Localization Method for Metro Stray Current Leakage Points Based on Tellegen’s Theorem
-
摘要:
为从源头定位地铁杂散电流泄漏点，首先建立地铁牵引供电系统等效电阻网络模型，根据钢轨绝缘损坏前后的等效电阻网络拓扑结构不变的特点，基于特勒根定理推导钢轨对地过渡电阻与牵引所及列车支路电压、电流的关系式；其次，考虑列车运行与牵引所、列车相关电气量的时空对应关系，构建多时间断面的钢轨对地过渡电阻求解方程组，并采用二分法对定位区间逐步细分以增加方程组维数，结合遗传算法对该方程组进行迭代寻优获取沿线钢轨对地过渡电阻分布；最后，将钢轨对地过渡电阻计算结果与杂散电流泄漏点判别阈值进行对比，以实现杂散电流泄漏点定位. 基于实际地铁线路参数及实测轧道车数据开展仿真验证，并从杂散电流泄漏点位置、泄漏程度及泄漏区间长度三方面分析所提方法的适用性. 结果表明：在不同泄漏点位置、不同泄漏程度及不同泄漏区间长度三类仿真场景下，最大定位误差分别为9.375 m、0 m、6.875 m，相对误差均低于0.4%，可见所提方法的定位结果与预设位置基本吻合. 综上所述，该方法能实现杂散电流泄漏点所在区段定位，可为钢轨扣件破损、局部绝缘劣化等场景下的杂散电流治理提供理论依据.
Abstract:To locate the metro stray current leakage points from the source, an equivalent resistance network model of the metro traction power supply system was first established. According to the characteristic of invariant topology of the equivalent resistance network before and after the rail insulation damage, the relationship between the rail-to-ground transition resistance and the branch voltages and currents of the traction substations and trains was derived based on Tellegen’s theorem. Secondly, by considering the spatiotemporal correspondence between train operations and the related electrical quantities of the traction substations and trains, a multi-time-section solving equation system for the rail-to-ground transition resistance was constructed. The locating interval was progressively subdivided by using the bisection method to increase the dimensionality of the equation system, and a genetic algorithm was combined to iteratively optimize the equation system to obtain the distribution of the rail-to-ground transition resistance along the line. Finally, the calculation results of the rail-to-ground transition resistance were compared with the identification threshold of stray current leakage points to realize the localization of stray current leakage points. Simulation verification was conducted based on actual metro line parameters and measured track inspection train data, and the applicability of the proposed localization method was analyzed from three aspects: stray current leakage point location, leakage severity, and leakage section length. The results show that under the three types of simulation scenarios of different leakage point locations, different leakage severities, and different leakage section lengths, the maximum localization errors are 9.375 m, 0 m, and 6.875 m, respectively, and the relative errors are all below 0.4%. It can be seen that the localization results of the proposed localization method are basically consistent with the preset locations. In summary, the method can realize the localization of the section where the stray current leakage points are located and can provide a theoretical basis for stray current mitigation in scenarios such as rail fastener damage and localized insulation degradation.
