电气化铁路牵引负荷的概率分布模型及其应用
|
摘要
电气化铁路在快速发展的同时,新建电气化铁路的投入运营对电力系统电能质量会产生诸多不利影响,主要是负序和谐波的污染。单相交流电气化铁路相比三相电力系统的特殊性,表现于它的特殊结构和各馈线(相)负荷的相互独立及随机波动性,因此,研究电气化铁路的无功、负序和谐波这三大技术问题在此基础上展开。
本文基于大量牵引负荷的实测数据,利用理论分布拟合与数值定义的方法分别获得了牵引负荷的概率密度函数。由于理论分布只需确定少数几个参数就能产生它的概率密度,应用方便,在对比了贝塔分布(Beta Distribution)、对数正态分布(Lognormal Distribution)以及瑞利分布(Reileigh Distribution)三种理论分布模型的拟合效果后,选择拟合效果最好的贝塔分布产生牵引负荷的概率密度函数,同时证明带电有效系数越小,贝塔分布拟合的误差越小。在确定了贝塔分布的拟合参数后,随机抽样产生牵引负荷的模拟数据并变换到牵引变压器一次侧验证了该方法的有效性。
由于贝塔函数拟合的局限性,本文采取了另一种方法,即利用数值定义的形式产生了牵引负荷的概率密度与概率分布模型,并通过特征参数的分类,找到了新建电气化铁路牵引负荷分布与既有电气化铁路牵引负荷分布的边界条件,预测了新建牵引变电所馈线电流的负荷数据。同样变换到牵引变压器一次侧验证了该方法的有效性。以新建遂渝线路为例,预测了遂渝线对重庆电网的负序影响。
从既有线路数据的角度出发,研究了YNdll和三相—二相平衡式接线牵引变电所的负序分布特性和牵引变压器的容量分布特征,并得出了相应的结论。
As the electrified railways rapid development and the same time new electric railways will produce many adverse impact on the main sequence, negative and harmonics pollution to quality of the power system. Contrast with a three-phase power system, the particularity of single-phase exchange electrified railway system reflect its specific structure and every line in the feeders (phase) of independence and random wave properties, therefore, based on this unfolding study the negative three technical problems of reactive power, needle sequence and harmonic.
Based on mass traction's load test data, and gained traction's load probability density function by using numerical definition and theoretical distribution fitting method. Because only a few theoretical distribution parameters determined could generate its probability density, applied conveniently, in contrast to the three theory fitting results of Distribution model with Beta Distribution, Lognormal Distribution and Rayleigh Distribution, choose the Beta Distribution which have best fitting effec produced probability density function of traction's load, and gives the conditions of beta function can accurate fitting load. After random sampling by current transform array verify the validity of this method.
Due to the limitations of Beta Distribution function fitting, in this paper using a numerical well-defined formalism produced traction's load probability density and probability distribution model, and found the boundary conditions of the new electrified railway traction's load distribution and existing electrified railway traction's load distribution by classification of the characteristic parameters, forecasts the new traction substation feeder current load data. Similarly transform to traction transformer primary side and proof the validity of this method. To new SuiYU line for example, combined with the power line, forecasts ChongQing grid lines negative sequence influence with the parameters of grid.
Data from the perspective of measured data, studies the YNd11 and three phase-two phase balance type wiring traction substation of negative sequence distribution charcteristics and traction transformer capacity distribution characteristics, and draws a conclusion.
