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A Review of Graph Neural Networks and Their Applications in Power Systems
Wenlong Liao, Birgitte Bak-Jensen, Jayakrishnan Radhakrishna Pillai, Yuelong Wang, Yusen Wang
TL;DR
Power-system applications increasingly produce graph-structured data whose topology and node interdependencies challenge Euclidean-domain DNNs. This paper comprehensively reviews GNN paradigms and their power-system applications, including fault analysis, forecasting, power flow, and data generation. It concludes that GNNs remain an active area with substantial challenges and opportunities for further development.
Problem
Graph-structured power-system data contains high-dimensional features and node interdependencies that challenge deep neural networks developed for Euclidean domains.
Method
The paper synthesizes classical GNN paradigms and reviews their applications, issues, and future directions in power systems.
Results
The review covers GNN applications in fault scenarios, time series prediction, power flow calculation, and data generation.
Takeaways & Limitations
GNNs and their power-system applications still face challenges and opportunities that are expected to attract further research.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
Power-system data and tasks increasingly involve complex, interdependent, non-Euclidean structures that conventional DNNs do not represent well. This paper reviews GNN paradigms, applications, limitations, and future directions for power systems.
- A. Background: Power systems are dynamic, nonlinear, large-scale systems whose multidirectional information makes coordinated optimization difficult.
- A. Background: DNNs have improved power-system tasks including load and renewable-energy forecasting, fault diagnosis, scenario generation, and operational control using Euclidean data.
- A. Background: Graph-structured power-system data preserves topology and node interdependencies that conventional models can miss when they impose an ordered Euclidean representation.
- A. Background: GNN research has expanded rapidly, with published articles showing strong growth during the final three years of 2010–2020.
- A. Background: Existing reviews often separate GNN theory from power-system applications, leaving limited comprehensive coverage of both areas together.
- C. Contributions and Organization: The paper introduces classical GNN paradigms, surveys power-system applications, and discusses model limitations, theoretical advantages, and future research directions.
A. Definitions of Graph-Structured Data
The paper defines graph-structured data through nodes, edges, features, adjacency, and Laplacian representations, then distinguishes spectral and spatial graph convolutions. It also compares their computational scalability, generalization, and graph-type flexibility.
- A. Definitions of Graph-Structured Data: A graph G=(V,E) consists of nodes and edges, with node neighborhoods, nodal features, edge features, and adjacency entries encoding connectivity.
- A. Definitions of Graph-Structured Data: Spatial-temporal graphs represent node features that change over time, while directed graphs use asymmetric adjacency matrices and undirected graphs use symmetric ones.
- B. Graph Convolutional Networks: Spectral GCNs perform graph convolution through Fourier-domain transformation, whereas spatial GCNs aggregate information directly from spatially close neighbors.
- B. Graph Convolutional Networks: ChebNet approximates graph filters with truncated Kth-order Chebyshev polynomials, making the operation K-localized.
- B. Graph Convolutional Networks: The renormalized GCN formulation adds self-loops and applies degree normalization before transforming node features with learned weights.
- B. Graph Convolutional Networks: DCNNs use degree-normalized transition matrices for graph convolution and can support graph and edge classification tasks.
- Comparison between spectral and spatial-based GCNs: Spatial-based GCNs can operate on batches of nodes and extend more readily to large-scale graphs than spectral methods that process whole graphs or require eigenvectors.
- Comparison between spectral and spatial-based GCNs: Spatial-based GCNs also accommodate directed, heterogeneous, edge-input, and signed graphs more flexibly than most spectral-based GCNs.
C. Graph Recurrent Neural Networks
Graph recurrent neural networks extend recurrent mechanisms to graph domains for sequence-producing tasks. Their gated variants propagate and combine temporal and neighboring-node information to address long-term dependencies.
- C. Graph Recurrent Neural Networks: GRNNs target graph-level and node-level problems that require sequence outputs.
- C. Graph Recurrent Neural Networks: Graph GRUs extend recurrent propagation to a fixed number of steps and compute gradients through back-propagation through time.
- C. Graph Recurrent Neural Networks: Gated GNNs use adjacency-based neighbor connections, learned gates, activation functions, and hidden states to update node representations.
- C. Graph Recurrent Neural Networks: Update and reset gates combine information from the previous time step with information from other nodes when updating each node’s hidden state.
- C. Graph Recurrent Neural Networks: Child-sum tree-LSTMs replace one forget gate with a separate gate for each child, allowing node states to aggregate child information accordingly.
D. Graph Attention Networks
Graph attention networks learn how strongly each neighbor influences a node rather than relying on equal or predefined aggregation weights. Multi-head attention and gated variants support more stable or flexible information gathering.
- D. Graph Attention Networks: GATs learn neighbor impacts during training because graph neighbors may contribute unequally to a node’s representation.
- D. Graph Attention Networks: The resulting attention coefficients weight information aggregated from neighboring nodes into updated hidden states.
