地铁杂散电流的数值模拟研究
摘要
目前的地铁和轻轨主要采用直流供电,车辆在运行过程中由于轨道绝缘方面的问题会产生杂散电流,不仅导致结构钢筋损耗,也容易造成地下管线腐蚀穿孔,危害结构和人民生命财产的安全,造成严重的经济损失。由于地铁杂散电流的客观存在,因此研究地铁杂散电流的分布对杂散电流的控制和危害的消除具有很重要的意义。
通常研究人员采用传统仿真方法对杂散电流的分布进行研究,但存在推导公式复杂,不能模拟单点或多点绝缘破坏,因此本文提出一种利用Pspice进行仿真的新方法。该方法的实质是通过编程生成地铁杂散电流电阻网络模型,通过基尔霍夫电压定律和电流定律直接计算复杂电阻网络的节点电压和每个元件的电流。
本文采用新的模拟方法分别模拟单边和双边供电杂散电流的分布规律,同时研究了不同的轨地过渡电阻率,供电电流和供电区间长度对于杂散电流的影响，得到如下结论：
(1)基于Pspice的模拟方法与基于微分方程的模拟方法在模拟不排流,全线绝缘的工况时得出的数据误差很小,均在5%以内。这说明基于Pspice的模拟方法是有效的。
(2)全线绝缘的情况下,不排流时,轨道电流,杂散电流均是抛物线分布。轨道电流在中点处于最小值,而杂散电流在中点处于最大值；排流时,轨道电流与杂散电流为半抛物线分布。轨道电压为直线分布,在牵引变电站处为0V,而在列车处取得最大值,且最大值是不排流时的两倍。
(3)随着轨道上泄漏点数目的增加,轨道电流降低,杂散电流升高。随着轨地过渡电阻率的减小,轨道电流降低,杂散电流升高。随着供电电流的增加,轨道电流,杂散电流,轨道电位最大值成比例的增长。随着供电区间长度增加,轨道电流降低,杂散电流升高。
(4)与单边供电相比,双边供电轨道电压较小,且杂散电流也远小于前者。
With the DC power supply of subway, the running rail may produce stray current, not only led to loss of structural steel even reducing the safety of the structures but also result in perforation of the underground pipeline and causing serious economic losses. Therefore, studying the distribution of the stray current will reduce the stray current leakage significance.
It's researched that the traditional simulation method has a huge flaw. In consideration of the limitations of traditional methods, this paper developed a simulation method based on Pspice. Kirchhoffs voltage law and current law are used to calculate of the voltage and current relationship in the complex resistor network, thus voltage, input current and output current at any node are obtained.
The simulation method based on Pspice simulates working conditions in unilateral and bilateral power supply. The distribution of stray current under various rail-ground resistivity, the supply current and the distance between traction substations is drawed. It mainly concludes:
(1) The simulation method based on Pspice and the simulation method based on differential equation in drainage and no-drainage reach a very small data error that is less than5%. It's showed that the simulation method base on Pspice is effective.
(2) Under electrical insulation without current drainage, the distribution of rail current and stray current is parabolic. In the mid-point railway current is at a minimum, and stray current is at a maximum.Under electrical insulation with current drainage, the distribution of rail current and stray current is semi-parabola. The distribution of rail potential is straight line, at the traction substation is zero, at the train is the maximum value, and the maximum is as twice as the value without current drainage.
(3) With the leak points increased, the rail current is reduced, stray current is increased. With the decrease of the rail-ground resistivity, the rail current is reduced, stray current is increased. With the increase of locomotive current, rail current, stray current, the maximum rail potential proportional to the growth. With the increase of power supply length, the rail current is reduced, stray current is increased.
(4) Compared with the unilateral power supply, bilateral power supply can effectively reduce the rail potential and stray current.
