谐波电能计量改进FFT算法研究
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摘要
非线性负荷特别是电力电子设备在电力系统中的广泛应用,导致电网谐波污染日益严重,使电能质量严重恶化,影响了用户的正常工作。实现电力谐波的精确分析和谐波电能的准确计量,可为电能的科学管理提供可靠依据。
快速傅立叶变换(FFT)因其易于嵌入式系统实现而被作为电力谐波分析的主要方法,但在电力谐波分析时很难做到同步采样和整数周期截断,由此造成的频谱泄漏将影响到谐波分析的结果。通过加窗以及采用插值修正算法可以改善计算谐波频率、相位和幅值的准确度。
针对已有算法在插值算法的实现、修正公式的求解及计算精度等方面存在的不足,本文提出了基于Nuttall窗双谱线插值FFT的电力谐波分析方法,探讨了基波频率、采样频率、截断信号的数据长度对谐波分析方法的精度的影响。用曲线拟合函数对算法中复杂的表达式进行曲线拟合,求出实用而简单的逼近公式,大大减少了计算量。进一步探讨了基于Nuttall窗双谱线插值FFT的谐波电能计量方法。仿真结果表明,在非同步采样和非整数周期截断条件下,本文提出的电力谐波分析方法具有很高的精确度。
针对电力行业谐波电能计量的迫切需求,提出了AD73360L+ADSP-BF533+M30624FGPFP的三相多功能谐波电能表构成方案,简述了电能表的工作原理,详细介绍了六路同步采样ADC的数据采集电路和以ADSP-BF533为核心的数据处理电路设计,给出了基于Nuttall窗双谱线插值FFT的谐波电能计量的软件流程,探讨了谐波电能计量的比差、角差校正方法。检测结果表明,基于本文方法研制的三相多功能谐波电能表的基波有功测量误差≤0.2%,基波无功测量误差≤1%,2-21次谐波电压测量误差≤2%、谐波电流测量误差≤5%、谐波相位测量误差≤5°,满足GB/T-14549-93的A类谐波测量仪器要求。
仿真实验和工程应用表明,本文提出的基于Nuttall窗双谱线插值FFT的电力谐波分析方法是可行的,能很好地抑制频谱泄漏和栅栏效应引起的误差,能实现电力谐波的精确分析和谐波电能的准确计量。
Nonlinear loads,such as electric and electronic equipments, are widely applied in power system, power harmonic pollution is becoming increasingly serious. Serious deterioration in the quality of power is affecting the user's normal work. The precise analysis and accurate measurement of harmonic energy can provide a reliable scientific basis for the power management.
The fast Fourier transform (FFT) has already become a main method of the electrical harmonic analysis since it’s easily realized in embedded system, but there are difficulties in performing synchronized sampling and integral period truncation in the electric power harmonic analysis, and the accuracy of analysis result will be disturbed by the frequency leakage. The window functions and interpolation algorithms are utilized to correct the measured frequency, phase and amplitude by FFT.
In order to overcome some shortcomings of existing methods in realizing the interpolation algorithm, in this paper, an approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT is presented. The effects of harmonic analysis precision brought by the fundamental frequency, sampling frequency and the the data length of truncation are dicussed. The applicable rectification formulas of the double-spectrum-line interpolation is obtained by using polynomial curve fit functions, and subsequently calculating burden is dramatically reduced. Further, the harmonic energy measurement method based on the Nuttall window double-spectrum-line interpolation FFT is discussed. The simulation results show that, under the non-synchronized sampling and non-integral period truncation conditions, the electricity harmonic analysis method proposed in this paper has very high accuracy.
To meet the urgent demand of electric power industry on harmonic energy measurement, a kind of three-phase multi-functional harmonic energy meter structure composed by AD73360L+ADSP-BF533+M30624FGPFP is presented. The operating principle of electric energy meter is described. The data acquisition circuit of six-channel synchronous-sampling A/D converter and the data processing circuit with the core of ADSP-BF533 are introduced in detail. Software process of the harmonic energy measurement method based on the Nuttall window double-spectrum-line interpolation FFT is proposed. Correction method of ratio error and phase error of harmonic energy measurement is discussed. Test results show that, three-phase multi-functional harmonic energy meter based on the algorithm proposed in this paper has its error of fundamental active power measurement lower than 0.2%, error of fundamental reactive power measurement lower than 1%, amplitude error of harmonic electric voltage lower than 2%, phase error of harmonic electric current lower than 5%, and phase angle error between harmonic voltage and electric current lower than 5°. Above data results meet the accuracy requirement of the A class harmonic measurement instruments according to GB/T-14549-93.
