In the context of the energy transition, the increasing penetration of nonprogrammable renewable sources, the process of electrification, and the simultaneous decommissioning of thermoelectric power plants place are putting increasing strain on the transmission grid. Its expansion needs to be planned in a robust manner to cope with the high level of uncertainty in the system, and must consider market-supplied flexibility resources (e.g., electrochemical storage systems, demand-side management) as possible candidates for solutions.

However, existing tools to support grid expansion planning are not applicable to large-scale systems. This is either because they cannot handle a large number of candidates or because the OPF (Optimal Power Flow) problem, which must be solved for each expansion candidate, acts as a computational bottleneck. This work aims to test whether the second limitation can be overcome by resorting to Graph Neural Network (GNN), based models that learn an approximate solution of the AC-OPF problem. This type of neural network is selected among others for its ability, fundamental in planning studies, to generalize to network topologies not seen in training.

Based on a review of the latest information on GNN applications for OPF, it was hypothesized and then empirically demonstrated that the performance of GNN models for OPF improves only when the receptive field is extended to the radius of the OPF problem. This is defined for a given electrical system as the length of the maximum shortest path of generator-to-load and generator-to-generator pairs. A fully connected neural network (FCNN) is used as a benchmark for comparison with GNN models, since it currently achieves the highest accuracy in predicting the solution of the OPF problem in the literature. The comparison is performed with a robust approach based on the method known as nested k-fold cross validation.

In addition, to obtain an unbiased performance estimate, the model size (i.e., total number of neurons) is fixed for a given network, while the learning rate (learning rate) is adjusted for each different architecture. Neural network models are trained, validated and tested in transductive mode (i.e., with fixed topology networks) using synthetic datasets for OPF generated for seven different test cases, where the number of nodes varies from 30 to 300. The models are evaluated not only in terms of neural network loss, but also in terms of other metrics that measure the feasibility of the prediction with respect to the AC-OPF domain.

All in all, the GNN models achieve comparable performance compared to their FCNN counterparts. The over-smoothing problem affects the accuracy of GNN models, especially if the receptive field is greater than 10 steps. Therefore, GNN models that solve this problem are needed for larger electrical networks. From the results obtained, regularization terms will be added in the future to account for the physical and operational constraints of the AC-OPF problem, and the analysis will be extended to an inductive context (i.e., with topological variation).