Research rticle Fast Flexible Direct Power Flow for Unbalanced and Balanced Distribution Systems Debasis Kumar Patel , Swapna Mansani, and Arup Kumar Goswami Electrical Engineering, NIT Silchar, Silchar 788010, ssam, India Correspondence should be addressed to Debasis Kumar Patel; debasispatel89@gmail.com Received 31 January 2022; Revised 21 October 2022; Accepted 26 October 2022; Published 29 November 2022 Academic Editor: Paulo Mois´ es Almeida Costa Copyright © 2022 Debasis Kumar Patel et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te study proposes a fast fexible direct power fow solution for radial distribution systems and a fast fexible direct weakly meshed power fow solution for weakly meshed distribution systems. Te algorithm is based on the direct forward sweep power fow solution, which is an updated version of the backward/forward sweep solution. Te fast fexible direct power fow uses a unique conversion matrix (CM) to rapidly determine the power fow solution. Te inverted conversion matrix and its slide•modifed matrix are used to solve the power fow 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 modifcation as for the radial network and employed in the fast fexible direct weakly meshed power fow (FFDWMPF) solution for the weakly meshed distribution network. Te usage of a single matrix in the power fow solution and advanced direct techniques decreases the number of iterations and CPU execution time when MATLAB programming is executed. Furthermore, the proposed method is fexible 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. 1. Introduction Analyzing the power fow of the distribution system is crucial to understanding its behavior. Te power fow study provides the steady•state value for the bus voltage and angle on an unspecifed bus. Tis bus voltage and angle data assist in determining the total system parameters in the power distribution network, such as power fow (real and reactive) and total line loss, which are critical for system stability analysis. Furthermore, the modern smart grid faces the challenge of collecting instant bus parameters (that is, the magnitude and angle of bus voltage) through sensors 1]. To fully meet the operational and planning requirements of modern distribution systems, a robust, fast, and fexible power fow technique is required. Numerous solutions to the power fow problem have been proposed since the mid•nineteenth century. Initially, Dusten 2] introduced the power fow using a digital ap• proach. Ward and Hale 3] successfully implemented this work. Following that, most power fow techniques solve power fow problems using the Ybus admittance matrix and the Gauss–Seidel iterative method. Due to the difculties associated with convergence, these methods have been replaced in power fow solutions for the power system’s primary transmission line by Newton–Raphson (NR) 4], decouple 5], and fast decouple 6] techniques. Tese updated methods are highly efcient for primary trans• mission lines, but inefective for distribution system power fow solutions. Since the distribution system has distinct characteristics from the transmission line of the power Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 2857358, 18 pages https://doi.org/10.1155/2022/2857358