Simulation and engineering applications show that, the proposed approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT is feasible, which can inhibit errors caused by the spectral leakage and fence, and is able to achieve the precise harmonic analysis and harmonic energy accurate measurement.
快速傅立叶变换(FFT)因其易于嵌入式系统实现而被作为电力谐波分析的主要方法,但在电力谐波分析时很难做到同步采样和整数周期截断,由此造成的频谱泄漏将影响到谐波分析的结果。通过加窗以及采用插值修正算法可以改善计算谐波频率、相位和幅值的准确度。
针对已有算法在插值算法的实现、修正公式的求解及计算精度等方面存在的不足,本文提出了基于Nuttall窗双谱线插值FFT的电力谐波分析方法,探讨了基波频率、采样频率、截断信号的数据长度对谐波分析方法的精度的影响。用曲线拟合函数对算法中复杂的表达式进行曲线拟合,求出实用而简单的逼近公式,大大减少了计算量。进一步探讨了基于Nuttall窗双谱线插值FFT的谐波电能计量方法。仿真结果表明,在非同步采样和非整数周期截断条件下,本文提出的电力谐波分析方法具有很高的精确度。
针对电力行业谐波电能计量的迫切需求,提出了AD73360L+ADSP-BF533+M30624FGPFP的三相多功能谐波电能表构成方案,简述了电能表的工作原理,详细介绍了六路同步采样ADC的数据采集电路和以ADSP-BF533为核心的数据处理电路设计,给出了基于Nuttall窗双谱线插值FFT的谐波电能计量的软件流程,探讨了谐波电能计量的比差、角差校正方法。检测结果表明,基于本文方法研制的三相多功能谐波电能表的基波有功测量误差≤0.2%,基波无功测量误差≤1%,2-21次谐波电压测量误差≤2%、谐波电流测量误差≤5%、谐波相位测量误差≤5°,满足GB/T-14549-93的A类谐波测量仪器要求。
仿真实验和工程应用表明,本文提出的基于Nuttall窗双谱线插值FFT的电力谐波分析方法是可行的,能很好地抑制频谱泄漏和栅栏效应引起的误差,能实现电力谐波的精确分析和谐波电能的准确计量。
Nonlinear loads,such as electric and electronic equipments, are widely applied in power system, power harmonic pollution is becoming increasingly serious. Serious deterioration in the quality of power is affecting the user's normal work. The precise analysis and accurate measurement of harmonic energy can provide a reliable scientific basis for the power management.
The fast Fourier transform (FFT) has already become a main method of the electrical harmonic analysis since it’s easily realized in embedded system, but there are difficulties in performing synchronized sampling and integral period truncation in the electric power harmonic analysis, and the accuracy of analysis result will be disturbed by the frequency leakage. The window functions and interpolation algorithms are utilized to correct the measured frequency, phase and amplitude by FFT.
In order to overcome some shortcomings of existing methods in realizing the interpolation algorithm, in this paper, an approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT is presented. The effects of harmonic analysis precision brought by the fundamental frequency, sampling frequency and the the data length of truncation are dicussed. The applicable rectification formulas of the double-spectrum-line interpolation is obtained by using polynomial curve fit functions, and subsequently calculating burden is dramatically reduced. Further, the harmonic energy measurement method based on the Nuttall window double-spectrum-line interpolation FFT is discussed. The simulation results show that, under the non-synchronized sampling and non-integral period truncation conditions, the electricity harmonic analysis method proposed in this paper has very high accuracy.
