Coupling effect of electromagnetic pulse to long rails with compensation capacitance of track circuit system
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摘要: 结合时域有限差分（FDTD）方法、传输线方程和长钢轨激励场快速计算方法，研究了一种高效的时域混合算法，实现长钢轨电容补偿电磁脉冲耦合效应的时域快速计算。首先，为避免对钢轨不规则结构的直接建模，根据趋肤效应，将钢轨等效为管状导体模型并提取对应的单位长度分布参数。然后，根据长钢轨激励场快速计算方法，快速计算长钢轨沿线电场分布，并结合传输线方程构建钢轨等效圆柱模型与补偿电容一体化的电磁耦合模型。最后，使用FDTD方法求解传输线方程，获取钢轨沿线各点的电磁脉冲耦合响应。研究结果表明，钢轨耦合电流波形不断展宽，但是峰值随长度增加到一定值后达到饱和状态，此结论可为轨道电路系统电磁防护设计提供重要的数据支撑。Abstract: At present, efficient time domain numerical methods used for the coupling effect analysis of electromagnetic pulse to long rails on infinite ground are still rare. An efficient time domain hybrid algorithm, consisting of the finite difference time domain (FDTD) method, the transmission line equation and the fast calculation method for the excitation fields of the long rails, is presented to realize fast electromagnetic pulse coupling simulation of the long rails with compensation capacitance in time domain. Firstly, to avoid direct modeling of the irregular structures of the rails, the rails are equivalent to the tubular conductor models based on the skin effect, and the corresponding per unit length distribution parameters are extracted. Then, the electric field distribution along the rails are calculated via the fast calculation method for the excitation fields of long rails rapidly, and the electromagnetic coupling model of the rails with compensation capacitance is constructed by the transmission line equation. Finally, the FDTD method is used to solve the transmission line equation to obtain the electromagnetic pulse coupling responses on the rails. The results show that the width of the coupling current waveform on the rails would extend, and the peak values of these currents would saturate with the rail length increasing to a certain value. This conclusion will provide important data for the electromagnetic protection design of track circuit system.
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Key words:
- long rail /
- track circuit /
- compensation capacitor /
- FDTD /
- transmission line equation
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图 2 P60钢轨和各半径对应圆柱模型在HEMP E1辐照下的电流响应
Figure 2. Current responses of P60 rail and cylinder models corresponding to each radius under HEMP E1 irradiation
图 3 不同长度的钢轨和圆柱模型在HEMP E1辐照下的电流响应
Figure 3. Current responses of rail and cylinder models with different lengths under HEMP E1 irradiation
图 4 双导线沿线电场和负载端垂直电场分布
Figure 4. Electric field distribution along the line and the vertical electric field at the load end of the double conductor
图 5 长传输线激励场快速计算方法处理示意图
Figure 5. Schematic diagram of processing method for fast calculation of excitation field of long transmission line
图 6 补偿电容对钢轨电容分布参数的影响
Figure 6. Influence of compensation capacitance on the distribution parameters of rail capacitance
图 7 电磁脉冲作用钢轨等效圆柱模型
Figure 7. Equivalent cylindrical model of rail under electromagnetic pulse
图 8 钢轨电磁耦合时域算法与CST的终端负载电流响应
Figure 8. Terminal load current response of rail electromagnetic coupling time domain (FDTD-TL) algorithm and CST calculation
图 9 不同钢轨长度下的终端负载电流响应
Figure 9. Termination load current response under different rail lengths
表 1 钢轨电磁耦合时域算法和CST计算所需内存和时间的对比
Table 1. Comparison of memory and time required for rail electromagnetic coupling time-domain algorithm and CST calculation
numerical methods memory/MB time/s rail electromagnetic
coupling time
domain algorithm50 16 CST 200 924 
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表 2 不同长度情况下的钢轨电磁耦合时域算法所需内存和时间
Table 2. Memory and time required by the time-domain algorithm for electromagnetic coupling of rails with different lengths
length/m memory/MB time/min 10 62 1 100 71 8 1000 87 58 10000 97 320
下载: 导出CSV
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