# Constraints and Variables Reduction for Optimal Power Flow Using Hierarchical Graph Neural Networks with Virtual Node-Splitting

arXiv: https://arxiv.org/abs/2411.06268 · HTML: https://mlsanity.com/paper/2411.06268/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 9 of 9)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Reduced Optimal Power Flow Using Graph Neural Network](https://mlsanity.com/paper/2206.13591/) (2022)
- [Neural Network-based Power Flow Model](https://mlsanity.com/paper/2112.08418/) (2021)
- [Long-Term Recurrent Convolutional Network-based Inertia Estimation using Ambient Measurements](https://mlsanity.com/paper/2112.00926/) (2021)
- [Spatio-Temporal Deep Learning-Assisted Reduced Security-Constrained Unit Commitment](https://mlsanity.com/paper/2306.01570/) (2023)
- [Graph Neural Network-based Power Flow Model](https://mlsanity.com/paper/2307.02049/) (2023)
- [N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network](https://mlsanity.com/paper/2402.06226/) (2024)
- [Graph Neural Network-Accelerated Network-Reconfigured Optimal Power Flow](https://mlsanity.com/paper/2410.17460/) (2024)

## Built on by (most cited first, 1 of 1)

- [A Theoretical Framework for Graph-based Digital Twins for Supply Chain Management and Optimization](https://mlsanity.com/paper/2504.03692/) (2025)

## Abstract (arXiv)

Power system networks are often modeled as homogeneous graphs, which limits the ability of graph neural network (GNN) to capture individual generator features at the same nodes. By introducing the proposed virtual node-splitting strategy, generator-level attributes like costs, limits, and ramp rates can be fully captured by GNN models, improving GNN's learning capacity and prediction accuracy. Optimal power flow (OPF) problem is used for real-time grid operations. Limited timeframe motivates studies to create size-reduced OPF (ROPF) models to relieve the computational complexity. In this paper, with virtual node-splitting, a novel two-stage adaptive hierarchical GNN is developed to (i) predict critical lines that would be congested, and then (ii) predict base generators that would operate at the maximum capacity. This will substantially reduce the constraints and variables needed for OPF, creating the proposed ROPFLG model with reduced monitor lines and reduced generator-specific variables and constraints. Two ROPF models, ROPFL and ROPFG, with just reduced lines or generators respectively, are also implemented as additional benchmark models. Case studies show that the proposed ROPFLG consistently outperforms the benchmark full OPF (FOPF) and the other two ROPF methods, achieving significant computational time savings while reliably finding optimal solutions.