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As phasor measurement units (PMUs) become more widely used in transmissionpower systems, a fast state estimation (SE) algorithm that can take advantageof their high sample rates is needed. To accomplish this, we present a methodthat uses graph neural networks (GNNs) to learn complex bus voltage estimatesfrom PMU voltage and current measurements. We propose an originalimplementation of GNNs over the power system's factor graph to simplify theintegration of various types and quantities of measurements on power systembuses and branches. Furthermore, we augment the factor graph to improve therobustness of GNN predictions. This model is highly efficient and scalable, asits computational complexity is linear with respect to the number of nodes inthe power system. Training and test examples were generated by randomlysampling sets of power system measurements and annotated with the exactsolutions of linear SE with PMUs. The numerical results demonstrate that theGNN model provides an accurate approximation of the SE solutions. Furthermore,errors caused by PMU malfunctions or communication failures that would normallymake the SE problem unobservable have a local effect and do not deteriorate theresults in the rest of the power system.

Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs