有损大地上传输线HEMP响应的研究
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摘要
针对电磁脉冲对传输线产生干扰的实际情况,基于传输线的频域二阶电流基本方程,建立了高空核爆电磁脉冲(HEMP)激励下有损大地上传输线电磁瞬态响应模型,利用伽辽金法和矢量匹配推导出关于传输线的时域有限元(FETD)迭代算法。该算法以电流为单变量进行迭代从而计算出沿线电流分布,通过在空间和时间上离散时域第二电报方程计算得到沿线的电压分布,从而大幅度提高了计算效率。通过对比FETD法计算结果与时域有限差分(FDTD)法计算结果,证实了FETD法的有效性和准确性。该研究为工程和科研人员评估、分析HEMP激励下传输线的瞬态响应问题提供了一种可靠的指导方法。
An accurate model for the transient response of overhead transmission line on lossy ground against high-attitude nuclear electromagnetic pulse(HEMP) plane wave was established based on the second-order telegrapher's equation of electric current. The time-domain finite-element formulas with respect to the electric current only are derived by using the Galerkin method and vector fitting method. The transmission line is divided into many segments, and in each segment the currents in the points are expressed by a linear combination of basis functions, so the residual formula is established in single segment. According the Kirchhoff's voltage law in circuit analysis, the segments about entire line are synthesized in the finite element time-domain(FETD) matrix equation, which the currents along the line can be computed. In order to solve the voltages along the line, the second time-domain telegrapher's equation is dealt with spatial and time discretization, so the voltages can be computed by means of the currents gained and previous voltages. Comparison with the results from the method of finite difference time-domain(FDTD) has verified the high efficiency and accuracy of the FETD method, which can provide reference for the transient response of transmission line excited by HEMP.
An accurate model for the transient response of overhead transmission line on lossy ground against high-attitude nuclear electromagnetic pulse(HEMP) plane wave was established based on the second-order telegrapher's equation of electric current. The time-domain finite-element formulas with respect to the electric current only are derived by using the Galerkin method and vector fitting method. The transmission line is divided into many segments, and in each segment the currents in the points are expressed by a linear combination of basis functions, so the residual formula is established in single segment. According the Kirchhoff's voltage law in circuit analysis, the segments about entire line are synthesized in the finite element time-domain(FETD) matrix equation, which the currents along the line can be computed. In order to solve the voltages along the line, the second time-domain telegrapher's equation is dealt with spatial and time discretization, so the voltages can be computed by means of the currents gained and previous voltages. Comparison with the results from the method of finite difference time-domain(FDTD) has verified the high efficiency and accuracy of the FETD method, which can provide reference for the transient response of transmission line excited by HEMP.
引文
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[17]Qi Lei,Bai Shuhua,Shuai Qi,et al.Finite-element time-domain method for multiconductor transmission lines based on the second-order wave equation[J].IEEE Transactions on Electromagnetic Compatibility,2014,56(5):1218-1227.
[18]Tesche F M,Ianoz M V,Karlsson T.EMC analysis methods and computational models[M].New York:John Wiley&Sons Incorporated,1997.
[19]Nucci C A,Guerrieri S,Teresa M,et al.Influence of corona on the voltage induced by nearby lighting on overhead distribution lines[J].IEEE Transactions on Power Delivery,2000,15(4):191-197.
[20]Kordi B,LoVetri J,Bridges G E,et al.Finitedifference analysis of dispersive transmission lines within a circuit simulator[J].IEEE Transactions on Power Delevery,2006,21(1):234-242.
[21]Gustavsen B.Improving the pole relocating properties of vector fitting[J].IEEE Transactions on Power Delivery,2006,21(3):1587-1592.
[22]Hendrickx W,Dhaene T.A discussion of rational approximation of frequency domain response by vector fitting[J].IEEE Transactions on Power Systems,2006,21(1):441-443.
[2]郝建红,公延飞,蒋璐行,等.内置电路板的复杂多腔体电磁串扰屏蔽效能的解析研究[J].电工技术学报,2018,33(3):670-679.Hao Jianhong,Gong Yanfei,Jiang Luhang,et al.Analytical formulation for the shielding effectiveness of electromagnetic crosstalk from a complex multiple enclosures with inner circuit board[J].Transactions of China Electrotechnical Society,2018,33(3):670-679.
[3]焦重庆,李明洋,崔翔.特高压气体绝缘开关设备套管的宽频等效电路建模[J].电工技术学报,2016,31(20):64-72.Jiao Chongqing,Li Mingyang,Cui Xiang.Broadband equivalent circuit mode of bushing for gas insulated switchgear in ultra high voltages substation[J].Transactions of China Electrotechnical Society,2016,31(20):64-72.
