基于信息熵原理的电气化铁道概率谐波研究
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摘要
电气化铁道在给交通带来方便、快捷、环保的同时也对电网带来了新的挑战。由于电力机车采用单相整流牵引技术,它所引起的谐波电流通过架空接触线流入周边电网,带来不可忽视的电能质量问题。
本文建立了机车、牵引网到电力系统的概率谐波模型,利用基于信息论的最大熵法来分析概率谐波样本,突破了基于最小二乘法原理的多项式逼近方法拟合概率密度函数的局限,并且结合蒙特卡罗法进行概率模拟,避免了用解析方法求取谐波概率分布的复杂运算过程,是概率谐波研究的一种新的尝试。
首先,在对比传统概率密度函数计算方法的基础上深入分析了基于信息论的最大熵法,推导了利用最大熵原理来拟合概率密度函数的计算公式和方法,为求取谐波95%概率大值和分析机车谐波的概率特征提供了准确有效的工具。
其次通过分析交直电力机车的控制系统,建立了适用于概率计算的机车主电路模型,考虑了机车运行中的多个随机因素;基于多端口降阶方法分析了牵引网谐波特性,实现了对电气化铁道牵引网的建模;以蒙特卡罗法模拟计算电气化铁道随机谐波电流,利用最大熵原理分析谐波电流的概率特征。
在概率模型的基础上分析了地区电网谐波潮流计算的三相不对称方法,建立了包含电气化铁道牵引负荷的电力系统谐波潮流计算模型。以电气化铁道注入110kV供电母线的谐波电流为谐波源分析评估谐波对地区电网的影响。
最后针对京沪电气化铁道南翔牵引变电站牵引区段以及其所在的地区电网作了实例计算分析。
As a modern transportation tool, Electrical railway has brought along a great benefit to the economy as well as challenges to power system, especially the problems of safety operation threatened by harmonics from electrical locomotives.
This paper utilizes Maximum Entropy method to analyze the probabilistic harmonic model. Combined with Monte Carlo method, Maximum Entropy method can avoid both the weakness of Cubic Polynomial Fitting method and the complexity of Analytic Method, which is a new experiment for probabilistic harmonic study.
Firstly, the Maximum Entropy method based on information theory is introduced, the formulae and practical method are deduced for fitting probabilistic density function, which offer an effective tool for calculating 95% probabilistic value and the probabilistic characteristics.
Secondly, by analyzing the control system of a typical AC-DC drive model locomotive, a mathematic model for probabilistic calculation is established, considering a set of probabilistic factors of locomotive’s operation. A deduced multi-port model is applied to analyze the influence on harmonic currents by traction network. Finally, the unbalanced harmonic power flow model is set up for regional power system using ATP software. These three models together establish the probabilistic harmonic calculation model including electrical railway and regional power system.
Thirdly, a calculation example is carried out at a detailed railway, using Monte Carlo method to simulate the probabilistic status and Maximum Entropy method to analyze the characteristic of probabilistic harmonics. The harmonic pollution in the regional power system is evaluated based on the analysis.
本文建立了机车、牵引网到电力系统的概率谐波模型,利用基于信息论的最大熵法来分析概率谐波样本,突破了基于最小二乘法原理的多项式逼近方法拟合概率密度函数的局限,并且结合蒙特卡罗法进行概率模拟,避免了用解析方法求取谐波概率分布的复杂运算过程,是概率谐波研究的一种新的尝试。
首先,在对比传统概率密度函数计算方法的基础上深入分析了基于信息论的最大熵法,推导了利用最大熵原理来拟合概率密度函数的计算公式和方法,为求取谐波95%概率大值和分析机车谐波的概率特征提供了准确有效的工具。
其次通过分析交直电力机车的控制系统,建立了适用于概率计算的机车主电路模型,考虑了机车运行中的多个随机因素;基于多端口降阶方法分析了牵引网谐波特性,实现了对电气化铁道牵引网的建模;以蒙特卡罗法模拟计算电气化铁道随机谐波电流,利用最大熵原理分析谐波电流的概率特征。
在概率模型的基础上分析了地区电网谐波潮流计算的三相不对称方法,建立了包含电气化铁道牵引负荷的电力系统谐波潮流计算模型。以电气化铁道注入110kV供电母线的谐波电流为谐波源分析评估谐波对地区电网的影响。
最后针对京沪电气化铁道南翔牵引变电站牵引区段以及其所在的地区电网作了实例计算分析。
As a modern transportation tool, Electrical railway has brought along a great benefit to the economy as well as challenges to power system, especially the problems of safety operation threatened by harmonics from electrical locomotives.
