混合自卷积窗谐波算法研究与FPGA方案
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摘要
快速傅里叶变换(fast Fourier transform, FFT)因其高效快捷比较适合对电力谐波进行实时分析,但其不足之处是非同步采样和非整数周期截断时易出现"频谱泄漏"与"栅栏效应"。为此,提出一种基于由Nuttall窗与Hanning窗混合卷积后再进行L阶自卷积的混合自卷积窗谐波算法。首先对混合自卷积窗进行双谱线插值改进与数值拟合修正,从而进一步提高了FFT算法的精确度;继而对采用混合自卷积窗的改进算法进行硬件结构方案设计与现场可编程门阵列(field-programmable gate array, FPGA)关键技术进行研究;最后利用混合自卷积窗与Nuttall窗和Hanning窗的算法,对电力谐波算例进行仿真对比。结果表明:采用混合自卷积窗谐波算法所得的相位误差稳定在0.000 01°,而幅值误差几乎为0,从而验证了该算法的有效性与实用性。
Fast Fourier transform(FFT) is suitable for real-time analysis of electric power harmonic due to its high efficiency and rapidity, but there are some shortages such as spectrum leakage and picket fence effect during asynchronous sampling and non-integer periodic truncation. Thus, this paper proposes a kind of hybrid self-convolution window harmonic algorithm which is firstly convoluted by Nuttall window and Hanning window and then L order. Double spectrum line interpolation improvement and numerical fitting correction are performed to improve precision of FFT algorithm and an improved algorithm based on the hybrid self-convolution window is used for hardware structure design and study on FPGA key technologies. Finally, the hybrid self-convolution window harmonic algorithm, the Nuttall window algorithm and the Hanning window algorithm are used for simulation comparison of electric power harmonic. The results indicate phase error calculated by the hybrid self-convolution window harmonic algorithm is stable at 0.000 01° and amplitude error is almost 0, which verifies effectiveness and practicability of this algorithm.
Fast Fourier transform(FFT) is suitable for real-time analysis of electric power harmonic due to its high efficiency and rapidity, but there are some shortages such as spectrum leakage and picket fence effect during asynchronous sampling and non-integer periodic truncation. Thus, this paper proposes a kind of hybrid self-convolution window harmonic algorithm which is firstly convoluted by Nuttall window and Hanning window and then L order. Double spectrum line interpolation improvement and numerical fitting correction are performed to improve precision of FFT algorithm and an improved algorithm based on the hybrid self-convolution window is used for hardware structure design and study on FPGA key technologies. Finally, the hybrid self-convolution window harmonic algorithm, the Nuttall window algorithm and the Hanning window algorithm are used for simulation comparison of electric power harmonic. The results indicate phase error calculated by the hybrid self-convolution window harmonic algorithm is stable at 0.000 01° and amplitude error is almost 0, which verifies effectiveness and practicability of this algorithm.
引文
[1]于燕平,方林,黄绘.基于非线性动力学和高斯混合模型的电能质量自动识别[J].广东电力,2016,29(3):67-71.YU Yanping,FANG Lin,HUANG Hui.Automatic identification for power quality based on nonlinear dynamics and Gaussian mixed model[J].Guangdong Electric Power,2016,29(3):67-71.
[2]袁小平,胡秀娟,孙英洲,等.基于加窗傅里叶变换的弱电网阻抗测量算法[J].电力系统保护与控制,2018,46(10):96-101.YUAN Xiaoping,HU Xiujuan,SUN Yingzhou,et al.A weak grid impedance detection method based on windowed Fourier transformation[J].Power System Protection and Control,2018,46(10):96-101.
[3]陈远周,杨芳.基于加窗插值FFT算法的低频振荡模式分析[J].广东电力,2016,29(3):61-66.CHEN Yuanzhou,YANG Fang.Analysis on low frequency oscillation mode based on windows and interpolated FFT[J].Guangdong Electric Power,2016,29(3):61-66.
[4]程浩忠,周荔丹,王丰华.电能质量[M].北京:清华大学出版社,2017.
[5]张逸,林焱,吴丹岳.电能质量监测系统研究现状及发展趋势[J].电力系统保护与控制,2015,1(26):139-145.ZHANG Yi,LIN Yan,WU Danyue.Current status and development trend of power quality monitoring system[J].Power System Protection and Control,2015,1(26):139-145.
[6]曾江,凌毓畅.光伏电站接入电网的电能质量分析及其应用[J].广东电力,2017,30(8):38-46.ZENG Jiang,LING Yuchang.Analysis and application of power quality of grid-connected photovoltaic power station[J].Guangdong Electric Power,2017,30(8):38-46.
