基于正则化的变电站局部放电定位方法
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摘要
基于特高频传感器阵列的变电站局部放电检测与定位方法得到应用,但获取多传感器到达时间差不可避免地存在误差,导致非线性定位方程组的解误差较大。提出基于正则化的变电站局部放电定位方法,为避免直接求解非线性定位方程组导致定位误差大、计算复杂等问题,通过消除二阶项,将非线性定位方程组转换为线性定位方程组。针对由传感器安装位置可能引起线性定位方程组存在病态问题,通过中心化法和平衡法对方程组处理,降低了方程组病态程度,用L曲线法计算正则化参数,最后使用Tikhonov正则化方法求解线性定位方程组,确定局部放电源坐标。仿真与模拟实验表明,到达时间差误差为3%～5%时,定位误差为1.58m;到达时间差误差为7%～10%时,定位误差为3.07m。在一定时间差误差下,正则化方法能够提高局部放电定位精度,实现变电站局部放电的精确定位。
The detection and location of partial discharge(PD) using ultra-high frequency(UHF) sensor array was applied in substations. However, the error of obtaining the time of arrival of multi-sensors is inevitable, which leads to a large error in solving the nonlinear location equations. In this paper,a PD location method in substations based on regularization was proposed. In order to avoid solving the nonlinear location equations directly, which leads to large location error and complex calculation, the nonlinear location equations were transformed into the linear location equations by eliminating the second order terms. As for the morbid problem of the linear location equations caused by the sensor installation position,the equations were processed by the centralization method and the balance method to reduce the morbidity of the equations.The regularization parameters were calculated by the L-curve method. Finally, the linear location equations were solved by using the Tikhonov regularization method to determine the coordinates of the PD source. Simulations and simulation experiments show that the location error is 1.58 m when the time-difference error is 3%～5%, and the location error is 3.07 m when the time-difference error is 7%～10%. The regularization method can improve the precision of partial discharge location and realize the accurate location of partial discharge in substations under certain time difference errors.
The detection and location of partial discharge(PD) using ultra-high frequency(UHF) sensor array was applied in substations. However, the error of obtaining the time of arrival of multi-sensors is inevitable, which leads to a large error in solving the nonlinear location equations. In this paper,a PD location method in substations based on regularization was proposed. In order to avoid solving the nonlinear location equations directly, which leads to large location error and complex calculation, the nonlinear location equations were transformed into the linear location equations by eliminating the second order terms. As for the morbid problem of the linear location equations caused by the sensor installation position,the equations were processed by the centralization method and the balance method to reduce the morbidity of the equations.The regularization parameters were calculated by the L-curve method. Finally, the linear location equations were solved by using the Tikhonov regularization method to determine the coordinates of the PD source. Simulations and simulation experiments show that the location error is 1.58 m when the time-difference error is 3%～5%, and the location error is 3.07 m when the time-difference error is 7%～10%. The regularization method can improve the precision of partial discharge location and realize the accurate location of partial discharge in substations under certain time difference errors.
引文
[1]郑书生,李成榕,何梦.变压器局部放电复数域牛顿迭代-网格搜索定位方法[J].中国电机工程学报,2013,33(9):155-161.Zheng Shusheng,Li Chengrong,He Meng.A novel method of Newton iteration in complex field and lattice search for locating partial discharges in transformers[J].Proceedings of the CSEE,2013,33(9):155-161(in Chinese).
[2]唐炬,张晓星,曾福平.组合电器设备局部放电特高频检测与故障诊断[M].北京:科学出版社,2016:6-9.Tang Ju,Zhang Xiaoxing,Zeng Fuping.UHF detection and fault diagnosis of partial discharge in combined electrical equipment[M].Beijing:Science Press,2016:6-9(in Chinese).
[3]Coenen S,Tenbohlen S.Location of PD sources in power transformers by UHF and acoustic measurements[J].IEEETransactions on Dielectrics and Electrical Insulation,2012,19(6):1934-1940.
[4]Xie Qing,Liu Xiong,Zhang Cheng,et al.Aging characteristics on epoxy resin surface under repetitive microsecond pulses in air at atmospheric pressure[J].Plasma Science and Technology,2016,18(3):325-330.
[5]辛晓虎,李继胜,纪海英,等.用于变压器中局部放电定位的十字形超声阵列传感器研究[J].中国电机工程学报,2013,33(21):154-162.Xin Xiaohu,Li Jisheng,Ji Haiying,et al.Study of cross-shaped ultrasonic array senor applied to partial discharge location in transformers[J].Proceedings of the CSEE,2013,33(21):154-162(in Chinese).
[6]廖瑞金,严家明,杨丽君,等.局部放电对油浸绝缘纸表面损伤特性研究[J].中国电机工程学报,2011,31(10):129-137.Liao Ruijin,Yan Jiaming,Yang Lijun,et al.Characteristics of partial discharge-caused surface damage for oil-impregnated insulation paper[J].Proceedings of the CSEE,2011,31(10):129-137(in Chinese).
[7]王丰华,周翔,高沛,等.基于绕组热分布的改进油浸式变压器绕组热点温度计算模型[J].高电压技术,2015,41(3):895-901.Wang Fenghua,Zhou Xiang,Gao Pei,et al.Improved thermal circuit model of hot spot temperature in oil-immersed transformers based on heat distribution of winding[J].High Voltage Engineering,2015,41(3):895-901(in Chinese).
[8]聂德鑫,王明渊,周远翔,等.操作冲击电压下油纸针板缺陷局部放电研究[J].高电压技术,2015,41(3):918-924.Nie Dexin,Wang Mingyuan,Zhou Yuanxiang,et al.Research on partial discharge of oil-paper insulation needle-plate electrode under switching pulse voltage[J].High Voltage Engineering,2015,41(3):918-924(in Chinese).
[9]姚陈果,周电波,陈攀,等.采用超高频法监测变电站设备局放水平及其早期预警[J].高电压技术,2011,37(7):1670-1676.Yao Cheguo,Zhou Dianbo,Chen Pan,et al.UHF-based Monitoring for equipment PD within the substation and early warning[J].High Voltage Engineering,2011,37(7):1670-1676(in Chinese).
[10]谢庆,李燕青,律方成,等.超声相控阵与宽带阵列信号处理相结合的油中局部放电定位方法[J].中国电机工程学报,2009,29(28):13-17.Xie Qing,Li Yanqing,LüFangcheng,et al.Method for PD location in oil combining ultrasonic phased array with wideband array signal processing[J].Proceedings of the CSEE,2009,29(28):13-17(in Chinese).
[11]侯慧娟,盛戈皞,苗培青,等.基于超高频电磁波的变电站局部放电空间定位[J].高电压技术,2012,38(6):1334-1340.Hou Huijuan,Sheng Gehao,Miao Peiqing,et al.Partial discharge location based on radio frequency antenna array in substation[J].High Voltage Engineering,2012,38(6):1334-1340(in Chinese).
[12]Moore P J,Portugues I E,Glover I A.Partial discharge investigation of a power transformer using wireless wideband radio-frequency measurements[J].IEEETransactions on Power Delivery,2006,21(1):528-530.
[13]Portugues I E,Moore P J,Glover I A,et al.RF-based partial discharge early warning system for air-insulated substations[J].IEEE Transactions on Power Delivery,2008,24(1):20-29.
[14]胡岳,王红斌,汤林,等.基于UHF天线阵列的变电站局部放电全站监测研究与实践[J].电工技术学报,2014(s1):502-509.Hu Yue,Wang Hongbin,Tang Lin,et al.Research and practice of partial discharge online monitoring and locating for substation using UHF sensor array[J].Transactions of China Electrotechnical Society,2014(s1):502-509(in Chinese).
[15]张冠军,朱明晓,王彦博,等.基于可移动特高频天线阵列的变电站站域放电源检测与定位研究[J].中国电机工程学报,2017,37(10):2761-2773.Zhang Guanjun,Zhu Mingxiao,Wang Yanbo,et al.Detection and localization of discharge sources in substation area using movable UHF antenna array[J].Proceedings of the CSEE,2017,37(10):2761-2773(in Chinese).
[16]唐炬,王存超,陈娇,等.变压器局部放电的泰勒-遗传综合定位法[J].电工技术学报,2010,25(7):165-171.Tang Ju,Wang Cunchao,Chen Jiao,et al.Taylor-genetic algorithm using for pd location in power transformer[J].Transactions of China Electrotechnical Society,2010,25(7):165-171(in Chinese).
[17]侯慧娟,盛戈皞,白万建,等.基于电磁波阵列信号处理和波达方向分析的变电站局部放电定位[J].高电压技术,2013,39(11):2692-2698.Hou Huijuan,Sheng Gehao,Bai Wanjian,et al.Partial discharge location in substation based on electromagnetic array signal processing and direction of arrival[J].High Voltage Engineering,2013,39(11):2692-2698(in Chinese).
[18]朱晓临.数值分析[M].2版.合肥:中国科学技术大学出版社,2014:66-67.Zhu Xiaolin.Numerical analysis[M].2nd Edition.Hefei:Press of University of Science and Technology of China,2014:66-67(in Chinese).
[19]何晓群,闵素芹.实用回归分析[M].2版.北京:高等教育出版社,2014:81-82.He Xiaoqun,Min Suqin.Practical regression analysis[M].2nd Edition.Beijing:Higher Education Press,2014:81-82(in Chinese).
[20]蔡锁章,杨明,雷英杰.数值计算方法[M].2版.北京:国防工业出版社,2016:59-60.Cai Suozhang,Yang Ming,Lei Yingjie.Numerical calculation method[M].2nd Edition.Beijing:National Defense Industry Press,2016:59-60(in Chinese).
[21]程久龙,宋广东,刘统玉,等.煤矿井下微震震源高精度定位研究[J].地球物理学报,2016,59(12):4513-4520.Cheng Jiulon,Song Guangdong,Liu Tongyu,et al.High precision location of micro-seismic sources in underground coal mine[J].Chinese Journal of Geophysics,2016,59(12):4513-4520(in Chinese).
[22]王堃,王广军,陈红,等.稳态传热边界温度分布的正则化共轭梯度反演[J].中国电机工程学报,2013,33(17):78-82.Wang Kun,Wang Guangjun,Chen Hong,et al.Regularization conjugate gradient inverse for the temperature distribution of steady-state heat transfer boundary[J].Proceedings of the CSEE,2013,33(17):78-82(in Chinese).
[23]Tikhonov A N,Arsenin V Y.Solutions of ill-posed problems[M].Washington:Halsted Press,1977:99-101.
[24]Eldén L.Algorithms for the regularization of ill-conditioned least squares problems[J].BIT,1977,17(2):134-145.
[25]Hansen P C.The L-curve and its use in the numerical treatment of inverse problems[J].Annals of the Association of American Geographers,2000,55:1-315.
[26]夏超男.基于L曲线的正则化参数选取研究[D].广州:暨南大学,2016.Xia Chaonan.Study on regularization parameter choiceBased on the L-curve[D].Guangzhou:Jinan University,2016(in Chinese).
[27]唐炬,陈娇,张晓星,等.用于局部放电信号定位的多样本能量相关搜索提取时间差算法[J].中国电机工程学报,2009,29(19):125-130.Tang Ju,Chen Jiao,Zhang Xiaoxing,et al.Time difference algorithm based on energy relevant search of multi-sample applied in PD location[J].Proceedings of the CSEE,2009,29(19):125-130(in Chinese).
[28]Hou H,Sheng G,Jiang X.Localization algorithm for the PD source in substation based on L-shaped antenna array signal processing[J].IEEE Transactions on Power Delivery,2015,30(1):472-479.
[2]唐炬,张晓星,曾福平.组合电器设备局部放电特高频检测与故障诊断[M].北京:科学出版社,2016:6-9.Tang Ju,Zhang Xiaoxing,Zeng Fuping.UHF detection and fault diagnosis of partial discharge in combined electrical equipment[M].Beijing:Science Press,2016:6-9(in Chinese).
[3]Coenen S,Tenbohlen S.Location of PD sources in power transformers by UHF and acoustic measurements[J].IEEETransactions on Dielectrics and Electrical Insulation,2012,19(6):1934-1940.
[4]Xie Qing,Liu Xiong,Zhang Cheng,et al.Aging characteristics on epoxy resin surface under repetitive microsecond pulses in air at atmospheric pressure[J].Plasma Science and Technology,2016,18(3):325-330.
[5]辛晓虎,李继胜,纪海英,等.用于变压器中局部放电定位的十字形超声阵列传感器研究[J].中国电机工程学报,2013,33(21):154-162.Xin Xiaohu,Li Jisheng,Ji Haiying,et al.Study of cross-shaped ultrasonic array senor applied to partial discharge location in transformers[J].Proceedings of the CSEE,2013,33(21):154-162(in Chinese).
[6]廖瑞金,严家明,杨丽君,等.局部放电对油浸绝缘纸表面损伤特性研究[J].中国电机工程学报,2011,31(10):129-137.Liao Ruijin,Yan Jiaming,Yang Lijun,et al.Characteristics of partial discharge-caused surface damage for oil-impregnated insulation paper[J].Proceedings of the CSEE,2011,31(10):129-137(in Chinese).
[7]王丰华,周翔,高沛,等.基于绕组热分布的改进油浸式变压器绕组热点温度计算模型[J].高电压技术,2015,41(3):895-901.Wang Fenghua,Zhou Xiang,Gao Pei,et al.Improved thermal circuit model of hot spot temperature in oil-immersed transformers based on heat distribution of winding[J].High Voltage Engineering,2015,41(3):895-901(in Chinese).
[8]聂德鑫,王明渊,周远翔,等.操作冲击电压下油纸针板缺陷局部放电研究[J].高电压技术,2015,41(3):918-924.Nie Dexin,Wang Mingyuan,Zhou Yuanxiang,et al.Research on partial discharge of oil-paper insulation needle-plate electrode under switching pulse voltage[J].High Voltage Engineering,2015,41(3):918-924(in Chinese).
[9]姚陈果,周电波,陈攀,等.采用超高频法监测变电站设备局放水平及其早期预警[J].高电压技术,2011,37(7):1670-1676.Yao Cheguo,Zhou Dianbo,Chen Pan,et al.UHF-based Monitoring for equipment PD within the substation and early warning[J].High Voltage Engineering,2011,37(7):1670-1676(in Chinese).
[10]谢庆,李燕青,律方成,等.超声相控阵与宽带阵列信号处理相结合的油中局部放电定位方法[J].中国电机工程学报,2009,29(28):13-17.Xie Qing,Li Yanqing,LüFangcheng,et al.Method for PD location in oil combining ultrasonic phased array with wideband array signal processing[J].Proceedings of the CSEE,2009,29(28):13-17(in Chinese).
[11]侯慧娟,盛戈皞,苗培青,等.基于超高频电磁波的变电站局部放电空间定位[J].高电压技术,2012,38(6):1334-1340.Hou Huijuan,Sheng Gehao,Miao Peiqing,et al.Partial discharge location based on radio frequency antenna array in substation[J].High Voltage Engineering,2012,38(6):1334-1340(in Chinese).
[12]Moore P J,Portugues I E,Glover I A.Partial discharge investigation of a power transformer using wireless wideband radio-frequency measurements[J].IEEETransactions on Power Delivery,2006,21(1):528-530.
[13]Portugues I E,Moore P J,Glover I A,et al.RF-based partial discharge early warning system for air-insulated substations[J].IEEE Transactions on Power Delivery,2008,24(1):20-29.
[14]胡岳,王红斌,汤林,等.基于UHF天线阵列的变电站局部放电全站监测研究与实践[J].电工技术学报,2014(s1):502-509.Hu Yue,Wang Hongbin,Tang Lin,et al.Research and practice of partial discharge online monitoring and locating for substation using UHF sensor array[J].Transactions of China Electrotechnical Society,2014(s1):502-509(in Chinese).
