基于幂迭代的电力系统模态谐振快速求解方法
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摘要
在谐波谐振分析方法中,模态分析方法可以揭示谐振频率、谐振幅度、谐振关键节点或位置等信息,得到了较快的推广和应用,但其计算效率尚有待提高。根据关键模态定义,即任一频率下的最大模态阻抗,只需求取每一个频率点处网络导纳矩阵的逆阵的最大特征值。采用幂迭代方法求取矩阵最大特征值及其对应的特征向量,通过采用新的迭代起始向量选取方法和迭代终止条件,有效减少了所需迭代次数;在优化方案中通过改进计算步长选择方法,进一步减少不必要的计算量。这些方法综合运用,获得了较高的计算速度。以IEEE 14母线系统作为算例,文中方法较一般模态分析方法计算速度提高了90%以上,验证了方法的有效性和高效性。
Among the harmonic resonance analysis methods, resonance mode assessment can reveal lot of useful information of the resonance, such as its frequency, amplitude, critical node or bus participation, etc. As a result, this method is widely used and studied. However, calculation speed of this method is not satisfactory in computing eigenvaluecomposition process at all frequency intervals. According to the definition of critical mode, namely the largest modal impedance at any frequency, it needs to calculate the largest eigenvalue of inverse matrix of network admittance matrix at each frequency interval. Power iteration is adopted to calculate the largest eigenvalue and corresponding eigenvector. Iterative times are reduced with new iteration starting vector selection method and iteration termination criteria. Furthermore, unnecessary calculation is further reduced by modifying calculation step selection method in prioritization scheme. Calculation speed increases remarkably with above methods synthetically. Simulation results on IEEE 14-bus test system illustrate high effectiveness of the proposed method, with an improvement of more than 90% calculation speed compared with conventional modal analysis method.
Among the harmonic resonance analysis methods, resonance mode assessment can reveal lot of useful information of the resonance, such as its frequency, amplitude, critical node or bus participation, etc. As a result, this method is widely used and studied. However, calculation speed of this method is not satisfactory in computing eigenvaluecomposition process at all frequency intervals. According to the definition of critical mode, namely the largest modal impedance at any frequency, it needs to calculate the largest eigenvalue of inverse matrix of network admittance matrix at each frequency interval. Power iteration is adopted to calculate the largest eigenvalue and corresponding eigenvector. Iterative times are reduced with new iteration starting vector selection method and iteration termination criteria. Furthermore, unnecessary calculation is further reduced by modifying calculation step selection method in prioritization scheme. Calculation speed increases remarkably with above methods synthetically. Simulation results on IEEE 14-bus test system illustrate high effectiveness of the proposed method, with an improvement of more than 90% calculation speed compared with conventional modal analysis method.
引文
[1]Huang Z.,Xu W,Dinavahi V R.A practical harmonic resonance guideline for shunt capacitor applications[J].IEEE Transactions on Power Delivery,2003,18(4):1382-1387.
[2]吴隆辉,卓放,张鹏博,等.一种用于配电系统谐振抑制及谐波治理的新型PAPF控制方法[J].中国电机工程学报,2008,28(27):70-77.Wu Longhui,Zhuo Fang,Zhang Pengbo,et al.A novel control method of PAPF for resonance damping and harmonics compensation in power system[J].Proceedings of the CSEE,2008,28(27):70-77(in Chinese).
[3]Temma K,Ishiguro F,Toki N,et al.Clarification and measurements of high frequency harmonic resonance by a voltage sourced converter[J].IEEE Transactions on Power Delivery,2005,20(1):450-457.
[4]史承逵.电网电容器组谐波谐振和谐波放大的研究[J].电力自动化设备,2001,21(7):36-38.Shi Chengkui.Study on harmonic resonance and harmonic enlargement of power network capacitor bank[J].Electric Power Automation Equipment,2001,21(7):36-38(in Chinese).
[5]Gustavsen B.Study of transformer resonant over-voltages caused by cable-transformer high-frequency interaction[J].IEEE Transactions on Power Delivery,2010,25(2):770-779.
[6]Chu X H,Tayjasanant T.Modeling wind power plants in harmonic resonance study-a case study in Thailand[C]//International Conference on Information Technology and Electrical Engineering(ICITEE),Yogyakarta,2013:385-390.
