# Machine Learning for Improved Gas Network Models in Coordinated Energy Systems

arXiv: https://arxiv.org/abs/2209.12731 · HTML: https://mlsanity.com/paper/2209.12731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 26 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2003.07939/) (2020)
- [Statistical Learning For DC Optimal Power Flow](https://mlsanity.com/paper/1801.07809/) (2018)
- [Supervised Learning for Optimal Power Flow as a Real-Time Proxy](https://mlsanity.com/paper/1612.06623/) (2016)
- [Convex Relaxations in Power System Optimization: A Brief Introduction](https://mlsanity.com/paper/1807.07227/) (2018)
- [Unit Commitment With Gas Network Awareness](https://mlsanity.com/paper/1902.03236/) (2019)
- [Moving from Linear to Conic Markets for Electricity](https://mlsanity.com/paper/2103.12122/) (2021)

## Abstract (arXiv)

The current energy transition promotes the convergence of operation between the power and natural gas systems. In that direction, it becomes paramount to improve the modeling of non-convex natural gas flow dynamics within the coordinated power and gas dispatch. In this work, we propose a neural-network-constrained optimization method which includes a regression model of the Weymouth equation, based on supervised machine learning. The Weymouth equation links gas flow to inlet and outlet pressures for each pipeline via a quadratic equality, which is captured by a neural network. The latter is encoded via a tractable mixed-integer linear program into the set of constraints. In addition, our proposed framework is capable of considering bidirectionality without having recourse to complex and potentially inaccurate convexification approaches. We further enhance our model by introducing a reformulation of the activation function, which improves the computational efficiency. An extensive numerical study based on the real-life Belgian power and gas systems shows that the proposed methodology yields promising results in terms of accuracy and tractability.