mlsanityData to 14 Oct 2026

Unsupervised Optimal Power Flow Using Graph Neural Networks

arXiv 2210.09277 ↗First posted 17 Oct 2022eess.SY cs.LG cs.SYcited by 14

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Abstract (arXiv)

Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this work, we propose to leverage graph signal processing and machine learning. More specifically, we use a graph neural network to learn a nonlinear parametrization between the power demanded and the corresponding allocation. We learn the solution in an unsupervised manner, minimizing the cost directly. In order to take into account the electrical constraints of the grid, we propose a novel barrier method that is differentiable and works on initially infeasible points. We show through simulations that the use of GNNs in this unsupervised learning context leads to solutions comparable to standard solvers while being computationally efficient and avoiding constraint violations most of the time.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 28 of its 68 references that are in the map. First posted on arXiv 17 Oct 2022.

Builds on

28 of 68 references.

References · 28

  1. 2021Convex optimizationcited by 2,515
  2. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  3. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  4. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  5. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
  6. 2019Stability Properties of Graph Neural Networkscited by 127
  7. 2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
  8. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 95
  9. 2019Optimal Wireless Resource Allocation with Random Edge Graph Neural Networkscited by 90
  10. 2017pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systemscited by 85
  11. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 75
  12. 2019Optimal Power Flow Using Graph Neural Networkscited by 63
16 more
  1. 2019Learning Decentralized Controllers for Robot Swarms with Graph Neural Networkscited by 62
  2. 2019DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flowcited by 50
  3. 2020DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problemscited by 47
  4. 2017PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulationscited by 33
  5. 2022Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutionscited by 28
  6. 2019Machine Learning for AC Optimal Power Flowcited by 24
  7. 2021Leveraging power grid topology in machine learning assisted optimal power flowcited by 22
  8. 2020Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulationcited by 19
  9. 2015Strong NP-hardness of AC power flows feasibilitycited by 14
  10. 2022Reduced Optimal Power Flow Using Graph Neural Networkcited by 11
  11. 2014Convex Relaxation of Optimal Power Flow, Part II: Exactnesscited by 10
  12. 2015Strong SOCP Relaxations for the Optimal Power Flow Problemcited by 9
  13. 2022Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competitioncited by 6
  14. 2018Lecture Notes on Optimal Power Flow (OPF)cited by 5
  15. 2015Convex Relaxations of Optimal Power Flow Problems: An Illustrative Examplecited by 3
  16. 2018Optimization-Based Bound Tightening using a Strengthened QC-Relaxation of the Optimal Power Flow Problemcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 5; 2026: 3.

14 papers.

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  1. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  2. 2023Dual Conic Proxies for AC Optimal Power Flowcited by 11
  3. 2023Unsupervised Learning of Sampling Distributions for Particle Filterscited by 8
  4. 2025Towards Generalization of Graph Neural Networks for AC Optimal Power Flowcited by 6
  5. 2024Sampling and Uniqueness Sets in Graphon Signal Processingcited by 5
  6. 2024N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Networkcited by 3
  7. 2024Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flowcited by 1
  8. 2025Revisiting Deep AC-OPFcited by 1
  9. 2025A General Approach of Automated Environment Design for Learning the Optimal Power Flowcited by 0
  10. 2025Learning to Optimally Dispatch Power: Performance on a Nation-Wide Real-World Datasetcited by 0
  11. 2025Optimizing Energy Management of Smart Grid using Reinforcement Learning aided by Surrogate models built using Physics-informed Neural Networkscited by 0
  12. 2026PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow with Continual Learningcited by 0
2 more
  1. 2026Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learningcited by 0
  2. 2026Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flowcited by 0