本文基于大量牵引负荷的实测数据,利用理论分布拟合与数值定义的方法分别获得了牵引负荷的概率密度函数。由于理论分布只需确定少数几个参数就能产生它的概率密度,应用方便,在对比了贝塔分布(Beta Distribution)、对数正态分布(Lognormal Distribution)以及瑞利分布(Reileigh Distribution)三种理论分布模型的拟合效果后,选择拟合效果最好的贝塔分布产生牵引负荷的概率密度函数,同时证明带电有效系数越小,贝塔分布拟合的误差越小。在确定了贝塔分布的拟合参数后,随机抽样产生牵引负荷的模拟数据并变换到牵引变压器一次侧验证了该方法的有效性。
由于贝塔函数拟合的局限性,本文采取了另一种方法,即利用数值定义的形式产生了牵引负荷的概率密度与概率分布模型,并通过特征参数的分类,找到了新建电气化铁路牵引负荷分布与既有电气化铁路牵引负荷分布的边界条件,预测了新建牵引变电所馈线电流的负荷数据。同样变换到牵引变压器一次侧验证了该方法的有效性。以新建遂渝线路为例,预测了遂渝线对重庆电网的负序影响。
从既有线路数据的角度出发,研究了YNdll和三相—二相平衡式接线牵引变电所的负序分布特性和牵引变压器的容量分布特征,并得出了相应的结论。
As the electrified railways rapid development and the same time new electric railways will produce many adverse impact on the main sequence, negative and harmonics pollution to quality of the power system. Contrast with a three-phase power system, the particularity of single-phase exchange electrified railway system reflect its specific structure and every line in the feeders (phase) of independence and random wave properties, therefore, based on this unfolding study the negative three technical problems of reactive power, needle sequence and harmonic.
Based on mass traction's load test data, and gained traction's load probability density function by using numerical definition and theoretical distribution fitting method. Because only a few theoretical distribution parameters determined could generate its probability density, applied conveniently, in contrast to the three theory fitting results of Distribution model with Beta Distribution, Lognormal Distribution and Rayleigh Distribution, choose the Beta Distribution which have best fitting effec produced probability density function of traction's load, and gives the conditions of beta function can accurate fitting load. After random sampling by current transform array verify the validity of this method.
Due to the limitations of Beta Distribution function fitting, in this paper using a numerical well-defined formalism produced traction's load probability density and probability distribution model, and found the boundary conditions of the new electrified railway traction's load distribution and existing electrified railway traction's load distribution by classification of the characteristic parameters, forecasts the new traction substation feeder current load data. Similarly transform to traction transformer primary side and proof the validity of this method. To new SuiYU line for example, combined with the power line, forecasts ChongQing grid lines negative sequence influence with the parameters of grid.
Data from the perspective of measured data, studies the YNd11 and three phase-two phase balance type wiring traction substation of negative sequence distribution charcteristics and traction transformer capacity distribution characteristics, and draws a conclusion.
引文
[1]蔡庆华.我国电气化铁路的发展与展望[J].中国铁路,1998,02
[2]李群湛.牵引变电所供电分析及综合补偿技术[M].北京：中国铁道出版社,2006
[3]李群湛,贺建闽.电气化铁路电能质量及其综合控制技术[M].西南交通大学电气工程学院,2007.
[4]李群湛.试论电气化铁道的电能质量问题[J].客运专线技术研讨会论文集,2006：1-6.
[5]GB-T 12325-2003.电能质量——供电电压偏差[S].北京：国家质量技术监督局,1993.
[6]GB-T 15543-1995.电能质量——三相电压不平衡[S].北京：国家质量技术监督局,1995.
[7]GB-T 12325-2003.电能质量——公用电网谐波[S].北京：国家质量技术监督局,2003.
[8]GB-T14549-1993.电能质量——电压波动和闪变[S].北京：国家质量技术监督局,1993.
[9]铁道部电气化工程局电气化勘测设计院编.电气化铁道设计手册——牵引供电系统[M].北京：中国铁道出版社,1988.
[10]卢志海,厉吉文,周剑.电气化铁路对电力系统的影响[J].继电器,32(11),2004：33-36
[11]李群湛.关于电气化铁道的负序影响与限制问题的研究[J].铁道学报,16(4),1994：21-27
[12]姚金雄,张涛,林榕,罗迪.牵引供电系统负序电流和谐波对电力系统的影响及其补偿措施[J].电网技术,32(9),2008：61-64
[13]陈立国著.工程随机变量优化设计方法——原理与应用[M].北京：科学出版社,1997.
