一种基于迭代抑制谱泄漏的改进相位差算法
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摘要
由于非同步采样所带来的频谱泄漏效应是影响相位差算法电参量测量精度的主要原因,利用高阶窗的旁瓣特性可抑制频谱泄漏,但二次谐波幅值的估计精度仍难以显著提升,并且由于高阶窗所带来频率分辨率损失的原因,通常需要增加待测信号的采样窗长,不利于频率波动和实时性要求较高的场合实现高精度测量。为此,提出一种加sine窗函数的改进型相位差算法,利用峰值谱线间相位差估计出的相对频偏,计算出除被测谐波分量之外的其他分量的长程谱泄漏对峰值谱线的干扰之和并将其减去后,重新利用其峰值谱线间的相位差计算相对频偏,循环迭代估计。基于该方法,与现有加窗相位差算法分别在无噪声、有噪声以及频率波动环境下进行仿真比较。实验结果表明,该方法迭代矫正计算4次即可,能有效抑制频谱泄露效应,减小估计偏差,提高电网电参量测量精度和实时性,能够满足电网测量需要。
The spectrum leakage effect caused by non-synchronous sampling is the main impact for the measurement precision of the phase difference algorithm,and the spectral leakage can be suppressed by the side lobe characteristic of highorder window function. However,the estimation accuracy of the secondary harmonic amplitude is still difficult to improve significantly,and the reason for the loss of frequency resolution due to high window function,the sampling window is usually increased,and it is not conducive to the frequency fluctuation and the real time requirement is higher. In this paper,a modified phase difference algorithm with sine window is presented,the relative frequency deviation is estimated by the phase difference between peak spectral lines,and the sum of the long range spectrum leakage of the components other than the measured harmonic components is calculated,as well as subtracts it from the measured component,we update relative frequency deviation by the phase difference between peak spectral lines,cyclic iterative estimation. Based on this method,the simulation is conducted by comparing with the existing phase difference algorithm in noise-free and noise environment and frequency fluctuation environment. Experimental results show that this method can be used for the iterative correction of 4 times,which can effectively suppress the spectrum leakage effect,reduce estimation error,and improve the measurement precision of power grid electrical parameters,as well as can meet the requirements of grid measurement.
The spectrum leakage effect caused by non-synchronous sampling is the main impact for the measurement precision of the phase difference algorithm,and the spectral leakage can be suppressed by the side lobe characteristic of highorder window function. However,the estimation accuracy of the secondary harmonic amplitude is still difficult to improve significantly,and the reason for the loss of frequency resolution due to high window function,the sampling window is usually increased,and it is not conducive to the frequency fluctuation and the real time requirement is higher. In this paper,a modified phase difference algorithm with sine window is presented,the relative frequency deviation is estimated by the phase difference between peak spectral lines,and the sum of the long range spectrum leakage of the components other than the measured harmonic components is calculated,as well as subtracts it from the measured component,we update relative frequency deviation by the phase difference between peak spectral lines,cyclic iterative estimation. Based on this method,the simulation is conducted by comparing with the existing phase difference algorithm in noise-free and noise environment and frequency fluctuation environment. Experimental results show that this method can be used for the iterative correction of 4 times,which can effectively suppress the spectrum leakage effect,reduce estimation error,and improve the measurement precision of power grid electrical parameters,as well as can meet the requirements of grid measurement.
引文
[1]李国庆,王鹤,张慧杰.微电网中基于逆变电源控制的重要节点电能质量管理方法[J].电工技术学报,2014,29(2):177-183Li Guoqing,Wang He,Zhang Huijie.Power quality management method based on inverter source control for important node in microgrid[J].Transactions of China Electrotechnical Society,2014,29(2):177-183.
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[4]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-spectrumline interpolation FFT[J].Proceedings of the CSEE,2008,28(25):153-158.
[5]蔡晓峰,张鸿博,鲁改凤.应用三谱线插值FFT分析电力谐波的改进算法[J].电力系统保护与控制,2015,43(2):33-39.Cai Xiaofeng,Zhang Hongbo,Lu Gaifeng.Improvement algorithm for harmonic analysis of power system using triple-spectrum-line interpolation algorithm based on window FFT[J].Power System Protection and Control,2015,43(2):33-39.
[6]刘冬梅,郑鹏,何怡刚,等.几种谐波检测加窗插值FFT算法的比较[J].电测与仪表,2013,50(12):51-55.Liu Dongmei,Zheng Peng,He Yigang,et al.Analysis and Comparison of Several Harmonic Detection Methods with Windowed and Interpolation FFT[J].Electrical Measurement&Instrumentation,2013,50(12):51-55.
