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

arXiv: https://arxiv.org/abs/2207.11465 · HTML: https://mlsanity.com/paper/2207.11465/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 23 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [Data-Driven Learning-Based Optimization for Distribution System State Estimation](https://mlsanity.com/paper/1807.01671/) (2018)
- [State Estimation in Electric Power Systems Leveraging Graph Neural Networks](https://mlsanity.com/paper/2201.04056/) (2022)
- [IGNNITION: Bridging the Gap Between Graph Neural Networks and Networking Systems](https://mlsanity.com/paper/2109.06715/) (2021)
- [Distributed Gauss-Newton Method for State Estimation Using Belief Propagation](https://mlsanity.com/paper/1702.05781/) (2017)
- [Robust and Fast Data-Driven Power System State Estimator Using Graph Neural Networks](https://mlsanity.com/paper/2206.02731/) (2022)

## Built on by (most cited first, 4 of 4)

- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Supporting Future Electrical Utilities: Using Deep Learning Methods in EMS and DMS Algorithms](https://mlsanity.com/paper/2303.00428/) (2023)
- [Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs](https://mlsanity.com/paper/2304.14680/) (2023)
- [On zero-shot learning in neural state estimation of power distribution systems](https://mlsanity.com/paper/2408.05787/) (2024)

## Abstract (arXiv)

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.