# Learning a Generalized Model for Substation Level Voltage Estimation in Distribution Networks

arXiv: https://arxiv.org/abs/2510.16063 · HTML: https://mlsanity.com/paper/2510.16063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Pre-trained Models for Natural Language Processing: A Survey](https://mlsanity.com/paper/2003.08271/) (2020)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Data-Driven Learning-Based Optimization for Distribution System State Estimation](https://mlsanity.com/paper/1807.01671/) (2018)
- [A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems](https://mlsanity.com/paper/1809.00057/) (2018)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Physics-informed Graphical Neural Network for Power System State Estimation](https://mlsanity.com/paper/2312.17738/) (2023)
- [Vulnerability Analysis and Consequences of False Data Injection Attack on Power System State Estimation](https://mlsanity.com/paper/1506.03774/) (2015)
- [Enhancing Observability in Distribution Grids using Smart Meter Data](https://mlsanity.com/paper/1612.06669/) (2016)
- [Voltage Estimation in Low-Voltage Distribution Grids with Distributed Energy Resources](https://mlsanity.com/paper/2011.05598/) (2020)

## Abstract (arXiv)

Accurate voltage estimation in distribution networks is critical for real-time monitoring and increasing the reliability of the grid. As DER penetration and distribution level voltage variability increase, robust distribution system state estimation (DSSE) has become more essential to maintain safe and efficient operations. Traditional DSSE techniques, however, struggle with sparse measurements and the scale of modern feeders, limiting their scalability to large networks. This paper presents a hierarchical graph neural network for substation-level voltage estimation that exploits both electrical topology and physical features, while remaining robust to the low observability levels common to real-world distribution networks. Leveraging the public SMART-DS datasets, the model is trained and evaluated on thousands of buses across multiple substations and DER penetration scenarios. Comprehensive experiments demonstrate that the proposed method achieves up to 2 times lower RMSE than alternative data-driven models, and maintains high accuracy with as little as 1% measurement coverage. The results highlight the potential of GNNs to enable scalable, reproducible, and data-driven voltage monitoring for distribution systems.