# Data driven approach towards more efficient Newton-Raphson power flow calculation for distribution grids

arXiv: https://arxiv.org/abs/2504.11650 · HTML: https://mlsanity.com/paper/2504.11650/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 2 of 2)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems](https://mlsanity.com/paper/2403.04578/) (2024)

## Built on by (most cited first, 2 of 2)

- [Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator](https://mlsanity.com/paper/2509.22458/) (2025)
- [Newton's Lantern: A Reinforcement Learning Framework for Finetuning AC Power Flow Warm Start Models](https://mlsanity.com/paper/2605.11102/) (2026)

## Abstract (arXiv)

Power flow (PF) calculations are fundamental to power system analysis to ensure stable and reliable grid operation. The Newton-Raphson (NR) method is commonly used for PF analysis due to its rapid convergence when initialized properly. However, as power grids operate closer to their capacity limits, ill-conditioned cases and convergence issues pose significant challenges. This work, therefore, addresses these challenges by proposing strategies to improve NR initialization, hence minimizing iterations and avoiding divergence. We explore three approaches: (i) an analytical method that estimates the basin of attraction using mathematical bounds on voltages, (ii) Two data-driven models leveraging supervised learning or physics-informed neural networks (PINNs) to predict optimal initial guesses, and (iii) a reinforcement learning (RL) approach that incrementally adjusts voltages to accelerate convergence. These methods are tested on benchmark systems. This research is particularly relevant for modern power systems, where high penetration of renewables and decentralized generation require robust and scalable PF solutions. In experiments, all three proposed methods demonstrate a strong ability to provide an initial guess for Newton-Raphson method to converge with fewer steps. The findings provide a pathway for more efficient real-time grid operations, which, in turn, support the transition toward smarter and more resilient electricity networks.