  Recently, there has been a major emphasis on developing data-driven
approaches involving machine learning (ML) for high-speed static state
estimation (SE) in power systems. The emphasis stems from the ability of ML to
overcome difficulties associated with model-based approaches, such as handling
of non-Gaussian measurement noise. However, topology changes pose a stiff
challenge for performing ML-based SE because the training and test environments
become different when such changes occur. This paper circumvents this challenge
by formulating a graph neural network (GNN)-based time-synchronized state
estimator that considers the physical connections of the power system during
the training itself. The results obtained using the IEEE 118-bus system
indicate that the GNN-based state estimator outperforms both the model-based
linear state estimator and a data-driven deep neural network-based state
estimator in the presence of non-Gaussian measurement noise and topology
changes, respectively.
