# Physics-informed Graphical Neural Network for Power System State Estimation

arXiv: https://arxiv.org/abs/2312.17738 · HTML: https://mlsanity.com/paper/2312.17738/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2023.

## Built on by (most cited first, 8 of 8)

- [Graph Neural Networks for Transmission Grid Topology Control: Busbar Information Asymmetry and Heterogeneous Representations](https://mlsanity.com/paper/2501.07186/) (2025)
- [Adaptive Informed Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2412.02659/) (2024)
- [SenseFlow: A Physics-Informed and Self-Ensembling Iterative Framework for Power Flow Estimation](https://mlsanity.com/paper/2505.12302/) (2025)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [Learning a Generalized Model for Substation Level Voltage Estimation in Distribution Networks](https://mlsanity.com/paper/2510.16063/) (2025)
- [A Graph Neural Network with Auxiliary Task Learning for Missing PMU Data Reconstruction](https://mlsanity.com/paper/2512.24542/) (2025)
- [Learning Without Adversarial Training: A Physics-Informed Neural Network for Secure Power System State Estimation under False Data Injection Attacks](https://mlsanity.com/paper/2604.22784/) (2026)
- [Graph Machine Learning: An Opportunity for Power Systems](https://mlsanity.com/paper/2608.16494/) (2026)

## Abstract (arXiv)

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.