通常研究人员采用传统仿真方法对杂散电流的分布进行研究,但存在推导公式复杂,不能模拟单点或多点绝缘破坏,因此本文提出一种利用Pspice进行仿真的新方法。该方法的实质是通过编程生成地铁杂散电流电阻网络模型,通过基尔霍夫电压定律和电流定律直接计算复杂电阻网络的节点电压和每个元件的电流。
本文采用新的模拟方法分别模拟单边和双边供电杂散电流的分布规律,同时研究了不同的轨地过渡电阻率,供电电流和供电区间长度对于杂散电流的影响，得到如下结论：
(1)基于Pspice的模拟方法与基于微分方程的模拟方法在模拟不排流,全线绝缘的工况时得出的数据误差很小,均在5%以内。这说明基于Pspice的模拟方法是有效的。
(2)全线绝缘的情况下,不排流时,轨道电流,杂散电流均是抛物线分布。轨道电流在中点处于最小值,而杂散电流在中点处于最大值；排流时,轨道电流与杂散电流为半抛物线分布。轨道电压为直线分布,在牵引变电站处为0V,而在列车处取得最大值,且最大值是不排流时的两倍。
(3)随着轨道上泄漏点数目的增加,轨道电流降低,杂散电流升高。随着轨地过渡电阻率的减小,轨道电流降低,杂散电流升高。随着供电电流的增加,轨道电流,杂散电流,轨道电位最大值成比例的增长。随着供电区间长度增加,轨道电流降低,杂散电流升高。
(4)与单边供电相比,双边供电轨道电压较小,且杂散电流也远小于前者。
With the DC power supply of subway, the running rail may produce stray current, not only led to loss of structural steel even reducing the safety of the structures but also result in perforation of the underground pipeline and causing serious economic losses. Therefore, studying the distribution of the stray current will reduce the stray current leakage significance.
It's researched that the traditional simulation method has a huge flaw. In consideration of the limitations of traditional methods, this paper developed a simulation method based on Pspice. Kirchhoffs voltage law and current law are used to calculate of the voltage and current relationship in the complex resistor network, thus voltage, input current and output current at any node are obtained.
The simulation method based on Pspice simulates working conditions in unilateral and bilateral power supply. The distribution of stray current under various rail-ground resistivity, the supply current and the distance between traction substations is drawed. It mainly concludes:
(1) The simulation method based on Pspice and the simulation method based on differential equation in drainage and no-drainage reach a very small data error that is less than5%. It's showed that the simulation method base on Pspice is effective.
(2) Under electrical insulation without current drainage, the distribution of rail current and stray current is parabolic. In the mid-point railway current is at a minimum, and stray current is at a maximum.Under electrical insulation with current drainage, the distribution of rail current and stray current is semi-parabola. The distribution of rail potential is straight line, at the traction substation is zero, at the train is the maximum value, and the maximum is as twice as the value without current drainage.
(3) With the leak points increased, the rail current is reduced, stray current is increased. With the decrease of the rail-ground resistivity, the rail current is reduced, stray current is increased. With the increase of locomotive current, rail current, stray current, the maximum rail potential proportional to the growth. With the increase of power supply length, the rail current is reduced, stray current is increased.
(4) Compared with the unilateral power supply, bilateral power supply can effectively reduce the rail potential and stray current.
引文
[1]SCHWALM L H, SANDOR J G. Stray current——the major cause of underground plant corrosion [J]. Materials Performance.1994,6:31-36.
[2]吴祥祖,张庆贺,高卫平.地铁杂散电流产生机理及其防护措施[J].建筑安全.2003,18(5)：28-30.
[3]EN 50122-2-2011, Railway applications-Fixed installations-Electrical safety, earthing and the return circuit——Part 2:Provisions against the effects of stray currents caused by d.c. traction systems[S].2011.
[4]BS EN 13636-2004, Cathodic protection of buried metallic tanks and related piping[S]. 2004.
[5]DIN EN 13509-2003, Cathodic protection measurement techniques [S].2003.
[6]CHEN S L, HSU S C, TSENG C T, et al. Analysis of rail potential and stray current for Taipei Metro[J]. Vehicular Technology, IEEE Transactions on.2006,55(1):67-75.
[7]MILLER R L, HARTT W H, BROWN R P. Stray current and galvanic corrosion of reinforcing steel in concrete[J]. Materials Performance.1976,15(5):20-27.
