Confronted with uncertainties, especially from large amounts of renewable energy sources, power flow studies need further analysis to cover the range of voltage magnitude and transferred power. To address this issue, this work proposes a novel interval power flow for the radial network by the use of an extended, simplified DistFlow formulation, which can be transformed into a set of interval linear equations. Furthermore, the Krawczyk iteration method, including an approximate inverse preconditioner using Frobenius norm minimisation, is employed to solve this problem. The approximate inverse preconditioner guarantees the convergence of the iterative method and has the potential for parallel implementation. In addition, to avoid generating a dense approximate inverse matrix in the preconditioning step, a dropping strategy is introduced to perform a sparse representation, which can significantly reduce the memory requirement and ease the matrix operation burden. The proposed methods are demonstrated on 33-bus, 69-bus, 123-bus, and several large systems. A comparison with interval LU decomposition, interval Gauss elimination method, and Monte Carlo simulation verifies its effectiveness.