[15]张冠军,朱明晓,王彦博,等.基于可移动特高频天线阵列的变电站站域放电源检测与定位研究[J].中国电机工程学报,2017,37(10):2761-2773.Zhang Guanjun,Zhu Mingxiao,Wang Yanbo,et al.Detection and localization of discharge sources in substation area using movable UHF antenna array[J].Proceedings of the CSEE,2017,37(10):2761-2773(in Chinese).
[16]唐炬,王存超,陈娇,等.变压器局部放电的泰勒-遗传综合定位法[J].电工技术学报,2010,25(7):165-171.Tang Ju,Wang Cunchao,Chen Jiao,et al.Taylor-genetic algorithm using for pd location in power transformer[J].Transactions of China Electrotechnical Society,2010,25(7):165-171(in Chinese).
[17]侯慧娟,盛戈皞,白万建,等.基于电磁波阵列信号处理和波达方向分析的变电站局部放电定位[J].高电压技术,2013,39(11):2692-2698.Hou Huijuan,Sheng Gehao,Bai Wanjian,et al.Partial discharge location in substation based on electromagnetic array signal processing and direction of arrival[J].High Voltage Engineering,2013,39(11):2692-2698(in Chinese).
[18]朱晓临.数值分析[M].2版.合肥:中国科学技术大学出版社,2014:66-67.Zhu Xiaolin.Numerical analysis[M].2nd Edition.Hefei:Press of University of Science and Technology of China,2014:66-67(in Chinese).
[19]何晓群,闵素芹.实用回归分析[M].2版.北京:高等教育出版社,2014:81-82.He Xiaoqun,Min Suqin.Practical regression analysis[M].2nd Edition.Beijing:Higher Education Press,2014:81-82(in Chinese).
[20]蔡锁章,杨明,雷英杰.数值计算方法[M].2版.北京:国防工业出版社,2016:59-60.Cai Suozhang,Yang Ming,Lei Yingjie.Numerical calculation method[M].2nd Edition.Beijing:National Defense Industry Press,2016:59-60(in Chinese).
[21]程久龙,宋广东,刘统玉,等.煤矿井下微震震源高精度定位研究[J].地球物理学报,2016,59(12):4513-4520.Cheng Jiulon,Song Guangdong,Liu Tongyu,et al.High precision location of micro-seismic sources in underground coal mine[J].Chinese Journal of Geophysics,2016,59(12):4513-4520(in Chinese).
[22]王堃,王广军,陈红,等.稳态传热边界温度分布的正则化共轭梯度反演[J].中国电机工程学报,2013,33(17):78-82.Wang Kun,Wang Guangjun,Chen Hong,et al.Regularization conjugate gradient inverse for the temperature distribution of steady-state heat transfer boundary[J].Proceedings of the CSEE,2013,33(17):78-82(in Chinese).
[23]Tikhonov A N,Arsenin V Y.Solutions of ill-posed problems[M].Washington:Halsted Press,1977:99-101.
[24]Eldén L.Algorithms for the regularization of ill-conditioned least squares problems[J].BIT,1977,17(2):134-145.
[25]Hansen P C.The L-curve and its use in the numerical treatment of inverse problems[J].Annals of the Association of American Geographers,2000,55:1-315.
[26]夏超男.基于L曲线的正则化参数选取研究[D].广州:暨南大学,2016.Xia Chaonan.Study on regularization parameter choiceBased on the L-curve[D].Guangzhou:Jinan University,2016(in Chinese).
[27]唐炬,陈娇,张晓星,等.用于局部放电信号定位的多样本能量相关搜索提取时间差算法[J].中国电机工程学报,2009,29(19):125-130.Tang Ju,Chen Jiao,Zhang Xiaoxing,et al.Time difference algorithm based on energy relevant search of multi-sample applied in PD location[J].Proceedings of the CSEE,2009,29(19):125-130(in Chinese).
[28]Hou H,Sheng G,Jiang X.Localization algorithm for the PD source in substation based on L-shaped antenna array signal processing[J].IEEE Transactions on Power Delivery,2015,30(1):472-479.