# Solving AC Power Flow with Graph Neural Networks under Realistic Constraints

arXiv: https://arxiv.org/abs/2204.07000 · HTML: https://mlsanity.com/paper/2204.07000/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Graph Neural Networks for Maximum Constraint Satisfaction](https://mlsanity.com/paper/1909.08387/) (2019)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)

## Built on by (most cited first, 11 of 11)

- [PowerGraph: A power grid benchmark dataset for graph neural networks](https://mlsanity.com/paper/2402.02827/) (2024)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [Physics-Guided Graph Neural Networks for Real-time AC/DC Power Flow Analysis](https://mlsanity.com/paper/2305.00216/) (2023)
- [Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator](https://mlsanity.com/paper/2509.22458/) (2025)
- [End-to-End Reinforcement Learning of Curative Curtailment with Partial Measurement Availability](https://mlsanity.com/paper/2405.03262/) (2024)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [PowerModelsGAT-AI: Physics-Informed Graph Attention for Multi-System Power Flow with Continual Learning](https://mlsanity.com/paper/2603.16879/) (2026)
- [BOOST-RPF: Boosted Sequential Trees for Radial Power Flow](https://mlsanity.com/paper/2603.21977/) (2026)
- [Differentiable Power-Flow Optimization](https://mlsanity.com/paper/2603.28203/) (2026)
- [Hierarchical GNNs for power flow: letting physics shape the hierarchy](https://mlsanity.com/paper/2609.26603/) (2026)

## Abstract (arXiv)

In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice to determine grid operating limits or analyze grid asset utilization in planning procedures. In our approach, we demonstrate the development of a framework that uses graph neural networks to learn the physical constraints of the power flow. We present our model architecture on which we perform unsupervised training to learn a general solution of the AC power flow formulation independent of the specific topologies and supply tasks used for training. Finally, we demonstrate, validate and discuss our results on medium voltage benchmark grids. In our approach, we focus on the physical and topological properties of distribution grids to provide scalable solutions for real grid topologies. Therefore, we take a data-driven approach, using large and diverse data sets consisting of realistic grid topologies, for the unsupervised training of the AC power flow graph neural network architecture and compare the results to a prior neural architecture and the Newton-Raphson method. Our approach shows a high increase in computation time and good accuracy compared to state-of-the-art solvers. It also out-performs that neural solver for power flow in terms of accuracy.