Whereas in the past, Distribution Systems played a passive role in connecting customers to electricity, Distribution System Operators (DSOs) will have to take in the future a more active role in monitoring and regulating the network to deal with the new behaviors and dynamics of the system brought by the energy transition. State Estimation, a task traditionally reserved for Transmission System Operators (TSOs), is, therefore, a needed tool for DSOs to properly monitor the distribution grid in the future. However, the implementation of Distribution System State Estimation (DSSE) faces several challenges. The distribution system lacks observability to get satisfying estimation accuracy, the denser network increases the complexity of the estimation process, and the lack of labeled data makes training Machine Learning alternatives difficult. To tackle these issues, we propose the Deep Statistical Solver for Distribution System State Estimation (DSS2), a Deep Learning model based on the Graph Neural Network (GNN) architecture and the Physic-Informed Machine Learning (PIML) framework.

The DSS2 model is based on the Deep Statistical Solver (DSS) framework, which seamlessly models power systems into GNN using Hyper-Heterogeneous Multi Graphs (H2MG), and emphasizes semi-supervised learning by learning to optimize, using optimization problem as a loss function. This thesis extends the DSS framework to the DSSE problem, using the traditional State Estimation algorithm as an optimization problem to learn, and incorporating the power flow equations in the loss function. This model is trained through a semi-supervised approach to learn the physics of the problem and alleviate the need for labels and uses the Deep Learning tools to improve accuracy and robustness in the DSSE task.

Case studies on 14-bus, 70-bus, and 179-bus networks show promising results, with the model outperforming the traditional WLS algorithm while showing better robustness. The model also competed in performance against supervised models and showed to be more suitable for the semi-supervised learning approach than simpler GNN architectures.