[14]解绍锋,李群湛,赵丽平.电气化铁道牵引负载谐波分布特征与概率模型研究[J].中国电机工程学报,2005(16)：79-83
[15]董祥.电气化铁路对电网电能质量影响的预测研究[D].西南交通大学硕士学位论文,2006
[16]张丽艳,李群湛,解绍锋.牵引变电所馈线电流的概率分布[J].西南交通大学学报,
[17]唐开林,李群湛,张丽艳.电气化铁路牵引网馈线电流概率分布[J].电力系统及其自动化,2010
[18]吴帆.基于实测数据的牵引变电所运行特性仿真及评价[D].西南交通大学硕士学位论文,2006
[19]张进思.电气化铁道负荷过程及负荷行为的计算机仿真[J].西南交通大学学报,1986,4：21-29.
[20]黄军.牵引负荷过程仿真[J].西南交通大学硕士学位论文,2006
[21]何俊文.牵引供电系统负荷过程仿真[J].西南交通大学硕士学位论文,2007
[22]黄石柱,李建华,赵娟,夏道止.电气化铁路牵引变电所概率谐波电流的仿真计算[J].电力系统自动化.2002(05)：26-31.
[23]李群湛,贺建闽.牵引供电系统分析[M].成都：西南交通大学出版社,2007.
[24]李群湛著.电气化铁道并联综合补偿及其应用[M].北京：中国铁道出版社,1993.
[25]清华大学电机工程系柔性输配电系统研究所.电气化铁道牵引供电系统初步研究[R].2006.
[26]陆旋.数理统计基础[M].北京：清华大学出版社,1998
[27]王岩,隋思莲,王爱青.数理统计与MATLAB工程数据分析[M].北京：清华大学出版社,2006.
[28]H. S. Ang, H. Tang, Probability Engineering Design, Marcel Dekker Inc, N. Y., 1983
[29]现代工程数学编委会,现代工程数学手册,华中理工大学出版社,1987
[30]李群湛.电牵引负荷概率分布建模[J].西南交通大学庆祝建校95周年学术报告会文集,1995
[31]杨振海,张忠占.应用数理统计[M].北京：高等教育出版社,2004
[32]李群湛.牵引变电所电气量的通用变换方法及其应用[J].铁道学报,1994
[33]R.E. Morrison, B.Sc, Ph.D., C.Eng., M.I.E.E. and A.D. Clark, B.Sc, C.Eng.,M.I.E.E.Probabilistic representation of harmonic currents in AC traction systems[J] Electric Power Applications, IEE Proceedings B. Volume 131, Issue 5, September 1984 Page(s):181-189
[33]Wang. Y.J, Pierrat. L, Wang. L.Summation of harmonic currents produced by AC/DC static power converters with randomly fluctuating loads[J]. Power Delivery, IEEE Transactions on Volume 9, Issue 2, April 1994 Page(s):1129-1135
[34]李群湛.电牵引负荷的概率分布及其应用.中国和学技术协会首届青年学术年会四川卫星会议论文集(上册).1992
[35]解绍锋,李群湛,王杰文,徐英雷.基于统计的牵引变压器典型负荷曲线分析[J].机车电传动,(6),2004：24-27
[36]新建遂渝线主要技术标准.西南电力设计院,2010
[37]Jasper van Casteren, Frederik Groeman.Harmonic Analysis of Rail Transportation Systems with Probabilistic Techniques [J] Probabilistic Methods Applied to Power Systems,2006. PMAPS 2006. International Conference on,11-15 June 2006 Page(s):1-4
[38]Jianhua Li, Shizhu Huang, Juan Zhao, Xia Daozhi.Simulation for Probabilistic Harmonic Currents of Electrical Railway Traction Substation [J]. Power System Technology,2002. Proceedings. PowerCon 2002. International Conference on. Volume 4,13-17 Oct.2002 Page(s):2511-2515 vol.4
[39]YE Zhongming, LO Edward, YUEN K. H., PONG M. H.Probabilistic Characterization of Current Harmonics of Electrical Traction Power Supply System by Analytic Method [J]. Industrial Electronics Society,1999. IECON'99 Proceedings. The 25th Annual Conference of the IEEE. Volume 1,29 Nov.-3 Dec.1999 Page(s):360-366 vol.1
[40]T.K. Ho, Y.L. Chi, J. Wang, K.K. Leung, L.K. Siu and C.T. Tse.Probabilistic load flow in AC electrified railways [J]. Electric Power Applications, IEE Proceedings. Volume 152, Issue 4,8 July 2005 Page(s):1003-1013
[41]Ho. T.K, Chi. Y.L, Wang. J, Leung. K.K.Load flow in electrified railway [J]. Power Electronics, Machines and Drives,2004. (PEMD 2004). Second International Conference on (Conf. Publ. No.498). Volume 2,31 March-2 April 2004 Page(s):498-503 Vol.2
[42]G.olguin, M.Aedo, M.Arias, A.Ortiz. A Monte Carlo Simulation Approach to the Method of Fault Positions for Stochastic Assessment of Voltage Dips(sags).IEEE/PES Transmission and Distribution conference & Exhibition:Asia and Pacific Dalian,China,2005:1-6.
