  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.
