Calculation of Lightning Induced Voltages on Overhead Lines Using an Analytical Fitting Representation of Electric Fields

The lightning electromagnetic field which illuminated the overhead line is the nonuniform field. When analyzing the lightning induced overvoltages on overhead lines by in frequency domain, to get an accurate response, the observation points of the horizontal electric field along the overhead line should be as many as possible. However, the expression of the horizontal electric field is formulated in the integral form and should be solved by the time-consuming numerical integration process at every observation point, which leads to a low calculation efficiency. This paper proposes an efficient method to avoid the numerical integration process at all the observation points and to enhance the calculation efficiency. In this method, the horizontal electric field at a few observation points along the line are calculated in the numerical way first, then the amplitudes and phases of the horizontal electric field along the line are fitted separately at every frequency with the fitting functions of the position $x$ along the line. The amplitudes are fitted by the Fourier series, and the phases are fitted by the polynomial functions. Based on the obtained analytical fitting representations, the transmission line response could be solved efficiently. The two different lightning electromagnetic pulse (LEMP) validation examples show the validity and general applicability of the proposed method.