# Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes

arXiv: https://arxiv.org/abs/2504.21260 · HTML: https://mlsanity.com/paper/2504.21260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 30 Apr 2025.

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

- [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)
- [Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach](https://mlsanity.com/paper/1906.06017/) (2019)
- [Gaussian Process Learning-based Probabilistic Optimal Power Flow](https://mlsanity.com/paper/2004.07757/) (2020)
- [Convex Relaxations and Linear Approximation for Optimal Power Flow in Multiphase Radial Networks](https://mlsanity.com/paper/1406.3054/) (2014)
- [Topology Estimation using Graphical Models in Multi-Phase Power Distribution Grids](https://mlsanity.com/paper/1803.06531/) (2018)
- [Power Flow Analysis Using Deep Neural Networks in Three-Phase Unbalanced Smart Distribution Grids](https://mlsanity.com/paper/2401.07465/) (2024)
- [Computing the Feasible Spaces of Optimal Power Flow Problems](https://mlsanity.com/paper/1608.00598/) (2016)
- [An Adaptive-Importance-Sampling-Enhanced Bayesian Approach for Topology Estimation in an Unbalanced Power Distribution System](https://mlsanity.com/paper/2110.09030/) (2021)

## Abstract (arXiv)

Learning-based approaches are increasingly leveraged to manage and coordinate the operation of grid-edge resources in active power distribution networks. Among these, model-based techniques stand out for their superior data efficiency and robustness compared to model-free methods. However, effective model learning requires a learning-based approximator for the underlying power flow model. This study extends existing work by introducing a data-driven power flow method based on Gaussian Processes (GPs) to approximate the multiphase power flow model, by mapping net load injections to nodal voltages. Simulation results using the IEEE 123-bus and 8500-node distribution test feeders demonstrate that the trained GP model can reliably predict the nonlinear power flow solutions with minimal training data. We also conduct a comparative analysis of the training efficiency and testing performance of the proposed GP-based power flow approximator against a deep neural network-based approximator, highlighting the advantages of our data-efficient approach. Results over realistic operating conditions show that despite an 85% reduction in the training sample size (corresponding to a 92.8% improvement in training time), GP models produce a 99.9% relative reduction in mean absolute error compared to the baselines of deep neural networks.