In the framework of the energy transition, the expansion of the power transmission network retains a central role and must be planned in a robust way to cope with the high level of uncertainty in the system evolution. This problem is inherently probabilistic and combinatorial, requiring solving many instances of the Optimal Power Flow (OPF) problem, and does not scale well to large power systems. Graph Neural Network (GNN) can be used in this context to approximate the solution of the OPF problem, since this NN type can generalise its solution to unseen topologies.

Specifically, this work simultaneously tackles two important and intertwined issues pertaining to this framework, namely the efficient generation of high quality, synthetic Alternating Current (AC) OPF datasets and the need for trustworthy NN models for the AC-OPF problem. A two-step methodology that builds upon the limited existing literature is developed to generate such datasets. The first step leverages on a relaxed formulation of the AC-OPF problem to iteratively trim the initial sampling hypervolume, which consists of the possible load states that characterise a given power system.

The reduced polytope is then sampled uniformly in terms of total load active power to generate the AC-OPF setpoints, using a technique to limit the number iterations. With reference to the need for trustworthy NNs, a physics-informed graph neural network (PiNN) architecture is developed. The NN model predicts the set of variables that fully characterise a power system in steady state (i.e. complex power injections and complex voltages). Based on these predictions, violation metrics are computed for every equality and inequality constraint of the AC-OPF and are added to the GNN loss function.

Overall, it is empirically proven that the PiNN model outperforms the physics agnostic GNN counterpart, effectively reducing the magnitude and frequency of constraint violations and enhancing NN generalisation capabilities. This is verified under the transductive learning framework (i.e., with fixed topology) by using the high-quality AC-OPF datasets generated with our methodology for seven power system test cases, ranging from 39 to 1354 buses. It is also preliminarily verified for three test cases that the PiNN model can generalise to topologies unseen during training and validation.