[43]Armando M.Leite da Silva, Leonidas C.Resende, Luiz A.F.Manso. Application of Monte Carlo Simulation to Well-being Analysis of Large Composition Power Systems.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-6.
[44]Chanan Singh, Joydeep Mitra.Monte Carlo Simulation for Reliability Analysis of Emergency and Standby Power Systems.IEEE,1995:2290-2295.
[45]Chanan Singh, Xiaochuan Luo, Hyungchul Kim. Power System Adequacy and Security Calculations Using Monte Carlo Simulation Incorporating Intelligent System Methodology.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-9.
[46]李曙辉.电气化铁道负荷统计特征的仿真分析[J].铁道学报,18(2),1994：40-46
[47]赵乾钊.电气化铁道谐波预测评估方法的研究[J].电气化铁道,2004,21(3)：1-7.
[48]李曙辉.电气化铁道负荷统计特征的仿真分析[J].铁道学报,1996,18(2)：40-46.
[49]李群湛.牵引负载的三相等效模型[J].电力系统自动化,18(12),1994：24-31
[50]Chun-lien S. Probabilistic load-flow computation using point estimate method[J]. Power Systems, IEEE Transactions on.2005,20(4):1843-1851.
[51]Borghetti.A,Nucci.C.A,Paolone.M.Statistical methods for evaluating lightning induced effects on distribution lines.Proceedings of the IEEE power Engineering Society Transmission and Distribution Conference,v2,2000:879
[52]YE Zhongming, PONG M. H., LO W. C., WEN K. H.Harrnonic Evaluation of Traction System by Monte Carlo Simulation [J] Power Electronics Specialists Conference, PESC 99.30th Annual IEEE, Volume 1,27 June-1 July 1999 Page(s):424-429 vol.1
[53]Yu.A.Shrelder. Method of Statistical Testing(Monte Carlo method)[M],1964 GE.Forsythe, B.A.Leibler.Matrix inversion by a Monte Carlo method, MTAC,4,1950: 127-129
[54]W.Wasow.A note on the inversion of matrix by random walks MTAC,6,1952:78-81 J.H.Curtiss.A theoretical Comparison of two Classical methods and a Monte Carlo method for Computing one Component of the solution of a set of linear algebraic eqution, (4):191-233.
[55]B.Spinard, et.al. An alignment Chart for Monte Carlo of the transport problem, (3):4-5.
[56]王猛.电力系统谐波、负序过程仿真及应用[D].西南交通大学硕士研究生学位论文,2003.
[57]张丽艳,李群湛.YNd11接线牵引变压器负序分析[J].变压器,2005,43(1)：21-25.
[58]铁道部电气化工程局电气化勘测设计院.牵引供电系统[M].中国铁道出版社,1989
[59]Andrea M.Rei, Marcus Th,Schilling, Albert C.GMelo. Monte Carlo Simulation and Contingency Enumeration in Bulk Power Systems Reliability Assessment.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-6.
[60]T.Solver, M.Amelin.State duration based Monte Carlo Simulation model with Independent Failures for Distribution System Reliability Analysis.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15.2006.
