基于复数域稳健回归的多谐波源污染责任量化方法
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摘要
主要针对多谐波源污染责任定量计算过程中,复最小二乘法对异常值敏感而传统稳健回归不是原问题的最小二乘解这一问题进行理论分析和研究,提出一种基于复数域多元模型的稳健回归方法。通过建立同时适用于集中式多谐波源和分布式多谐波源的等效电路模型和数学模型,理论推导复数域稳健回归的算法原理,并选用IEEE 14节点系统对所提出的算法进行仿真验证。研究结果表明:与复最小二乘法相比,该方法可较好地消减异常值对回归结果的影响,且比传统稳健回归的结果误差更小。
In the process of quantifying harmonic pollution responsibilities,Aimed at defects problem of CLSM(Complex Least Squares Method)as well as Usual Robust Regression,Theoretical analysis and research is studied. A new method,called Robust Regression in Complex Domain,is proposed to eliminate this question. Mathematical model and equivalent circuit model of multiple harmonic sources at the same bus and different buses are established. Algorithm principle of robust regression in complex domain is theoretically derived. And the analysis of simulation is studied with IEEE 14-bus system. The results show that this method is better to waken the influence of bad data than the CLSM,and its regression error is smaller than common Robust Regression.
In the process of quantifying harmonic pollution responsibilities,Aimed at defects problem of CLSM(Complex Least Squares Method)as well as Usual Robust Regression,Theoretical analysis and research is studied. A new method,called Robust Regression in Complex Domain,is proposed to eliminate this question. Mathematical model and equivalent circuit model of multiple harmonic sources at the same bus and different buses are established. Algorithm principle of robust regression in complex domain is theoretically derived. And the analysis of simulation is studied with IEEE 14-bus system. The results show that this method is better to waken the influence of bad data than the CLSM,and its regression error is smaller than common Robust Regression.
引文
[1]惠锦,杨洪耕,叶茂清.多谐波源条件下的谐波污染责任划分研究[J].中国电机工程学报,2011,31(13):48—54.[1] Hui Jin,Yang Honggeng,Ye Maoqing. Research on the responsibility partition of harmonic pollution of multiple harmonic sources[J]. Proceedings of the CSEE,2011,31(13):48—53.
[2]贾秀芳,华回春,曹东升,等.基于复线性最小二乘法的谐波责任定量划分[J].中国电机工程学报,2013,33(4):149—155,20.[2] Jia Xiufang,Hua Huichun,Cao Dongsheng,et al.Determining harmonic contributions based on complex least squares method[J]. Proceedings of the CSEE,2013,33(4):149—155,20.
[3]龚华麟,肖先勇,刘亚梅,等.基于主导波动量筛选原理的用户谐波发射水平估计方法[J].中国电机工程学报,2010,30(4):22—27.[3] Gong Hualin,Xiao Xianyong,Liu Yamei,et al. A method for assessing customer harmonic emission level based on the dominant fluctuation filtering principle[J].Proceedings of the CSEE,2010,30(4):22—27.
[4]车权,杨洪耕.基于稳健回归的谐波发射水平估计方法[J].中国电机工程学报,2004,24(4):39—42.[4] Che Quan,Yang Honggeng. Assessing the harmonic emission level based on robust regression method[J].Proceedings of the CSEE,2004,24(4):39—42.
[5]孙媛媛,尹志明.基于M估计稳健回归的多谐波源责任区分[J].中国电机工程学报,2012,32(31):166—173,233.[5] Sun Yuanyuan, Yin Zhiming. Quantifying harmonic responsibilities of multiple harmonic sources based on M-estimation robust regression[J]. Proceedings of the CSEE,2012,32(31):166—173,233.
[6]黄舜,徐永海.基于偏最小二乘回归的系统谐波阻抗与谐波发射水平的评估方法[J].中国电机工程学报,2007,27(1):93—97.[6] Huang Shun, Xu Yonghai. Assessing harmonic impedance and the harmonic emission level based on partial least-squares regression method[J]. Proceedings of the CSEE,2007,27(1):93—97.