[8]CHARALAMBOUS C, COTTON I. Influence of soil structures on corrosion performance of floating-DC transit systems[J]. Electric Power Applications.2007,1(1):9-16.
[9]COTTON I, CHARALAMBOUS C, AYLOTT P, et al. Stray current control in DC mass transit systems[J]. Vehicular Technology, IEEE Transactions on.2005,54(2):722-730.
[10]LIU Y C, CHEN J F. Control scheme for reducing rail potential and stray current in MRT systems[J]. Electric Power Applications.2005,152(3):612-618.
[11]PHAM K D, THOMAS R S, STINGER W E. Analysis of stray current, track-to-earth potentials and substation negative grounding in DC traction electrification system[C]. Proceedings of the 2001 IEEE/ASME Joint Railroad Conference. New York:Institute of Electrical and Electronics Engineers Inc.,2001:141-160.
[12]SIM W M, CHAN C F. Stray current monitoring and control on Singapore MRT system[C]. Anon.2004 International Conference on Power System Technology. New York:Institute of Electrical and Electronics Engineers Inc.,2004,1:1898-1903.
[13]JAMALI S, ALAMUTI M M, SAVAGHEBI M. Effects of different earthing schemes on the stray current in rail transit systems[C].43rd International Universities Power Engineering Conference. New York:Institute of Electrical and Electronics Engineers Inc. 2008,1:1261-1265.
[14]PAUL D. DC traction power system grounding[J]. Industry Applications, IEEE Transactions on.2002,38(3):818-824.
[15]BRICHAU F, DRIESENS T, DECONINCK J. Modeling of underground cathodic protection stray currents[J]. Corrosion.1996,52(06):480-488.
[16]NIASATI M, GHOLAMI A. Overview of stray current control in DC railway systems[C]. Anon.2008 International Conference on Railway Engineering. Hong Kong:The Institution of Engineering and Technology,2008:237-242.
[17]SHAFFER R E, FITZGERALD III J H. STRAY EARTH CURRENT CONTROL--ASHINGTON, DC METRO SYSTEM[J]. Materials Performance.1981,20(4):9-15.
[18]TREVELYAN J, HACK H P. Analysis of stray current corrosion problems using the boundary element method[J]. Boundary Element Technology IX.199-4:347-356.
[19]TZENG Y S, LEE C H. Analysis of Rail Potential and Stray Currents in a Direct-Current Transit System[J]. Power Delivery, IEEE Transactions on.2010,25(3):1516-1525.
[20]YU J G. The effects of earthing strategies on rail potential and stray currents in DC transit railways[C]. International Conference on Developments in Mass Transit Systems. London:Institution of Electrical Engineers,1998:303-309.
[21]YU J G, GOODMAN C J. Modelling of rail potential rise and leakage current in DC rail transit systems[C]. IEE Colloquium on'Stray Current Effects of DC Railways and Tramways'. London:Institution of Electrical Engineers,1990:1-6.
[22]MOODY K J. Stray current characteristics of DC transit systems[J]. Materials performance.1994,33(6):15-19.
[23]张英梅.煤矿井下杂散电流分布规律的研究[J].煤炭学报.2005,30(1)：129-132.
[24]赵宇辉,周晓军.地铁杂散电流分布的数值分析[J].城市轨道交通研究.2009,12(12)：42-47.
[25]周晓军,高波.地铁杂散电流分布及其对砼衬砌耐久性的影响[J].西部探矿工程.1999,11(6)：31-35.
[26]刘燕,王京梅,赵丽等.地铁杂散电流分布的数学模型[J].工程数学学报.2009,26(4)：571-576.
[27]靳富群.城市轨道交通杂散电流分布与监控系统研究[D].河南：郑州大学,2009.
[28]庞原冰.城市轨道交通杂散电流研究[D].四川：西南交通大学,2008.
[29]吕伟杰,地铁杂散电流的防护方案研究与设计[D].四川：西南交通大学,2007.
[30]战鹏.地铁杂散电流对钢筋混凝土结构腐蚀影响研究及防护[D].北京：北京交通大学,2009.
