Analysis of approximate formulas of internal impedance for the study of high-frequency transients in high-voltage underground cables
This study presents an analysis of approximate formulas of internal impedance for the study of high-frequency transients in high voltage underground cables. The analysis is conducted in the frequency domain, and converted to the time domain performed using a Fast Fourier Transform. The cable is modeled as a multiconductor transmission line, using modal analysis and two-port network theory. The approximate internal impedance formulas analyzed are those proposed by Gary and Wedepohl-Wilcox, used in modeling overhead and underground transmission lines, respectively. To conduct the analysis, formulas are compared with the exact model of internal impedance and the relative error of each formula is determined for real and imaginary values. The results show that the approximate formula proposed by Gary for modeling overhead transmission lines can be used to analyze high-frequency electromagnetic transient phenomena in underground cables with acceptable results. In order to carry out a comparative study of the approximate formulas of internal impedance, a series of case studies are presented, in which the magnitude of the transient voltage, the transit time and wave attenuation are determined in different lengths of single-phase underground line.
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