多相耦合输电线路频率相关模型的动态分段非解耦算法
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摘要
多相耦合输电线路的频率相关分布参数模型是分析任意多回交、直流输电线路最实用的模型,其非解耦算法具有计算精确、适用于不对称参数等优点,但应用于谐波稳态计算时,存在运算复杂、数值规模大及计算需要分段等问题。该文对频率相关模型非解耦算法的计算效率和计算精度进行了定量分析。在此基础上,推导了1种输电线路最优分段长度的计算方法,提出了1种频率相关模型的动态分段非解耦算法。该算法根据预设的计算精度,对各次谐波频率动态选取分段长度。验证算例表明,该文所提算法计算精度高,可根据需求任意指定精度,同时可以提高计算效率、降低软件复杂度,因此对电力系统谐波稳态分析软件的设计实现具有参考价值。
The frequency-dependent distributed parameter model of multi-phase coupled transmission line is the most practical method for analyzing multiple AC/DC transmission lines, and its non-decoupling numerical algorithms have advantages of accuracy in calculation and applicability under unbalanced parameters. However, when applied to harmonic analysis, the current algorithms also show many problems such as complex algorithm, large numerical scale and segmented calculation. This paper analyzed the efficiency and accuracy of the current non-decoupling numerical algorithms in a quantitative way. On this basis, a novel method for calculating the optimal segment length of transmission lines was designed,and a flexibly segmented non-decoupling algorithm of frequency-dependent distributed parameter model of multiphase coupled transmission line was proposed, in which the segment length for each harmonic order is selected separately according to a requested accuracy. Calculating example shows that the proposed algorithm has good accuracy, and was effective in simplifying software flow and optimizing computational efficiency. So it is of reference value to the design of harmonic analysis software for power systems.
The frequency-dependent distributed parameter model of multi-phase coupled transmission line is the most practical method for analyzing multiple AC/DC transmission lines, and its non-decoupling numerical algorithms have advantages of accuracy in calculation and applicability under unbalanced parameters. However, when applied to harmonic analysis, the current algorithms also show many problems such as complex algorithm, large numerical scale and segmented calculation. This paper analyzed the efficiency and accuracy of the current non-decoupling numerical algorithms in a quantitative way. On this basis, a novel method for calculating the optimal segment length of transmission lines was designed,and a flexibly segmented non-decoupling algorithm of frequency-dependent distributed parameter model of multiphase coupled transmission line was proposed, in which the segment length for each harmonic order is selected separately according to a requested accuracy. Calculating example shows that the proposed algorithm has good accuracy, and was effective in simplifying software flow and optimizing computational efficiency. So it is of reference value to the design of harmonic analysis software for power systems.
引文
[1]张开迪.分布参数电路模型及其在特高压线路保护中的应用研究[D].重庆:重庆大学,2014.Zhang Kaidi.Research on the distributed parameter circuit model and its application in UHV transmission line protection[D].Chongqing:Chongqing University,2014(in Chinese).
[2]段慧,肖龙海,徐政.基于潮流数据的输电线路谐波模型和电磁暂态模型研究[J].华东电力,2007,35(9):9-11.Duan Hui,Xiao Longhai,Xu Zheng.Harmonic models and electromagnetic transient models of transmission lines based on power flow data[J].East China Electric Power,2007,35(9):9-11(in Chinese).
[3]Task Force on Harmonies Modeling and Simulation.Modeling and simulation of the propagation of harmonics in electric power networks-part I[J].IEEETransaction on Power Delivery,1996,11(1):452-465.
[4]索南加乐,吴亚萍,宋国兵,等.基于分布参数的同杆双回线单线故障准确测距原理[J].中国电机工程学报,2003,23(5):40-44.Suonan Jiale,Wu Yaping,Song Guobing,et al.New accurate fault location algorithm for parallel lines on the same tower based on distribute parameter[J].Proceedings of the CSEE,2003,23(5):40-44(in Chinese).
[5]肖遥,邓军,夏谷林,等.高压直流输电线路分布参数测量新方法[J].中国电机工程学报,2015,35(20):5375-5383.Xiao Yao,Deng Jun,Xia Gulin,et al.A novel distributed parameters measurement method of HVDC transmission line[J].Proceedings of the CSEE,2015,35(20):5375-5383(in English).
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[7]邓军,肖遥,范毅,等.基于两相电源的高压直流输电线路分布参数计算方法及直流工程的应用研究[J].高电压技术,2015,41(7):2451-2456.Deng Jun,Xiao Yao,Fan Yi,et al.Calculation method of distributed parameters and application of DC projects in HVDC transmission lines based on two phase power resource[J].High Voltage Engineering,2015,41(7):2451-2456(in Chinese).