[31]曹阿林,朱庆军,张胜涛等.埋地金属管道杂散电流影响因素模拟研究[J].煤气与热力.2010,30(5)：6-8.
[32]高敬宇,易友祥.地铁杂散电流的分析[J].天津理工学院学报.1996,12(3)：52-55.
[33]胡云进,钟振,方镜平.地铁杂散电流场的有限元模拟[J].中国铁道科学.2011,32(6)：129-133.
[34]李威.地铁杂散电流的监测与防治[J].城市轨道交通研究.2003,6(4)：48-52.
[35]谭建红,张胜涛,曹阿林等.土壤环境中钢的杂散电流腐蚀研究[J].材料导报.2011,25(4)：107-110.
[36]李威.地铁杂散电流腐蚀监测及防护技术[M].江苏：中国矿业大学出版社,2004：23-98.
[37]WANG Y, LI W, YANG X, et al. Modeling and simulation the distribution of metro stray current [C].2010 International Conference on Computer Application and System Modeling. New York:Institute of Electrical and Electronics Engineers Inc.,2010:704-707.
[38]NILSSON J W. Introduction to PSpice for Electric Circuits [M]. New York: Pearson Education, Inc.,1992:33-50.
[39]吴建强编.PSpice仿真实践[M].黑龙江：哈尔滨工业大学出版社,2001：60-77.
[40]周润景.PSpice电子电路设计与分析[M].北京：机械工业出版社2011：103-120.
[41]CJJ 49-1992,地铁杂散电流腐蚀防护技术规程[s].1992.
[2]吴祥祖,张庆贺,高卫平.地铁杂散电流产生机理及其防护措施[J].建筑安全.2003,18(5)：28-30.
[3]EN 50122-2-2011, Railway applications-Fixed installations-Electrical safety, earthing and the return circuit——Part 2:Provisions against the effects of stray currents caused by d.c. traction systems[S].2011.
[4]BS EN 13636-2004, Cathodic protection of buried metallic tanks and related piping[S]. 2004.
[5]DIN EN 13509-2003, Cathodic protection measurement techniques [S].2003.
[6]CHEN S L, HSU S C, TSENG C T, et al. Analysis of rail potential and stray current for Taipei Metro[J]. Vehicular Technology, IEEE Transactions on.2006,55(1):67-75.
[7]MILLER R L, HARTT W H, BROWN R P. Stray current and galvanic corrosion of reinforcing steel in concrete[J]. Materials Performance.1976,15(5):20-27.
[8]CHARALAMBOUS C, COTTON I. Influence of soil structures on corrosion performance of floating-DC transit systems[J]. Electric Power Applications.2007,1(1):9-16.
[9]COTTON I, CHARALAMBOUS C, AYLOTT P, et al. Stray current control in DC mass transit systems[J]. Vehicular Technology, IEEE Transactions on.2005,54(2):722-730.
[10]LIU Y C, CHEN J F. Control scheme for reducing rail potential and stray current in MRT systems[J]. Electric Power Applications.2005,152(3):612-618.
[11]PHAM K D, THOMAS R S, STINGER W E. Analysis of stray current, track-to-earth potentials and substation negative grounding in DC traction electrification system[C]. Proceedings of the 2001 IEEE/ASME Joint Railroad Conference. New York:Institute of Electrical and Electronics Engineers Inc.,2001:141-160.
[12]SIM W M, CHAN C F. Stray current monitoring and control on Singapore MRT system[C]. Anon.2004 International Conference on Power System Technology. New York:Institute of Electrical and Electronics Engineers Inc.,2004,1:1898-1903.
[13]JAMALI S, ALAMUTI M M, SAVAGHEBI M. Effects of different earthing schemes on the stray current in rail transit systems[C].43rd International Universities Power Engineering Conference. New York:Institute of Electrical and Electronics Engineers Inc. 2008,1:1261-1265.
[14]PAUL D. DC traction power system grounding[J]. Industry Applications, IEEE Transactions on.2002,38(3):818-824.