[61]Yaw-juen W, Yaw-juen W, Pierrat L. Probabilistic modelling of current harmonics produced by an AC/DC converter under voltage unbalance [J]. Power Delivery, IEEE Transactions on.1993,8(4):2060-2066.
[62]Kazibwe E W, Kazibwe E W, Ortmeyer T H, et al. Summation of probabilistic harmonic vectors [power systems][J]. Power Delivery, IEEE Transactions on.1989,4(1): 621-628.
[63]Martinon J, Martinon J, Fauquembergue P, et al. Anew statistical approach of harmonic propagation in transmission systems[J]. Power Delivery, IEEE Transactions on.1996, 11(2):1032-1040.
[64]Carpinelli G, Carpinelli G, Esposito T, et al. First-order probabilistic harmonic power flow First-order probabilistic harmonic power flow[J]. Generation, Transmission and Distribution, IEE Proceedings-.2001,148(6):541-548.
[65]Pei Z, Pei Z, Lee S T. Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J]. Power Systems, IEEE Transactions on.2004,19(1):676-682.
[2]李群湛.牵引变电所供电分析及综合补偿技术[M].北京：中国铁道出版社,2006
[3]李群湛,贺建闽.电气化铁路电能质量及其综合控制技术[M].西南交通大学电气工程学院,2007.
[4]李群湛.试论电气化铁道的电能质量问题[J].客运专线技术研讨会论文集,2006：1-6.
[5]GB-T 12325-2003.电能质量——供电电压偏差[S].北京：国家质量技术监督局,1993.
[6]GB-T 15543-1995.电能质量——三相电压不平衡[S].北京：国家质量技术监督局,1995.
[7]GB-T 12325-2003.电能质量——公用电网谐波[S].北京：国家质量技术监督局,2003.
[8]GB-T14549-1993.电能质量——电压波动和闪变[S].北京：国家质量技术监督局,1993.
[9]铁道部电气化工程局电气化勘测设计院编.电气化铁道设计手册——牵引供电系统[M].北京：中国铁道出版社,1988.
[10]卢志海,厉吉文,周剑.电气化铁路对电力系统的影响[J].继电器,32(11),2004：33-36
[11]李群湛.关于电气化铁道的负序影响与限制问题的研究[J].铁道学报,16(4),1994：21-27
[12]姚金雄,张涛,林榕,罗迪.牵引供电系统负序电流和谐波对电力系统的影响及其补偿措施[J].电网技术,32(9),2008：61-64
[13]陈立国著.工程随机变量优化设计方法——原理与应用[M].北京：科学出版社,1997.
[14]解绍锋,李群湛,赵丽平.电气化铁道牵引负载谐波分布特征与概率模型研究[J].中国电机工程学报,2005(16)：79-83
[15]董祥.电气化铁路对电网电能质量影响的预测研究[D].西南交通大学硕士学位论文,2006
[16]张丽艳,李群湛,解绍锋.牵引变电所馈线电流的概率分布[J].西南交通大学学报,
[17]唐开林,李群湛,张丽艳.电气化铁路牵引网馈线电流概率分布[J].电力系统及其自动化,2010
[18]吴帆.基于实测数据的牵引变电所运行特性仿真及评价[D].西南交通大学硕士学位论文,2006
[19]张进思.电气化铁道负荷过程及负荷行为的计算机仿真[J].西南交通大学学报,1986,4：21-29.
[20]黄军.牵引负荷过程仿真[J].西南交通大学硕士学位论文,2006
[21]何俊文.牵引供电系统负荷过程仿真[J].西南交通大学硕士学位论文,2007
[22]黄石柱,李建华,赵娟,夏道止.电气化铁路牵引变电所概率谐波电流的仿真计算[J].电力系统自动化.2002(05)：26-31.
[23]李群湛,贺建闽.牵引供电系统分析[M].成都：西南交通大学出版社,2007.
[24]李群湛著.电气化铁道并联综合补偿及其应用[M].北京：中国铁道出版社,1993.