-
图 2 地铁牵引供电系统等效电阻网络
Figure 2. Equivalent resistance network of metro traction power supply system
图 5 杂散电流泄漏点定位求解收敛曲线
Figure 5. Solving convergence curve for stray current leakage point localization
图 6 钢轨对地过渡电阻计算结果
Figure 6. Calculation results of rail-to-ground transition resistance
表 1 模型纵向导体参数
Table 1. Longitudinal conductor parameters of model
金属导体 参数 数值 钢轨 半径/m 0.0683 阻值（Ω•km-1） 0.02 接触网 半径/m 0.009 阻值/（Ω•km-1） 0.008 钢轨涂层电阻率 阻值（kΩ•m） 650 
下载: 导出CSV
表 2 不同杂散电流泄漏点位置的仿真场景
Table 2. Simulation scenarios for different stray current leakage point locations
序号 泄漏点位置区间/m 钢轨对地过渡电阻/（Ω•km） 工况2 [356.250, 375.000] 2.500 工况3 [890.625, 909.375] 2.500 工况4 [ 2043.750 ,2062.5 ]2.500
下载: 导出CSV
表 3 工况2～4的定位结果
Table 3. Localization results for case 2–case 4
序号 定位结果区间/m 定位误差/m 工况2 [356.250, 375.000] 0 工况3 [900.000, 918.750] 9.375 工况4 [ 2043.750 ,2062.500 ]0
下载: 导出CSV
表 4 不同杂散电流泄漏程度的仿真场景
Table 4. Simulation scenarios for different stray current leakage severities
序号 泄漏点位置区间/m 钢轨对地过渡电阻/（Ω•km） 工况5 [918.250, 937.000] 3.000 工况6 [918.250, 937.000] 2.500 工况7 [918.250, 937.000] 1.000
下载: 导出CSV
表 5 工况5-工况7的定位结果
Table 5. Localization results for case 5–case 7
序号 定位结果区间/m 定位误差/m 工况5 [918.250, 937.000] 0 工况6 [918.250, 937.000] 0 工况7 [918.250, 937.000] 0
下载: 导出CSV
表 6 不同杂散电流泄漏区间长度的仿真场景
Table 6. Simulation scenarios for different stray current leakage section lengths
序号 泄漏点位置区间/m 钢轨对地过渡电阻/（Ω•km） 工况8 [920.000, 945.000] 1.000 工况9 [918.250, 937.500] 1.000 工况10 [920.000, 930.000] 1.000
下载: 导出CSV
表 7 工况8-工况10的定位结果
Table 7. Localization results for case 8–case 10
序号 定位结果区间/m 定位误差/m 工况8 [918.250, 937.000] 6.875 工况9 [918.250, 937.000] 0 工况10 [918.250, 937.000] 3.125
下载: 导出CSV
-
[1] Lin S, Wang A M, Liu M J, et al. A multiple section model of stray current of DC metro systems[J]. IEEE Transactions on Power Delivery, 2021, 36(3): 1582-1593. doi: 10.1109/TPWRD.2020.3011574 [2] Liu W, Li T, Zheng J, et al. Evaluation of the effect of stray current collection system in DC-electrified railway system[J]. IEEE Transactions on Vehicular Technology, 2021, 70(7): 6542-6553. doi: 10.1109/TVT.2021.3084340 [3] 王爱民, 林圣, 李俊逸, 等. 城市轨道交通长线路杂散电流仿真模型[J]. 高电压技术, 2020, 46(4): 1379-1386.Wang Aimin, Lin Sheng, Li Junyi, et al. Stray current simulation model of the long line of DC metro systems[J]. High Voltage Engineering, 2020, 46(4): 1379-1386. [4] Wang S K, Zhou L M, Xiong D Y, et al. Zero-resistance-branch electrical drainage system to solve the adverse influence of stray current on buried pipelines[J]. IEEE Transactions on Industrial Electronics, 2024, 71(5): 4618-4628. doi: 10.1109/TIE.2023.3283675 [5] Wang A M, Lin S, Wu J Z, et al. Relationship analysis between metro rail potential and neutral direct current of nearby transformers[J]. IEEE Transactions on Transportation Electrification, 2021, 7(3): 1795-1804. doi: 10.1109/TTE.2021.3053340 [6] 程宏波, 钟文帆, 陈艳华, 等. 一种基于Lasso理论的牵引变电所接地网腐蚀诊断方法[J]. 