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The study proposes a fast flexible direct power flow solution for radial distribution systems and a fast flexible direct weakly meshed power flow solution for weakly meshed distribution systems. The algorithm is based on the direct forward sweep power flow solution, which is an updated version of the backward/forward sweep solution. The fast flexible direct power flow uses a unique conversion matrix (CM) to rapidly determine the power flow solution. The inverted conversion matrix and its slide-modified matrix are used to solve the power flow problem in a single forward sweep step, which is a novel feature of this work. To ensure the invertibility of the conversion matrix, it is constructed to have a small condition number and a determinant of minus one, and all of its eigenvalues must be equal to that of minus one. Additionally, by modifying the conversion matrix to accommodate the loop branch using the break-point idea, a new weakly meshed conversion matrix (WMCM) is generated with the same following modification as for the radial network and employed in the fast flexible direct weakly meshed power flow (FFDWMPF) solution for the weakly meshed distribution network. The usage of a single matrix in the power flow solution and advanced direct techniques decreases the number of iterations and CPU execution time when MATLAB programming is executed. Furthermore, the proposed method is flexible enough to incorporate any changes in the radial or weakly meshed distribution system just by incorporating the changes in the CM and WMCM for any radial or weakly meshed system. Moreover, the robustness of FFDPF and FFDWMPF is evaluated under various loading scenarios on balanced radial and weakly meshed distribution networks. Finally, to validate the proposed algorithm, the proposed strategy is applied to numerous balanced and unbalanced distribution systems.

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