[7]惠锦,杨洪耕,林顺富.基于独立随机矢量协方差特性的谐波发射水平评估方法[J].电力系统自动化,2009,33(7):27—31.[7] Hui Jin, Yang Honggeng, Lin Shunfu. Assessment method of harmonic emission level based on covariance characteristic of random vectors[J]. Automation of Electric Power Systems,2009,33(7):27—31.
[8]赵熙,杨洪耕.基于快速独立分量分析的系统侧谐波阻抗计算方法[J].电力系统自动化,2015,39(23):139—144,151.[8] Zhao Xi, Yang Honggeng. Methods of calculating system-side harmonic impedance based on FastICA[J]Automation of Electric Power Systems,2015,39(23):139—144,151.
[9]赵熙,杨洪耕.基于贝叶斯定理的系统谐波阻抗估计[J].中国电机工程学报,2016,36(11):2935—2943.[9] Zhao Xi,Yang Honggeng. Utility harmonic impedance estimation based on bayes theorem[J]. Proceedings of the CSEE,2016,36(11):2935—2943.
[10]解绍锋.基于秩次回归的系统谐波阻抗分析与谐波评估方法[J].电力自动化设备,2010,30(11):29—33.[10] Xie Shaofeng. Harmonic impedance analysis and harmonic assessment based on rank regression[J].Electric Power Automation Equipment,2010,30(11):29—33.
[11]杨洪耕,王磊.基于拉盖尔多项式的非线性负荷谐波发射水平估计[J].中国电机工程学报,2005,25(7):81—85.[11] Yang Honggeng, Wang Lei. Assessing harmonic emission levels from non-loads using Laguerre polynomials[J]. Proceedings of the CSEE,2005,25(7):81—85.
[12]张巍,杨洪耕.基于二元线性回归的谐波发射水平估计方法[J].中国电机工程学报,2004,24(6):54—57.[12] Zhang Wei,Yang Honggeng. A methods for assessing harmonic emission level based of binary linear regression[J]. Proceedings of the CSEE,2004,24(6):50—54.
[13]惠锦,杨洪耕,叶茂清.基于阻抗归一化趋势判别的谐波发射水平估计[J].中国电机工程学报,2011,31(10):73—80.[13] Hui Jin, Yang Honggeng, Ye Maoqing. Assessing harmonic emission level based on the impedance gathering thrend discrimination[J]. Proceedings of the CSEE,2011,31(13):48—53.
[14] Hamzah N, Mohamed A, Hussain A. Methods for determining utility and customer harmonic contributions at the point of common coupling[A]. Power Engineering Conference,2003[C],Bangi,Malaysia,2003,167—171.
[15] Omran W A,El-Goharey H S K,Kazerani M,et al.Identification and measurement of harmonic pollution for radial and nonradial systems[J]. IEEE Transactions on Power Delivery,2009,24(6):1642—1650.
[16]孙媛媛,李佳奇,尹志明.基于实测数据的集中式多谐波源责任评估[J].中国电机工程学报,2014,34(13):2164—2171.[16] Sun Yuanyuan,Li Jiaqi,Yin Zhiming. Quantifying harmonic impacts for concentrated multiple harmonic sources using actual data[J]. Proceedings of the CSEE,2014,34(13):2164—2171.
[17]王瑜,臧天磊,符玲,等.考虑背景谐波电压变化的多谐波源谐波责任划分[J].电力系统自动化,2015,39(18):55—61.[17] Wang Yu,Zang Tianling,Fu Ling,et al. Harmonic contribution patition of multiple harmonic sources considering background harmonic voltage fluctuation[J]. Automation of Electric Power Systems,2015,39(18):55—61.
[18]陈静,符玲,臧天磊,等.考虑背景谐波波动的谐波责任划分方法[J].电力自动化设备,2016,36(5):61—66.[18] Chen Jing,Fu Ling,Zang Tianling,et al. Harmonic contribution patition of multiple harmonic sources considering background harmonic fluctuation[J].Automation of Electric Power Systems,2016,36(5):61—66.
[19]贾秀芳,岳娜.基于岭估计方法的多谐波源责任划分[J].电力系统自动化,2015,39(21):87—92.[19] Jia Xiufang, Yue Na. Quantifying harmonic responsibilities of multiple harmonic sources based on ridge-estimation[J]. Automation of Electric Power Systems,2015,39(21):87—92.
[20]华回春,贾秀芳,曹东升,等.电能质量数据交换格式下的谐波责任估计[J].电网技术,2013,37(11):3110—3117.[20] Hua Huichun,Jia Xiufang,Cao Dongsheng,et al.Harmonic contribution estimation under power quality data interchange format[J]. Power System Technology,2013,37(11):3110—3117.
[21]何晓群,闵素芹.实用回归分析[M].北京:高等教育出版社,2014.[21] He Xiaoqun,Min Suqin. Applied regression analysis[M]. Beijing:Higher Education Press,2014.
[2]贾秀芳,华回春,曹东升,等.基于复线性最小二乘法的谐波责任定量划分[J].中国电机工程学报,2013,33(4):149—155,20.[2] Jia Xiufang,Hua Huichun,Cao Dongsheng,et al.Determining harmonic contributions based on complex least squares method[J]. Proceedings of the CSEE,2013,33(4):149—155,20.
[3]龚华麟,肖先勇,刘亚梅,等.基于主导波动量筛选原理的用户谐波发射水平估计方法[J].中国电机工程学报,2010,30(4):22—27.[3] Gong Hualin,Xiao Xianyong,Liu Yamei,et al. A method for assessing customer harmonic emission level based on the dominant fluctuation filtering principle[J].Proceedings of the CSEE,2010,30(4):22—27.
[4]车权,杨洪耕.基于稳健回归的谐波发射水平估计方法[J].中国电机工程学报,2004,24(4):39—42.[4] Che Quan,Yang Honggeng. Assessing the harmonic emission level based on robust regression method[J].Proceedings of the CSEE,2004,24(4):39—42.
[5]孙媛媛,尹志明.基于M估计稳健回归的多谐波源责任区分[J].中国电机工程学报,2012,32(31):166—173,233.[5] Sun Yuanyuan, Yin Zhiming. Quantifying harmonic responsibilities of multiple harmonic sources based on M-estimation robust regression[J]. Proceedings of the CSEE,2012,32(31):166—173,233.
[6]黄舜,徐永海.基于偏最小二乘回归的系统谐波阻抗与谐波发射水平的评估方法[J].中国电机工程学报,2007,27(1):93—97.[6] Huang Shun, Xu Yonghai. Assessing harmonic impedance and the harmonic emission level based on partial least-squares regression method[J]. Proceedings of the CSEE,2007,27(1):93—97.
[7]惠锦,杨洪耕,林顺富.基于独立随机矢量协方差特性的谐波发射水平评估方法[J].电力系统自动化,2009,33(7):27—31.[7] Hui Jin, Yang Honggeng, Lin Shunfu. Assessment method of harmonic emission level based on covariance characteristic of random vectors[J]. Automation of Electric Power Systems,2009,33(7):27—31.
[8]赵熙,杨洪耕.基于快速独立分量分析的系统侧谐波阻抗计算方法[J].电力系统自动化,2015,39(23):139—144,151.[8] Zhao Xi, Yang Honggeng. Methods of calculating system-side harmonic impedance based on FastICA[J]Automation of Electric Power Systems,2015,39(23):139—144,151.
[9]赵熙,杨洪耕.基于贝叶斯定理的系统谐波阻抗估计[J].中国电机工程学报,2016,36(11):2935—2943.[9] Zhao Xi,Yang Honggeng. Utility harmonic impedance estimation based on bayes theorem[J]. Proceedings of the CSEE,2016,36(11):2935—2943.