[7]Agorreta J L,Borrega M,López J,et al.Modeling and control of N-paralleled grid-connected inverters with LCL filter coupled due to grid impedance in PV plants[J].IEEE Transactions on Power Electronics,2011,26(3-4):770-785.
[8]何正友,胡海涛,方雷,等.高速铁路牵引供电系统谐波及其传输特性研究[J].中国电机工程学报,2011,31(16):55-62.He Zhengyou,Hu Haitao,Fang Lei,et al.Research on the harmonic in high-speed railway traction power supply system and its transmission characteristic[J].Proceedings of the CSEE,2011,31(16):55-62(in Chinese).
[9]He Z,Hu H,Zhang Y,et al.Harmonic resonance assessment to traction power-supply system considering train model in China high-speed railway[J].IEEE Transactions on Power Delivery,2014,29(4):1735-1743.
[10]CEA Technology Inc.Impact of harmonics on utility equipment:a survey and review of published work[R].Canada:Report no.T024700-5117,2003.
[11]刘心旸,蒋维勇,李亚男,等.青海电网二次谐波传导机理与抑制措施[J].电网技术,2015,39(8):2277-2282.Liu Xinyang,Jiang Weiyong,Li Yanan,et al.Second harmonic transmission mechanism and suppression measures in Qinghai Power Grid[J].Power System Technology,2015,39(8):2277-2282(in Chinese).
[12]陈甜甜,胡蓉,金祖洋,等.邻近直流输电落点的城市电网谐波传导特性分析[J].电网技术,2015,39(10):3000-3004.Chen Tiantian,Hu Rong,Jin Zuyang,et al.Analysis research on harmonic transmission characteristics of urban power network adjacent to UHVDC terminal location[J].Power System Technology,2015,39(10):3000-3004(in Chinese).
[13]熊希聪,王强钢,周念成,等.基于谐波解析的电动汽车充电对配电变压器影响概率评估方法[J].电网技术,2015,39(8):2283-2290.Xiong Xicong,Wang Qianggang,Zhou Niancheng,et al.Probability assessment of electric vehicle charging impact on distribution transformer based on harmonic analysis[J].Power System Technology,2015,39(8):2283-2290(in Chinese).
[14]余光正,林涛,徐遐龄,等.基于2m+1点估计法的考虑风力发电接入时电力系统谐波概率潮流算法[J].电网技术,2015,39(11):3260-3265.Yu Guangzheng,Lin Tao,Xu Xialing,et al.An algorithm based on2m+1 point estimate method for harmonic probabilistic load flow calculation of power systems incorporating wind power[J].Power System Technology,2015,39(11):3260-3265(in Chinese).
[15]江友华,王林,曹以龙,等.树状分布的多谐波源治理系统解耦与稳定性寻优[J].电网技术,2015,39(3):817-822.Jiang Youhua,Wang Lin,Cao Yilong,et al.Decoupling and stability optimization of dendroid-distributed multi-harmonic source management system[J].Power System Technology,2015,39(3):817-822(in Chinese).
[16]Xiao J,Gole A.A frequency scanning method for the identification of harmonic instabilities in HVDC systems[J].IEEE Transactions on Power Delivery,1995,10(4):1875-1881.
[17]徐文远,张大海.基于模态分析的谐波谐振评估方法[J].中国电机工程学报,2005,25(22):89-93.Xu Wilsun,Zhang Dahai.A modal analysis method for harmonic resonance assessment[J].Proceedings of the CSEE,2005,25(22):89-93(in Chinese).
[18]周辉,吴耀武,娄素华,等.基于模态分析和虚拟支路法的串联谐波谐振分析[J].中国电机工程学报,2007,27(28):84-89.Zhou Hui,Wu Yaowu,Lou Suhua,et al.Series resonance analysis based on modal analysis and dummy branch method[J].Proceedings of the CSEE,2007,27(28):84-89(in Chinese).
[19]Varricchio S L,Martins N,Lima L T G.A Newton-Raphson method based on eigenvalue sensitivities to improve harmonic voltage performance[J].IEEE Transactions on Power Delivery,2003,18(1):334-342.
[20]Varricchio S L,Gomes S,Martins N.Modal analysis of industrial system harmonics using the s-domain approach[J].IEEE Transactions on Power Delivery,2004,19(3):1232-1237.
[21]Xu W,Huang Z,Cui Y,et al.Harmonic resonance mode analysis[J].IEEE Transactions on Power Delivery,2005,20(2):1182-1190.
