Graph Neural Network-Based Distribution System State Estimators

State estimation is an essential tool for situational awareness and control to ensure safe operation. While current state-of-the-art techniques, such as model-based sparsity-aware state estimators, provide superior performance over conventional approaches, they have poor scalability and require large computational times. These limitations can be overcome by utilizing deep learning models such as deep neural networks (DNNs). However, DNNs are prone to over-fitting and cannot incorporate structural information of networks. Furthermore, current model-based approaches require detailed knowledge of network parameters that may be unavailable in large systems. Therefore, new models with comparable performance are desired that either do not require network parameters or that can work using partial knowledge of these parameters. Recently, graph neural networks (GNNs) have become popular deep learning models that extend neural models to graph structures and incorporate structural information of the networks through graph structures. Therefore, this article proposes GNN-based state estimators by modeling the state estimation problem in distribution systems as node-level prediction problems on their graph representations with state measurement matrices and tensors as input features. Feature scaling and pseudo-measurement generation phases are introduced to enhance their performance. These approaches are evaluated on the IEEE 33, 37-node systems, and an unbalanced three-phase 559-node system. The proposed approaches provide comparable performance to sparsity-aware state estimators while using significantly lower computational times. The GNN-based approaches produce state estimates conforming to the power flow constraints without prior knowledge of the network parameters, thus suggesting that the proposed models can learn the system's underlying physical flows.