To meet the urgent demand of electric power industry on harmonic energy measurement, a kind of three-phase multi-functional harmonic energy meter structure composed by AD73360L+ADSP-BF533+M30624FGPFP is presented. The operating principle of electric energy meter is described. The data acquisition circuit of six-channel synchronous-sampling A/D converter and the data processing circuit with the core of ADSP-BF533 are introduced in detail. Software process of the harmonic energy measurement method based on the Nuttall window double-spectrum-line interpolation FFT is proposed. Correction method of ratio error and phase error of harmonic energy measurement is discussed. Test results show that, three-phase multi-functional harmonic energy meter based on the algorithm proposed in this paper has its error of fundamental active power measurement lower than 0.2%, error of fundamental reactive power measurement lower than 1%, amplitude error of harmonic electric voltage lower than 2%, phase error of harmonic electric current lower than 5%, and phase angle error between harmonic voltage and electric current lower than 5°. Above data results meet the accuracy requirement of the A class harmonic measurement instruments according to GB/T-14549-93.
Simulation and engineering applications show that, the proposed approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT is feasible, which can inhibit errors caused by the spectral leakage and fence, and is able to achieve the precise harmonic analysis and harmonic energy accurate measurement.
引文
[1] George J.Wakileh.电力系统谐波—基本原理、分析方法和滤波器设计.北京:机械工业出版社,2003:1-5
[2] 中华人民共和国国家标准.GB/T-14549-93 电能质量公用电网谐波.北京:国家技术监督局,1993:1-7
[3] Rife D C,Vincent G A.Use of the discrete Fourier transform in the measurement of frequencies and levels of tones.The Bell System Technical Journal,1970,49(2):197-228
[4] Ortmeyer T H,Chakravarthi K R,Mahmoud A A.The effects of power system harmonics on power system equipment and loads.IEEE Transactions on Power Apparatus and Systems,1985,104(9):2555-2563
[5] Grandke T.Interpolation algorithms for discrete Fourier transforms of weighted signals. IEEE Transactions on Instrumentation and Measurement, 1983,IM-32(2):350-355
[6] Chu R F,Burns J J.Impact of cycloconverter harmonics.IEEE Transactions on Industry Applications,1989,25(3):427-435
[7] Steffan Hansen,Peter Nielsen,Frede Blaabjerg.Harmonic cancellation by mixing nonlinear single-phase and three-phase loads.IEEE Transactions on Industry applications,2000,36(1):152-159
[8] Davis E J , Emanuel A E . Harmonics pollution metering : theoretical consideration. IEEE Transactions on Power Delivery,2000,1(15):19-23
[9] 林海雪,孙树勤.电力网中的谐波.北京:中国电力出版社,2000:2-11
[10] Subjak J S,McQuilkin J S.Hanonics-causes,effects,measurements,and analysis: an update.IEEE Transactions on Industry Applications,1990,26(6):1034-1042
