Peaks Times of Transients in Transmission Systems based on Laplace Transform in Modal Coordinates

Abstract

The current paper presents an analysis for the dependency of propagation self-parameters (propagation coefficient, attenuation factor and wave velocity) of some typical transmission lines (500, 330, 220, 110 kV) besides the distribution lines of 35 and 10 kV. The wave-mode parameters are deduced in modal coordinates (a, b, 0). Carson's equations for computation of frequency dependent parameters of overhead transmission lines are modified for the homogenous earth and the optimal number of terms of Carson's series is considered. The standard dimensions of towers are implanted, and the corresponding accurate propagation parameters of overhead transmission lines are obtained. Different arrangements of conductors for transmission lines are studied for the voltage levels of 500 and 220 kV. The mutual inductance and potential coefficient (mutual capacitance) of such arrangements are based (mirror effect). The time response for the first 5 peaks of transients for a long duration is intended and analyzed. The per unit system is accounted and the comparison is applied where the points of overvoltage are derived based on the convolution theorem and Laplace inverse structure. The voltages are computed for the specified points on the line (as SE, ¼ , ½ , ¾ , and RE) for considered voltage levels where a tailored comparison has been analyzed for the major parameters of propagation (Propagation Coefficient, Wave Velocity, Attenuation Factor). It is concluded that the time dependency is linearly with the rise of standard voltage of a line.