This paper utilizes Maximum Entropy method to analyze the probabilistic harmonic model. Combined with Monte Carlo method, Maximum Entropy method can avoid both the weakness of Cubic Polynomial Fitting method and the complexity of Analytic Method, which is a new experiment for probabilistic harmonic study.
Firstly, the Maximum Entropy method based on information theory is introduced, the formulae and practical method are deduced for fitting probabilistic density function, which offer an effective tool for calculating 95% probabilistic value and the probabilistic characteristics.
Secondly, by analyzing the control system of a typical AC-DC drive model locomotive, a mathematic model for probabilistic calculation is established, considering a set of probabilistic factors of locomotive’s operation. A deduced multi-port model is applied to analyze the influence on harmonic currents by traction network. Finally, the unbalanced harmonic power flow model is set up for regional power system using ATP software. These three models together establish the probabilistic harmonic calculation model including electrical railway and regional power system.
Thirdly, a calculation example is carried out at a detailed railway, using Monte Carlo method to simulate the probabilistic status and Maximum Entropy method to analyze the characteristic of probabilistic harmonics. The harmonic pollution in the regional power system is evaluated based on the analysis.
引文
[1]孟丽萍.电气化铁路负序影响及对策[J].应用能源技术, 2007, (8):38-40.
[2]解绍峰.电气化铁道谐波过程分析与推荐限值制定思路研究[D].成都:西南交通大学, 2004.
[3] Limits for Harmonics in the United Kingdom Electricity Supply System, Engineering RecommendationG5/3,1976.
[4]李建华,夏道止.铁路电气化在电力系统中引起的谐波计算方法[J].电力系统及其自动化学报,1993,5(1):10-19.
[5]徐春侠,李庚银,赵成勇,等.韶山IV型电力机车谐波分析[J].华北电力大学学报, 1998,25(3):13-16.
[6]李明,连级三. 6K机车功率因数计算及谐波电流分析[J].机车电传动, 1994, (2): 7-12.
[7]连级三.电力牵引控制系统.北京:中国铁道出版社, 1994.
[8]王刚.随机谐波概率模型研究[D].成都:四川大学, 2006.
[9]叶忠明,钱照明,庞敏熙.谐波电流的概率分析[J].电工电能新技术, 1998, (4):31-35.
[10]王磊.用概率密度函数近似计算谐波发射水平[J].高电压技术, 2007, 33(11):891-895.
[11] K.H.Yuen, Z.M.Ye. Modeling of traction harmonic current using statistical method. Proceeding the International Conference on Power Electronics and Drive Systems, Jul27-Jul29,1999
[12]Z.M.YE, M.H.Pong. Harmonic evaluation of traction system by Monte Carlo simulation. IEEE Annual Power Electronics Specialists Conference, Jun27-Jun29,1999
[13]王磊.多谐波源求和问题的研究[D].成都:四川大学, 2005.
[14]J.B.Billingsley. A.Farina. Statistical analysis of measured radar ground data. IEEE Trans. on Antennas and Propagation, 1999, 35(2): 579-593
[15]A.C. Frery, H.J.Muller. A model for extremely heterogeneous clutter. IEEE Trans. on Geoscience and Remote Sensing, 1997, 35(3):648-659
[16]J.S.Daba, M.R.Bell. Statistic of the scattering Cross-Section of a Small Number of random scatters. IEEE Trans. on Antennas Propagat.,1995,43(5):773-783
[17]F.I.Meno. Mobile radio fading in Scandinavian terrain. IEEE Trans. on Veh. Technol.,1997,26(9):335-340
[18]徐红红,陈小川,张雷,等.全并联AT供电牵引网断线接地阻抗计算与分析[J].继电器, 2008, 36(2): 6-9.