[11] Wagner V E,Balda J C.Effects of harmonics on equipment,Report of the IEEE Task Force on the Effects of Harmonics on Equipment.IEEE Transactions on Power Delivery,1993,8(2):672-680
[12] Read J C . The calculation of rectifier and converter performance characteristics.journal IEF,1945,92(0):495-590
[13] Kimbark E W.Direct current transmission.Vol.1,chapter 8,New York:John Wiley & Sons,1971:856-1035
[14] 付周兴,赵永秀.电网谐波测量技术的现状与发展.工矿自动化,2004,2(2):18-21
[15] Arrillaga J,Bradley D A,Bodger P S.电力系统谐波.徐州:中国矿业大学出版社,1991:5-13
[16] IEEE Working Group on Power System Harmonics . Power system harmonics.Short course,84EHO211-2-PWR.IEEE Power Engineering Society,New York,1984:86-89
[17] IEEE Std.Harmonic Control in Electric Power Systems.IEEE Recommended Practices and Requirements.New York,1993:519-528
[18] IEEE std . Monitoring Electric Power Quality . IEEE Recommended Practice.New York,1995:256-274
[19] IEEE Std . the Transfer of Power Quality Data . IEEE Recommended Practice. New York,2003:874-901
[20] 肖雁鸿,毛 筱,周靖林.电力系统谐波测量方法综述.电网技术,2002,26(6):61-64
[21] 孙传奇.基于小波包变换的谐波电能计量技术研究:[湖南大学硕士学位论文].长沙:湖南大学,2004:2-3
[22] Akagi H,Kanazawa Y,Nabae A.Instantaneous reactive Power compensators comprising switching devices without energy storage components . IEEE Transactions on Industry Applications,1984,20(3):625-630
[23] Fangzheng Peng, Ott G W, Adams D J. Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory for three-Phase four-wire systems.IEEE Transactions on Power Electronics,1998,13(6):1174-1181
[24] Soares V,Verdelho P,Marques G.Active power fi1ter control circuit based on the instantaneous active and reactive current id-iq method.28th Annual IEEE Power Electronics Specialists Conference,1997,0(2):1096-1101
[25] 李庚银,陈志业,丁巧林.dp()坐标系下广义瞬时无功功率定义及其补偿.中国电机工程学报,1996,16(3):176-179
[26] 张波,易颂文,何晓敏.基于广义 d-q 旋转坐标变换的谐波电流检测方法.电力系统及其自动化学报,2001,0(3):5-29
[27] 粟时平,郑小平,金维宇.电力系统谐波检测方法及其实现技术的发展.电气开关,2004,0(1):33-38
[28] Xi Jiangtao.A new algorithm for improving the accuracy of periodic signal analysis.IEEE Transactions on Instrumentation and Measurement,1996,57(8):827-830
[29] 李庚银,陈志业,宁宇.快速傅立叶变换的两种改进算法.电力系统自动化,1997,21(12):37-40
[30] 张伏生,耿中行,葛耀中.电力系统谐波分析的高精度 FFT 算法.中国电机工程学报,1999,l9(3):63-66
[31] 潘文,钱俞寿,周鹗.基于加窗插值 FFT 的电力谐波测量理论( Ⅱ )双插值 FFT理论.电工技术学报,1994,9(2):53-56
[32] 庞浩,李东霞,俎云霄.应用 FFT 进行电力系统谐波分析的改进算法.中国电机工程学报,2003,23(6):50-54
[33] Jain V K,Collins W L,Davis D C.High-accuracy analog measurements via interpolated FFT.IEEE Transactions on Instrumentation and Measurement,1979,28(2):113-122
[34] 周俊,王小海,祁才君.基于 Blackman 窗函数的插值 FFT 在电网谐波信号分析中的应用.浙江大学学报:理学版,2006,33(6):650-653
[35] Harris F J.On the use of windows for harmonic analysis with the discrete Fourier transform.Processing IEEE,1978,66(1):51-83
[36] 许珉,张鸿博.基于 Blackman-harris 窗的加窗 FFT 插值修正算法.郑州大学学报:工学版,2005,26(4):99-101
