一般情况下完全无法计算。 在这项工作中, 我们提议利用图形信号处理和机器学习。 更具体地说, 我们使用图形神经网络学习所需电量和相应分配之间的非线性平衡。 我们以不受监督的方式学习解决方案, 直接将成本降到最低。 为了考虑到电网的电力限制, 我们提出了一种新的屏障方法, 这种方法是不同的, 最初在不可行的点上运行。 我们通过模拟显示, 在这种不受监督的学习环境中使用 GNNs 会导致与标准求解器相似的解决方案, 同时进行高效的计算, 并避免在大部分时间里违反限制 。