[19]孙林.电气化铁路接触网上谐波的分布[J].北京邮电学院学报, 1991, 14(2): 72-77.
[20]李自良,陈薇.交流牵引网两边供电研究总结[J].华东交通大学学报, 1993, 10(2): 48-53.
[21]张莹.牵引网供电质量改善问题研究[J].电气开关, 2005, 2: 30-33.
[22]姚楠.电气化铁道牵引网基波与谐波模型研究[D].北京:北京交通大学, 2008.
[23]李曙辉.电牵引负荷在复线牵引网的分布[J].西南交通大学学报. 1993, (1): 98-106.
[24]刘学军.牵引供电系统牵引网的四端网络级联模型及其仿真[J].铁道学报, 1995, 17:32-35.
[25]李洪波.电力系统谐波潮流计算算法综述.重庆电力高等专科学校学报,2004,9(3):1-4.
[26]王刚,杨洪耕.基于最小二乘法的正交多项式级数在谐波估计中的应用.继电器,2006,34(12):25-29.
[27]郑成德. Padé逼近若干问题研究[D].大连:大连理工大学, 2004.
[28]章光,朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报,1995,14(2):119-129.
[29] Ernani V Volpe,Donald Baganoff. Maximum entropy pdfs and the moment problem under near-Gaussian conditions[J] . Probabilistic Engineering Mechanics,2003,18(1):17～29.
[30]邓建,李夕兵,古德生.岩石力学参数概率分布的信息熵推断.岩石力学与工程学报, 2004,23(13):2177-2181 .
[31]姚荣涵.居民出行分布的熵模型(D).吉林:吉林大学,2003-2004.
[32] Jaynes E.T. Information theory and statistical mechanics[J]. Physical Review. 1957,106(4):620-630.
[33]俞礼军,成耀荣.交通流统计分布密度函数优度拟合方法研究[J].长沙交通学院学报, 2002(2): 17-20.
[34] J.B.Billingsley. A.Farina. Statistical analysis of measured radar ground data. IEEE Trans. on Antennas and Propagation, 1999, 35(2): 579-593.
[35]林磊.电气化铁路对电力系统影响的分析研究[D].杭州:浙江大学,2005.
[36]廖洪涛. SS9型客运电力机车[3]-主电路[J].电力机车技术, 1999, (4): 4-8.
[37]刘学军.牵引供电系统牵引网的四端网络级联模型及其仿真[J].铁道学报, 1995, 17:32-35
[38] J. H. Song and H. M.Hwang. Estimation of harmonics on power system on ac electric railway. KIEE Int. Trans. Power Eng., vol. 52B, no. 2, pp.68–79, 2003.
[39] Y. Mochinaga. Higher harmonics resonance on at feeding circuit and countermeasures to suppress it. Trans. Inst. Elect. Eng. Jpn., vol. 114-D, no. 10, 1994.
[40]柯尊平.牵引网电抗参数的简易算法[J].铁道学报, 1997, 19(2): 43-48.
[41]何正友,方雷,郭东,等.基于AT等值电路的牵引网潮流计算方法[J].西南交通大学学报, 2008, 43(1): 1-7
[42] D. Xia, G.T. Heydt. Harmonic Power Flow Studies [J]. IEEE Trans. on PAS, 1982, 101(6):1257-1270.
[43]潘云江,赵书强,陈斌发,沈琦.电力系统不对称谐波潮流的一种实用计算方法[J].电力系统自动化, 2000, 24(9):60-62.
[44]顾伟,陈谦,蒋平.采用对称分量坐标的谐波潮流部分解耦算法[J].电力自动化设备, 2004, 24(2):9-13.
[45]卢恩,张步涵,龚世缨.电力系统谐波潮流的一种解耦算法[J].电网技术, 2003, 27(2):34-36.
