  Nonlinear state estimation (SE), with the goal of estimating complex bus
voltages based on all types of measurements available in the power system, is
usually solved using the iterative Gauss-Newton method. The nonlinear SE
presents some difficulties when considering inputs from both phasor measurement
units and supervisory control and data acquisition system. These include
numerical instabilities, convergence time depending on the starting point of
the iterative method, and the quadratic computational complexity of a single
iteration regarding the number of state variables. This paper introduces an
original graph neural network based SE implementation over the augmented factor
graph of the nonlinear power system SE, capable of incorporating measurements
on both branches and buses, as well as both phasor and legacy measurements. The
proposed regression model has linear computational complexity during the
inference time once trained, with a possibility of distributed implementation.
Since the method is noniterative and non-matrix-based, it is resilient to the
problems that the Gauss-Newton solver is prone to. Aside from prediction
accuracy on the test set, the proposed model demonstrates robustness when
simulating cyber attacks and unobservable scenarios due to communication
irregularities. In those cases, prediction errors are sustained locally, with
no effect on the rest of the power system's results.