- D. Graph Attention Networks: The attention mechanism computes coefficients from transformed node representations, concatenation, a learned function, LeakyReLU, and Softmax normalization.
- D. Graph Attention Networks: Multi-head GATs use K independent attention mechanisms and concatenate their resulting features to stabilize learning.
- D. Graph Attention Networks: GaAN replaces average aggregation with dot-product and key-value attention, while self-attention gathers information from different heads.
E. Graph Generative Networks
Graph generative networks generate new graph-structured data by learning from historical samples. Their main paradigms include graph autoencoders, variational graph autoencoders, and graph generative adversarial networks.
- GGNs generate new graph-structured data by learning from historical samples.
- The principal GGN paradigms are GAEs, VGAEs, and GGANs.
- GAEs use an encoder and decoder to process node features, adjacency information, and graph embeddings.The encoder receives X and A to obtain the graph embedding matrix Z.
GAE GAE GAE
GAEs reconstruct graph structure from learned embeddings, while VGAEs introduce probability to address limited diversity and quantity. GGANs use adversarial training to improve generated graph quality.
- GAE decoders reconstruct the graph adjacency matrix from the encoder’s embedding matrix.
- GAE-generated graph data lacks diversity and is limited in quantity, motivating VGAEs’ probabilistic extension.
- VGAEs optimize a variational lower bound involving reconstruction likelihood and Kullback-Leibler divergence.The formulation includes a Gaussian prior and latent noise.
- VGAEs produce limited-quality graph data because they approximate only the lower bound of the nodes’ logarithm likelihood.
- GGAN generators model likely node connections, while discriminators estimate whether node pairs are ground-truth neighbors or generated.
- GGAN training alternates generator minimization and discriminator maximization of a two-player min-max loss.The discriminator and generator parameters are updated alternately during training.
F. Spatial-Temporal Graph Neural Networks
Spatial-temporal GNNs capture changing spatial and temporal dependencies in graph data, including correlated wind-farm power curves. RNN-based and CNN-based architectures provide different computational trade-offs.
- STGNNs simultaneously capture temporal-spatial dependencies to predict node values or graph labels.
- RNN-based models: RNN-based models filter hidden states and node inputs using graph convolutional operations to model temporal-spatial dependencies.The graph-recurrent formulation uses the node feature matrix at time t, prior hidden states, and the adjacency matrix.
- RNN-based models: Examples combine GRUs with diffusion graph convolution, LSTMs with ChebNet, or edge-level and node-level RNNs.The edge-level and node-level recurrent structures separately process temporal information from edges and nodes before merging spatial information.
- RNN-based models: RNN-based models face gradient vanishing problems and time-consuming iterative propagation.
- CNN-based models: CNN-based models process temporal-spatial graphs non-recursively, providing stable gradients, parallel computing, and low memory requirements.
G. Hybrid forms of GNNs
Hybrid GNN forms combine graph neural networks with reinforcement learning or transfer learning. These combinations target graph-based decision-making and reuse knowledge across related tasks.
- GRL combines reinforcement-learning decision-making with GNN-based perception for graph-structured tasks requiring control and perception.
- GTL transfers prior knowledge from old problems to new but related problems.
- Transferable GNN frameworks can reuse learned geometric information for related target-domain tasks without training a new model from scratch.
III. APPLICATIONS IN POWER SYSTEMS
Applications of GNNs in power systems remain relatively limited, although publications have increased since 2018. Existing work covers fault scenarios, time-series prediction, power-flow calculation, and data generation.
- Most GNN applications have focused on computer science and biology, while power-system applications remain relatively limited.
- Existing power-system applications include fault scenarios, time-series prediction of renewable-energy sources and loads, power-flow calculation, and data generation.
- Table II catalogs existing applications of graph neural networks in power systems.
A. Fault scenario application
Fault-scenario applications use GNNs to address limitations of conventional methods in transformer diagnosis, fault location, fault detection and isolation, outage prediction, and photovoltaic fault classification. The section also identifies ensemble GNNs, CNN-style pooling, and broader classification tasks as research directions.
- Fault-scenario applications target failure detection to help avoid power outages and support safe power-system operation.
- A1. Transformer fault diagnosis: Transformer fault diagnosis commonly uses dissolved gas analysis, with existing approaches including model-based, distance-based, and hybrid methods.The passage identifies CNNs, k-nearest neighbors, and ensemble models as examples of these categories.
- A2. Fault location: Traditional distribution-network fault-location methods struggle to combine measurements across buses, particularly with data loss, and have difficulty modeling network topology.
- A3. Fault detection and isolation: GCNs improve fault detection and isolation over several baselines by modeling dependencies among multiple components; community-varying GCNs help identify highly correlated components.
- A4. Power outages prediction: GNN-based methods address limited accuracy in outage prediction by representing weather-station measurements as a graph, while graph signal processing supports photovoltaic fault detection with limited historical data.
