  As phasor measurement units (PMUs) become more widely used in transmission
power systems, a fast state estimation (SE) algorithm that can take advantage
of their high sample rates is needed. To accomplish this, we present a method
that uses graph neural networks (GNNs) to learn complex bus voltage estimates
from PMU voltage and current measurements. We propose an original
implementation of GNNs over the power system's factor graph to simplify the
integration of various types and quantities of measurements on power system
buses and branches. Furthermore, we augment the factor graph to improve the
robustness of GNN predictions. This model is highly efficient and scalable, as
its computational complexity is linear with respect to the number of nodes in
the power system. Training and test examples were generated by randomly
sampling sets of power system measurements and annotated with the exact
solutions of linear SE with PMUs. The numerical results demonstrate that the
GNN model provides an accurate approximation of the SE solutions. Furthermore,
errors caused by PMU malfunctions or communication failures that would normally
make the SE problem unobservable have a local effect and do not deteriorate the
results in the rest of the power system.