[37] Zhang Fusheng,Geng Zhongxing,Yuan Wei.The algorithm of interpolating windowed FFT for harmonic analysis of electric power system . IEEE Transactions on Power Delivery,2001,l6(2):160-164
[38] T.X. Zhu.Exact harmonics/interharmonics calculation using adaptive window width.IEEE Transactions on Power Delivery,2007,22(4):2279-2288
[39] Irini S. Reljin,Branimir D. Reljin,Veljko D.Papic.Extremely flat-top windows for harmonic analysis.IEEE Transactions on Instrumentation and Measurement,2007,56(3):1025-1041
[40] 薛蕙,杨仁刚.基于 FFT 的高精度谐波检测算法.中国电机工程学报,2002,22(12):106-110
[41] 柴旭峥,文习山,关根志.一种高精度的电力系统谐波分析算法.中国电机工程学报,2003,23(9):67-70
[42] H.Xue,R.Yang.Optimal interpolating windowed discrete Fourier transform algorithm for harmonic analysis in power system.IEE Proceedings Generation Transmission Distribution,2003,150(5):583-587
[43] A.Testa , D.Gallo , R.Langella . On the processing of harmonics and interharmonics : using Hanning window in standard framework . IEEETransactions on Power Delivery,2004,19(1):28-34
[44] 张介秋,梁昌洪,陈砚圃.基于卷积窗的电力系统谐波理论分析与算法.中国电机工程学报,2004,24(11):48-52
[45] 杨冠鲁,姚若苹,余尤好.采用加窗插值 FFT 与逐幅谐波消去法的电机谐波算法.福州大学学报:自然科学版,2006,34(3):352-356
[46] H.C.Lin,C.S.Lee.Enhanced FFT-based parametric algorithm for simultaneous multiple harmonics analysis . IEE Proceedings Generation Transmission Distribution,2001,148(3):209-214
[47] Hao Qian,Rongxiang Zhao,Tong Chen.Interharmonics analysis based on interpolating windowed FFT algorithm.IEEE Transactions on Power Delivery,2007,22(2):1064-1069
[48] 赵文春,马伟明,胡安.电机测试中谐波分析的高精度 FFT 算法.中国电机工程学报,2001,21(12):83-87
[49] 孙宏伟,李梅,袁健华.用于电力系统谐波分析的加窗插值 FFT 算法研究.高电压技术,2004,30(8):52-55
[50] Offelli C , Petri D . The influence of windowing on the accuracy of multi-frequency signal parameter estimation . IEEE Transactions on Instrumentation and Measurement,1992,41(4):256-261
[51] 王建赜,冉启文.基于小波变换的时变谐波检测.电力系统自动化,l998,22(8):52-54
[52] AngrisaniL , Daponte P . A Measurement Method based on the Wavelet Transform for Power Quality Analysis.IEEE Transactions on Power Delivery,1998,13(4):990-998
[53] S.Santoso,W.M.Grady,E.J.Powers.Characterization of distribution power quality events with Fourier and Wavelet transforms.IEEE Transactions on Power Delivery,2000,15(1):247-254
[54] 张乃饶.神经网络与模糊控制.北京:清华大学出版社,1998:120-183
[55] 危韧勇,李志勇.基于人工神经元网络的电力谐波测量方法.电网技术,1999,23(12):20-23
[56] 王群,吴宁,王兆安.一种基于人工神经网络的电力谐波测量方法.电力系统自动化,1998,0(11):35-39
[57] 金明,刘远龙.用于电力系统谐波分析的 ANN 算法.电网技术,l997,0(5):52-54
[58] 舒双焰,丁洪发,段献忠.基于自适应数字滤波的谐波检测.电力自动化设备,2000,0(6):13-16
[59] 肖雁鸿,毛筱,罗瑞琼.神经网络理论在谐波测量中的应用.电工技术学报,2002,17(2):101-104
[60] 杨晓科,张忠怀,金维.谐波下的电能计量及电能质量分析方法.电测与仪表,2004,0(8):16-19
[61] 肖湘宁.电能质量分析与控制.北京:中国电力出版社,2004:10-32
[62] 南京工学院数学教研组编.工程数学-积分变换.北京:高等教育出版社,2002:3-9
[63] 王世一.数字信号处理.北京:北京理工大学出版社,2005:123-150
[64] Vinay K. Ingle,John G. Proakis.Digital Signal Processing Using MTALB.北京:科学出版社,2003:116-172
[65] 文俊浩,何光辉.图像重建算法中的窗函数研究.哈尔滨工业大学学报,2006,38(2):287-289
[66] 乔新愚,肖建红,郑术力.动态信号测量中的周期截断与加窗技术.电子产品可靠性与环境试验,2005,0(12):158-160
[67] 潘文,钱俞寿,周鹗.基于加窗插值 FFT 的电力谐波测量理论( Ⅰ )窗函数研究.电工技术学报,1994,9(2):50-54
[68] 林明邦,吴亦谦,金翠芬.频谱分析中的窗函数.振动、测试与诊断,1989,9(1):19-27
[69] 侯朝焕,阎世尊,蒋银林.实用 FFT 信号处理技术.北京:海洋出版社,1990:49-87
[70] 肖学亮.窗函数应用中的几个问题.动态分析与测试技术,1989,0(1):10-19
[71] 卿柏元,滕召胜,高云鹏.基于 Nuttall 窗双谱线插值 FFT 的电力谐波分析方法.中国电机工程学报,2008,0(0):0-0
[72] Nuttall A H . Some windows with very good sidelobe behavior . IEEE Transactions on Acoustics Speech Signal Processing,1981,ASSP-29(1):84-91
[73] 刘宏友,李莉.MATLAB 6 基础及应用.重庆:重庆大学出版社,2002:4-5
[74] 李庆扬,王能超,易大义.数值分析.武汉:华中科技大学出版社,1986:68-69
[75] Zhang Lixia,Yan Xiangwu,Li Heming.Modified on-line detection technology of harmonics in power system.Industry Applications Conference,2005,3(10):1900-1903
[2] 中华人民共和国国家标准.GB/T-14549-93 电能质量公用电网谐波.北京:国家技术监督局,1993:1-7
[3] Rife D C,Vincent G A.Use of the discrete Fourier transform in the measurement of frequencies and levels of tones.The Bell System Technical Journal,1970,49(2):197-228
[4] Ortmeyer T H,Chakravarthi K R,Mahmoud A A.The effects of power system harmonics on power system equipment and loads.IEEE Transactions on Power Apparatus and Systems,1985,104(9):2555-2563
[5] Grandke T.Interpolation algorithms for discrete Fourier transforms of weighted signals. IEEE Transactions on Instrumentation and Measurement, 1983,IM-32(2):350-355
[6] Chu R F,Burns J J.Impact of cycloconverter harmonics.IEEE Transactions on Industry Applications,1989,25(3):427-435
[7] Steffan Hansen,Peter Nielsen,Frede Blaabjerg.Harmonic cancellation by mixing nonlinear single-phase and three-phase loads.IEEE Transactions on Industry applications,2000,36(1):152-159
[8] Davis E J , Emanuel A E . Harmonics pollution metering : theoretical consideration. IEEE Transactions on Power Delivery,2000,1(15):19-23
[9] 林海雪,孙树勤.电力网中的谐波.北京:中国电力出版社,2000:2-11
[10] Subjak J S,McQuilkin J S.Hanonics-causes,effects,measurements,and analysis: an update.IEEE Transactions on Industry Applications,1990,26(6):1034-1042
[11] Wagner V E,Balda J C.Effects of harmonics on equipment,Report of the IEEE Task Force on the Effects of Harmonics on Equipment.IEEE Transactions on Power Delivery,1993,8(2):672-680
[12] Read J C . The calculation of rectifier and converter performance characteristics.journal IEF,1945,92(0):495-590
[13] Kimbark E W.Direct current transmission.Vol.1,chapter 8,New York:John Wiley & Sons,1971:856-1035
[14] 付周兴,赵永秀.电网谐波测量技术的现状与发展.工矿自动化,2004,2(2):18-21
[15] Arrillaga J,Bradley D A,Bodger P S.电力系统谐波.徐州:中国矿业大学出版社,1991:5-13
[16] IEEE Working Group on Power System Harmonics . Power system harmonics.Short course,84EHO211-2-PWR.IEEE Power Engineering Society,New York,1984:86-89
[17] IEEE Std.Harmonic Control in Electric Power Systems.IEEE Recommended Practices and Requirements.New York,1993:519-528
[18] IEEE std . Monitoring Electric Power Quality . IEEE Recommended Practice.New York,1995:256-274
[19] IEEE Std . the Transfer of Power Quality Data . IEEE Recommended Practice. New York,2003:874-901
[20] 肖雁鸿,毛 筱,周靖林.电力系统谐波测量方法综述.电网技术,2002,26(6):61-64
[21] 孙传奇.基于小波包变换的谐波电能计量技术研究:[湖南大学硕士学位论文].长沙:湖南大学,2004:2-3
[22] Akagi H,Kanazawa Y,Nabae A.Instantaneous reactive Power compensators comprising switching devices without energy storage components . IEEE Transactions on Industry Applications,1984,20(3):625-630
[23] Fangzheng Peng, Ott G W, Adams D J. Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory for three-Phase four-wire systems.IEEE Transactions on Power Electronics,1998,13(6):1174-1181
[24] Soares V,Verdelho P,Marques G.Active power fi1ter control circuit based on the instantaneous active and reactive current id-iq method.28th Annual IEEE Power Electronics Specialists Conference,1997,0(2):1096-1101
[25] 李庚银,陈志业,丁巧林.dp()坐标系下广义瞬时无功功率定义及其补偿.中国电机工程学报,1996,16(3):176-179
[26] 张波,易颂文,何晓敏.基于广义 d-q 旋转坐标变换的谐波电流检测方法.电力系统及其自动化学报,2001,0(3):5-29
[27] 粟时平,郑小平,金维宇.电力系统谐波检测方法及其实现技术的发展.电气开关,2004,0(1):33-38
[28] Xi Jiangtao.A new algorithm for improving the accuracy of periodic signal analysis.IEEE Transactions on Instrumentation and Measurement,1996,57(8):827-830
[29] 李庚银,陈志业,宁宇.快速傅立叶变换的两种改进算法.电力系统自动化,1997,21(12):37-40
[30] 张伏生,耿中行,葛耀中.电力系统谐波分析的高精度 FFT 算法.中国电机工程学报,1999,l9(3):63-66
[31] 潘文,钱俞寿,周鹗.基于加窗插值 FFT 的电力谐波测量理论( Ⅱ )双插值 FFT理论.电工技术学报,1994,9(2):53-56
[32] 庞浩,李东霞,俎云霄.应用 FFT 进行电力系统谐波分析的改进算法.中国电机工程学报,2003,23(6):50-54
[33] Jain V K,Collins W L,Davis D C.High-accuracy analog measurements via interpolated FFT.IEEE Transactions on Instrumentation and Measurement,1979,28(2):113-122
[34] 周俊,王小海,祁才君.基于 Blackman 窗函数的插值 FFT 在电网谐波信号分析中的应用.浙江大学学报:理学版,2006,33(6):650-653
[35] Harris F J.On the use of windows for harmonic analysis with the discrete Fourier transform.Processing IEEE,1978,66(1):51-83
[36] 许珉,张鸿博.基于 Blackman-harris 窗的加窗 FFT 插值修正算法.郑州大学学报:工学版,2005,26(4):99-101
[37] Zhang Fusheng,Geng Zhongxing,Yuan Wei.The algorithm of interpolating windowed FFT for harmonic analysis of electric power system . IEEE Transactions on Power Delivery,2001,l6(2):160-164
[38] T.X. Zhu.Exact harmonics/interharmonics calculation using adaptive window width.IEEE Transactions on Power Delivery,2007,22(4):2279-2288
[39] Irini S. Reljin,Branimir D. Reljin,Veljko D.Papic.Extremely flat-top windows for harmonic analysis.IEEE Transactions on Instrumentation and Measurement,2007,56(3):1025-1041
[40] 薛蕙,杨仁刚.基于 FFT 的高精度谐波检测算法.中国电机工程学报,2002,22(12):106-110
[41] 柴旭峥,文习山,关根志.一种高精度的电力系统谐波分析算法.中国电机工程学报,2003,23(9):67-70
[42] H.Xue,R.Yang.Optimal interpolating windowed discrete Fourier transform algorithm for harmonic analysis in power system.IEE Proceedings Generation Transmission Distribution,2003,150(5):583-587
