# State Estimation in Electric Power Systems Leveraging Graph Neural Networks

arXiv: https://arxiv.org/abs/2201.04056 · HTML: https://mlsanity.com/paper/2201.04056/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 14 references that are in the map.
- First posted on arXiv 11 Jan 2022.

## Builds on (most cited first, 8 of 8)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [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)
- [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)
- [Gauss-Newton Unrolled Neural Networks and Data-driven Priors for Regularized PSSE with Robustness](https://mlsanity.com/paper/2003.01667/) (2020)

## Built on by (most cited first, 12 of 12)

- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks](https://mlsanity.com/paper/2207.11465/) (2022)
- [Near Real-Time Distributed State Estimation via AI/ML-Empowered 5G Networks](https://mlsanity.com/paper/2207.11117/) (2022)
- [Graph Neural Networks for Electric and Hydraulic Data Fusion to Enhance Short-term Forecasting of Pumped-storage Hydroelectricity](https://mlsanity.com/paper/2404.03368/) (2024)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Towards Practical Physics-Informed ML Design and Evaluation for Power Grid](https://mlsanity.com/paper/2205.03673/) (2022)
- [Robust and Fast Data-Driven Power System State Estimator Using Graph Neural Networks](https://mlsanity.com/paper/2206.02731/) (2022)
- [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)
- [Scalability and Sample Efficiency Analysis of Graph Neural Networks for Power System State Estimation](https://mlsanity.com/paper/2303.00105/) (2023)
- [Unified Heterogeneous Graph Neural Network solver for Power Flow, Optimal Power Flow and State Estimation](https://mlsanity.com/paper/2609.16738/) (2026)
- [Sensor-Aware Joint Data Fusion and State Estimation under Sparse Multi-rate Distribution Grid Sensing](https://mlsanity.com/paper/2610.15156/) (2026)

## Abstract (arXiv)

The goal of the state estimation (SE) algorithm is to estimate complex bus voltages as state variables based on the available set of measurements in the power system. Because phasor measurement units (PMUs) are increasingly being used in transmission power systems, there is a need for a fast SE solver that can take advantage of high sampling rates of PMUs. This paper proposes training a graph neural network (GNN) to learn the estimates given the PMU voltage and current measurements as inputs, with the intent of obtaining fast and accurate predictions during the evaluation phase. GNN is trained using synthetic datasets, created by randomly sampling sets of measurements in the power system and labelling them with a solution obtained using a linear SE with PMUs solver. The presented results display the accuracy of GNN predictions in various test scenarios and tackle the sensitivity of the predictions to the missing input data.