[7]王玲,康健,邹宏亮,等.实时电能质量监测系统的构建及应用[J].电力系统保护与控制,2011,39(2):108-111.WANG Ling,KANG Jian,ZOU Hongliang,et al.Construction and application of real-time power quality monitoring system[J].Power System Protection and Control,2011,39(2):108-111.
[8]翁国庆.现代电能质量监测、分析与控制技术[M].北京:机械工业出版社,2016.
[9]International Electrotechnical Commission.IEC 61000-4-7,General guide on harmonics and interharmonics for power supply systems and equipment connected thereto[S].
[10]全国电压电流等级和频率标准化技术委员会.GB/T14549-1993,电能质量公用电网谐波[S].北京:中国标准出版社,1993.
[11]卿柏元,滕召胜,高云鹏,等.基于Nuttall窗双谱线插值FFT的电力谐波分析方法[J].中国电机工程学报,2008,28(25):153-158.QING Baiyuan,TENG Zhaosheng,GAO Yunpeng,et al.An approach for electrical harmonic analysis based on Nuttall window double-spectrum line interpolation FFT[J].Proceedings of the CSEE,2008,28(25):153-158.
[12]曾博,唐求,卿柏元,等.基于Nuttall自卷积窗的改进FFT谱分析方法[J].电工技术学报,2014,29(7):59-65.ZENG Bo,TANG Qiu,QING Baiyuan,et al.Spectral analysis method based on improved FFT Nuttall selfconvolution window[J].Transactions of China Electrotechnical Society,2014,29(7):59-65.
[13]温和,滕召胜,卿柏元.Hanning自卷积窗及其在谐波分析中的应用[J].电工技术学报,2009,24(2):164-169.WEN He,TENG Zhaosheng,QING Baiyuan.Hanning selfconvolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[14]李德民.基于混合卷积窗与改进FFT算法的电力系统谐波分析[D].合肥:合肥工业大学,2016.
[15]孙鹏,杨永越.五点加权FFT介质损耗角测量算法的研究[J].高压电器,2015,51(3):88-92.SUN Peng,YANG Yongyue.Five weighted FFTdielectric loss angle measurement algorithm studies[J].High Voltage Electrical Appliances,2015,51(3):88-92.
[16]张红瑛,滕召胜,温和,等.九点变换改进FFT高精度谐波分析方法[J].电力系统及其自动化学报,2010,22(6):38-43.ZHANG Hongying,TENG Zhaosheng,WEN He,et al.Nine pointspolynomial transform improved FFT for high precise harmonic analysis[J].Proceedings of the CSU-EPSA,2010,22(6):38-43.
[17]LIN H C.Power harmonics and interharmonics measurement using recursive group-harmonic power minimizing algorithm[J].IEEE Transactions on Industrial Electronics,2012,59(2):1184-1193.
[18]ZENG B,TENG Z S.Parameter estimation of power system signals based on cosine self-convolution window with desirable side-lobe behaviors[J].IEEE Transactions on Power Delivery,2011,26(1):250-257.
[19]黄建明,李晓明.结合短时傅里叶变换和谱峭度的电力系统谐波检测方法[J].电力系统保护与控制,2017,45(7):43-50.HUANG Jianming,LI Xiaoming.Detection of harmonic in power system based on short-time Fourier transform and spectral kurtosis[J].Power System Protection and Control,2017,45(7):43-50.
[20]宋知用.MATLAB数字信号处理85个实用案例精讲[M].北京:北京航天航空大学出版社,2016.
[21]彭曦,刘开培,李登云.Kaiser窗的组合余弦窗拟合及其在频谱分析中的应用[J].电测与仪表,2018,55(19):93-96.PENG Xi,LIU Kaipei,LI Dengyun.A fitting combined cosine window based on Kaiser window and its application in spectral analysis[J].Electrical Measurement&Instrumentation,2018,55(19):93-96.
[2]袁小平,胡秀娟,孙英洲,等.基于加窗傅里叶变换的弱电网阻抗测量算法[J].电力系统保护与控制,2018,46(10):96-101.YUAN Xiaoping,HU Xiujuan,SUN Yingzhou,et al.A weak grid impedance detection method based on windowed Fourier transformation[J].Power System Protection and Control,2018,46(10):96-101.
[3]陈远周,杨芳.基于加窗插值FFT算法的低频振荡模式分析[J].广东电力,2016,29(3):61-66.CHEN Yuanzhou,YANG Fang.Analysis on low frequency oscillation mode based on windows and interpolated FFT[J].Guangdong Electric Power,2016,29(3):61-66.
[4]程浩忠,周荔丹,王丰华.电能质量[M].北京:清华大学出版社,2017.
[5]张逸,林焱,吴丹岳.电能质量监测系统研究现状及发展趋势[J].电力系统保护与控制,2015,1(26):139-145.ZHANG Yi,LIN Yan,WU Danyue.Current status and development trend of power quality monitoring system[J].Power System Protection and Control,2015,1(26):139-145.
[6]曾江,凌毓畅.光伏电站接入电网的电能质量分析及其应用[J].广东电力,2017,30(8):38-46.ZENG Jiang,LING Yuchang.Analysis and application of power quality of grid-connected photovoltaic power station[J].Guangdong Electric Power,2017,30(8):38-46.
[7]王玲,康健,邹宏亮,等.实时电能质量监测系统的构建及应用[J].电力系统保护与控制,2011,39(2):108-111.WANG Ling,KANG Jian,ZOU Hongliang,et al.Construction and application of real-time power quality monitoring system[J].Power System Protection and Control,2011,39(2):108-111.
[8]翁国庆.现代电能质量监测、分析与控制技术[M].北京:机械工业出版社,2016.
[9]International Electrotechnical Commission.IEC 61000-4-7,General guide on harmonics and interharmonics for power supply systems and equipment connected thereto[S].
[10]全国电压电流等级和频率标准化技术委员会.GB/T14549-1993,电能质量公用电网谐波[S].北京:中国标准出版社,1993.
[11]卿柏元,滕召胜,高云鹏,等.基于Nuttall窗双谱线插值FFT的电力谐波分析方法[J].中国电机工程学报,2008,28(25):153-158.QING Baiyuan,TENG Zhaosheng,GAO Yunpeng,et al.An approach for electrical harmonic analysis based on Nuttall window double-spectrum line interpolation FFT[J].Proceedings of the CSEE,2008,28(25):153-158.
[12]曾博,唐求,卿柏元,等.基于Nuttall自卷积窗的改进FFT谱分析方法[J].电工技术学报,2014,29(7):59-65.ZENG Bo,TANG Qiu,QING Baiyuan,et al.Spectral analysis method based on improved FFT Nuttall selfconvolution window[J].Transactions of China Electrotechnical Society,2014,29(7):59-65.
[13]温和,滕召胜,卿柏元.Hanning自卷积窗及其在谐波分析中的应用[J].电工技术学报,2009,24(2):164-169.WEN He,TENG Zhaosheng,QING Baiyuan.Hanning selfconvolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[14]李德民.基于混合卷积窗与改进FFT算法的电力系统谐波分析[D].合肥:合肥工业大学,2016.
[15]孙鹏,杨永越.五点加权FFT介质损耗角测量算法的研究[J].高压电器,2015,51(3):88-92.SUN Peng,YANG Yongyue.Five weighted FFTdielectric loss angle measurement algorithm studies[J].High Voltage Electrical Appliances,2015,51(3):88-92.
[16]张红瑛,滕召胜,温和,等.九点变换改进FFT高精度谐波分析方法[J].电力系统及其自动化学报,2010,22(6):38-43.ZHANG Hongying,TENG Zhaosheng,WEN He,et al.Nine pointspolynomial transform improved FFT for high precise harmonic analysis[J].Proceedings of the CSU-EPSA,2010,22(6):38-43.
[17]LIN H C.Power harmonics and interharmonics measurement using recursive group-harmonic power minimizing algorithm[J].IEEE Transactions on Industrial Electronics,2012,59(2):1184-1193.
[18]ZENG B,TENG Z S.Parameter estimation of power system signals based on cosine self-convolution window with desirable side-lobe behaviors[J].IEEE Transactions on Power Delivery,2011,26(1):250-257.
[19]黄建明,李晓明.结合短时傅里叶变换和谱峭度的电力系统谐波检测方法[J].电力系统保护与控制,2017,45(7):43-50.HUANG Jianming,LI Xiaoming.Detection of harmonic in power system based on short-time Fourier transform and spectral kurtosis[J].Power System Protection and Control,2017,45(7):43-50.
[20]宋知用.MATLAB数字信号处理85个实用案例精讲[M].北京:北京航天航空大学出版社,2016.
[21]彭曦,刘开培,李登云.Kaiser窗的组合余弦窗拟合及其在频谱分析中的应用[J].电测与仪表,2018,55(19):93-96.PENG Xi,LIU Kaipei,LI Dengyun.A fitting combined cosine window based on Kaiser window and its application in spectral analysis[J].Electrical Measurement&Instrumentation,2018,55(19):93-96.