[15]BRICHAU F, DRIESENS T, DECONINCK J. Modeling of underground cathodic protection stray currents[J]. Corrosion.1996,52(06):480-488.
[16]NIASATI M, GHOLAMI A. Overview of stray current control in DC railway systems[C]. Anon.2008 International Conference on Railway Engineering. Hong Kong:The Institution of Engineering and Technology,2008:237-242.
[17]SHAFFER R E, FITZGERALD III J H. STRAY EARTH CURRENT CONTROL--ASHINGTON, DC METRO SYSTEM[J]. Materials Performance.1981,20(4):9-15.
[18]TREVELYAN J, HACK H P. Analysis of stray current corrosion problems using the boundary element method[J]. Boundary Element Technology IX.199-4:347-356.
[19]TZENG Y S, LEE C H. Analysis of Rail Potential and Stray Currents in a Direct-Current Transit System[J]. Power Delivery, IEEE Transactions on.2010,25(3):1516-1525.
[20]YU J G. The effects of earthing strategies on rail potential and stray currents in DC transit railways[C]. International Conference on Developments in Mass Transit Systems. London:Institution of Electrical Engineers,1998:303-309.
[21]YU J G, GOODMAN C J. Modelling of rail potential rise and leakage current in DC rail transit systems[C]. IEE Colloquium on'Stray Current Effects of DC Railways and Tramways'. London:Institution of Electrical Engineers,1990:1-6.
[22]MOODY K J. Stray current characteristics of DC transit systems[J]. Materials performance.1994,33(6):15-19.
[23]张英梅.煤矿井下杂散电流分布规律的研究[J].煤炭学报.2005,30(1)：129-132.
[24]赵宇辉,周晓军.地铁杂散电流分布的数值分析[J].城市轨道交通研究.2009,12(12)：42-47.
[25]周晓军,高波.地铁杂散电流分布及其对砼衬砌耐久性的影响[J].西部探矿工程.1999,11(6)：31-35.
[26]刘燕,王京梅,赵丽等.地铁杂散电流分布的数学模型[J].工程数学学报.2009,26(4)：571-576.
[27]靳富群.城市轨道交通杂散电流分布与监控系统研究[D].河南：郑州大学,2009.
[28]庞原冰.城市轨道交通杂散电流研究[D].四川：西南交通大学,2008.
[29]吕伟杰,地铁杂散电流的防护方案研究与设计[D].四川：西南交通大学,2007.
[30]战鹏.地铁杂散电流对钢筋混凝土结构腐蚀影响研究及防护[D].北京：北京交通大学,2009.
[31]曹阿林,朱庆军,张胜涛等.埋地金属管道杂散电流影响因素模拟研究[J].煤气与热力.2010,30(5)：6-8.
[32]高敬宇,易友祥.地铁杂散电流的分析[J].天津理工学院学报.1996,12(3)：52-55.
[33]胡云进,钟振,方镜平.地铁杂散电流场的有限元模拟[J].中国铁道科学.2011,32(6)：129-133.
[34]李威.地铁杂散电流的监测与防治[J].城市轨道交通研究.2003,6(4)：48-52.
[35]谭建红,张胜涛,曹阿林等.土壤环境中钢的杂散电流腐蚀研究[J].材料导报.2011,25(4)：107-110.
[36]李威.地铁杂散电流腐蚀监测及防护技术[M].江苏：中国矿业大学出版社,2004：23-98.
[37]WANG Y, LI W, YANG X, et al. Modeling and simulation the distribution of metro stray current [C].2010 International Conference on Computer Application and System Modeling. New York:Institute of Electrical and Electronics Engineers Inc.,2010:704-707.
[38]NILSSON J W. Introduction to PSpice for Electric Circuits [M]. New York: Pearson Education, Inc.,1992:33-50.
[39]吴建强编.PSpice仿真实践[M].黑龙江：哈尔滨工业大学出版社,2001：60-77.
[40]周润景.PSpice电子电路设计与分析[M].北京：机械工业出版社2011：103-120.
[41]CJJ 49-1992,地铁杂散电流腐蚀防护技术规程[s].1992.