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Optimal Power Flow Using Graph Neural Networks

arXiv 1910.09658 ↗First posted 21 Oct 2019eess.SY cs.SYcited by 60

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Abstract (arXiv)

Optimal power flow (OPF) is one of the most important optimization problems in the energy industry. In its simplest form, OPF attempts to find the optimal power that the generators within the grid have to produce to satisfy a given demand. Optimality is measured with respect to the cost that each generator incurs in producing this power. The OPF problem is non-convex due to the sinusoidal nature of electrical generation and thus is difficult to solve. Using small angle approximations leads to a convex problem known as DC OPF, but this approximation is no longer valid when power grids are heavily loaded. Many approximate solutions have been since put forward, but these do not scale to large power networks. In this paper, we propose using graph neural networks (which are localized, scalable parametrizations of network data) trained under the imitation learning framework to approximate a given optimal solution. While the optimal solution is costly, it is only required to be computed for network states in the training set. During test time, the GNN adequately learns how to compute the OPF solution. Numerical experiments are run on the IEEE-30 and IEEE-118 test cases.

Key facts. Cited by 60 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Oct 2019.

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Citing papers per year: 2020: 1; 2021: 16; 2022: 13; 2023: 5; 2024: 5; 2025: 12; 2026: 8.

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  1. 2021A Review of Graph Neural Networks and Their Applications in Power Systemscited by 62
  2. 2025Position: Graph Learning Will Lose Relevance Due To Poor Benchmarkscited by 52
  3. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  4. 2021Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatchcited by 29
  5. 2022Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutionscited by 28
  6. 2021Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networkscited by 26
  7. 2021Graph Neural Networks Based Detection of Stealth False Data Injection Attacks in Smart Gridscited by 24
  8. 2021Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systemscited by 21
  9. 2021Leveraging power grid topology in machine learning assisted optimal power flowcited by 21
  10. 2021Power Flow Balancing with Decentralized Graph Neural Networkscited by 19
  11. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  12. 2022Unsupervised Optimal Power Flow Using Graph Neural Networkscited by 13
38 more
  1. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  2. 2022Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitmentscited by 12
  3. 2022Solving AC Power Flow with Graph Neural Networks under Realistic Constraintscited by 11
  4. 2022Reduced Optimal Power Flow Using Graph Neural Networkcited by 11
  5. 2022GNN at the Edge: Cost-Efficient Graph Neural Network Processing over Distributed Edge Serverscited by 11
  6. 2023Compact Optimization Learning for AC Optimal Power Flowcited by 11
  7. 2021Predicting Basin Stability of Power Grids using Graph Neural Networkscited by 10
  8. 2021Cyberattack Detection in Large-Scale Smart Grids using Chebyshev Graph Convolutional Networkscited by 8
  9. 2021Embedding Power Flow into Machine Learning for Parameter and State Estimationcited by 6
  10. 2021Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approachcited by 5
  11. 2021Graph Neural Networks for Learning Real-Time Prices in Electricity Marketcited by 5
  12. 2021Learning to Solve the AC Optimal Power Flow via a Lagrangian Approachcited by 5
  13. 2024Sampling and Uniqueness Sets in Graphon Signal Processingcited by 5
  14. 2024SafePowerGraph: Safety-aware Evaluation of Graph Neural Networks for Transmission Power Gridscited by 5
  15. 2025Towards Generalization of Graph Neural Networks for AC Optimal Power Flowcited by 5
  16. 2022Proximal Policy Optimization with Graph Neural Networks for Optimal Power Flowcited by 4
  17. 2022Toward Dynamic Stability Assessment of Power Grid Topologies using Graph Neural Networkscited by 3
  18. 2022Bucketized Active Sampling for Learning ACOPFcited by 3
  19. 2022Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Dualitycited by 3
  20. 2023Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generationcited by 3
  21. 2024N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Networkcited by 3
  22. 2025PowerGNN: A Topology-Aware Graph Neural Network for Electricity Gridscited by 3
  23. 2021Structured Convolutional Kernel Networks for Airline Crew Schedulingcited by 2
  24. 2022Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flowcited by 2
  25. 2022Towards dynamic stability analysis of sustainable power grids using graph neural networkscited by 2
  26. 2023Physics-Guided Graph Neural Networks for Real-time AC/DC Power Flow Analysiscited by 2
  27. 2025Graph Neural Networks for Transmission Grid Topology Control: Busbar Information Asymmetry and Heterogeneous Representationscited by 2
  28. 2026LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learningcited by 2
  29. 2022Towards Practical Physics-Informed ML Design and Evaluation for Power Gridcited by 1
  30. 2023Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networkscited by 1
  31. 2024End-to-End Reinforcement Learning of Curative Curtailment with Partial Measurement Availabilitycited by 1
  32. 2024Physics-Informed Heterogeneous Graph Neural Networks for DC Blocker Placementcited by 1
  33. 2025SenseFlow: A Physics-Informed and Self-Ensembling Iterative Framework for Power Flow Estimationcited by 1
  34. 2025Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operatorcited by 1
  35. 2025Constraint-Informed Active Learning for End-to-End ACOPF Optimization Proxiescited by 1
  36. 2021Neural Predictive Control for the Optimization of Smart Grid Flexibility Schedulescited by 0
  37. 2025Learning to Optimally Dispatch Power: Performance on a Nation-Wide Real-World Datasetcited by 0
  38. 2025Revisiting Deep AC-OPFcited by 0

50 most cited of 60 All 60 (JSON)

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  1. 2025Refining Graphical Neural Network Predictions Using Flow Matching for Optimal Power Flow with Constraint-Satisfaction Guarantee
  2. 2026FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow
  3. 2025Power Grid Control with Graph-Based Distributed Reinforcement Learning
  4. 2021Reinforcement Learning for Battery Energy Storage Dispatch augmented with Model-based Optimizer
  5. 2026Newton's Lantern: A Reinforcement Learning Framework for Finetuning AC Power Flow Warm Start Models
  6. 2024Imitation Learning for Intra-Day Power Grid Operation through Topology Actions
  7. 2025Learning Topology Actions for Power Grid Control: A Graph-Based Soft-Label Imitation Learning Approach
  8. 2025Constrained Diffusion Models for Synthesizing Representative Power Flow Datasets