[4]Ianoz M,Nicoara B I C,Radasky W A.Modeling of an EMP conducted environment[J].IEEE Transactions on Electromagnetic Compatibility,1996,38(3):400-413.
[5]Xie Haiyan,Li Yong,Qiao Hailiang,et al.Empirical formula of effective coupling length for transmission lines illuminated by E1 HEMP[J].IEEE Transactions on Electromagnetic Compatibility,2016,58(2):518-525.
[6]Sabath F,Potthast S.Tolerance values and the confidence level for high-altitude electromagnetic puls(HEMP)field tests[J].IEEE Transactions on Electromagnetic Compatibility,2013,55(3):1529-1538.
[7]Xie Haiyan,Du Taijiao,Zhang Maoyu,et al.Theoretical and experimental study of effective coupling length for transmission lines illuminated by HEMP[J].IEEE Transactions on Electromagnetic Compatibility,2015,57(6):1529-1538.
[8]朱峰,邱日强,牛大鹏,等.基于有源传输线模型的地-架空屏蔽线缆耦合特性分析与参数计算[J].电工技术学报,2016,31(4):22-28.Zhu Feng,Qiu Riqiang,Niu Dapeng,et al.Coupling characteristic analysis and parameters calculation of ground and above-ground shielded cables based on transmission line with a distributed source model[J].Transactions of China Electrotechnical Society,2016,31(4):22-28.
[9]Jiang Luhang,Hao Jianhong,Gong Yanfei.Electromagnetic coupling to an aperture enclosure via a penetrated transmission line based on electromagnetic topology[J].Journal of Electromagnetic Waves and Applications,2018,32(5):609-623.
[10]文刚,齐世举,姜勤波,等.大地水平分层电导率对架空线缆HEMP响应的影响[J].电工技术学报,2016,31(1):91-95.Wen Gang,Qi Shiju,Jiang Qinbo,et al.Impact of horizontal stratified earth conductivity on overhead cable HEMP response[J].Transactions of China Electrotechnical Society,2016,31(1):91-95.
[11]Afrooz K,Abdipour A.Efficient method for timedomain analysis of lossy nonuniform multiconductor transmission line driven by a modulated signal using FDTD technique[J].IEEE Transactions on Electromagnetic Compatibility,2012,54(2):482-494.
[12]Ye Zhihong,Xiong Xiangzheng,Zhang Min,et al.Atime-domain hybrid method for coupling problems of long cables excited by electromagnetic pulses[J].IEEE Transactions on Electromagnetic Compatibility,2016,58(6):1710-1716.
[13]Lucic R,Jovic V,Kurtovic M.Simulation of electromagnetic transients on single transmission line via the finite element method[C]//International Conference and Exhibition on Electromagnetic Compatibility,York,1999:41-46.
[14]刘磊,崔翔,齐磊.时域有限元法求解传输线瞬态波过程[J].中国电机工程学报,2008,28(3):112-118.Liu Lei,Cui Xiang,Qi Lei.Transients analysis of transmission line by time domain finite element method[J].Proceedings of the CSEE,2008,28(3):112-118.
[15]Liu Lei,Cui Xiang,Qi Lei.Simulation of electromagnetic transients of the bus bar in substation by the time-domain finite-element method[J].IEEETransactions on Electromagnetic Compatibility,2009,51(4):1017-1025.
[16]Liu Xin,Cui Xiang,Qi Lei.Time-domain finiteelement method for the transient response of multiconductor transmission lines excited by an electromagnetic field[J].IEEE Transactions on Electromagnetic Compatibility,2011,53(2):462-474.
[17]Qi Lei,Bai Shuhua,Shuai Qi,et al.Finite-element time-domain method for multiconductor transmission lines based on the second-order wave equation[J].IEEE Transactions on Electromagnetic Compatibility,2014,56(5):1218-1227.
[18]Tesche F M,Ianoz M V,Karlsson T.EMC analysis methods and computational models[M].New York:John Wiley&Sons Incorporated,1997.
[19]Nucci C A,Guerrieri S,Teresa M,et al.Influence of corona on the voltage induced by nearby lighting on overhead distribution lines[J].IEEE Transactions on Power Delivery,2000,15(4):191-197.
[20]Kordi B,LoVetri J,Bridges G E,et al.Finitedifference analysis of dispersive transmission lines within a circuit simulator[J].IEEE Transactions on Power Delevery,2006,21(1):234-242.
[21]Gustavsen B.Improving the pole relocating properties of vector fitting[J].IEEE Transactions on Power Delivery,2006,21(3):1587-1592.
[22]Hendrickx W,Dhaene T.A discussion of rational approximation of frequency domain response by vector fitting[J].IEEE Transactions on Power Systems,2006,21(1):441-443.