[25]清华大学电机工程系柔性输配电系统研究所.电气化铁道牵引供电系统初步研究[R].2006.
[26]陆旋.数理统计基础[M].北京：清华大学出版社,1998
[27]王岩,隋思莲,王爱青.数理统计与MATLAB工程数据分析[M].北京：清华大学出版社,2006.
[28]H. S. Ang, H. Tang, Probability Engineering Design, Marcel Dekker Inc, N. Y., 1983
[29]现代工程数学编委会,现代工程数学手册,华中理工大学出版社,1987
[30]李群湛.电牵引负荷概率分布建模[J].西南交通大学庆祝建校95周年学术报告会文集,1995
[31]杨振海,张忠占.应用数理统计[M].北京：高等教育出版社,2004
[32]李群湛.牵引变电所电气量的通用变换方法及其应用[J].铁道学报,1994
[33]R.E. Morrison, B.Sc, Ph.D., C.Eng., M.I.E.E. and A.D. Clark, B.Sc, C.Eng.,M.I.E.E.Probabilistic representation of harmonic currents in AC traction systems[J] Electric Power Applications, IEE Proceedings B. Volume 131, Issue 5, September 1984 Page(s):181-189
[33]Wang. Y.J, Pierrat. L, Wang. L.Summation of harmonic currents produced by AC/DC static power converters with randomly fluctuating loads[J]. Power Delivery, IEEE Transactions on Volume 9, Issue 2, April 1994 Page(s):1129-1135
[34]李群湛.电牵引负荷的概率分布及其应用.中国和学技术协会首届青年学术年会四川卫星会议论文集(上册).1992
[35]解绍锋,李群湛,王杰文,徐英雷.基于统计的牵引变压器典型负荷曲线分析[J].机车电传动,(6),2004：24-27
[36]新建遂渝线主要技术标准.西南电力设计院,2010
[37]Jasper van Casteren, Frederik Groeman.Harmonic Analysis of Rail Transportation Systems with Probabilistic Techniques [J] Probabilistic Methods Applied to Power Systems,2006. PMAPS 2006. International Conference on,11-15 June 2006 Page(s):1-4
[38]Jianhua Li, Shizhu Huang, Juan Zhao, Xia Daozhi.Simulation for Probabilistic Harmonic Currents of Electrical Railway Traction Substation [J]. Power System Technology,2002. Proceedings. PowerCon 2002. International Conference on. Volume 4,13-17 Oct.2002 Page(s):2511-2515 vol.4
[39]YE Zhongming, LO Edward, YUEN K. H., PONG M. H.Probabilistic Characterization of Current Harmonics of Electrical Traction Power Supply System by Analytic Method [J]. Industrial Electronics Society,1999. IECON'99 Proceedings. The 25th Annual Conference of the IEEE. Volume 1,29 Nov.-3 Dec.1999 Page(s):360-366 vol.1
[40]T.K. Ho, Y.L. Chi, J. Wang, K.K. Leung, L.K. Siu and C.T. Tse.Probabilistic load flow in AC electrified railways [J]. Electric Power Applications, IEE Proceedings. Volume 152, Issue 4,8 July 2005 Page(s):1003-1013
[41]Ho. T.K, Chi. Y.L, Wang. J, Leung. K.K.Load flow in electrified railway [J]. Power Electronics, Machines and Drives,2004. (PEMD 2004). Second International Conference on (Conf. Publ. No.498). Volume 2,31 March-2 April 2004 Page(s):498-503 Vol.2
[42]G.olguin, M.Aedo, M.Arias, A.Ortiz. A Monte Carlo Simulation Approach to the Method of Fault Positions for Stochastic Assessment of Voltage Dips(sags).IEEE/PES Transmission and Distribution conference & Exhibition:Asia and Pacific Dalian,China,2005:1-6.
[43]Armando M.Leite da Silva, Leonidas C.Resende, Luiz A.F.Manso. Application of Monte Carlo Simulation to Well-being Analysis of Large Composition Power Systems.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-6.
