电网畸变电流快速自适应检测方法
|
摘要
应用有源电力滤波器(Active Power Filter, APF)提高电能质量,需要获取电网相关电流分量如畸变电流或谐波,实时精确的测量有利于提高有源电力滤波器的性能。实时精确的电网畸变电流或谐波检测是电能质量控制的重要问题。
本文选择LMS (Least Mean Square)自适应算法作为电网畸变电流检测系统的核心环节进行理论与算法研究。在理论方面,阐明了基于LMS算法自适应系统的线性时变特性,分析了电网畸变电流检测系统的瞬态特性；由于迭代步长是自适应算法的关键因素之一,本文研究了自适应LMS算法的步长选择原理。通过分析基于LMS的自适应电网畸变电流检测算法的缺陷,提出了改进型LMS算法并研究其在电网畸变电流检测中的应用,这些算法包括：1)基于嵌入低通滤波器的改进型自适应畸变电流检测算法,运用低通滤波器滤去权值或误差迭代中的高频分量,提高算法稳态精度与收敛速度。分析嵌入均值滤波的aLPF-LMS算法自适应谐波检测的稳定性。2)研究了OVS-LMS与ROVS-LMS变步长算法,提高检测的稳态精度,改善了收敛速度。3)基于双LMS构成自适应组合系统,通过兼顾自适应的快速性能与稳定性能改善电网畸变电流的检测。4)通过在自适应系统输入信号环节预置带通滤波器,改善LMS算法电网畸变电流检测的稳态误差,提高检测收敛速度。研究改进LMS算法在单相谐波检测中的应用。
基于LMS算法探索三相系统畸变电流的自适应检测方法,研究了三相平衡系统与三相不平衡系统的自适应畸变电流检测问题。研究了基于瞬时无功功率理论的自适应三相电网谐波检测方法,包括改进型LMS算法自适应三相谐波检测方法与基于重采样原理的自适应三相谐波检测方法,克服了基于瞬时无功功率理论实现三相谐波检测的缺陷,提高了三相谐波检测的稳态精度与跟随性能。
本文对提出的基于LMS改进算法的单相以及三相自适应畸变电流与谐波检测方法进行了仿真验证,分析基于LMS改进算法自适应畸变电流或谐波检测的稳态精度与动态跟随性能。
最后,对改进的LPFw-LMS、LPFd-LMS、LPFwd-LMS算法进行了实验分析,测试了改进型自适应畸变电流检测算法的性能。
In APF (Active Power Filter), it is necessary to get distorted current components or harmonics in electric distribution network for suppressing distorted currents or harmonics, and real-time and accurate detection of currents can improve APF's quality. So real-time and accurate distorted current detection is an important problem in electric power quality control.
This dissertation made a selection which employs least mean square (LMS) adaptive algorithm to distorted current detection system as the key, and discussed theories and algorithms of the adaptive system. In theory, research included some characters of linearity and time-varying of the adaptive system based on LMS algorithm, and instantaneous characters of adaptive distorted current detection system. For the key facter of adaptive algorithm, this dissertation proved principle of selecting step-size to accelerate convergence based on LMS algorithm. This dissertation discussed errors and drawbacks of adaptive distorted current detection system based on LMS, and proposed methods to improve performance of distorted current detection in power system. These methods included:1) Improved adaptive distorted current detection method based on embedded low pass filter. By filtering fluctuation of weights and errors in LMS algorithm, the adaptive system can detect distorted currents timely and accurately. This dissertation analyzed stability of an LMS algorithm which adopts an average filter to eliminate fluctuation (aLPF-LMS) in harmonic detection.2) Optimal variable step-size LMS algorithm (OVS-LMS) and recursion optimal variable step-size LMS algorithm (ROVS-LMS).The algorithm can improve adaptive convergence speed reduce errors of steady state in distorted current and harmonic detection.3) Combined LMS which improves precision of distorted current detection. When keeping dynamics of detecting distorted current, the combination can reduce errors of steady state with twin-LMS.4) Employing band pass filter (BPF) to pretreate input of adaptive system based on LMS algorithm. The LMS algorithm can reduce the errors of steady state of harmonic current detection and improve convergence speed of system. This dissertation also discussed adaptive harmonic detection methods based on improved LMS algorithm.
This dissertation discussed adaptive distorted current detection methods of3-phase circuits based on LMS algorithm, and discussed distorted current detection of3-phase balance system and3-phase unbalance system. For three phase symmetrical system, this dissertation discussed harmonic detection methods based on the instantaneous reactive power theory and adaptive LMS algorithm. These methods include adaptive3-phase harmonic detection method based on improved LMS algorithm and resampling LMS algorithm, overcoming the drawback of harmonic detection based on the instantaneous reactive power theory, improving dynamic performance and reducing the steady state errors in3-phase harmonic detection.
In these studies, simulations of adaptive distorted current detection or harmonic detection methods based on modified LMS algorithms have been done by using MATLAB, dynamics and steady state errors of these algorithms have been analyzed, including3-phase circuits.
Finally, modified algorithms including LPFw-LMS, LPFd-LMS and LPFwd-LMS have been tested and verified by experiments. According to experimental results, these algorithms are proved to detect distorted current efficiently.
本文选择LMS (Least Mean Square)自适应算法作为电网畸变电流检测系统的核心环节进行理论与算法研究。在理论方面,阐明了基于LMS算法自适应系统的线性时变特性,分析了电网畸变电流检测系统的瞬态特性；由于迭代步长是自适应算法的关键因素之一,本文研究了自适应LMS算法的步长选择原理。通过分析基于LMS的自适应电网畸变电流检测算法的缺陷,提出了改进型LMS算法并研究其在电网畸变电流检测中的应用,这些算法包括：1)基于嵌入低通滤波器的改进型自适应畸变电流检测算法,运用低通滤波器滤去权值或误差迭代中的高频分量,提高算法稳态精度与收敛速度。分析嵌入均值滤波的aLPF-LMS算法自适应谐波检测的稳定性。2)研究了OVS-LMS与ROVS-LMS变步长算法,提高检测的稳态精度,改善了收敛速度。3)基于双LMS构成自适应组合系统,通过兼顾自适应的快速性能与稳定性能改善电网畸变电流的检测。4)通过在自适应系统输入信号环节预置带通滤波器,改善LMS算法电网畸变电流检测的稳态误差,提高检测收敛速度。研究改进LMS算法在单相谐波检测中的应用。
基于LMS算法探索三相系统畸变电流的自适应检测方法,研究了三相平衡系统与三相不平衡系统的自适应畸变电流检测问题。研究了基于瞬时无功功率理论的自适应三相电网谐波检测方法,包括改进型LMS算法自适应三相谐波检测方法与基于重采样原理的自适应三相谐波检测方法,克服了基于瞬时无功功率理论实现三相谐波检测的缺陷,提高了三相谐波检测的稳态精度与跟随性能。
本文对提出的基于LMS改进算法的单相以及三相自适应畸变电流与谐波检测方法进行了仿真验证,分析基于LMS改进算法自适应畸变电流或谐波检测的稳态精度与动态跟随性能。
最后,对改进的LPFw-LMS、LPFd-LMS、LPFwd-LMS算法进行了实验分析,测试了改进型自适应畸变电流检测算法的性能。
In APF (Active Power Filter), it is necessary to get distorted current components or harmonics in electric distribution network for suppressing distorted currents or harmonics, and real-time and accurate detection of currents can improve APF's quality. So real-time and accurate distorted current detection is an important problem in electric power quality control.
This dissertation made a selection which employs least mean square (LMS) adaptive algorithm to distorted current detection system as the key, and discussed theories and algorithms of the adaptive system. In theory, research included some characters of linearity and time-varying of the adaptive system based on LMS algorithm, and instantaneous characters of adaptive distorted current detection system. For the key facter of adaptive algorithm, this dissertation proved principle of selecting step-size to accelerate convergence based on LMS algorithm. This dissertation discussed errors and drawbacks of adaptive distorted current detection system based on LMS, and proposed methods to improve performance of distorted current detection in power system. These methods included:1) Improved adaptive distorted current detection method based on embedded low pass filter. By filtering fluctuation of weights and errors in LMS algorithm, the adaptive system can detect distorted currents timely and accurately. This dissertation analyzed stability of an LMS algorithm which adopts an average filter to eliminate fluctuation (aLPF-LMS) in harmonic detection.2) Optimal variable step-size LMS algorithm (OVS-LMS) and recursion optimal variable step-size LMS algorithm (ROVS-LMS).The algorithm can improve adaptive convergence speed reduce errors of steady state in distorted current and harmonic detection.3) Combined LMS which improves precision of distorted current detection. When keeping dynamics of detecting distorted current, the combination can reduce errors of steady state with twin-LMS.4) Employing band pass filter (BPF) to pretreate input of adaptive system based on LMS algorithm. The LMS algorithm can reduce the errors of steady state of harmonic current detection and improve convergence speed of system. This dissertation also discussed adaptive harmonic detection methods based on improved LMS algorithm.
This dissertation discussed adaptive distorted current detection methods of3-phase circuits based on LMS algorithm, and discussed distorted current detection of3-phase balance system and3-phase unbalance system. For three phase symmetrical system, this dissertation discussed harmonic detection methods based on the instantaneous reactive power theory and adaptive LMS algorithm. These methods include adaptive3-phase harmonic detection method based on improved LMS algorithm and resampling LMS algorithm, overcoming the drawback of harmonic detection based on the instantaneous reactive power theory, improving dynamic performance and reducing the steady state errors in3-phase harmonic detection.
In these studies, simulations of adaptive distorted current detection or harmonic detection methods based on modified LMS algorithms have been done by using MATLAB, dynamics and steady state errors of these algorithms have been analyzed, including3-phase circuits.
Finally, modified algorithms including LPFw-LMS, LPFd-LMS and LPFwd-LMS have been tested and verified by experiments. According to experimental results, these algorithms are proved to detect distorted current efficiently.
引文
[1]王兆安,杨君,刘进军.谐波抑制和无功功率补偿[M].1998,北京：机械工业出版社.
[2]罗安.电网谐波治理和无功补偿技术及装备[M].2006,北京：中国电力出版社.
[3]吴竞昌.供电系统谐波[M].1998,北京：中国电力出版社.
[4]林海雪,孙树勤.电力网中的谐波[M].1998,北京：中国电力出版社.
[5]奥本海姆.离散时间信号处理[M].2002,西安：西安交通大学出版.
[6]张贤达.现代信号处理[M].2002,北京：清华大学出版社.
[7]程佩青.数字信号处理教程[M].2001,北京：清华大学出版社.
[8]胡广书.数字信号处理[M].1997,北京：清华大学出版社.
[9]沈福民.自适应信号处理[M].2001,西安：西安电子科技大学大学出版社.
[10]B.Widrow, E.Walach自适应逆控制[M].2000,西安：西安交通大学出版.
[11]Paulo S.R.Diniz自适应滤波算法与实现[M].2004,北京：电子工业出版社.
[12]胡寿松.自动控制原理[M].2001,第四版,北京：科学出版社.
[13]郭雷,程代展,冯德兴.控制理论导论—从基本概念到研究前沿[M].2005,北京：科学出版社.
[14]Sanjit K. Mitra. Digital Signal Processing-A Compute-Based Approach[M]2001,北京：清华大学出版社.
[15]Simon Haykin. Adaptive Filter Theory(Fourth Edition) [M].2002, Beijing:Publishing House of Electronics Industry.
[16]Edward W. Kamen, Bonnie S. Heck. Fundamentals of Signals and Systems Using the Web and MATLAB (Second Edition) [M].2002, Beijing:Publishing House of Electronics Industry.
[17]高大威.电力系统谐波、无功和负序电流综合补偿的研究[D].2001,华北电力大学博士论文.
[18]李燕青,陈志业,李鹏,谢红玲.电力系统谐波抑制技术[J].华北电力大学学报,2001,28(4)：19-22.
[19]童立青,钱照明,彭方正.有源电力滤波器电路拓扑研究综述[J].电力电子技术,2009(10)：2-4.
[20]M.EI-Habrouk, M.K.Darwish, P.Mehta. Active Power Filter:A Review. IEE Proc. Electr. Power. Appl.,2000,147(5):403-413.
[21]Pigazo A., Moreno V. M., Liserre M., et al. FBD-method based controller for shunt active power filters in marine vessels[M].2008:2253-2257.
[22]胡振华,王海滨,张健毅.工业电力系统谐波分析的高精度FFT算法[J].电力系统及其自动化学报.2009(3)：46-52.
[23]李波,张林利,王广柱等.用于APF的神经网络自适应谐波电流检测方法[J].电力自动化设备,2004,24(5)：38-40.
[24]付青,罗安,王莉娜.基于自适应智能控制的混合有源电力滤波器复合控制[J].中国电机工程学报,2005,25(14)：46-5.
[25]盘宏斌,罗安,唐杰等.一种改进的基于最小二乘法的自适应谐波检测方法[J].中国电机工程学报,2008,28(13)：144-151.
[26]王群,周洛维,吴宁.一种基于神经网络的自适应谐波电流检测方法[J].重庆大学学报(自然科学版),1997,5(20)：6-11.
[27]王群,吴宁,王兆安.神经元自适应谐波电流检测系统的仿真研究[J].西安交通大学学报,1999,2(3)：1-5.
[28]于群,谢品芳,吴宁等.模拟电路实现的神经元自适应谐波电流检测方法[J].中国电机工程学报,1999,19(6)：42-46.
[29]Qun Wang, Ning Wu, Zhaoan Wang. A Neuron Adaptive Detecting Approach of Harmonic Current for APF and Its Realization of Analog Circuit[J]. IEEE TRANSACTION ON POWER DELIVERY,2001,2(50):77-84.
[30]Raymond H. Kwong, Edward W. Johnston. A variable step size LMS algorithm[J]. IEEE Transactions on signal processing,1992,40(7):1633-1642.
[31]谷源涛.LMS算法收敛性能研究及应用[D].2003.4,清华大学博士学位论文.
[32]S. Luo, Z. Hou. An adaptive detecting method for harmonic and reactive currents[J]. IEEE Trans. On industrial Electronics,1995,42(1):85-89.
[33]K.Mayyas, F.Momani. An LMS adaptive algoritm with a new step-size control equation[J]. Joural of the Franklin Institute,2011,348(1):589-605.
[34]T.Aboulnasr, K.Mayyas. A robust variable step-size LMS-type algorithm analysis and simulations[J]. IEEE Trans. Signal Processing,1997,45(3):631-639.
[35]Houshang Karimi, Masound Karimi-Ghartrmani, M.Reza Iravani, etc. An Adaptive Filter for Synchronous Extraction of Harmonics and Distortions [J]. IEEE TRANSACTION ON POWER DELIVERY,2003,10(8):1350-1356.
[36]Fei Liu,Yunping Zou,Kai Ding, A novel real-time algorithm for harmonic detecting[M]. Industrial Electronics Society,2003. IECON '03, The 29th Annual Conference of the IEEE, 2003,3(2-6):2561-2565.
[37]李圣清,彭玉楼,周有庆.一种改进型自适应谐波电流检测方法的研究[J].高电压技术,2002,12(28)：3-5.
[38]王群,姚为正,王兆安.高通和低通滤波器对谐波检测电路检测效果的影响研究[J].电工技术学报,1999,14(5)：22-26.
[39]王群,姚为正,王兆安.低通滤波器对谐波检测电路的影响[J].西安交通大学学报,1999,4(33)：5-8.
[40]Shengkui Zhao, Zhihong Man, Suiyang Khoo, Hong Ren Wu. Variable step-size LMS algorithm with a quotient form[J]. Signal Processing,2009,89:67-76.
[41]覃景繁,欧阳景正.一种新的变步长LMS自适应滤波算法[J].数据采集与处理.1997,12(3)：171-174.
[42]包明，王云亮.改进的变步长自适应谐波检测算法[J].电力自动化设备,2011,31(1)：71-74.
[43]王置.基于自适应神经网络的畸变电流检测方法[D].2004,武汉大学硕士毕业论文.
[44]曹建光.基于自适应神经网络的畸变电流检测方法研究[D].2004,武汉大学硕士毕业论文.
[45]刘开培,张俊敏.基于DFT的瞬时谐波检测方法[J].电力自动化设备.2003,23(3)：8-10.
[46]刘传林,刘开培.电力有源滤波器中对指定整数次谐波的DFT算法[J].电测与仪表,2005,42(1)：4-7.
[47]G.Manchur, C.C.Erven. Development of a model for predicting filter from electric arc furnaces[J]. IEEE Trans.on Power Delivery,1992,7(1):416-420.
[48]P.Enjeti,S.A. Choudhury. A new control strategy to improve the performance of a PWM AC to DC converter under unbalanced operating conditions[M].1991 IEEE Industry Application Society Annual Meeting:382-389.
[49]Mukul Rastogi, Rajendra Naik, Ned Mohan. A comparative evaluation of harmonic reduction techniques[J].1994,30(5):1149-1155.
[50]Luis Moran, Phoivs D.Ziogas,Geza joos. Design aspects of synchronous PWM rectifier-inverter systems under unbalanced input voltage conditions[J]. IEEE Transaction on Industry Application,1992,28(6):1286-1293.
[51]P.D.Ziogas, L.Moran,G.Joos, D.Vincenti. A refined PWM scheme for voltage and current source converters[M].1990 IEEE Industry Application Society Annual Meeting:977-983.
[52]Phoivas D.Ziogas,Eduardo P.Wiechmanm,Victor R.Stefanovic. A computer analysis and design approach for static voltage source inverters[J]. IEEE Trans, on IA,1985, 21(5):1234-1241.
[53]Luo Shiguo,Hou Zhengcheng. An adaptive detecting method for harmonic and reactive current[J]. IEEE Trans on Industrial Electronics,1995,42(1):85-89.
[54]Dxion J W, Garcia J J,Moran L. Control system for three-phase active power filter which simultaneously compensates power factor and unbalanced loads[J]. IEEE Trans on Industrial Electronics,1995,42(6):636-641.
[55]王兆安,李民,卓放.三相电路瞬时无功功率理论的研究[J].电工技术学报,1992,7(3)：55-59.
[56]刘进军,刘波,王兆安.基于瞬时无功功率理论的串联混合型单相电力有源滤波器[J].中国电机工程学报,1997,17(1)：37-41.
[57]蒋兵,颜钢峰,赵光宇.单相电路瞬时谐波及无功电流实时检测新方法[J].电力系统自动化,2000,(10)：35-38.
[58]杨君,王兆安.三相电路谐波电流两种检测方法的对比研究[J].电工技术学报,1995,2：43-48.
[59]黄玲,刘骥,曹滨,朱东柏.基于瞬时无功功率理论的谐波电流检测法[J].哈尔滨工业大学学报,2001,6(4)：104-106.
[60]戴朝波,林海雪,雷林绪.两种谐波电流检测方法的比较[J].中国电机工程学报,2002,1(22)：80-84.
[61]陶骏,刘正之.谐波及无功电流检测方法的研究[J].电力系统自动化,2001,25(1)：31-33.
[62]刘开培,张俊敏,陈艳慧.基于重采样的三相谐波检测瞬时无功功率法[J].电力系统自动化,2003,27(12)：45-47.
[63]刘开培,张俊敏,宣扬.基于重采样和均值滤波的三相电路谐波检测方法[J].中国电机工程学报,2003,23(9)：78-82.
[64]Liu Kaipei, Zhang Junmin, Xuan Yang. Hamonics detection for three-phase circuits based on resampling theory and mean filtering [M]. Proceedings of the CSEE,2003,23(9):78-82.
[65]高大威,孙孝瑞.基于自适应线性神经网络的三相畸变电流检测方法及实现[J].中国电机工程学报,2001,21(3)：50-53.
[66]汤赐,罗安,舒适等.基于瞬时无功理论的谐波检测方法及其实现技术[J].变流技术与电力牵引,2007(4)：1-5.
[67]郑征,杜翠静,常万仓.三相不对称系统中谐波电流检测的新方法[J].电力系统及其自动化学报,2010(3)：50-54.
[68]H. M. John, C. G. Tim. The predictive transient-following control of shunt and series active power filter[J]. IEEE Tran. Power Electronics,2002,17 (4):574-584.
[69]Akagi H, Kanazawa, A. Nabae. Generalized theory of instantaneous reactive power in three-phase circuits[M]. IEEE & JIEE. Proceeding IPEC. Tokyo:IEEE,1983:1375-1386.
[70]Akagi H, Kanazawa Y, Nabae A. Instantaneous reactive power compensator comprising switching devices without energy storage components[J]. IEEE Trans on IA,1984,20(3): 625-630.
[71]H. Akagi, Y. Kanazawa, A. Nabae. Instantaneous reactive power compensators comprising switching devices without energy storage components[J]. IEEE Trans. Ind. Applicat.,1984, 20(3):625-633.
[72]A. Nabae, T. Tanaka. A new definition of approach of instantaneous active-reactive current and power based on instantaneous space vectors on polar coordinates in three-phase circuits[J]. IEEE Trans. Power De-livery,1996,11:625-633.
[73]H. Akagi. New trends in active filters for power conditioning[J]. IEEE Trans. Ind. Applicat., 1996,32:1312-1322.
[74]F. Z. Peng, J.S. Lai. Generalized instantaneous reactive power theory for three-phase power systems[J]. IEEE Trans. Instrumentation and Measurement,1996,45(1):293-297.
[75]Neil J. Bershad, Jose Carlos, M. Bermudez, Jean-Yves Tourneret. An Affine Combination of Two LMS Adaptive Filters-Transient Mean-Square Analysis[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING,2008,56(5):1853-1864.
[76]N.J. Bershad, J.C. M. Bermudez, J.-Y. Tourneret. On Performance Bounds for an Affine Combination of Two LMS Adaptive filters[M]. IEEE ICASSP 2008:3297-3300.
[77]Magno T. M. Silva, Vitor H. Nascimento. Convex combination of adaptive filters with different tracking capabilities. IEEE ICASSP 2007.
[78]T.Dai, B.Shahrrava, X.Chen. A variable step-size affine projection algorithm with a weighted projection matrix[M].IEEE Canadian Conference (CCECE),2005:320-323.
[79]Gitlin R D, Weinstein S B. On the design of gradient algorithms for digitally implemented adaptive filtere[J]. IEEE Trens on CT,1973,(2):125-136.
[80]Yasukaws H, Shimads S. Furukraws, and et al.. Acoustic echo conceller with high speech quality[M].ICASSP'87:2125-2128.
[81]Gitlin R D, Weinsitein S B.The effects of large interference on the tracking capability of digitally implemented echo cancellers[J]. IEEE Trans on COM,1978,(6):833-839.
[82]Clark C A, Mitra S K, Parker S R. Block implementation of adaptive digital filters [J]. IEEE Trans on AS-SP,1981(3):744-752.
[83]Liu Kaipei, Zhang Junmin, Harmonic Detection Based on the TLS Estimation Algorithm[M]. IEEE IPEMC 2006.
[84]Zhao Shengkui, Man Zhihong, Khoo Suiyang. Modified LMS and NLMS Algorithms with a New Variable Step Size[M]. IEEE ICARCV 2006. Control, Automation, Robotics and Vision, 2006. ICARCV'06.9th International Conference on.
[85]Zhao Shengkui, Man Zhihong, Khoo Suiyang. A Fast Variable Step-Size LMS Algorithm with System Identification.2007, Second IEEE Conference on Industrial Electronics and Applications,2340-2345.
[86]Z. Ramadan, A. Poularikas, Performance analysis of a new variable step-size LMS algorithm with error nonlinearities[M]. Proc. of the 36th IEEE Southeastern Symposium on System Theory (SSST),2004:384-388.
[87]Z. Ramadan, A. Poularikas. A variable step-size adaptive noise canceller using signal to noise ratio as the controlling factor[M]. Proc. of the 36th IEEE Southeastern Symposium on System Theory (SSST),2004:456-461.
[88]R. H. Kwong, E. W. Johnston. A variable step-size LMS algorithm[J]. IEEE Trans. Signal Procesing,1992,40:1633-1642.
[89]Dong-Wook Kim, Han-Bit Kang, Myoung-Su Eun, Jong-Soo Choi. A variable step-size algorithm using normalized absolute estimation error[M]. IEEE Proceedings of the 38th Midwest Symposium on Circuits and Systems,1995,2:979-982.
[90]T. Aboulnasr, K. Mayyas. A robust variable step-size LMS-type algorithm:Analysis and simulations[J].IEEE Transactions on Signal Processing,1997,45(3):631-639.
[91]W. A. Harrison, J. S. Lim, E. Singer. A new application of adaptive noise cancellation, IEEE Trans. Acoust., Speech, Signal, Signal Processing,1986,34(1):21-27.
[92]Scott. C. Douglas, Teresa H.-Y. Meng. Normalized data nonlinearities for LMS adaptation[J]. IEEE Trans. On Signal Processing,1994,42(6):1352-1365.
[93]B. Farhang-Boroujeny. On statistical efficiency of the LMS algorithm in system modeling[J]. IEEE Trans. Signal Process,1993,41:1947-1951.
[94]S. Ikeda, A. Sugiyama. An adaptive noise canceller with low signal distortion for speech codecs[J]. IEEE Trans, on Signal Processing,1999,47(3):665-674.
[95]J. E. Greenberg.Modified LMS algorithms for speech processing with an adaptive noise canceller[J]. IEEE Trans. On Speech and Audio Processing,1998,6(4):338-358.
[96]GAO Ying, XIE Sheng-li. A variable step size LMS adaptive filtering algorithm and its analyses[M]. ACTA Electronica Sinica,2001:1094-1097.
[97]Junmin Zhang, Kaipei Liu. Harmonic detection for three-phase circuit based on the improved analog LMS algorithm[M]. Electrical Machines and Systems, ICEMS 2008. International Conference on,2008:3978-3982.
[98]何娜.电力系统谐波检测及有源抑制技术的研究[D].2008,哈尔滨工业大学.
[99]杨建宁,陈婕,关佳军,李自成.一种改进变步长的自适应谐波检测算法[J].电力系统保护与控制,2011,39(6)：40-52.
[100]TA1420系列立式穿芯小型精密交流电流互感器[EB/OL].2008,北京.
[101]TA1005系列母线内置式微型精密交流电流互感器[EB/OL].2008,北京.
[2]罗安.电网谐波治理和无功补偿技术及装备[M].2006,北京：中国电力出版社.
[3]吴竞昌.供电系统谐波[M].1998,北京：中国电力出版社.
[4]林海雪,孙树勤.电力网中的谐波[M].1998,北京：中国电力出版社.
[5]奥本海姆.离散时间信号处理[M].2002,西安：西安交通大学出版.
[6]张贤达.现代信号处理[M].2002,北京：清华大学出版社.
[7]程佩青.数字信号处理教程[M].2001,北京：清华大学出版社.
[8]胡广书.数字信号处理[M].1997,北京：清华大学出版社.
[9]沈福民.自适应信号处理[M].2001,西安：西安电子科技大学大学出版社.
[10]B.Widrow, E.Walach自适应逆控制[M].2000,西安：西安交通大学出版.
[11]Paulo S.R.Diniz自适应滤波算法与实现[M].2004,北京：电子工业出版社.
[12]胡寿松.自动控制原理[M].2001,第四版,北京：科学出版社.
[13]郭雷,程代展,冯德兴.控制理论导论—从基本概念到研究前沿[M].2005,北京：科学出版社.
[14]Sanjit K. Mitra. Digital Signal Processing-A Compute-Based Approach[M]2001,北京：清华大学出版社.
[15]Simon Haykin. Adaptive Filter Theory(Fourth Edition) [M].2002, Beijing:Publishing House of Electronics Industry.
[16]Edward W. Kamen, Bonnie S. Heck. Fundamentals of Signals and Systems Using the Web and MATLAB (Second Edition) [M].2002, Beijing:Publishing House of Electronics Industry.
[17]高大威.电力系统谐波、无功和负序电流综合补偿的研究[D].2001,华北电力大学博士论文.
[18]李燕青,陈志业,李鹏,谢红玲.电力系统谐波抑制技术[J].华北电力大学学报,2001,28(4)：19-22.
[19]童立青,钱照明,彭方正.有源电力滤波器电路拓扑研究综述[J].电力电子技术,2009(10)：2-4.
[20]M.EI-Habrouk, M.K.Darwish, P.Mehta. Active Power Filter:A Review. IEE Proc. Electr. Power. Appl.,2000,147(5):403-413.
[21]Pigazo A., Moreno V. M., Liserre M., et al. FBD-method based controller for shunt active power filters in marine vessels[M].2008:2253-2257.
[22]胡振华,王海滨,张健毅.工业电力系统谐波分析的高精度FFT算法[J].电力系统及其自动化学报.2009(3)：46-52.
[23]李波,张林利,王广柱等.用于APF的神经网络自适应谐波电流检测方法[J].电力自动化设备,2004,24(5)：38-40.
[24]付青,罗安,王莉娜.基于自适应智能控制的混合有源电力滤波器复合控制[J].中国电机工程学报,2005,25(14)：46-5.
[25]盘宏斌,罗安,唐杰等.一种改进的基于最小二乘法的自适应谐波检测方法[J].中国电机工程学报,2008,28(13)：144-151.
[26]王群,周洛维,吴宁.一种基于神经网络的自适应谐波电流检测方法[J].重庆大学学报(自然科学版),1997,5(20)：6-11.
[27]王群,吴宁,王兆安.神经元自适应谐波电流检测系统的仿真研究[J].西安交通大学学报,1999,2(3)：1-5.
[28]于群,谢品芳,吴宁等.模拟电路实现的神经元自适应谐波电流检测方法[J].中国电机工程学报,1999,19(6)：42-46.
[29]Qun Wang, Ning Wu, Zhaoan Wang. A Neuron Adaptive Detecting Approach of Harmonic Current for APF and Its Realization of Analog Circuit[J]. IEEE TRANSACTION ON POWER DELIVERY,2001,2(50):77-84.
[30]Raymond H. Kwong, Edward W. Johnston. A variable step size LMS algorithm[J]. IEEE Transactions on signal processing,1992,40(7):1633-1642.
[31]谷源涛.LMS算法收敛性能研究及应用[D].2003.4,清华大学博士学位论文.
[32]S. Luo, Z. Hou. An adaptive detecting method for harmonic and reactive currents[J]. IEEE Trans. On industrial Electronics,1995,42(1):85-89.
[33]K.Mayyas, F.Momani. An LMS adaptive algoritm with a new step-size control equation[J]. Joural of the Franklin Institute,2011,348(1):589-605.
[34]T.Aboulnasr, K.Mayyas. A robust variable step-size LMS-type algorithm analysis and simulations[J]. IEEE Trans. Signal Processing,1997,45(3):631-639.
[35]Houshang Karimi, Masound Karimi-Ghartrmani, M.Reza Iravani, etc. An Adaptive Filter for Synchronous Extraction of Harmonics and Distortions [J]. IEEE TRANSACTION ON POWER DELIVERY,2003,10(8):1350-1356.
[36]Fei Liu,Yunping Zou,Kai Ding, A novel real-time algorithm for harmonic detecting[M]. Industrial Electronics Society,2003. IECON '03, The 29th Annual Conference of the IEEE, 2003,3(2-6):2561-2565.
[37]李圣清,彭玉楼,周有庆.一种改进型自适应谐波电流检测方法的研究[J].高电压技术,2002,12(28)：3-5.
[38]王群,姚为正,王兆安.高通和低通滤波器对谐波检测电路检测效果的影响研究[J].电工技术学报,1999,14(5)：22-26.
[39]王群,姚为正,王兆安.低通滤波器对谐波检测电路的影响[J].西安交通大学学报,1999,4(33)：5-8.
[40]Shengkui Zhao, Zhihong Man, Suiyang Khoo, Hong Ren Wu. Variable step-size LMS algorithm with a quotient form[J]. Signal Processing,2009,89:67-76.
[41]覃景繁,欧阳景正.一种新的变步长LMS自适应滤波算法[J].数据采集与处理.1997,12(3)：171-174.
[42]包明，王云亮.改进的变步长自适应谐波检测算法[J].电力自动化设备,2011,31(1)：71-74.
[43]王置.基于自适应神经网络的畸变电流检测方法[D].2004,武汉大学硕士毕业论文.
[44]曹建光.基于自适应神经网络的畸变电流检测方法研究[D].2004,武汉大学硕士毕业论文.
[45]刘开培,张俊敏.基于DFT的瞬时谐波检测方法[J].电力自动化设备.2003,23(3)：8-10.
[46]刘传林,刘开培.电力有源滤波器中对指定整数次谐波的DFT算法[J].电测与仪表,2005,42(1)：4-7.
[47]G.Manchur, C.C.Erven. Development of a model for predicting filter from electric arc furnaces[J]. IEEE Trans.on Power Delivery,1992,7(1):416-420.
[48]P.Enjeti,S.A. Choudhury. A new control strategy to improve the performance of a PWM AC to DC converter under unbalanced operating conditions[M].1991 IEEE Industry Application Society Annual Meeting:382-389.
[49]Mukul Rastogi, Rajendra Naik, Ned Mohan. A comparative evaluation of harmonic reduction techniques[J].1994,30(5):1149-1155.
[50]Luis Moran, Phoivs D.Ziogas,Geza joos. Design aspects of synchronous PWM rectifier-inverter systems under unbalanced input voltage conditions[J]. IEEE Transaction on Industry Application,1992,28(6):1286-1293.
[51]P.D.Ziogas, L.Moran,G.Joos, D.Vincenti. A refined PWM scheme for voltage and current source converters[M].1990 IEEE Industry Application Society Annual Meeting:977-983.
[52]Phoivas D.Ziogas,Eduardo P.Wiechmanm,Victor R.Stefanovic. A computer analysis and design approach for static voltage source inverters[J]. IEEE Trans, on IA,1985, 21(5):1234-1241.
[53]Luo Shiguo,Hou Zhengcheng. An adaptive detecting method for harmonic and reactive current[J]. IEEE Trans on Industrial Electronics,1995,42(1):85-89.
[54]Dxion J W, Garcia J J,Moran L. Control system for three-phase active power filter which simultaneously compensates power factor and unbalanced loads[J]. IEEE Trans on Industrial Electronics,1995,42(6):636-641.
[55]王兆安,李民,卓放.三相电路瞬时无功功率理论的研究[J].电工技术学报,1992,7(3)：55-59.
[56]刘进军,刘波,王兆安.基于瞬时无功功率理论的串联混合型单相电力有源滤波器[J].中国电机工程学报,1997,17(1)：37-41.
[57]蒋兵,颜钢峰,赵光宇.单相电路瞬时谐波及无功电流实时检测新方法[J].电力系统自动化,2000,(10)：35-38.
[58]杨君,王兆安.三相电路谐波电流两种检测方法的对比研究[J].电工技术学报,1995,2：43-48.
[59]黄玲,刘骥,曹滨,朱东柏.基于瞬时无功功率理论的谐波电流检测法[J].哈尔滨工业大学学报,2001,6(4)：104-106.
[60]戴朝波,林海雪,雷林绪.两种谐波电流检测方法的比较[J].中国电机工程学报,2002,1(22)：80-84.
[61]陶骏,刘正之.谐波及无功电流检测方法的研究[J].电力系统自动化,2001,25(1)：31-33.
[62]刘开培,张俊敏,陈艳慧.基于重采样的三相谐波检测瞬时无功功率法[J].电力系统自动化,2003,27(12)：45-47.
[63]刘开培,张俊敏,宣扬.基于重采样和均值滤波的三相电路谐波检测方法[J].中国电机工程学报,2003,23(9)：78-82.
[64]Liu Kaipei, Zhang Junmin, Xuan Yang. Hamonics detection for three-phase circuits based on resampling theory and mean filtering [M]. Proceedings of the CSEE,2003,23(9):78-82.
[65]高大威,孙孝瑞.基于自适应线性神经网络的三相畸变电流检测方法及实现[J].中国电机工程学报,2001,21(3)：50-53.
[66]汤赐,罗安,舒适等.基于瞬时无功理论的谐波检测方法及其实现技术[J].变流技术与电力牵引,2007(4)：1-5.
[67]郑征,杜翠静,常万仓.三相不对称系统中谐波电流检测的新方法[J].电力系统及其自动化学报,2010(3)：50-54.
[68]H. M. John, C. G. Tim. The predictive transient-following control of shunt and series active power filter[J]. IEEE Tran. Power Electronics,2002,17 (4):574-584.
[69]Akagi H, Kanazawa, A. Nabae. Generalized theory of instantaneous reactive power in three-phase circuits[M]. IEEE & JIEE. Proceeding IPEC. Tokyo:IEEE,1983:1375-1386.
[70]Akagi H, Kanazawa Y, Nabae A. Instantaneous reactive power compensator comprising switching devices without energy storage components[J]. IEEE Trans on IA,1984,20(3): 625-630.
[71]H. Akagi, Y. Kanazawa, A. Nabae. Instantaneous reactive power compensators comprising switching devices without energy storage components[J]. IEEE Trans. Ind. Applicat.,1984, 20(3):625-633.
[72]A. Nabae, T. Tanaka. A new definition of approach of instantaneous active-reactive current and power based on instantaneous space vectors on polar coordinates in three-phase circuits[J]. IEEE Trans. Power De-livery,1996,11:625-633.
[73]H. Akagi. New trends in active filters for power conditioning[J]. IEEE Trans. Ind. Applicat., 1996,32:1312-1322.
[74]F. Z. Peng, J.S. Lai. Generalized instantaneous reactive power theory for three-phase power systems[J]. IEEE Trans. Instrumentation and Measurement,1996,45(1):293-297.
[75]Neil J. Bershad, Jose Carlos, M. Bermudez, Jean-Yves Tourneret. An Affine Combination of Two LMS Adaptive Filters-Transient Mean-Square Analysis[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING,2008,56(5):1853-1864.
[76]N.J. Bershad, J.C. M. Bermudez, J.-Y. Tourneret. On Performance Bounds for an Affine Combination of Two LMS Adaptive filters[M]. IEEE ICASSP 2008:3297-3300.
[77]Magno T. M. Silva, Vitor H. Nascimento. Convex combination of adaptive filters with different tracking capabilities. IEEE ICASSP 2007.
[78]T.Dai, B.Shahrrava, X.Chen. A variable step-size affine projection algorithm with a weighted projection matrix[M].IEEE Canadian Conference (CCECE),2005:320-323.
[79]Gitlin R D, Weinstein S B. On the design of gradient algorithms for digitally implemented adaptive filtere[J]. IEEE Trens on CT,1973,(2):125-136.
[80]Yasukaws H, Shimads S. Furukraws, and et al.. Acoustic echo conceller with high speech quality[M].ICASSP'87:2125-2128.
[81]Gitlin R D, Weinsitein S B.The effects of large interference on the tracking capability of digitally implemented echo cancellers[J]. IEEE Trans on COM,1978,(6):833-839.
[82]Clark C A, Mitra S K, Parker S R. Block implementation of adaptive digital filters [J]. IEEE Trans on AS-SP,1981(3):744-752.
[83]Liu Kaipei, Zhang Junmin, Harmonic Detection Based on the TLS Estimation Algorithm[M]. IEEE IPEMC 2006.
[84]Zhao Shengkui, Man Zhihong, Khoo Suiyang. Modified LMS and NLMS Algorithms with a New Variable Step Size[M]. IEEE ICARCV 2006. Control, Automation, Robotics and Vision, 2006. ICARCV'06.9th International Conference on.
[85]Zhao Shengkui, Man Zhihong, Khoo Suiyang. A Fast Variable Step-Size LMS Algorithm with System Identification.2007, Second IEEE Conference on Industrial Electronics and Applications,2340-2345.
[86]Z. Ramadan, A. Poularikas, Performance analysis of a new variable step-size LMS algorithm with error nonlinearities[M]. Proc. of the 36th IEEE Southeastern Symposium on System Theory (SSST),2004:384-388.
[87]Z. Ramadan, A. Poularikas. A variable step-size adaptive noise canceller using signal to noise ratio as the controlling factor[M]. Proc. of the 36th IEEE Southeastern Symposium on System Theory (SSST),2004:456-461.
[88]R. H. Kwong, E. W. Johnston. A variable step-size LMS algorithm[J]. IEEE Trans. Signal Procesing,1992,40:1633-1642.
[89]Dong-Wook Kim, Han-Bit Kang, Myoung-Su Eun, Jong-Soo Choi. A variable step-size algorithm using normalized absolute estimation error[M]. IEEE Proceedings of the 38th Midwest Symposium on Circuits and Systems,1995,2:979-982.
[90]T. Aboulnasr, K. Mayyas. A robust variable step-size LMS-type algorithm:Analysis and simulations[J].IEEE Transactions on Signal Processing,1997,45(3):631-639.
[91]W. A. Harrison, J. S. Lim, E. Singer. A new application of adaptive noise cancellation, IEEE Trans. Acoust., Speech, Signal, Signal Processing,1986,34(1):21-27.
[92]Scott. C. Douglas, Teresa H.-Y. Meng. Normalized data nonlinearities for LMS adaptation[J]. IEEE Trans. On Signal Processing,1994,42(6):1352-1365.
[93]B. Farhang-Boroujeny. On statistical efficiency of the LMS algorithm in system modeling[J]. IEEE Trans. Signal Process,1993,41:1947-1951.
[94]S. Ikeda, A. Sugiyama. An adaptive noise canceller with low signal distortion for speech codecs[J]. IEEE Trans, on Signal Processing,1999,47(3):665-674.
[95]J. E. Greenberg.Modified LMS algorithms for speech processing with an adaptive noise canceller[J]. IEEE Trans. On Speech and Audio Processing,1998,6(4):338-358.
[96]GAO Ying, XIE Sheng-li. A variable step size LMS adaptive filtering algorithm and its analyses[M]. ACTA Electronica Sinica,2001:1094-1097.
[97]Junmin Zhang, Kaipei Liu. Harmonic detection for three-phase circuit based on the improved analog LMS algorithm[M]. Electrical Machines and Systems, ICEMS 2008. International Conference on,2008:3978-3982.
[98]何娜.电力系统谐波检测及有源抑制技术的研究[D].2008,哈尔滨工业大学.
[99]杨建宁,陈婕,关佳军,李自成.一种改进变步长的自适应谐波检测算法[J].电力系统保护与控制,2011,39(6)：40-52.
[100]TA1420系列立式穿芯小型精密交流电流互感器[EB/OL].2008,北京.
[101]TA1005系列母线内置式微型精密交流电流互感器[EB/OL].2008,北京.