采用新穎格式FDTD計(jì)算大地垂直分層雷電電磁場(chǎng)
金濤斌1，王龍飛2，劉正文2，羅雨2
（1 呼和浩特市城市軌道交通建設(shè)管理有限責(zé)任公司，內(nèi)蒙古 呼和浩特 010000；2 北京石油化工學(xué)院 機(jī)械工程學(xué)院，北京 102617）
摘 要：雷電電磁脈沖會(huì)通過(guò)耦合作用產(chǎn)生瞬時(shí)高電壓和大電流干擾，研究雷電放電過(guò)程并快速、精確計(jì)算雷電電磁場(chǎng)分布，可有效減少設(shè)備損失，降低事故率。在二維柱坐標(biāo)系下，提出了一種新穎格式的FDTD算法，能夠更精確計(jì)算大地垂直分層且分界面離雷電通道較近情況下的雷電電磁場(chǎng)分布，計(jì)算結(jié)果表明：對(duì)大地垂直分層且分界面離雷電通道較近時(shí)，計(jì)算離雷電通道50 m范圍內(nèi)的雷電電磁場(chǎng)，新穎FDTD的計(jì)算精度較傳統(tǒng)FDTD有顯著提高，而計(jì)算離雷電通道50 m范圍外的雷電電磁場(chǎng)，其計(jì)算結(jié)果與傳統(tǒng)FDTD計(jì)算結(jié)果趨于一致，這說(shuō)明提出的新穎格式FDTD具有傳統(tǒng)FDTD的所有優(yōu)點(diǎn)，并且在計(jì)算大地垂直分層情況下，較傳統(tǒng)FDTD具有更高的計(jì)算精度，在計(jì)算雷電電磁場(chǎng)時(shí)，具有更廣泛的適用性。
關(guān)鍵詞：雷電電磁脈沖；雷電電磁場(chǎng)；二維柱坐標(biāo)系；大地垂直分層
中圖分類號(hào)：TM863 文獻(xiàn)標(biāo)識(shí)碼：A 文章編號(hào)：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
參考文獻(xiàn)
[1] 李涵，鄧雨榮，朱時(shí)陽(yáng)，等. 海- 陸混合路徑對(duì)雷電電磁場(chǎng)傳播的影響[J]. 電工技術(shù)學(xué)報(bào)，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] 張巖，劉福貴，汪友華，等. 改進(jìn)的雙指數(shù)函數(shù)雷電流波形及其輻射電磁場(chǎng)的計(jì)算[J]. 電工技術(shù)學(xué)報(bào)，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] 樊亞?wèn)|，于建新，詹清華，等. 基于多階FDTD雷電感應(yīng)過(guò)電壓計(jì)算新方法[J]. 電工技術(shù)學(xué)報(bào)，2015，30(12)：336-343.
[11] 劉榮美，汪友華，張巖. 建筑結(jié)構(gòu)中雷電流和磁場(chǎng)分布特性的頻域有限元方法分析[J]. 電工技術(shù)學(xué)報(bào)，2013，28(2)：140-145.
[12] 葛德彪，閆玉波. 電磁波時(shí)域有限差分方法[M]. 西安：西安電子科技大學(xué)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] 金濤斌. 考慮大地分層時(shí)雷電瞬態(tài)輻射場(chǎng)的計(jì)算[D]. 北京：清華大學(xué)，2013.
