雷电水平电场时域近似算法研究及精度验证

Research and Accuracy Validation of Approximate Time-domain Method for Lightning-horizontal Electric Field

雷电水平电场是计算雷电感应过电压的关键参数。为了准确高效的求解出雷电水平电场,利用Barbosa和Paulino所提出的雷电水平电场时域近似算法（B-P方程）对距离闪电通道100~1 000 m范围内雷电水平电场进行模拟,分析了不同雷电参数及大地电参数对水平电场特性所产生的影响,并应用2-D FDTD方法对B-P方程的精度进行检验。结果表明：若模拟中地面电导率σ设置越低、观测点距地面高度h设置越低、观测点到闪击点距离r0设置越远、回击速度v设置越大时,电磁场所包含的高频分量比重越大,模拟出水平电场波形的双极性特征越明显;相比于首次回击电流,当模拟中采用继后回击电流时,模拟出水平电场波形的双极性特征更明显;除了电导率σ较低时（σ≤0.001 S/m）B-P方程的计算精度会受传播效应的影响外,其模拟出的水平电场波形与2-D FDTD的模拟结果基本一致,且B-P方程的峰值计算误差均在±5%之内。综上,由于B-P方程的计算时间仅为0.01 s左右,因此在提高计算效率的同时能保证较好的计算精度。

The lightning horizontal electric field is a key parameter for calculating lightninginduced over-voltage. In or- der to study and calculate the lightning horizontal electric field more accurately and efficiently, we calculated the lightning-radiated horizontal electric field within distances from 100 to 1 000 m from the lightning channel and analyzed the different lightning and soil parameters which influence the characteristics of lightning horizontal electric field by the time-domain method presented by Barbosa and Paulino （B-P formula）. We also validated the accuracy of B-P formula us- ing the 2-D FDTD method as the exact solution. The results show that, if the soil conductivity（a） is set lower, the observation point height to ground （h） is set lower, the observation point distance to lightning channel（r0） is set farther and the return stroke speed（v）is set larger in simulation, the electromagnetic field contains more high frequency components and the bipolar characteristics of the simulated waveform is obvious; Compared with the first return-stroke current, the bipolar characteristics of the simulated waveform is more obvious when subsequent return-stroke current is adopted in simulation; Except the waveform influenced by propagation effect caused by lower soil conductivities （σ≤0.001 S/m）, the waveform predicted by B-P formula is basically the same as the 2-D FDTD result and the peak value accuracy of the B-P formula is within ＋5% range. It is concluded that, because the computational time is only about 0.01 s, the B-P formula can improve the calculation efficiency and ensure the accuracy simultaneously.