Calculation Of Lightning Electromagnetic Field And Lightning-Induced Voltages Based On FDTD Method

Lightning is a key factor threatening the safety of overhead lines, and the design and implementation of the lightning protection project for transmission lines should be based on characteristics of overvoltage. Therefore, it is necessary to discuss the electromagnetic fields produced by lighting return strokes and the method to calculate the lightning-induced voltages of transmission lines considering the complex surface area. So far, there are limitations in precision and applicability of frequency-domain approximate formulas, which are widely used in calculating the lightning electromagnetic fields. Besides, there are comparatively inadequate researches on algorithms and compromise theory of estimation of the lightning-induced voltages considering the non-homogeneous soil. To overcome these shortcomings, the relevant researches are carried out and the results obtained are showed as follows:(1) A Finite-Difference Time-Domain method in three-dimensional Cartesian coordinates (3-D FDTD) is developed, with has a good precision in calculating the lightning electromagnetic fields considering the non-uniform ground. By comparing the horizontal electrical fields obtained by extended formulas of Coory-Rubstein (C-R) approximate algorithm with this3-D FDTD method, it can be found that the error of the negative peak value obtained by Delfino algorithm increases with the decrease of the electrical conductivity of the ground, and Delfino algorithm is not suitable in the case of poor conductivity (e.g.,0.001S/m) and a distance of over1km from the lightning channel; Shoory algorithm has a higher accuracy when the upper layer has a higher conductivity than the lower layer; Zhang algorithm has excellent accuracy within1km from the lightning channel, but it has a so-called "angle-problem", which means that it applies only to propagation path perpendicular to the interface between the different soil, meaning that it do not apply to the case of vertically stratified ground in calculating the lightning-induced voltages on overhead lines.(2) A new numerical method with the "field-line" integration based on the three-dimensional FDTD method for calculating the lightning-induced voltages is proposed. Also, its validity and efficiency are confirmed. Overvoltages can be simulated considering the stratified conducting ground by using this method. At the same time, the calculating process can realize the dynamic visualization of the lightning electromagnetic field distribution.(3) In the condition of the horizontally stratified conducting ground, the lightning induced voltage increases obviously with the depth of the first layer, and we should consider the influence of the stratified ground when the conductivity of the first layer is less than that of the second layer in engineering calculation; Conversely, we could just simplified the ground as the homogenous soil with the electrical parameters of the first layer in calculation when the first layer is over2meters depth with high conductivity (e.g.,0.1S/m).(4) The traditional "two-step" algorithm is extended to the case of the horizontally stratified conducting ground. The simulations show that the results calculated by using "two-step" algorithm with two-dimensional FDTD method are highly consistent with those of three-dimensional FDTD method, and the relative errors are within3%. However, C-R approximate algorithm underestimates the peak values to some extent, and its relative error decreases with the increase of the conductivity of the first layer, but no more than10%.(5) In the condition of the vertically stratified conducting ground, we should consider the influence of the mixed propagation on the lightning-induced voltages on overhead lines if only the ground is of low conductivity covering a range of more than2meters around the line, even the lightning strikes over the sea, ponds, farmland or some other areas of high conductivity; Conversely, only when the ground of low resistivity covers a range of less than30meters around the line should we consider the influence of the mixed propagation path when the conductivity of the ground near the strike point is less than that of the overhead lines, otherwise a simplified process can be carried out in engineering calculation by using alone the electrical parameters of the highly conducting ground near the lines.