一种适用于二维分形粗糙地表的雷电水平场计算的新算法  

The New Formula for Calculating Lightning-Radiated Horizontal Electric Field of Two-Dimensional(2-D) Rough Ground Surface

作　　者：刘涛[1,2] 李东帅[1,2] 张其林[1,2] 

机构地区：[1]南京信息工程大学中国气象局气溶胶与云降水重点开放实验室,南京210044 [2]南京信息工程大学大气物理学院,南京210044

出　　处：《电瓷避雷器》2016年第6期68-72,76,共6页Insulators and Surge Arresters

基　　金：国家自然科学基金项目(编号:40975002)

摘　　要：由雷电引起的浪涌电压和电流是造成电子设备失效甚至损坏的主要因素。雷电辐射电磁场的水平电场分量在雷电瞬态过电压的研究计算中占据重要位置,然而目前针对雷电辐射水平电场的近似算法均是将地表假设成光滑地表,但现实中的地表常常存在高低起伏的特征。针对上述问题,基于Cooray-Rubinstein算法(简称C-R算法)提出了一种适用于二维分形粗糙地表的雷电水平场计算的新算法,并利用三维时域有限差分方法对其适用范围和精度进行了检验。结果表明:相比于光滑地表,粗糙地表对雷电水平电场的衰减不容忽视,尤其在回击开始的几个微秒范围内,水平电场的幅值会出现明显的衰减;当高度均方根δ=5 m时,水平电场的幅值可衰减到原来的一半;当地面电导率的变化范围从0.1 S/m到0.01 S/m时,新算法的结果与三维时域有限差分方法的结果相比具有较好的适用精度,且节约了运算时间和计算成本,更利于推广到雷电定位技术和架空配电线路的雷电防护工程计算中。Surge voltage or surge current caused by lightning is the main damage reason of electronic equipment. The Lightning-radiated horizontal electric field is the most widely used for the lightning location technology and the lightning-induced voltages on overhead line. However, all the approximate formulas of the lightning-radiated horizontal electric field are over the smooth ground surface, but the natural ground surface is always irregular and not smooth. Therefore, it is more valuable to study the formulas of lightning-radiated horizontal field over the rough land than that over the smooth ground surface. Above all, we will simulate the rough ground surface with the fractal geometry and estimate the propagation effect of the rough ground on the lightning horizontal field, and then validate the accuracy of the C-R formula by using three-dimensional （3-D） finite-difference time-domain （FDTD） method. The results show that, compared with the smooth surface, the attenuation of rough terrain cannot be ignored, especially in the initial several seconds of the return stroke, the amplitude of the horizontal electric field will significantly affected by the rough ground. The amplitude of the horizontal electric field can be reduced to half of the original height when the rootmean-square height （δ） is 5 m. When the conductivity of the ground ranges from 0.1 S/m to 0.01 S/m, the new formula has a good accuracy with the FDTD method and greatly shortened the time of calculation and computational cost, which is more valuable to generalize to the lightning location technology and the lightning-induced voltages on overhead line.

关 键 词：C-R算法 FDTD 水平电场 

分 类 号：TM863[电气工程—高电压与绝缘技术]