# Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs

arXiv: https://arxiv.org/abs/2304.14680 · HTML: https://mlsanity.com/paper/2304.14680/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Real-time Power System State Estimation and Forecasting via Deep Neural Networks](https://mlsanity.com/paper/1811.06146/) (2018)
- [Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks](https://mlsanity.com/paper/1812.09464/) (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)
- [A General Framework for quantifying Aleatoric and Epistemic uncertainty in Graph Neural Networks](https://mlsanity.com/paper/2205.09968/) (2022)
- [A Graph Policy Network Approach for Volt-Var Control in Power Distribution Systems](https://mlsanity.com/paper/2109.12073/) (2021)
- [Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks](https://mlsanity.com/paper/2207.11465/) (2022)

## Built on by (most cited first, 1 of 1)

- [Decoding Quantum LDPC Codes Using Graph Neural Networks](https://mlsanity.com/paper/2408.05170/) (2024)

## Abstract (arXiv)

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.