[44]Chanan Singh, Joydeep Mitra.Monte Carlo Simulation for Reliability Analysis of Emergency and Standby Power Systems.IEEE,1995:2290-2295.
[45]Chanan Singh, Xiaochuan Luo, Hyungchul Kim. Power System Adequacy and Security Calculations Using Monte Carlo Simulation Incorporating Intelligent System Methodology.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-9.
[46]李曙辉.电气化铁道负荷统计特征的仿真分析[J].铁道学报,18(2),1994：40-46
[47]赵乾钊.电气化铁道谐波预测评估方法的研究[J].电气化铁道,2004,21(3)：1-7.
[48]李曙辉.电气化铁道负荷统计特征的仿真分析[J].铁道学报,1996,18(2)：40-46.
[49]李群湛.牵引负载的三相等效模型[J].电力系统自动化,18(12),1994：24-31
[50]Chun-lien S. Probabilistic load-flow computation using point estimate method[J]. Power Systems, IEEE Transactions on.2005,20(4):1843-1851.
[51]Borghetti.A,Nucci.C.A,Paolone.M.Statistical methods for evaluating lightning induced effects on distribution lines.Proceedings of the IEEE power Engineering Society Transmission and Distribution Conference,v2,2000:879
[52]YE Zhongming, PONG M. H., LO W. C., WEN K. H.Harrnonic Evaluation of Traction System by Monte Carlo Simulation [J] Power Electronics Specialists Conference, PESC 99.30th Annual IEEE, Volume 1,27 June-1 July 1999 Page(s):424-429 vol.1
[53]Yu.A.Shrelder. Method of Statistical Testing(Monte Carlo method)[M],1964 GE.Forsythe, B.A.Leibler.Matrix inversion by a Monte Carlo method, MTAC,4,1950: 127-129
[54]W.Wasow.A note on the inversion of matrix by random walks MTAC,6,1952:78-81 J.H.Curtiss.A theoretical Comparison of two Classical methods and a Monte Carlo method for Computing one Component of the solution of a set of linear algebraic eqution, (4):191-233.
[55]B.Spinard, et.al. An alignment Chart for Monte Carlo of the transport problem, (3):4-5.
[56]王猛.电力系统谐波、负序过程仿真及应用[D].西南交通大学硕士研究生学位论文,2003.
[57]张丽艳,李群湛.YNd11接线牵引变压器负序分析[J].变压器,2005,43(1)：21-25.
[58]铁道部电气化工程局电气化勘测设计院.牵引供电系统[M].中国铁道出版社,1989
[59]Andrea M.Rei, Marcus Th,Schilling, Albert C.GMelo. Monte Carlo Simulation and Contingency Enumeration in Bulk Power Systems Reliability Assessment.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15,2006:1-6.
[60]T.Solver, M.Amelin.State duration based Monte Carlo Simulation model with Independent Failures for Distribution System Reliability Analysis.9th International Conference on Probabilistic Methods Applied to Power Systems KTH, Stockholm, Sweden-June 11-15.2006.
[61]Yaw-juen W, Yaw-juen W, Pierrat L. Probabilistic modelling of current harmonics produced by an AC/DC converter under voltage unbalance [J]. Power Delivery, IEEE Transactions on.1993,8(4):2060-2066.
[62]Kazibwe E W, Kazibwe E W, Ortmeyer T H, et al. Summation of probabilistic harmonic vectors [power systems][J]. Power Delivery, IEEE Transactions on.1989,4(1): 621-628.
[63]Martinon J, Martinon J, Fauquembergue P, et al. Anew statistical approach of harmonic propagation in transmission systems[J]. Power Delivery, IEEE Transactions on.1996, 11(2):1032-1040.
[64]Carpinelli G, Carpinelli G, Esposito T, et al. First-order probabilistic harmonic power flow First-order probabilistic harmonic power flow[J]. Generation, Transmission and Distribution, IEE Proceedings-.2001,148(6):541-548.
[65]Pei Z, Pei Z, Lee S T. Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J]. Power Systems, IEEE Transactions on.2004,19(1):676-682.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |