高压局部放电定位模型转换求解与改进K-means聚类优化方法
|
摘要
非线性定位方程组的求解是变压器局部放电(PD)定位技术的重要手段。针对目前非线性定位方程组求解时出现的迭代算法的选择困难、迭代不收敛、运算时间长、对到时误差敏感等问题,提出了局部放电定位模型转换求解与改进K-means聚类优化方法,建立多超声波传感器定位模型。首先通过消除非线性定位方程组的二阶项,将非线性方程组转换为线性方程组,从而避免了求解方程组对迭代算法选择的依赖,运算时间短,不会出现迭代不收敛。当传感器数量大于6个时,一次测量并求解得到多样本初值,最后采用改进的K-means聚类算法对样本初值进行聚类优化,确定最优的PD源坐标,有效解决了因到时误差导致定位结果较差的难题。仿真与模拟实验表明,当到时误差小于0.03 ms时,定位误差为3.07 cm。
The solution of nonlinear location equations is an important means of transformer partial discharge location technology. At present, there are many problems in solving nonlinear location equations, such as the difficulty of selection of iterative algorithm, the non-convergence of iteration, the long calculation time and the sensitivity to arrival error. Based on this, a partial discharge location model conversion solution and an improved K-means cluster optimization method were proposed, and a multi-ultrasonic sensor location model was established. Firstly, by eliminating the second-order terms of nonlinear location equations, they are transformed into linear equations, thus avoiding the dependence of solving equations on the selection of iterative algorithms. In this way, the calculation time is short and the iteration does not converge. When the number of sensors is more than 6, the initial values of multiple samples are obtained. Finally, the improved K-means clustering algorithm is used to cluster and optimize the initial value of the samples, to determine the optimal PD source coordinates, which effectively solves the problem of poor location result due to the arrival time error. The simulation experiments show that the location error is 3.07 cm when the arrival time error is less than 0.03 ms.
The solution of nonlinear location equations is an important means of transformer partial discharge location technology. At present, there are many problems in solving nonlinear location equations, such as the difficulty of selection of iterative algorithm, the non-convergence of iteration, the long calculation time and the sensitivity to arrival error. Based on this, a partial discharge location model conversion solution and an improved K-means cluster optimization method were proposed, and a multi-ultrasonic sensor location model was established. Firstly, by eliminating the second-order terms of nonlinear location equations, they are transformed into linear equations, thus avoiding the dependence of solving equations on the selection of iterative algorithms. In this way, the calculation time is short and the iteration does not converge. When the number of sensors is more than 6, the initial values of multiple samples are obtained. Finally, the improved K-means clustering algorithm is used to cluster and optimize the initial value of the samples, to determine the optimal PD source coordinates, which effectively solves the problem of poor location result due to the arrival time error. The simulation experiments show that the location error is 3.07 cm when the arrival time error is less than 0.03 ms.
引文
[1] MONTANARI G C, CAVALLINI A. Partial discharge diagnostics: From apparatus monitoring to smart grid assessment[J]. IEEE Electrical Insulation Magazine, 2013, 29(3):8-17.
[2] WU M, CAO H, CAO J, et al. An overview of state-of-the-art partial discharge analysis techniques for condition monitoring[J]. IEEE Electrical Insulation Magazine, 2015, 31(6):22-35.
[3] 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.TANG J, ZHANG X X, ZENG F P. UHF Detection and Fault Diagnosis of Partial Discharge in Combined Electrical Equipment[M]. Beijing: Science Press, 2016.
[4] COENEN S, TENBOHLEN S.Location of PD sources in power transformers by UHF and acoustic measurements[J].IEEE Transactions on Dielectrics and Electrical Insulation,2012,19(6):1934-1940.
[5] XIE Q,LIU X,ZHANG CH,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.
[6] 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 H H, LI J SH, JI H Y, 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.
[7] 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 R J, YAN J M, YANG L J, et al. Characteristics of partial discharge-caused surface damage for oil-impregnated insulation paper[J]. Proceedings of the CSEE, 2011, 31(10): 129-137.
[8] 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 F H, ZHOU X, GAO P, 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.
[9] 刘克民, 韩克俊, 李军,等. 局部放电光学检测技术研究进展[J]. 电子测量技术, 2015, 38(1):100-103.LIU K M, HAN K J, LI J, et al. Research progress of partial discharge detection on optical methods[J]. Electronic Measurement Technology, 2015, 38(1):100-103.
[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(28):13-17.XIE Q, LI Y Q, LV F CH, et al. Method for PD location in oil combining ultrasonic phased array with wideband array signal processing[J]. Proceedings of the CSEE, 2009(28):13-17.
[11] 程述一, 律方成, 谢庆,等. 基于暂态对地电压和超声阵列信号的变压器局放定位方法[J]. 电工技术学报, 2012, 27(4):255-262.CHENG SH Y, LV F CH, XIE Q, et al. Study of partial discharge locating method in transformer based on transient earth voltage and ultrasonic array signals[J]. Transactions of China Electrotechnical Society, 2012, 27(4):255-262.
[12] 律方成, 谢庆. 电气设备局部放电超声阵列定位[M]. 北京:中国电力出版社, 2016.LV F CH, XIE Q. Partial Discharge Ultrasonic Array Positioning of Electrical Equipment[M]. Beijing: China Electric Power Press, 2016.
[13] 李昕, 罗更生, 龙盛蓉,等. 钢板声发射时间反转聚焦增强定位方法[J]. 仪器仪表学报, 2016, 37(8):1792-1799.LI X, LUO G SH, LONG SH R, et al. Location method of acoustic emission by time reversal focusing and enhancing for steel plate[J]. Chinese Journal of Scientific Instrument, 2016, 37(8):1792-1799.
[14] 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 J, WANG C CH, CHEN J, et al. Taylor-genetic algorithm using for PD location in power transformer[J]. Transactions of China Electrotechnical Society, 2010, 25(7):165-171.
[15] 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 H J, SHENG G H, MIAO P Q, et al. Partial discharge location based on radio frequency antenna array in substation[J]. High Voltage Engineering, 2012, 38(6):1334-1340.
[16] 刘化龙, 胡钋. 序列二次规划-遗传算法及其在变压器局部放电超声定位中的应用[J]. 电网技术, 2015, 39(1):130-135.LIU H L, HU P. Sequential quadratic programming-genetic algorithm and its application in ultrasonic localization of partial discharge in power transformers[J]. Power System Technology, 2015, 39(1):130-135.
[17] MARKALOUS S M, TENBOHLEN S, FESER K. Detection and location of partial discharges in power transformers using acoustic and electromagnetic signals[J]. IEEE Transactions on Dielectrics & Electrical Insulation, 2008, 15(6):1576-1583.
[18] 郑书生, 李成榕, 周冰. 用于变压器局部放电定位的复数域牛顿迭代算法[J]. 高电压技术, 2011, 37(8):2017-2023.ZHENG SH SH, LI CH R, ZHOU B. Newton’s method in complex field for locating partial discharge in transformers[J]. High Voltage Engineering, 2011, 37(8):2017-2023.
[19] DONG L J, SHU W W, LI X B, et al. Three dimensional comprehensive analytical solutions for locating sources of sensor networks in unknown velocity mining system[J]. IEEE Access, 2017, 5(99):11337-11351.
[20] 董陇军, 李夕兵, 马举,等. 未知波速系统中声发射与微震震源三维解析综合定位方法及工程应用[J]. 岩石力学与工程学报, 2017, 36(1):186-197.DONG L J, LI X B, MA J, et al. Three-dimensional analytical comprehensive solutions for acoustic emission/microseismic sources of unknown velocity system[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(1):186-197.
[21] 张姝, 杨健维, 何正友,等. 基于线路暂态重心频率的配电网故障区段定位[J]. 中国电机工程学报, 2015, 35(10):2463-2470.ZHANG SH, YANG J W, HE ZH Y, et al. Fault section location of the distribution network based on transient center frequency[J]. Proceedings of the CSEE, 2015, 35(10):2463-2470.
[22] 蔡娟, 李东新. 基于优化K均值建模的运动目标检测算法[J]. 国外电子测量技术, 2016, 35(12):20-23.CAI J, LI D X. Movingtarget detection algorithm based on K-means optimized modeling[J]. Foreign Electronic Measurement Technology, 2016, 35(12):20-23.
[23] 孙云亭, 蔡振江, 程曼,等. 多超声波传感器局部放电源定位方法的研究[J]. 电子测量与仪器学报, 2016, 30(3):416-422.SUN Y T, CAI ZH J, CHENG M, et al. Research on partial discharge source localization method of multi-ultrasonic-sensor[J]. Journal of Electronic Measurement and Instrumentation, 2016, 30(3):416-422.
[24] 李亚, 刘丽平, 李柏青,等. 基于改进K-means聚类和BP神经网络的台区线损率计算方法[J]. 中国电机工程学报, 2016, 36(17):4543-4551.LI Y, LIU L P, LI B Q, et al. Calculation of line loss rate in transformer district based on improved K-means clustering algorithm and BP neural network[J]. Proceedings of the CSEE, 2016, 36(17):4543-4551.
[25] 张淑美, 王福利, 谭帅,等. 多模态过程的全自动离线模态识别方法[J]. 自动化学报, 2016, 42(1):60-80.ZHANG SH M, WANG F L, TAN SH, et al. A fully automatic offline mode Identification method for multi-mode processes[J]. Acta Automatica Sinica, 2016, 42(1):60-80.
[26] 唐炬, 黄亮, 曾福平,等. 一种多样本信息的局部放电源逐次逼近定位方法[J]. 电工技术学报, 2016, 31(10):119-126.TANG J, HUANG L, ZENG F P, et al. A positioning approach based on successive approximation of multi-samples for partial discharge source[J]. Transactions of China Electrotechnical Society, 2016, 31(10):119-126.
[27] 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 SH SH, LI CH R, HE M. 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.
[2] WU M, CAO H, CAO J, et al. An overview of state-of-the-art partial discharge analysis techniques for condition monitoring[J]. IEEE Electrical Insulation Magazine, 2015, 31(6):22-35.
[3] 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.TANG J, ZHANG X X, ZENG F P. UHF Detection and Fault Diagnosis of Partial Discharge in Combined Electrical Equipment[M]. Beijing: Science Press, 2016.
[4] COENEN S, TENBOHLEN S.Location of PD sources in power transformers by UHF and acoustic measurements[J].IEEE Transactions on Dielectrics and Electrical Insulation,2012,19(6):1934-1940.
[5] XIE Q,LIU X,ZHANG CH,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.
[6] 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 H H, LI J SH, JI H Y, 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.
[7] 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 R J, YAN J M, YANG L J, et al. Characteristics of partial discharge-caused surface damage for oil-impregnated insulation paper[J]. Proceedings of the CSEE, 2011, 31(10): 129-137.
[8] 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 F H, ZHOU X, GAO P, 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.
[9] 刘克民, 韩克俊, 李军,等. 局部放电光学检测技术研究进展[J]. 电子测量技术, 2015, 38(1):100-103.LIU K M, HAN K J, LI J, et al. Research progress of partial discharge detection on optical methods[J]. Electronic Measurement Technology, 2015, 38(1):100-103.
[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(28):13-17.XIE Q, LI Y Q, LV F CH, et al. Method for PD location in oil combining ultrasonic phased array with wideband array signal processing[J]. Proceedings of the CSEE, 2009(28):13-17.
[11] 程述一, 律方成, 谢庆,等. 基于暂态对地电压和超声阵列信号的变压器局放定位方法[J]. 电工技术学报, 2012, 27(4):255-262.CHENG SH Y, LV F CH, XIE Q, et al. Study of partial discharge locating method in transformer based on transient earth voltage and ultrasonic array signals[J]. Transactions of China Electrotechnical Society, 2012, 27(4):255-262.
[12] 律方成, 谢庆. 电气设备局部放电超声阵列定位[M]. 北京:中国电力出版社, 2016.LV F CH, XIE Q. Partial Discharge Ultrasonic Array Positioning of Electrical Equipment[M]. Beijing: China Electric Power Press, 2016.
[13] 李昕, 罗更生, 龙盛蓉,等. 钢板声发射时间反转聚焦增强定位方法[J]. 仪器仪表学报, 2016, 37(8):1792-1799.LI X, LUO G SH, LONG SH R, et al. Location method of acoustic emission by time reversal focusing and enhancing for steel plate[J]. Chinese Journal of Scientific Instrument, 2016, 37(8):1792-1799.
[14] 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 J, WANG C CH, CHEN J, et al. Taylor-genetic algorithm using for PD location in power transformer[J]. Transactions of China Electrotechnical Society, 2010, 25(7):165-171.
[15] 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 H J, SHENG G H, MIAO P Q, et al. Partial discharge location based on radio frequency antenna array in substation[J]. High Voltage Engineering, 2012, 38(6):1334-1340.
[16] 刘化龙, 胡钋. 序列二次规划-遗传算法及其在变压器局部放电超声定位中的应用[J]. 电网技术, 2015, 39(1):130-135.LIU H L, HU P. Sequential quadratic programming-genetic algorithm and its application in ultrasonic localization of partial discharge in power transformers[J]. Power System Technology, 2015, 39(1):130-135.
[17] MARKALOUS S M, TENBOHLEN S, FESER K. Detection and location of partial discharges in power transformers using acoustic and electromagnetic signals[J]. IEEE Transactions on Dielectrics & Electrical Insulation, 2008, 15(6):1576-1583.
[18] 郑书生, 李成榕, 周冰. 用于变压器局部放电定位的复数域牛顿迭代算法[J]. 高电压技术, 2011, 37(8):2017-2023.ZHENG SH SH, LI CH R, ZHOU B. Newton’s method in complex field for locating partial discharge in transformers[J]. High Voltage Engineering, 2011, 37(8):2017-2023.
[19] DONG L J, SHU W W, LI X B, et al. Three dimensional comprehensive analytical solutions for locating sources of sensor networks in unknown velocity mining system[J]. IEEE Access, 2017, 5(99):11337-11351.
[20] 董陇军, 李夕兵, 马举,等. 未知波速系统中声发射与微震震源三维解析综合定位方法及工程应用[J]. 岩石力学与工程学报, 2017, 36(1):186-197.DONG L J, LI X B, MA J, et al. Three-dimensional analytical comprehensive solutions for acoustic emission/microseismic sources of unknown velocity system[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(1):186-197.
[21] 张姝, 杨健维, 何正友,等. 基于线路暂态重心频率的配电网故障区段定位[J]. 中国电机工程学报, 2015, 35(10):2463-2470.ZHANG SH, YANG J W, HE ZH Y, et al. Fault section location of the distribution network based on transient center frequency[J]. Proceedings of the CSEE, 2015, 35(10):2463-2470.
[22] 蔡娟, 李东新. 基于优化K均值建模的运动目标检测算法[J]. 国外电子测量技术, 2016, 35(12):20-23.CAI J, LI D X. Movingtarget detection algorithm based on K-means optimized modeling[J]. Foreign Electronic Measurement Technology, 2016, 35(12):20-23.
[23] 孙云亭, 蔡振江, 程曼,等. 多超声波传感器局部放电源定位方法的研究[J]. 电子测量与仪器学报, 2016, 30(3):416-422.SUN Y T, CAI ZH J, CHENG M, et al. Research on partial discharge source localization method of multi-ultrasonic-sensor[J]. Journal of Electronic Measurement and Instrumentation, 2016, 30(3):416-422.
[24] 李亚, 刘丽平, 李柏青,等. 基于改进K-means聚类和BP神经网络的台区线损率计算方法[J]. 中国电机工程学报, 2016, 36(17):4543-4551.LI Y, LIU L P, LI B Q, et al. Calculation of line loss rate in transformer district based on improved K-means clustering algorithm and BP neural network[J]. Proceedings of the CSEE, 2016, 36(17):4543-4551.
[25] 张淑美, 王福利, 谭帅,等. 多模态过程的全自动离线模态识别方法[J]. 自动化学报, 2016, 42(1):60-80.ZHANG SH M, WANG F L, TAN SH, et al. A fully automatic offline mode Identification method for multi-mode processes[J]. Acta Automatica Sinica, 2016, 42(1):60-80.
[26] 唐炬, 黄亮, 曾福平,等. 一种多样本信息的局部放电源逐次逼近定位方法[J]. 电工技术学报, 2016, 31(10):119-126.TANG J, HUANG L, ZENG F P, et al. A positioning approach based on successive approximation of multi-samples for partial discharge source[J]. Transactions of China Electrotechnical Society, 2016, 31(10):119-126.
[27] 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 SH SH, LI CH R, HE M. 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.