# Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems

arXiv: https://arxiv.org/abs/2403.04578 · HTML: https://mlsanity.com/paper/2403.04578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2024.

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

- [RL-ADN: A High-Performance Deep Reinforcement Learning Environment for Optimal Energy Storage Systems Dispatch in Active Distribution Networks](https://mlsanity.com/paper/2408.03685/) (2024)
- [Data driven approach towards more efficient Newton-Raphson power flow calculation for distribution grids](https://mlsanity.com/paper/2504.11650/) (2025)

## Abstract (arXiv)

In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore glscpu and glsgpu parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the practical operational point, which is the solution of high-voltage and low-current. The proof is validated using numerical simulations showing the robustness of the FPI algorithm compared to the classical glsnr approach. In the case study, a benchmark with different PF solution methods is performed, showing that for applications requiring a yearly simulation at 1-minute resolution the computation time is decreased by a factor of 164, compared to the NR in its sparse formulation.