[22]Huang Z,Cui Y,Xu W.Application of modal sensitivity for power system harmonic resonance analysis[J].IEEE Transactions on Power Systems,2007,22(1):222-231.
[23]Cui Y,Wang X.Modal frequency sensitivity for power system harmonic resonance analysis[J].IEEE Transactions on Power Delivery,2012,27(2):1010-1017.
[24]Hu H,He Z,Zhang Y,et al.Modal frequency sensitivity analysis and application using complex nodal matrix[J].IEEE Transactions on Power Delivery,2014,29(2):969-971.
[25]Bellman R.Introduction to matrix analysis[M].Second Edition,New York:Mc Graw-Hill,1970.
[26]陈建兵,敖鸿斐.乘幂法求矩阵特征向量与特征值的初始向量及循环控制[J].数学的实践与认识,2001,31(2):148-152.Chen Jianbing,Ao Hongfei.Initial vector and iterating control in the solution to eigenvalue and eigenvector of a matrix by the matrix iteration method[J].Mathematics in Practice and Theory,2001,31(2):148-152(in Chinese).
[27]Lin F,Cohen W W.Power iteration clustering[C]//27 th International Conference on Machine Learning(ICML),Haifa,Israel,2010:655-662.
[28]IEEE Harmonics Model and Simulation Task Force.Test systems for harmonics modeling and simulation[J].IEEE Transactions on Power Delivery,1999,14(2):579-587.
[2]吴隆辉,卓放,张鹏博,等.一种用于配电系统谐振抑制及谐波治理的新型PAPF控制方法[J].中国电机工程学报,2008,28(27):70-77.Wu Longhui,Zhuo Fang,Zhang Pengbo,et al.A novel control method of PAPF for resonance damping and harmonics compensation in power system[J].Proceedings of the CSEE,2008,28(27):70-77(in Chinese).
[3]Temma K,Ishiguro F,Toki N,et al.Clarification and measurements of high frequency harmonic resonance by a voltage sourced converter[J].IEEE Transactions on Power Delivery,2005,20(1):450-457.
[4]史承逵.电网电容器组谐波谐振和谐波放大的研究[J].电力自动化设备,2001,21(7):36-38.Shi Chengkui.Study on harmonic resonance and harmonic enlargement of power network capacitor bank[J].Electric Power Automation Equipment,2001,21(7):36-38(in Chinese).
[5]Gustavsen B.Study of transformer resonant over-voltages caused by cable-transformer high-frequency interaction[J].IEEE Transactions on Power Delivery,2010,25(2):770-779.
[6]Chu X H,Tayjasanant T.Modeling wind power plants in harmonic resonance study-a case study in Thailand[C]//International Conference on Information Technology and Electrical Engineering(ICITEE),Yogyakarta,2013:385-390.
[7]Agorreta J L,Borrega M,López J,et al.Modeling and control of N-paralleled grid-connected inverters with LCL filter coupled due to grid impedance in PV plants[J].IEEE Transactions on Power Electronics,2011,26(3-4):770-785.
[8]何正友,胡海涛,方雷,等.高速铁路牵引供电系统谐波及其传输特性研究[J].中国电机工程学报,2011,31(16):55-62.He Zhengyou,Hu Haitao,Fang Lei,et al.Research on the harmonic in high-speed railway traction power supply system and its transmission characteristic[J].Proceedings of the CSEE,2011,31(16):55-62(in Chinese).
[9]He Z,Hu H,Zhang Y,et al.Harmonic resonance assessment to traction power-supply system considering train model in China high-speed railway[J].IEEE Transactions on Power Delivery,2014,29(4):1735-1743.
[10]CEA Technology Inc.Impact of harmonics on utility equipment:a survey and review of published work[R].Canada:Report no.T024700-5117,2003.
[11]刘心旸,蒋维勇,李亚男,等.青海电网二次谐波传导机理与抑制措施[J].电网技术,2015,39(8):2277-2282.Liu Xinyang,Jiang Weiyong,Li Yanan,et al.Second harmonic transmission mechanism and suppression measures in Qinghai Power Grid[J].Power System Technology,2015,39(8):2277-2282(in Chinese).