铁道学报, 2024, 46(5): 58-65.Cheng Hongbo, Zhong Wenfan, Chen Yanhua, et al. Research on corrosion diagnosis of grounding grid based on Lasso theory[J]. Journal of the China Railway Society, 2024, 46(5): 58-65. [7] Wang A M, Lin S, He Z Y, et al. Probabilistic evaluation method of transformer neutral direct current distribution in urban power grid caused by DC metro stray current[J]. IEEE Transactions on Power Delivery, 2023, 38(1): 541-552. doi: 10.1109/TPWRD.2022.3200953 [8] 刘炜, 李松原, 唐宇宁. 轨道交通直流干扰的车-地-网动态耦合仿真[J]. 西南交通大学学报, 2025, 60(1): 156-165. doi: 10.3969/j.issn.0258-2724.20230052Liu Wei, Li Songyuan, Tang Yuning. Simulation of dynamic coupling of metro-earth-grid for DC interference in rail transit[J]. Journal of Southwest Jiaotong University, 2025, 60(1): 156-165. doi: 10.3969/j.issn.0258-2724.20230052 [9] Du G F, Wang J, Jiang X X, et al. Evaluation of rail potential and stray current with dynamic traction networks in multitrain subway systems[J]. IEEE Transactions on Transportation Electrification, 2020, 6(2): 784-796. doi: 10.1109/TTE.2020.2980745 [10] 朱峰, 李嘉成, 曾海波, 等. 城市轨道交通轨地过渡电阻对杂散电流分布特性的影响[J]. 高电压技术, 2018, 44(8): 2738-2745. doi: 10.13336/j.1003-6520.hve.20180731034Zhu Feng, Li Jiacheng, Zeng Haibo, et al. Influence of rail-to-ground resistance of urban transit systems on distribution characteristics of stray current[J]. High Voltage Engineering, 2018, 44(8): 2738-2745. doi: 10.13336/j.1003-6520.hve.20180731034 [11] GB/T 28026.2—2018 轨道交通 地面装置 电气安全、接地和回流 第2部分: 直流牵引供电系统杂散电流的防护措施[S]. [12] 李诗晨, 禹贤虎, 李景龙. 城市轨道交通轨排过渡电阻新型测量方法[J]. 城市轨道交通研究, 2025, 28(5): 232-237. doi: 10.16037/j.1007-869x.2025.05.039Li Shichen, Yu Xianhu, Li Jinglong. New measurement methods for transition re-sistance of rail tracks in urban rail transit[J]. Urban Mass Transit, 2025, 28(5): 232-237. doi: 10.16037/j.1007-869x.2025.05.039 [13] 洪子杰, 赵文彬, 谭乃久, 等. 基于地电位特征和Chan算法的轨道交通钢轨绝缘破损点定位方法[J]. 上海电力大学学报, 2024, 40(3): 251-258.Hong Zijie, Zhao Wenbin, Tan Naijiu, et al. A method for locating insulation damage points on rail transit based on ground potential and Chan algorithm[J]. Journal of Shanghai University of Electric Power, 2024, 40(3): 251-258. [14] 苏宁宁. 地铁轨道对地局部绝缘损坏点定位方法研究[D]. 徐州: 中国矿业大学, 2022. [15] 卢昱瑾. 地铁轨地过渡电阻测试技术研究[D]. 徐州: 中国矿业大学, 2021. [16] 赵珊鹏, 刘俊, 李亚宁, 等. 基于响应面法的城市轨道交通杂散电流多因素影响分析[J/OL]. 西南交通大学学报, 2026-04-13. https://link.cnki.net/urlid/51.1277.U.20260411.1825.014.Zhao Shanpeng, Liu Jun, Li Yaning, et al. Multi-factor influence analysis of stray current in urban rail transit based on response surface methodology[J/OL]. Journal of Southwest Jiaotong University, 2026-04-13. https://link.cnki.net/urlid/51.1277.U.20260411.1825.014. [17] 刘炜, 吴拓剑, 禹皓元, 等. 直流牵引供电系统地面储能装置建模与仿真分析[J]. 电工技术学报, 2020, 35(19): 4207-4215. doi: 10.19595/j.cnki.1000-6753.tces.191308Liu Wei, Wu Tuojian, Yu Haoyuan, et al. Modeling and simulation of way-side energy storage devices in DC traction power supply system[J]. Transactions of China Electrotechnical Society, 2020, 35(19): 4207-4215. doi: 10.19595/j.cnki.1000-6753.tces.191308 [18] 唐泽洋, 梅欣, 阮羚, 等. 