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The load flow problem (LFP) in power distribution networks allows us to find the nodal voltage values within the electrical systems. These values, along with the system parameters, are useful to identify the (technical, economic, and environmental) operational indices and constraints that describe the system's behavior under an established load scenario. The solution of the LFP requires the implementation of numerical methods due to its mathematical model's nonlinear and non-convex nature. In the specialized literature, multiple classical and modern methods seek to improve the solutions achieved in terms of convergence and processing times. However, the most efficient method in both radial and meshed networks has not been determined. Consequently, this study identified the most widely used and efficient classical and modern methods reported in the literature: Newton–Raphson (NR), Gauss-Seidel (GS), Iterative Sweep (IS), Successive Approximations (SA), Taylor's Series (TS), and Triangular Method (TM). The analysis also identified and selected the most common test scenarios to validate the effectiveness of the proposed solution methods: 10-, 33-, and 69-node systems in radial and meshed topologies. The software employed to validate the processing times and convergence of the numerical methods was MATLAB. The results obtained by the different methods were compared, taking the NR methodology as the base case. Thanks to its convergence, this method is used in commercial software packages to solve the LFP, as is the case of DIgSILENT. After analyzing the results of this study, we can state that all the selected methods were suitable in terms of convergence. The greatest errors were 6.064×10−07 for power losses and 8.017×10−04 for nodal voltages, which are negligible values for practical purposes in radial and meshed networks. In this work, processing time was employed as the selection criterion, and TM was identified as the most efficient method for solving the AC power flow in radial and meshed topologies for all the scenarios analyzed.
Grisales-Noreña et al. (Thu,) studied this question.