[12]陈甜甜,胡蓉,金祖洋,等.邻近直流输电落点的城市电网谐波传导特性分析[J].电网技术,2015,39(10):3000-3004.Chen Tiantian,Hu Rong,Jin Zuyang,et al.Analysis research on harmonic transmission characteristics of urban power network adjacent to UHVDC terminal location[J].Power System Technology,2015,39(10):3000-3004(in Chinese).
[13]熊希聪,王强钢,周念成,等.基于谐波解析的电动汽车充电对配电变压器影响概率评估方法[J].电网技术,2015,39(8):2283-2290.Xiong Xicong,Wang Qianggang,Zhou Niancheng,et al.Probability assessment of electric vehicle charging impact on distribution transformer based on harmonic analysis[J].Power System Technology,2015,39(8):2283-2290(in Chinese).
[14]余光正,林涛,徐遐龄,等.基于2m+1点估计法的考虑风力发电接入时电力系统谐波概率潮流算法[J].电网技术,2015,39(11):3260-3265.Yu Guangzheng,Lin Tao,Xu Xialing,et al.An algorithm based on2m+1 point estimate method for harmonic probabilistic load flow calculation of power systems incorporating wind power[J].Power System Technology,2015,39(11):3260-3265(in Chinese).
[15]江友华,王林,曹以龙,等.树状分布的多谐波源治理系统解耦与稳定性寻优[J].电网技术,2015,39(3):817-822.Jiang Youhua,Wang Lin,Cao Yilong,et al.Decoupling and stability optimization of dendroid-distributed multi-harmonic source management system[J].Power System Technology,2015,39(3):817-822(in Chinese).
[16]Xiao J,Gole A.A frequency scanning method for the identification of harmonic instabilities in HVDC systems[J].IEEE Transactions on Power Delivery,1995,10(4):1875-1881.
[17]徐文远,张大海.基于模态分析的谐波谐振评估方法[J].中国电机工程学报,2005,25(22):89-93.Xu Wilsun,Zhang Dahai.A modal analysis method for harmonic resonance assessment[J].Proceedings of the CSEE,2005,25(22):89-93(in Chinese).
[18]周辉,吴耀武,娄素华,等.基于模态分析和虚拟支路法的串联谐波谐振分析[J].中国电机工程学报,2007,27(28):84-89.Zhou Hui,Wu Yaowu,Lou Suhua,et al.Series resonance analysis based on modal analysis and dummy branch method[J].Proceedings of the CSEE,2007,27(28):84-89(in Chinese).
[19]Varricchio S L,Martins N,Lima L T G.A Newton-Raphson method based on eigenvalue sensitivities to improve harmonic voltage performance[J].IEEE Transactions on Power Delivery,2003,18(1):334-342.
[20]Varricchio S L,Gomes S,Martins N.Modal analysis of industrial system harmonics using the s-domain approach[J].IEEE Transactions on Power Delivery,2004,19(3):1232-1237.
[21]Xu W,Huang Z,Cui Y,et al.Harmonic resonance mode analysis[J].IEEE Transactions on Power Delivery,2005,20(2):1182-1190.
[22]Huang Z,Cui Y,Xu W.Application of modal sensitivity for power system harmonic resonance analysis[J].IEEE Transactions on Power Systems,2007,22(1):222-231.
[23]Cui Y,Wang X.Modal frequency sensitivity for power system harmonic resonance analysis[J].IEEE Transactions on Power Delivery,2012,27(2):1010-1017.
[24]Hu H,He Z,Zhang Y,et al.Modal frequency sensitivity analysis and application using complex nodal matrix[J].IEEE Transactions on Power Delivery,2014,29(2):969-971.
[25]Bellman R.Introduction to matrix analysis[M].Second Edition,New York:Mc Graw-Hill,1970.
[26]陈建兵,敖鸿斐.乘幂法求矩阵特征向量与特征值的初始向量及循环控制[J].数学的实践与认识,2001,31(2):148-152.Chen Jianbing,Ao Hongfei.Initial vector and iterating control in the solution to eigenvalue and eigenvector of a matrix by the matrix iteration method[J].Mathematics in Practice and Theory,2001,31(2):148-152(in Chinese).
[27]Lin F,Cohen W W.Power iteration clustering[C]//27 th International Conference on Machine Learning(ICML),Haifa,Israel,2010:655-662.
[28]IEEE Harmonics Model and Simulation Task Force.Test systems for harmonics modeling and simulation[J].IEEE Transactions on Power Delivery,1999,14(2):579-587.