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Nonlinear state estimation (SE), with the goal of estimating complex busvoltages based on all types of measurements available in the power system, isusually solved using the iterative Gauss-Newton method. The nonlinear SEpresents some difficulties when considering inputs from both phasor measurementunits and supervisory control and data acquisition system. These includenumerical instabilities, convergence time depending on the starting point ofthe iterative method, and the quadratic computational complexity of a singleiteration regarding the number of state variables. This paper introduces anoriginal graph neural network based SE implementation over the augmented factorgraph of the nonlinear power system SE, capable of incorporating measurementson both branches and buses, as well as both phasor and legacy measurements. Theproposed regression model has linear computational complexity during theinference time once trained, with a possibility of distributed implementation.Since the method is noniterative and non-matrix-based, it is resilient to theproblems that the Gauss-Newton solver is prone to. Aside from predictionaccuracy on the test set, the proposed model demonstrates robustness whensimulating cyber attacks and unobservable scenarios due to communicationirregularities. In those cases, prediction errors are sustained locally, withno effect on the rest of the power system's results.

Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks