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The radial distribution network structure is exploited in developing a fast and flexible radial power flow (FFRPF) solution technique. The cornerstone of this technique is constructing one single building block matrix, called the radial configuration matrix (RCM), which is utilized in carrying out the radial power flow backward/forward iterative steps. The RCM is designed to have a small condition number with a determinant and all of its eigenvalues be equal to one to ensure its invertibility. By incorporating this matrix and its direct descendant matrices in solving the power flow problem, the CPU execution time is decreased compared with other methods. The FFRPF method is flexible in accommodating any changes that may take place in an existing radial distribution system since these changes can be exclusively incorporated within this matrix. The FFRPF is tested by using several balanced and unbalanced three-phase radial distribution systems.