In this letter, a methodology is proposed for automatically (and locally) obtaining the shape factor c for the Gaussian basis functions, for each support domain, in order to increase numerical precision and mainly to avoid matrix inversion impossibilities. The concept of calibration function is introduced, which is used for obtaining c. The methodology developed was applied for a 2-D numerical experiment, which results are compared to analytical solution. This comparison revels that the results associated to the developed methodology are very close to the analytical solution for the entire bandwidth of the excitation pulse. The proposed methodology is called in this work Local Shape Factor Calibration Method (LSFCM). Index Terms − improved numerical precision, matrix inversion difficulties, optimum shape factor calculation, radial point interpolation method (RPIM). I. INTRODUCTION One of the most used numerical methods for solving Maxwell's equations in time domain is the finite-difference (FD) technique, on which the finite-difference time-domain method (FDTD) is based [1], [2]. Meshless methods, such as the Radial Point Interpolation Method (RPIM), have become an important alternative to solve numerically problems involving partial differential equations [3], [4], [5], [6], due to the fact it provides greater geometric flexibility [7], [8] than FD-based methods. This kind of methdology employs a set of points for representing the analysis region, instead of grids. The field components are locally interpolated by using subgroups of points, called support domains [3] (Fig. 1).
In this work, voltages and currents induced due to lightning occurrence on the transformers' courtyard of Tucuruí hydroelectric generation plant are calculated by employing the Finite-Difference Time-Domain method. The transient functions are obtained for 500 kV-transmission lines at the output of the power plant. In order to the simulations become viable from the computational point of view, it was necessary to use parallel processing for dividing the analysis region into 24 subdomains (24 computer cores were used). The simulated problem in this work consists on an 1 kA-lightning stroke on phase A of the output transmission system of the Tucuruí's plant.
In this work, induced voltages between the phase A of the line and the following reference points were obtained: a) the courtyard grounding mesh for voltage transformers, b) ground grid in the first floor concrete, c) rock (basalt) surface at the base of the plant, d) the soil's layer and water surfaces. Transient voltages induced between the phases A, B and V of the transmission line are also analyzed. These data are important because the electrical system is based on voltage differences between phases.It is also noticed that, in this case, the maximum induced voltage between phases A and B is approximately 157.9 kV/kA. It is also performed a study regarding voltage supportability for line insulators on the structure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.