# A Review of Graph Neural Networks and Their Applications in Power Systems

arXiv: https://arxiv.org/abs/2101.10025 · HTML: https://mlsanity.com/paper/2101.10025/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 112 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks](https://mlsanity.com/paper/1503.00075/) (2015)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [Structural-RNN: Deep Learning on Spatio-Temporal Graphs](https://mlsanity.com/paper/1511.05298/) (2015)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Transfer Learning of Graph Neural Networks with Ego-graph Information Maximization](https://mlsanity.com/paper/2009.05204/) (2020)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Graph Transformation Policy Network for Chemical Reaction Prediction](https://mlsanity.com/paper/1812.09441/) (2018)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [RouteNet: Leveraging Graph Neural Networks for network modeling and optimization in SDN](https://mlsanity.com/paper/1910.01508/) (2019)
- [Fault Location in Power Distribution Systems via Deep Graph Convolutional Networks](https://mlsanity.com/paper/1812.09464/) (2018)
- [Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks](https://mlsanity.com/paper/2003.11702/) (2020)

## Built on by (most cited first, 30 of 63)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems](https://mlsanity.com/paper/2102.06349/) (2021)
- [Graph Neural Networks Designed for Different Graph Types: A Survey](https://mlsanity.com/paper/2204.03080/) (2022)
- [PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2311.03415/) (2023)
- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [Graph Neural Networks for Text Classification: A Survey](https://mlsanity.com/paper/2304.11534/) (2023)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Reduced Optimal Power Flow Using Graph Neural Network](https://mlsanity.com/paper/2206.13591/) (2022)
- [Hierarchical Reinforcement Learning for Power Network Topology Control](https://mlsanity.com/paper/2311.02129/) (2023)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Forecasting Unobserved Node States with spatio-temporal Graph Neural Networks](https://mlsanity.com/paper/2211.11596/) (2022)
- [Graph Reinforcement Learning for Power Grids: A Comprehensive Survey](https://mlsanity.com/paper/2407.04522/) (2024)
- [Residual connections provably mitigate oversmoothing in graph neural networks](https://mlsanity.com/paper/2501.00762/) (2025)
- [Embedding Power Flow into Machine Learning for Parameter and State Estimation](https://mlsanity.com/paper/2103.14251/) (2021)
- [Spatio-Temporal Deep Learning-Assisted Reduced Security-Constrained Unit Commitment](https://mlsanity.com/paper/2306.01570/) (2023)
- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [SafePowerGraph: Safety-aware Evaluation of Graph Neural Networks for Transmission Power Grids](https://mlsanity.com/paper/2407.12421/) (2024)
- [Attention-based Deep Neural Networks for Battery Discharge Capacity Forecasting](https://mlsanity.com/paper/2202.06738/) (2022)
- [Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI](https://mlsanity.com/paper/2208.08485/) (2022)
- [Proximal Policy Optimization with Graph Neural Networks for Optimal Power Flow](https://mlsanity.com/paper/2212.12470/) (2022)
- [PowerFlowMultiNet: Multigraph Neural Networks for Unbalanced Three-Phase Distribution Systems](https://mlsanity.com/paper/2403.00892/) (2024)
- [Graph-PHPA: Graph-based Proactive Horizontal Pod Autoscaling for Microservices using LSTM-GNN](https://mlsanity.com/paper/2209.02551/) (2022)
- [Graph Isomorphic Networks for Assessing Reliability of the Medium-Voltage Grid](https://mlsanity.com/paper/2310.01181/) (2023)
- [N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network](https://mlsanity.com/paper/2402.06226/) (2024)
- [Edge Graph Intelligence: Reciprocally Empowering Edge Networks with Graph Intelligence](https://mlsanity.com/paper/2407.15320/) (2024)
- [xAI-Drop: Don't Use What You Cannot Explain](https://mlsanity.com/paper/2407.20067/) (2024)
- [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)
- [Predicting Fault-Ride-Through Probability of Inverter-Dominated Power Grids using Machine Learning](https://mlsanity.com/paper/2406.08917/) (2024)
- [Optimal Power Grid Operations with Foundation Models](https://mlsanity.com/paper/2409.02148/) (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)

## Abstract (arXiv)

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many publications generalizing deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks) are summarized, and key applications in power systems, such as fault scenario application, time series prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.