- A5. Further ideas for fault scenario application: Future directions include combining multiple GNNs or GNNs with traditional DNNs, developing pooling methods that retain feature information, and applying the framework to transformer and other power-system classification tasks.Suggested applications include power-quality disturbance classification and transient-stability assessment.
B. Time series prediction
The review covers graph-neural-network applications for time-series prediction of renewable-energy generation, wind speed, and residential loads. It also identifies hybrid graph architectures and other research directions for improving temporal and spatial modeling.
- B. Time series prediction: The section is organized around three application categories and additional research directions for time-series prediction.A spatio-temporal graph deep neural network is also identified for short-term wind-speed prediction.
- B. Time series prediction: Graph neural networks are reviewed for solar power, wind power and speed, and residential load prediction.The section explicitly groups these applications into three categories.
- B1. Solar power prediction: CNN-based spatio-temporal GNNs and graph autoencoders are used to capture spatial-temporal relationships in photovoltaic systems and power measurements.The reviewed models represent measurement units or sites as graph nodes and encode mutual relationships through edges.
- B2. Wind power and wind speed prediction: Superposition graph neural networks are proposed to represent temporal and spatial information in offshore wind-power forecasting.The motivation is that offshore wind-power fluctuations and intermittence challenge power-system operation and planning.
- B3. Residential load prediction: A graph-based residential-load model clusters appliances and forecasts their individual power curves before aggregating them into the total load curve.Each appliance is treated as a node, with branches constructed from appliance state-duration probabilities; simulations report greater accuracy than existing approaches.
- B4. Further ideas for time series prediction: The review proposes combining GCNs with GRNNs, extending TCNs to graph domains, and applying ensemble learning to graph-based forecasting.These directions aim to combine feature extraction, temporal modeling, and ensemble strategies for renewable-energy and load prediction.
C. Power flow calculation
The review covers GNN applications in power-flow-related tasks and adjacent power-system problems, emphasizing topology-aware modeling, computational performance, and open research directions.
- C1. Power flow approximation: Power-flow calculation uses GCNs to model node features and network topology for approximating flows, voltages, and distribution characteristics.Spatial GCNs use active and reactive power as node features, while branch flows and node voltages are prediction targets; spectral GCNs and ChebNet address related calculations.
- C2. Optimal power flow: Spectral GCNs approximate optimal reactive-power solutions by mining distribution-network topology, with local solutions outperforming comparable methods.The models use adjacency matrices to represent node correlations and approximate the output of an interior-point optimizer.
- C2. Optimal power flow: Existing optimal-power-flow GNNs generally do not account for operating constraints or changing network topology, motivating constrained and dynamic extensions.The review specifically identifies voltage and current constraints, reconfiguration, and time-varying adjacency matrices and node features as open issues.
- C3. Optimal load shedding: GCNs support optimal load shedding by representing voltage, power, and topology information as graph inputs, significantly outperforming MLPs and linear regressions across testing systems.The review also highlights the need to study how pooling and dropout affect accuracy and computing time.
- C4. Further ideas for power flow calculation: Future power-flow research should address small-sample training and may use GGANs to expand datasets for GNN training.The review also suggests generalizing DBNs from Euclidean domains to graph domains for optimal power flow.
- Other applications: Beyond power flow, reviewed applications include scenario and feeder generation, electric-vehicle control, knowledge reasoning, economic dispatch, topology identification, and temporal or physics-informed modeling.These studies combine graph representations with GAE, GGAN, GRL, heterogeneous GNN, ChebNet, recurrent, or physics-induced architectures.
IV. KEY ISSUES AND FUTURE DEVELOPMENT
The review identifies unresolved issues limiting GNN deployment in power systems, including data-specific architecture design, practical reliability, shallow depth, and changing graph structures. It concludes that these challenges define substantial opportunities for future development.
- A. Main issues: GNN parameters and structures developed for computer-vision data may not suit one-dimensional power-system time series and require data-specific adjustment.The review calls for architectures with stronger feature extraction and high-quality solutions for power-system data characteristics.
- A. Main issues: GNN applications in power systems have rarely been commercially viable or practical because their theory remains at an exploratory stage and control requires stability and reliability.Current GNNs are described as relying on statistical laws and probability, while power-system control approaches face stringent reliability requirements.
- B. Future development: Most GNNs are no more than three layers, making the design of genuinely deep GNN structures an open research challenge.The review contrasts this with traditional DNNs, which can improve representation by stacking hundreds of layers.
- B. Future development: Current GNNs cannot adapt well to dynamic graph structures in which power-system nodes and branches change over time.Developing dynamic GNNs is presented as important for improving general-model adaptability and stability.
- Conclusion: The paper provides a comprehensive review of classical GNN paradigms, power-system applications, current challenges, and future development directions.Its surveyed applications include fault scenarios, time-series prediction, power-flow calculation, and data generation.