[8]王峰,朱光友,游广增,等.高压直流输电直流侧谐波电流计算[J].高电压技术,2009,35(9):2275-2279.Wang Feng,Zhu Guangyou,You Guangzeng,et al.Calculation of DC side harmonic currents for HVDCtransmission[J].High Voltage Engineering,2009,35(9):2275-2279(in Chinese).
[9]肖遥,范毅,程澜,等.单回及同塔双回交流输电线路参数测量理论[J].中国电机工程学报,2016,36(20):5515-5522,5727.Xiao Yao,Fan Yi,Cheng Lan,et al.A parameter measurement theory of single and double circuit ACtransmission lines[J].Proceedings of the CSEE,2016,36(20):5515-5522,5727(in Chinese).
[10]徐政.耦合长线稳态分析的非解耦模型及其算法[J].中国电机工程学报,1995,15(5):342-346,353.Xu Zheng.Coupled model and its computation for steady state analysis of multiphase transmission lines[J].Proceedings of the CSEE,1995,15(5):342-346,353(in Chinese).
[11]徐韬,翁华,徐政,等.高压直流输电非解耦线路模型改进算法[J].中国电机工程学报,2011,31(7):71-76.Xu Tao,Weng Hua,Xu Zheng,et al.An improved calculating method for the coupled line model of HVDCtransmission[J].Proceedings of the CSEE,2011,31(7):71-76(in Chinese).
[12]李英第.C语言代码分析与函数时间复杂度计算的研究[D].天津:天津大学,2014.Li Yingdi.The research of C language’s code analysis and calculating the time complexity of functions[D].Tianjin:Tianjin University,2014(in Chinese).
[13]谢东垒,刘宗行,陈显圣.均匀传输线电路模型参数的测试[J].重庆大学学报:自然科学版,2006,29(5),24-27.Xie Donglei,Liu Zonghang,Chen Xiansheng.A genetic based fault location algorithm for transmission lines[J].Journal of Chongqing University:Natural Science Edition,2006,29(5):24-27(in Chinese).
[14]李娟,薛永端,徐丙垠,等.单相均匀传输线暂态模型参数计算[J].电网技术,2013,37(4):1083-1089.Li Juan,Xue Yongduan,Xu Bingyin,et al.A method to calculate parameters of transient model for single-phase uniform transmission line[J].Power System Technology,2013,37(4):1083-1089(in Chinese).
[15]滕福生,滕欢.面向波阻抗的长距离输电研究[J].电网技术,2007,31(S1):70-72.Teng Fusheng,Teng Huan.Study on long distance power transmission with oriented wave impedance[J].Power System Technology,2007,31(S1):70-72(in Chinese).
[16]邓培民,王云葵.关于伯努利数结构的讨论[J].广西师范大学学报:自然科学版,1995,13(4):4-9.Deng Peimin,Wang Yunkui.Discourse on the structure of bernoulli’s numbers[J].Journal of Guangxi Normal University:Natural Science,1995,13(4):4-9(in Chinese).
[17]钟玉泉.复变函数论[M].北京:高等教育出版社,1988:177-186.
[18]邱启荣.矩阵理论及其应用[M].北京:中国电力出版社,2008:98-105.
[19]沈赞埙,夏道止.高压双极直流输电线路方程式及参数[J].西安交通大学学报,1984,18(3):31-42.Shen Zanxun,Xia Daozhi.Bipolar HVDC transmission line equation and parameters[J].Journal of Xi'an Jiaotong University,1984,18(3):31-42(in Chinese).
[20]朱光友.换流站交流侧谐波电流计算与交流滤波器设计研究[D].杭州:浙江大学,2007.
[2]段慧,肖龙海,徐政.基于潮流数据的输电线路谐波模型和电磁暂态模型研究[J].华东电力,2007,35(9):9-11.Duan Hui,Xiao Longhai,Xu Zheng.Harmonic models and electromagnetic transient models of transmission lines based on power flow data[J].East China Electric Power,2007,35(9):9-11(in Chinese).
[3]Task Force on Harmonies Modeling and Simulation.Modeling and simulation of the propagation of harmonics in electric power networks-part I[J].IEEETransaction on Power Delivery,1996,11(1):452-465.
[4]索南加乐,吴亚萍,宋国兵,等.基于分布参数的同杆双回线单线故障准确测距原理[J].中国电机工程学报,2003,23(5):40-44.Suonan Jiale,Wu Yaping,Song Guobing,et al.New accurate fault location algorithm for parallel lines on the same tower based on distribute parameter[J].Proceedings of the CSEE,2003,23(5):40-44(in Chinese).
