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Analysis of load surge of overhead transmission line under indirect lightning stroke introduction the surge voltage of indirect lightning stroke on transmission line is an important cause of power line surge, electromagnetic disturbance and permanent damage of electronic and electrical equipment. At the same time, the effect of external electromagnetic fields on transmission lines is also the basic content of EMC Research. We will continue to implement three major special projects: advanced CNC machine tools and basic manufacturing equipment, large aircraft, aero engines and gas turbines. Using the finite difference method to analyze the coupling between the external electromagnetic field and the transmission line [1~3], the surge voltage and current at any point of the line can be calculated. However, this method is difficult to deal with the calculation of parameters varying with frequency. In engineering applications, people are mainly concerned about the surge voltage and current at the load end. BLT equation is an effective method to calculate the surge voltage and current at the load end in frequency domain. This paper studies the load surge voltage of transmission line under indirect lightning according to the following steps:

(1) establish the mathematical model of lightning return current

(2) calculate the electromagnetic field generated by lightning channel current in space, so as to consider the influence of finite earth conductivity on the electric field component

(3) establish the mathematical model of coupling electromagnetic field and transmission line in frequency domain

(4) the frequency domain solution of load surge voltage is obtained by using BLT equation, and the transient solution of load surge voltage is obtained by inverse FFT transformation

2 model of return stroke current

there are different methods for modeling lightning return stroke current. Theoretical analysis and experimental results show that when studying the coupling of electromagnetic field and transmission line, the influence caused by the inclination of lightning channel is small [4]. Therefore, this paper adopts the so-called "improved transmission line model (MTL)" (as shown in Figure 1) [1]. In the figure, the lightning point is taken as the coordinate origin, the lightning channel is the Z axis, the parallel direction along the conductor is the X axis, the vertical direction with the conductor is the Y axis, and the xoy plane is the ground plane. The model assumes that the ground is a good conductor and the ground surface is the mirror interface of lightning channel. The lightning current is expressed as the pulsating traveling wave I (Z ', t) propagating upward along the vertical channel. The inclination angle of the lever fulcrum end is controlled within ± 0.5 °. At any instant, I (Z', t) decays exponentially with the height Z '

i (Z ', t) can be expressed as

where a is the attenuation constant, and its value is related to the charge distribution stored in the ionosphere and the subsequent return stroke discharge, with a variation range of 0.5 ~ 1.0KM; V is the effective propagation velocity of pulsating current along the return stroke channel, and its variation range is 0.6 ~ 2.0 × 108 m/s； I (0, t-z '/v) is the value of the return stroke current at the ground, and the typical waveform can be expressed as the sum of two exponential functions. That is, where I0I is the current amplitude at the bottom of the channel; τ 1I is the rise time constant; τ 2I is the delay time constant; N is the index (n=2,4,... 10). Adjust I0I, τ 1i， τ The value of 2I can change the maximum value of current amplitude and slope, etc

the basic current waveform of lightning channel determined by the parameters in Table 1 is used in this calculation, as shown in Figure 2. 3 Calculation of the induced electric field generated by the return stroke current

3.1 calculation of the induced electric field when the earth is a good conductor

to solve the coupling problem between the electromagnetic field and the transmission line, we must know the vertical and horizontal components of the induced electric field along the transmission line, which can be calculated by integration according to the distribution of the channel current and the position of the observation point

if the lightning strike point is close to the transmission line (within a few hundred meters), at this time, the earth can be regarded as a good conductor when calculating the electric field generated by the lightning strike current that has passed the acceptance of the expert group [1]. Since the conductivity of the earth is a function of frequency, in order to consider the influence of the earth on the load surge voltage more generally, it is more effective to solve the coupling problem between the external electromagnetic field and the transmission line in the frequency domain. In this section, it is assumed that the earth is a good conductor to calculate the electric field distribution around the channel. The influence of earth conductivity on surge voltage will be discussed in section 6.3. Suppose that there is a vertically oriented Hertz dipole idz 'at the height Z', and the vertical component of the electric field of the Hertz dipole at the observation point P (Z, R, t) is [5]

where Z0 is the wave impedance in free space Z0 = 377w; K is the wave number k =w/c; C is the propagation speed of electromagnetic wave in vacuum; R is the distance from the dipole to the observation point. The electric field generated by the current of the whole lightning channel at point P shall be integrated along the channel. Since the channel current is a pulsating traveling wave, the integrand function should be equal to zero before it is transferred to the integration point. Assuming the height of lightning channel is h, the total excitation electric field intensity of observation point P (Z, R) is

it is reported that the variation range of channel height h is generally 7km. When h 1/a (a is the attenuation constant in formula (1)), the value of H has little effect on the calculation results, and h can be taken as infinity in practical application

3.2 effect of finite earth conductivity on induced electric field

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