# Power Flow Balancing with Decentralized Graph Neural Networks

arXiv: https://arxiv.org/abs/2111.02169 · HTML: https://mlsanity.com/paper/2111.02169/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 3 Nov 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE](https://mlsanity.com/paper/1603.01533/) (2016)
- [Fast Power system security analysis with Guided Dropout](https://mlsanity.com/paper/1801.09870/) (2018)

## Built on by (most cited first, 20 of 20)

- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Decentralized Channel Management in WLANs with Graph Neural Networks](https://mlsanity.com/paper/2210.16949/) (2022)
- [PFDelta: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations](https://mlsanity.com/paper/2510.22048/) (2025)
- [Graph Kalman Filters](https://mlsanity.com/paper/2303.12021/) (2023)
- [Toward Dynamic Stability Assessment of Power Grid Topologies using Graph Neural Networks](https://mlsanity.com/paper/2206.06369/) (2022)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [DPFAGA-Dynamic Power Flow Analysis and Fault Characteristics: A Graph Attention Neural Network](https://mlsanity.com/paper/2503.15563/) (2025)
- [Linearization of ReLU Activation Function for Neural Network-Embedded Optimization: Optimal Day-Ahead Energy Scheduling](https://mlsanity.com/paper/2310.01758/) (2023)
- [Revisiting Deep AC-OPF](https://mlsanity.com/paper/2509.00655/) (2025)
- [Physics-Informed Inductive Biases for Voltage Prediction in Distribution Grids](https://mlsanity.com/paper/2509.25158/) (2025)
- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)
- [Operational risk quantification of power grids using graph neural network surrogates of the DC OPF](https://mlsanity.com/paper/2311.03661/) (2023)
- [Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes](https://mlsanity.com/paper/2504.21260/) (2025)
- [Rebuild AC Power Flow Models with Graph Attention Networks](https://mlsanity.com/paper/2509.22733/) (2025)
- [Physics-Aware Heterogeneous GNN Architecture for Real-Time BESS Optimization in Unbalanced Distribution Systems](https://mlsanity.com/paper/2512.09780/) (2025)
- [Scale-Adaptive Power Flow Analysis with Local Topology Slicing and Multi-Task Graph Learning](https://mlsanity.com/paper/2601.01387/) (2026)
- [BOOST-RPF: Boosted Sequential Trees for Radial Power Flow](https://mlsanity.com/paper/2603.21977/) (2026)
- [Inductive Power Grid Cascading Failure Analysis with GRU-Gated Graph Attention](https://mlsanity.com/paper/2605.07010/) (2026)
- [Learning by Examples: Power Grid Steady State Analysis with a Tabular Foundation Model](https://mlsanity.com/paper/2610.20462/) (2026)

## Abstract (arXiv)

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that is accurate and robust to changes in topology. In addition, by using specialized GNN layers, we are able to build a very deep architecture that accounts for large neighborhoods on the graph, while implementing only localized operations. We perform three different experiments to evaluate: i) the benefits of using localized rather than global operations and the tendency of deep GNN models to oversmooth the quantities on the nodes; ii) the resilience to perturbations in the graph topology; and iii) the capability to train the model simultaneously on multiple grid topologies and the consequential improvement in generalization to new, unseen grids. The proposed framework is efficient and, compared to other solvers based on deep learning, is robust to perturbations not only to the physical quantities on the grid components, but also to the topology.