城市轨道交通地铁线路对变压器中性点直流电流的影响分析[J/OL]. 西南交通大学学报, 2026-03-19. https://link.cnki.net/urlid/51.1277.U.20260319.1209.004.Tang Zeyang, Mei Xin, Ruan Ling, et al. Influence analysis of urban rail transit metro line on the DC current at the neutral point of transformer[J/OL]. Journal of Southwest Jiaotong University, 2026-03-19. https://link.cnki.net/urlid/51.1277.U.20260319.1209.004. [19] Zhou Q, Lin S, Lin X H, et al. A uniform model for stray current of long-line DC metro systems[J]. IEEE Transactions on Transportation Electrification, 2022, 8(2): 2915-2927. doi: 10.1109/TTE.2021.3120466 [20] Zhou Q, Lin S, Zhang W J. Analysis and mitigation of stray current in modern metro systems with OVPD and PSD[J]. IEEE Transactions on Transportation Electrification, 2024, 10(2): 3153-3166. doi: 10.1109/TTE.2023.3300750 [21] 王丰华, 王劭菁, 刘亚东, 等. 采用地表电位和磁感应强度进行变电站接地网故障诊断的效果对比[J]. 高电压技术, 2016, 42(7): 2281-2289.Wang Fenghua, Wang Shaojing, Liu Yadong, et al. Comparison of substation grounding grid fault diagnosis results using surface potential and magnetic induction intensity[J]. High Voltage Engineering, 2016, 42(7): 2281-2289. [22] 许磊, 李琳. 基于电网络理论的变电站接地网腐蚀及断点诊断方法[J]. 电工技术学报, 2012, 27(10): 270-276.Xu Lei, Li Lin. Fault diagnosis for grounding grids based on electric network theory[J]. Transactions of China Electrotechnical Society, 2012, 27(10): 270-276. [23] 倪砚茹, 曾祥君, 喻锟, 等. 地铁杂散电流引起动态地电位分布建模及影响因素分析[J]. 中国电机工程学报, 2023, 43(23): 9059-9071.Ni Yanru, Zeng Xiangjun, Yu Kun, et al. Modeling and influencing factors analysis of dynamic potential distribution caused by metro stray current[J]. Proceedings of the Chinese Society for Electrical Engineering, 2023, 43(23): 9059-9071. [24] 夏能弘, 唐文涛, 李怀慎, 等. 地铁轨道局部绝缘损坏下动态杂散电流及地电位梯度建模与分析[J]. 电力系统保护与控制, 2023, 51(4): 53-61.Xia Nenghong, Tang Wentao, Li Huaishen, et al. Modeling and analysis of dynamic stray current and ground potential gradient under partial insulation damage of a metro track[J]. Power System Protection and Control, 2023, 51(4): 53-61. [25] CJJ 49—1992 地铁杂散电流腐蚀防护技术规程[S]. [26] 徐超, 李鲲鹏, 曹晓斌, 等. 城市轨道交通钢轨扣件对地绝缘组成及影响因素研究[J]. 城市轨道交通研究, 2019, 22(6): 129-132, 137. doi: 10.16037/j.1007-869x.2019.06.029Xu Chao, Li Kunpeng, Cao Xiaobin, et al. Ground insulat ion composition and influencing factors of rail fastener in urban rail transit[J]. Urban Mass Transit, 2019, 22(6): 129-132,137. doi: 10.16037/j.1007-869x.2019.06.029 [27] 杨雯暄, 王爱民, 王军, 等. 基于过渡电阻灵敏度分析的地铁轨地绝缘劣化区域定位方法[J/OL]. 高电压技术, 2025-11-17. https://link.cnki.net/urlid/42.1239.tm.20251114.1648.005.Yang Wenxuan, Wang Aimin, Wang Jun, et al. Method for locating the defective areas of rail-to-ground insulation in metro rail systems based on transition resistance sensitivity analysis[J/OL]. High Voltage Engineering, 2025-11-17. https://link.cnki.net/urlid/42.1239.tm.20251114.1648.005. -
下载:
点击查看大图
计量
- 文章访问数: 37
- HTML全文浏览量: 33
- PDF下载量: 0
- 被引次数: 0