[46] Dommel H. W. EMTP Theory Book. Microtran Power System Analysis Corporation, 1992
[47]崔威,李建华,赵娟.供电网络谐波潮流分析[J].电力自动化设备, 2003, 23(2):11-14. Cui Wei, Li Jianhua, Zhao Juan. Harmonic flow calculation in power supply system[J]. Electric Power Automation Equipment, 2003, 23(2):11-14.
[48]吴笃贵,徐政.电力负荷的谐波建模[J].电网技术, 2004, 28(3): 20-24. Wu Dugui, Xu Zheng. Harmonic Modeling of Electric Loads[J]. Power System technology, 2004, 28(3): 20-24.
[49] GB12325-1990.电能质量-供电电压允许偏差.北京:国家技术监督局, 1990
[50] George J. Wakileh. Power Systems Harmonics[M]. Berlin: Springer, 2001.
[51] Davor Vujatovic, Zhang Qingping. Harmonics Generated from Railway Operation[C]. IEEE Power Engineering Society General Meeting, 18-22, 2006, Montréal Quebéc.Canada
[2]解绍峰.电气化铁道谐波过程分析与推荐限值制定思路研究[D].成都:西南交通大学, 2004.
[3] Limits for Harmonics in the United Kingdom Electricity Supply System, Engineering RecommendationG5/3,1976.
[4]李建华,夏道止.铁路电气化在电力系统中引起的谐波计算方法[J].电力系统及其自动化学报,1993,5(1):10-19.
[5]徐春侠,李庚银,赵成勇,等.韶山IV型电力机车谐波分析[J].华北电力大学学报, 1998,25(3):13-16.
[6]李明,连级三. 6K机车功率因数计算及谐波电流分析[J].机车电传动, 1994, (2): 7-12.
[7]连级三.电力牵引控制系统.北京:中国铁道出版社, 1994.
[8]王刚.随机谐波概率模型研究[D].成都:四川大学, 2006.
[9]叶忠明,钱照明,庞敏熙.谐波电流的概率分析[J].电工电能新技术, 1998, (4):31-35.
[10]王磊.用概率密度函数近似计算谐波发射水平[J].高电压技术, 2007, 33(11):891-895.
[11] K.H.Yuen, Z.M.Ye. Modeling of traction harmonic current using statistical method. Proceeding the International Conference on Power Electronics and Drive Systems, Jul27-Jul29,1999
[12]Z.M.YE, M.H.Pong. Harmonic evaluation of traction system by Monte Carlo simulation. IEEE Annual Power Electronics Specialists Conference, Jun27-Jun29,1999
[13]王磊.多谐波源求和问题的研究[D].成都:四川大学, 2005.
[14]J.B.Billingsley. A.Farina. Statistical analysis of measured radar ground data. IEEE Trans. on Antennas and Propagation, 1999, 35(2): 579-593
[15]A.C. Frery, H.J.Muller. A model for extremely heterogeneous clutter. IEEE Trans. on Geoscience and Remote Sensing, 1997, 35(3):648-659
[16]J.S.Daba, M.R.Bell. Statistic of the scattering Cross-Section of a Small Number of random scatters. IEEE Trans. on Antennas Propagat.,1995,43(5):773-783
[17]F.I.Meno. Mobile radio fading in Scandinavian terrain. IEEE Trans. on Veh. Technol.,1997,26(9):335-340
[18]徐红红,陈小川,张雷,等.全并联AT供电牵引网断线接地阻抗计算与分析[J].继电器, 2008, 36(2): 6-9.
[19]孙林.电气化铁路接触网上谐波的分布[J].北京邮电学院学报, 1991, 14(2): 72-77.
[20]李自良,陈薇.交流牵引网两边供电研究总结[J].华东交通大学学报, 1993, 10(2): 48-53.
[21]张莹.牵引网供电质量改善问题研究[J].电气开关, 2005, 2: 30-33.
[22]姚楠.电气化铁道牵引网基波与谐波模型研究[D].北京:北京交通大学, 2008.
[23]李曙辉.电牵引负荷在复线牵引网的分布[J].西南交通大学学报. 1993, (1): 98-106.
[24]刘学军.牵引供电系统牵引网的四端网络级联模型及其仿真[J].铁道学报, 1995, 17:32-35.
