采用新颖格式FDTD计算大地垂直分层雷电电磁场
金涛斌1，王龙飞2，刘正文2，罗雨2
（1 呼和浩特市城市轨道交通建设管理有限责任公司，内蒙古 呼和浩特 010000；2 北京石油化工学院 机械工程学院，北京 102617）
摘 要：雷电电磁脉冲会通过耦合作用产生瞬时高电压和大电流干扰，研究雷电放电过程并快速、精确计算雷电电磁场分布，可有效减少设备损失，降低事故率。在二维柱坐标系下，提出了一种新颖格式的FDTD算法，能够更精确计算大地垂直分层且分界面离雷电通道较近情况下的雷电电磁场分布，计算结果表明：对大地垂直分层且分界面离雷电通道较近时，计算离雷电通道50 m范围内的雷电电磁场，新颖FDTD的计算精度较传统FDTD有显著提高，而计算离雷电通道50 m范围外的雷电电磁场，其计算结果与传统FDTD计算结果趋于一致，这说明提出的新颖格式FDTD具有传统FDTD的所有优点，并且在计算大地垂直分层情况下，较传统FDTD具有更高的计算精度，在计算雷电电磁场时，具有更广泛的适用性。
关键词：雷电电磁脉冲；雷电电磁场；二维柱坐标系；大地垂直分层
中图分类号：TM863 文献标识码：A 文章编号：1007-3175(2020)07-0024-05
Calculation of the Lightning Electromagnetic Field for Vertically Stratified Ground Using Novel Scheme FDTD
JIN Tao-bin1, WANG Long-fei2, LIU Zheng-wen2, LUO Yu2
（1 Hohhot Rail Transit Construction Management Co., Ltd, Hohhot 010000, China;
2 School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China）
Abstract: Lightning electromagnetic pulses will generate instantaneous high voltage and high current interference through coupling, studying on the lightning process and calculating the lightning electromagnetic field quickly and accurately can effectively reduce equipment losses and accident rate.In the two dimensional cylindrical coordinate system, a novel format of FDTD (NFDTD) algorithm is proposed which can calculate the lightning electromagnetic field distribution more accurately in the case that the ground is vertically layered and the interface is near the lightning channels.The numerical result shows that for vertically stratified ground when the vertical interface is not far away from the lightning channels, the NFDTD has higher precision than the TFDTD within the range of 50 m from the lightning channels, and the results using the NFDTD and the TFDTD tend to come together beyond the range.It is shown that the NFDTD has a great advantage over the TFDTD and the NFDTD has a wide applicability in calculating the lightning electromagnetic field.
Key words: lightning electromagnetic pulse; lightning electromagnetic field; 2-D cylindrical coordinate system; vertical stratification of the earth
参考文献
[1] 李涵，邓雨荣，朱时阳，等. 海- 陆混合路径对雷电电磁场传播的影响[J]. 电工技术学报，2014，29(1)：229-235.
[2] DELFINO F, PROCOPIO R, ROSSI M, et al.Lightning return stroke current radiation in presence of a conducting ground:1 Theory and numerical evaluation of the electromagnetic fields[J]. Journal of Geophysical Research Atmospheres，2008，113：D05110.
[3] DELFINO F, PROCOPIO R, ROSSI M, et al.Lightning return stroke current radiation in presence of a conducting ground: 2 Validity assessment of simplified approaches[J]. Journal of Geophysical Research Atmospheres，2008，113：D05111.
[4] ZOU J, JIN T B, LI W W, et al.Fast numerical evaluation of the horizontal electric field radiated by a lightning channel using the moment technique[J]. IEEE Transactions on Electromagnetic Compatibility，2012，54(6)：1244-1251.
[5] ZOU J, JIN T B, LI W W, et al.A hermite interpolation model to accelerate the calculation of the horizontal electric field of a lightning channel along a transmission line[J]. IEEE Transactions on Electromagnetic Compatibility，2013，55(1)：124-131.
[6] 张岩，刘福贵，汪友华，等. 改进的双指数函数雷电流波形及其辐射电磁场的计算[J]. 电工技术学报，2013，28(z2)：133-138.
[7] SARTORI C A F, CARDOSO J R.An analytical FDTD method for near LEMP calculation[J]. IEEE Transactions on Electromagnetic Compatibility，2000，42(4)：1631-1634.
[8] YANG C S, ZHOU B H. Calculation methods of electromagnetic fields very close to lightning[J]. IEEE Transactions on Electromagnetic Compatibility，2004，46(1)：133-141.
[9] YANG B, ZHOU B, GAO H C, et al.Using a two-step finite difference time domain method to analyze lightning induced voltages on transmission lines[J]. IEEE Transactions on Electromagnetic Compatibility，2011，53(1)：256-260.
[10] 樊亚东，于建新，詹清华，等. 基于多阶FDTD雷电感应过电压计算新方法[J]. 电工技术学报，2015，30(12)：336-343.
[11] 刘荣美，汪友华，张岩. 建筑结构中雷电流和磁场分布特性的频域有限元方法分析[J]. 电工技术学报，2013，28(2)：140-145.
[12] 葛德彪，闫玉波. 电磁波时域有限差分方法[M]. 西安：西安电子科技大学出版社，2005：178-185.
[13] ZHANG Q L, LI D S, ZHANG Y Y, et al.On the accuracy of Wait's formula along a mixed propagation path within 1 km from the lightning channel[J].IEEE Transactions on Electromagnetic Compatibility，2012，54(5)：1042-1047.
[14] COORAY V.Horizontal electric field above-and underground produced by lightning flashes[J]. IEEE Transactions on Electromagnetic Compatibility，2010，52(4)：936-943.
[15] 金涛斌. 考虑大地分层时雷电瞬态辐射场的计算[D]. 北京：清华大学，2013.