[10]解绍锋.基于秩次回归的系统谐波阻抗分析与谐波评估方法[J].电力自动化设备,2010,30(11):29—33.[10] Xie Shaofeng. Harmonic impedance analysis and harmonic assessment based on rank regression[J].Electric Power Automation Equipment,2010,30(11):29—33.
[11]杨洪耕,王磊.基于拉盖尔多项式的非线性负荷谐波发射水平估计[J].中国电机工程学报,2005,25(7):81—85.[11] Yang Honggeng, Wang Lei. Assessing harmonic emission levels from non-loads using Laguerre polynomials[J]. Proceedings of the CSEE,2005,25(7):81—85.
[12]张巍,杨洪耕.基于二元线性回归的谐波发射水平估计方法[J].中国电机工程学报,2004,24(6):54—57.[12] Zhang Wei,Yang Honggeng. A methods for assessing harmonic emission level based of binary linear regression[J]. Proceedings of the CSEE,2004,24(6):50—54.
[13]惠锦,杨洪耕,叶茂清.基于阻抗归一化趋势判别的谐波发射水平估计[J].中国电机工程学报,2011,31(10):73—80.[13] Hui Jin, Yang Honggeng, Ye Maoqing. Assessing harmonic emission level based on the impedance gathering thrend discrimination[J]. Proceedings of the CSEE,2011,31(13):48—53.
[14] Hamzah N, Mohamed A, Hussain A. Methods for determining utility and customer harmonic contributions at the point of common coupling[A]. Power Engineering Conference,2003[C],Bangi,Malaysia,2003,167—171.
[15] Omran W A,El-Goharey H S K,Kazerani M,et al.Identification and measurement of harmonic pollution for radial and nonradial systems[J]. IEEE Transactions on Power Delivery,2009,24(6):1642—1650.
[16]孙媛媛,李佳奇,尹志明.基于实测数据的集中式多谐波源责任评估[J].中国电机工程学报,2014,34(13):2164—2171.[16] Sun Yuanyuan,Li Jiaqi,Yin Zhiming. Quantifying harmonic impacts for concentrated multiple harmonic sources using actual data[J]. Proceedings of the CSEE,2014,34(13):2164—2171.
[17]王瑜,臧天磊,符玲,等.考虑背景谐波电压变化的多谐波源谐波责任划分[J].电力系统自动化,2015,39(18):55—61.[17] Wang Yu,Zang Tianling,Fu Ling,et al. Harmonic contribution patition of multiple harmonic sources considering background harmonic voltage fluctuation[J]. Automation of Electric Power Systems,2015,39(18):55—61.
[18]陈静,符玲,臧天磊,等.考虑背景谐波波动的谐波责任划分方法[J].电力自动化设备,2016,36(5):61—66.[18] Chen Jing,Fu Ling,Zang Tianling,et al. Harmonic contribution patition of multiple harmonic sources considering background harmonic fluctuation[J].Automation of Electric Power Systems,2016,36(5):61—66.
[19]贾秀芳,岳娜.基于岭估计方法的多谐波源责任划分[J].电力系统自动化,2015,39(21):87—92.[19] Jia Xiufang, Yue Na. Quantifying harmonic responsibilities of multiple harmonic sources based on ridge-estimation[J]. Automation of Electric Power Systems,2015,39(21):87—92.
[20]华回春,贾秀芳,曹东升,等.电能质量数据交换格式下的谐波责任估计[J].电网技术,2013,37(11):3110—3117.[20] Hua Huichun,Jia Xiufang,Cao Dongsheng,et al.Harmonic contribution estimation under power quality data interchange format[J]. Power System Technology,2013,37(11):3110—3117.
[21]何晓群,闵素芹.实用回归分析[M].北京:高等教育出版社,2014.[21] He Xiaoqun,Min Suqin. Applied regression analysis[M]. Beijing:Higher Education Press,2014.