Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems
<|reference_start|>Tensor Power Flow Formulations for Multidimensional Analyses in Distribution Systems: 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 \gls{cpu} and \gls{gpu} 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 \gls{nr} 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.<|reference_end|>
@article{duque2024tensor,
    title={Tensor Power Flow Formulations for Multidimensional Analyses in
  Distribution Systems},
    author={Edgar Mauricio Salazar Duque, Juan S. Giraldo, Pedro P. Vergara,
  Phuong H. Nguyen, Han (J.G.) Slootweg},
    journal={arXiv preprint arXiv:2403.04578},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04578},
    primaryClass={eess.SY cs.SY}
}