[43] A.Testa , D.Gallo , R.Langella . On the processing of harmonics and interharmonics : using Hanning window in standard framework . IEEETransactions on Power Delivery,2004,19(1):28-34
[44] 张介秋,梁昌洪,陈砚圃.基于卷积窗的电力系统谐波理论分析与算法.中国电机工程学报,2004,24(11):48-52
[45] 杨冠鲁,姚若苹,余尤好.采用加窗插值 FFT 与逐幅谐波消去法的电机谐波算法.福州大学学报:自然科学版,2006,34(3):352-356
[46] H.C.Lin,C.S.Lee.Enhanced FFT-based parametric algorithm for simultaneous multiple harmonics analysis . IEE Proceedings Generation Transmission Distribution,2001,148(3):209-214
[47] Hao Qian,Rongxiang Zhao,Tong Chen.Interharmonics analysis based on interpolating windowed FFT algorithm.IEEE Transactions on Power Delivery,2007,22(2):1064-1069
[48] 赵文春,马伟明,胡安.电机测试中谐波分析的高精度 FFT 算法.中国电机工程学报,2001,21(12):83-87
[49] 孙宏伟,李梅,袁健华.用于电力系统谐波分析的加窗插值 FFT 算法研究.高电压技术,2004,30(8):52-55
[50] Offelli C , Petri D . The influence of windowing on the accuracy of multi-frequency signal parameter estimation . IEEE Transactions on Instrumentation and Measurement,1992,41(4):256-261
[51] 王建赜,冉启文.基于小波变换的时变谐波检测.电力系统自动化,l998,22(8):52-54
[52] AngrisaniL , Daponte P . A Measurement Method based on the Wavelet Transform for Power Quality Analysis.IEEE Transactions on Power Delivery,1998,13(4):990-998
[53] S.Santoso,W.M.Grady,E.J.Powers.Characterization of distribution power quality events with Fourier and Wavelet transforms.IEEE Transactions on Power Delivery,2000,15(1):247-254
[54] 张乃饶.神经网络与模糊控制.北京:清华大学出版社,1998:120-183
[55] 危韧勇,李志勇.基于人工神经元网络的电力谐波测量方法.电网技术,1999,23(12):20-23
[56] 王群,吴宁,王兆安.一种基于人工神经网络的电力谐波测量方法.电力系统自动化,1998,0(11):35-39
[57] 金明,刘远龙.用于电力系统谐波分析的 ANN 算法.电网技术,l997,0(5):52-54
[58] 舒双焰,丁洪发,段献忠.基于自适应数字滤波的谐波检测.电力自动化设备,2000,0(6):13-16
[59] 肖雁鸿,毛筱,罗瑞琼.神经网络理论在谐波测量中的应用.电工技术学报,2002,17(2):101-104
[60] 杨晓科,张忠怀,金维.谐波下的电能计量及电能质量分析方法.电测与仪表,2004,0(8):16-19
[61] 肖湘宁.电能质量分析与控制.北京:中国电力出版社,2004:10-32
[62] 南京工学院数学教研组编.工程数学-积分变换.北京:高等教育出版社,2002:3-9
[63] 王世一.数字信号处理.北京:北京理工大学出版社,2005:123-150
[64] Vinay K. Ingle,John G. Proakis.Digital Signal Processing Using MTALB.北京:科学出版社,2003:116-172
[65] 文俊浩,何光辉.图像重建算法中的窗函数研究.哈尔滨工业大学学报,2006,38(2):287-289
[66] 乔新愚,肖建红,郑术力.动态信号测量中的周期截断与加窗技术.电子产品可靠性与环境试验,2005,0(12):158-160
[67] 潘文,钱俞寿,周鹗.基于加窗插值 FFT 的电力谐波测量理论( Ⅰ )窗函数研究.电工技术学报,1994,9(2):50-54
[68] 林明邦,吴亦谦,金翠芬.频谱分析中的窗函数.振动、测试与诊断,1989,9(1):19-27
[69] 侯朝焕,阎世尊,蒋银林.实用 FFT 信号处理技术.北京:海洋出版社,1990:49-87
[70] 肖学亮.窗函数应用中的几个问题.动态分析与测试技术,1989,0(1):10-19
[71] 卿柏元,滕召胜,高云鹏.基于 Nuttall 窗双谱线插值 FFT 的电力谐波分析方法.中国电机工程学报,2008,0(0):0-0
[72] Nuttall A H . Some windows with very good sidelobe behavior . IEEE Transactions on Acoustics Speech Signal Processing,1981,ASSP-29(1):84-91
[73] 刘宏友,李莉.MATLAB 6 基础及应用.重庆:重庆大学出版社,2002:4-5
[74] 李庆扬,王能超,易大义.数值分析.武汉:华中科技大学出版社,1986:68-69
[75] Zhang Lixia,Yan Xiangwu,Li Heming.Modified on-line detection technology of harmonics in power system.Industry Applications Conference,2005,3(10):1900-1903
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