[5]肖遥,邓军,夏谷林,等.高压直流输电线路分布参数测量新方法[J].中国电机工程学报,2015,35(20):5375-5383.Xiao Yao,Deng Jun,Xia Gulin,et al.A novel distributed parameters measurement method of HVDC transmission line[J].Proceedings of the CSEE,2015,35(20):5375-5383(in English).
[6]鲍乐.输电线路参数在线测量方法与应用研究[D].济南:山东大学,2015.Bao Le.Study on transmission line parameters on-line measurement and application[D].Jinan:Shandong University,2015(in Chinese).
[7]邓军,肖遥,范毅,等.基于两相电源的高压直流输电线路分布参数计算方法及直流工程的应用研究[J].高电压技术,2015,41(7):2451-2456.Deng Jun,Xiao Yao,Fan Yi,et al.Calculation method of distributed parameters and application of DC projects in HVDC transmission lines based on two phase power resource[J].High Voltage Engineering,2015,41(7):2451-2456(in Chinese).
[8]王峰,朱光友,游广增,等.高压直流输电直流侧谐波电流计算[J].高电压技术,2009,35(9):2275-2279.Wang Feng,Zhu Guangyou,You Guangzeng,et al.Calculation of DC side harmonic currents for HVDCtransmission[J].High Voltage Engineering,2009,35(9):2275-2279(in Chinese).
[9]肖遥,范毅,程澜,等.单回及同塔双回交流输电线路参数测量理论[J].中国电机工程学报,2016,36(20):5515-5522,5727.Xiao Yao,Fan Yi,Cheng Lan,et al.A parameter measurement theory of single and double circuit ACtransmission lines[J].Proceedings of the CSEE,2016,36(20):5515-5522,5727(in Chinese).
[10]徐政.耦合长线稳态分析的非解耦模型及其算法[J].中国电机工程学报,1995,15(5):342-346,353.Xu Zheng.Coupled model and its computation for steady state analysis of multiphase transmission lines[J].Proceedings of the CSEE,1995,15(5):342-346,353(in Chinese).
[11]徐韬,翁华,徐政,等.高压直流输电非解耦线路模型改进算法[J].中国电机工程学报,2011,31(7):71-76.Xu Tao,Weng Hua,Xu Zheng,et al.An improved calculating method for the coupled line model of HVDCtransmission[J].Proceedings of the CSEE,2011,31(7):71-76(in Chinese).
[12]李英第.C语言代码分析与函数时间复杂度计算的研究[D].天津:天津大学,2014.Li Yingdi.The research of C language’s code analysis and calculating the time complexity of functions[D].Tianjin:Tianjin University,2014(in Chinese).
[13]谢东垒,刘宗行,陈显圣.均匀传输线电路模型参数的测试[J].重庆大学学报:自然科学版,2006,29(5),24-27.Xie Donglei,Liu Zonghang,Chen Xiansheng.A genetic based fault location algorithm for transmission lines[J].Journal of Chongqing University:Natural Science Edition,2006,29(5):24-27(in Chinese).
[14]李娟,薛永端,徐丙垠,等.单相均匀传输线暂态模型参数计算[J].电网技术,2013,37(4):1083-1089.Li Juan,Xue Yongduan,Xu Bingyin,et al.A method to calculate parameters of transient model for single-phase uniform transmission line[J].Power System Technology,2013,37(4):1083-1089(in Chinese).
[15]滕福生,滕欢.面向波阻抗的长距离输电研究[J].电网技术,2007,31(S1):70-72.Teng Fusheng,Teng Huan.Study on long distance power transmission with oriented wave impedance[J].Power System Technology,2007,31(S1):70-72(in Chinese).
[16]邓培民,王云葵.关于伯努利数结构的讨论[J].广西师范大学学报:自然科学版,1995,13(4):4-9.Deng Peimin,Wang Yunkui.Discourse on the structure of bernoulli’s numbers[J].Journal of Guangxi Normal University:Natural Science,1995,13(4):4-9(in Chinese).
[17]钟玉泉.复变函数论[M].北京:高等教育出版社,1988:177-186.
[18]邱启荣.矩阵理论及其应用[M].北京:中国电力出版社,2008:98-105.
[19]沈赞埙,夏道止.高压双极直流输电线路方程式及参数[J].西安交通大学学报,1984,18(3):31-42.Shen Zanxun,Xia Daozhi.Bipolar HVDC transmission line equation and parameters[J].Journal of Xi'an Jiaotong University,1984,18(3):31-42(in Chinese).
[20]朱光友.换流站交流侧谐波电流计算与交流滤波器设计研究[D].杭州:浙江大学,2007.