[25]李洪波.电力系统谐波潮流计算算法综述.重庆电力高等专科学校学报,2004,9(3):1-4.
[26]王刚,杨洪耕.基于最小二乘法的正交多项式级数在谐波估计中的应用.继电器,2006,34(12):25-29.
[27]郑成德. Padé逼近若干问题研究[D].大连:大连理工大学, 2004.
[28]章光,朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报,1995,14(2):119-129.
[29] Ernani V Volpe,Donald Baganoff. Maximum entropy pdfs and the moment problem under near-Gaussian conditions[J] . Probabilistic Engineering Mechanics,2003,18(1):17～29.
[30]邓建,李夕兵,古德生.岩石力学参数概率分布的信息熵推断.岩石力学与工程学报, 2004,23(13):2177-2181 .
[31]姚荣涵.居民出行分布的熵模型(D).吉林:吉林大学,2003-2004.
[32] Jaynes E.T. Information theory and statistical mechanics[J]. Physical Review. 1957,106(4):620-630.
[33]俞礼军,成耀荣.交通流统计分布密度函数优度拟合方法研究[J].长沙交通学院学报, 2002(2): 17-20.
[34] J.B.Billingsley. A.Farina. Statistical analysis of measured radar ground data. IEEE Trans. on Antennas and Propagation, 1999, 35(2): 579-593.
[35]林磊.电气化铁路对电力系统影响的分析研究[D].杭州:浙江大学,2005.
[36]廖洪涛. SS9型客运电力机车[3]-主电路[J].电力机车技术, 1999, (4): 4-8.
[37]刘学军.牵引供电系统牵引网的四端网络级联模型及其仿真[J].铁道学报, 1995, 17:32-35
[38] J. H. Song and H. M.Hwang. Estimation of harmonics on power system on ac electric railway. KIEE Int. Trans. Power Eng., vol. 52B, no. 2, pp.68–79, 2003.
[39] Y. Mochinaga. Higher harmonics resonance on at feeding circuit and countermeasures to suppress it. Trans. Inst. Elect. Eng. Jpn., vol. 114-D, no. 10, 1994.
[40]柯尊平.牵引网电抗参数的简易算法[J].铁道学报, 1997, 19(2): 43-48.
[41]何正友,方雷,郭东,等.基于AT等值电路的牵引网潮流计算方法[J].西南交通大学学报, 2008, 43(1): 1-7
[42] D. Xia, G.T. Heydt. Harmonic Power Flow Studies [J]. IEEE Trans. on PAS, 1982, 101(6):1257-1270.
[43]潘云江,赵书强,陈斌发,沈琦.电力系统不对称谐波潮流的一种实用计算方法[J].电力系统自动化, 2000, 24(9):60-62.
[44]顾伟,陈谦,蒋平.采用对称分量坐标的谐波潮流部分解耦算法[J].电力自动化设备, 2004, 24(2):9-13.
[45]卢恩,张步涵,龚世缨.电力系统谐波潮流的一种解耦算法[J].电网技术, 2003, 27(2):34-36.
[46] Dommel H. W. EMTP Theory Book. Microtran Power System Analysis Corporation, 1992
[47]崔威,李建华,赵娟.供电网络谐波潮流分析[J].电力自动化设备, 2003, 23(2):11-14. Cui Wei, Li Jianhua, Zhao Juan. Harmonic flow calculation in power supply system[J]. Electric Power Automation Equipment, 2003, 23(2):11-14.
[48]吴笃贵,徐政.电力负荷的谐波建模[J].电网技术, 2004, 28(3): 20-24. Wu Dugui, Xu Zheng. Harmonic Modeling of Electric Loads[J]. Power System technology, 2004, 28(3): 20-24.
[49] GB12325-1990.电能质量-供电电压允许偏差.北京:国家技术监督局, 1990
[50] George J. Wakileh. Power Systems Harmonics[M]. Berlin: Springer, 2001.
[51] Davor Vujatovic, Zhang Qingping. Harmonics Generated from Railway Operation[C]. IEEE Power Engineering Society General Meeting, 18-22, 2006, Montréal Quebéc.Canada