# Unsupervised Optimal Power Flow Using Graph Neural Networks

arXiv: https://arxiv.org/abs/2210.09277 · HTML: https://mlsanity.com/paper/2210.09277/

## 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 (most cited first, 28 of 28)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations](https://mlsanity.com/paper/1711.01728/) (2017)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation](https://mlsanity.com/paper/2008.11827/) (2020)
- [Strong NP-hardness of AC power flows feasibility](https://mlsanity.com/paper/1512.07315/) (2015)
- [Reduced Optimal Power Flow Using Graph Neural Network](https://mlsanity.com/paper/2206.13591/) (2022)
- [Convex Relaxation of Optimal Power Flow, Part II: Exactness](https://mlsanity.com/paper/1405.0814/) (2014)
- [Strong SOCP Relaxations for the Optimal Power Flow Problem](https://mlsanity.com/paper/1504.06770/) (2015)
- [Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition](https://mlsanity.com/paper/2206.07843/) (2022)
- [Lecture Notes on Optimal Power Flow (OPF)](https://mlsanity.com/paper/1811.00943/) (2018)
- [Convex Relaxations of Optimal Power Flow Problems: An Illustrative Example](https://mlsanity.com/paper/1510.04330/) (2015)
- [Optimization-Based Bound Tightening using a Strengthened QC-Relaxation of the Optimal Power Flow Problem](https://mlsanity.com/paper/1809.04565/) (2018)

## Built on by (most cited first, 14 of 14)

- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [Unsupervised Learning of Sampling Distributions for Particle Filters](https://mlsanity.com/paper/2302.01174/) (2023)
- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [Sampling and Uniqueness Sets in Graphon Signal Processing](https://mlsanity.com/paper/2401.06279/) (2024)
- [N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network](https://mlsanity.com/paper/2402.06226/) (2024)
- [Physics-Informed Graph Neural Networks for Robust AC-Optimal Power Flow](https://mlsanity.com/paper/2410.04818/) (2024)
- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [A General Approach of Automated Environment Design for Learning the Optimal Power Flow](https://mlsanity.com/paper/2505.07832/) (2025)
- [Learning to Optimally Dispatch Power: Performance on a Nation-Wide Real-World Dataset](https://mlsanity.com/paper/2505.24505/) (2025)
- [Optimizing Energy Management of Smart Grid using Reinforcement Learning aided by Surrogate models built using Physics-informed Neural Networks](https://mlsanity.com/paper/2510.17380/) (2025)
- [PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow with Continual Learning](https://mlsanity.com/paper/2603.16879/) (2026)
- [Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning](https://mlsanity.com/paper/2609.36310/) (2026)
- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)

## 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.