  The power system state estimation (SE) algorithm estimates the complex bus
voltages based on the available set of measurements. Because phasor measurement
units (PMUs) are becoming more widely employed in transmission power systems, a
fast SE solver capable of exploiting PMUs' high sample rates is required. To
accomplish this, we present a method for training a model based on graph neural
networks (GNNs) to learn estimates from PMU voltage and current measurements,
which, once it is trained, has a linear computational complexity with respect
to the number of nodes in the power system. We propose an original GNN
implementation over the power system's factor graph to simplify the
incorporation of various types and numbers of measurements both on power system
buses and branches. Furthermore, we augment the factor graph to improve the
robustness of GNN predictions. 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.
Additionally, errors caused by PMU malfunctions or the communication failures
that make the SE problem unobservable have a local effect and do not
deteriorate the results in the rest of the power system.