[7]刘涛,庄双勇,陈晓伟,等.基于四阶Hanning自乘窗FFT三峰插值的电能计量新算法[J].电测与仪表,2017,54(21):1-6,41.Liu Tao,Zhuang Shuangyong,Chen Xiaowei,et al.A new algorithm for electric energy measurement based on four-order Hanning self-multiplication window triple-spectrum-line interpolation FFT[J].Electrical Measurement&Instrumentation,2017,54(21):1-6,41.
[8]曾博,滕召胜.纳托尔自卷积窗加权电力谐波分析方法[J].电网技术,2011,35(8):134-139.Zeng Bo,Teng Zhaosheng.A Nuttall self-convolution window-based approach to weighted analysis on power system harmonic[J].Power System Technology,2011,35(8):134-139.
[9]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 self-convolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[10]曾博,唐求,卿柏元.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.Spectral analysis method based on improved FFT by nuttall self-convolution window[J].Transactions of China Electrotechnical Society,2014,29(7):59-65.
[11]孙仲民,何正友,臧天磊.一种混合卷积窗及其在谐波分析中的应用[J].电工技术学报,2016,31(16):207-214.Sun Zhongmin,He Zhengyou,Zang Tianlei.A kind of hybrid convolution window and its application in harmonic analysis[J].Transactions of China Electrotechnical Society,2016,31(16):207-214.
[12]黄威威,蔡念,王晗,等.基于VSS窗的改进相位差电力谐波分析方法[J].电测与仪表,2014,51(22):76-81.Huang Weiwei,Cai Nian,Wang Han,et al.Improved Phase Difference Method Based on Variation Semi-Sinusoidal Window for Power Harmonic Analysis[J].Electrical Measurement&Instrumentation,2014,51(22):76-81.
[13]张鸿博,蔡晓峰,鲁改凤.基于全相位FFT改进相位差法的自动准同期并列参数测量[J].电力系统保护与控制,2016,44(4):76-83.Zhang Hongbo,Cai Xiaofeng,Lu Gaifeng.Generator quasi synchronization parameter measurement method based on improved phase difference method of all-phase fast Flourier transform[J].Power System Protection and Control,2016,44(4):76-83.
[14]GB/T 15945-2008,电能质量电力系统频率偏差[S].北京:中国标准出版社,2008.
[2]潘文,钱俞寿,周鹗.基于加窗插值FFT的电力谐波测量理论(|)窗函数研究[J].电工技术学报,1994,9(1):50-54.Pan Wen,Qian Yushou,Zhou E.Power harmonics measurement based on windows and interpolated FFT(|)study of windows[J].Transactions of China Electrotechnical Society,1994,9(1):50-54.
[3]谢明,丁康.频谱分析的校正方法[J].振动工程学报,1994,7(2):172-178.Xie Ming,Ding Kang.Rectifying technique of spectrum analysis[J].Journal of Vibration Engineering,1994,7(2):172-178.
[4]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-spectrumline interpolation FFT[J].Proceedings of the CSEE,2008,28(25):153-158.
[5]蔡晓峰,张鸿博,鲁改凤.应用三谱线插值FFT分析电力谐波的改进算法[J].电力系统保护与控制,2015,43(2):33-39.Cai Xiaofeng,Zhang Hongbo,Lu Gaifeng.Improvement algorithm for harmonic analysis of power system using triple-spectrum-line interpolation algorithm based on window FFT[J].Power System Protection and Control,2015,43(2):33-39.
[6]刘冬梅,郑鹏,何怡刚,等.几种谐波检测加窗插值FFT算法的比较[J].电测与仪表,2013,50(12):51-55.Liu Dongmei,Zheng Peng,He Yigang,et al.Analysis and Comparison of Several Harmonic Detection Methods with Windowed and Interpolation FFT[J].Electrical Measurement&Instrumentation,2013,50(12):51-55.
[7]刘涛,庄双勇,陈晓伟,等.基于四阶Hanning自乘窗FFT三峰插值的电能计量新算法[J].电测与仪表,2017,54(21):1-6,41.Liu Tao,Zhuang Shuangyong,Chen Xiaowei,et al.A new algorithm for electric energy measurement based on four-order Hanning self-multiplication window triple-spectrum-line interpolation FFT[J].Electrical Measurement&Instrumentation,2017,54(21):1-6,41.
[8]曾博,滕召胜.纳托尔自卷积窗加权电力谐波分析方法[J].电网技术,2011,35(8):134-139.Zeng Bo,Teng Zhaosheng.A Nuttall self-convolution window-based approach to weighted analysis on power system harmonic[J].Power System Technology,2011,35(8):134-139.
[9]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 self-convolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[10]曾博,唐求,卿柏元.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.Spectral analysis method based on improved FFT by nuttall self-convolution window[J].Transactions of China Electrotechnical Society,2014,29(7):59-65.
[11]孙仲民,何正友,臧天磊.一种混合卷积窗及其在谐波分析中的应用[J].电工技术学报,2016,31(16):207-214.Sun Zhongmin,He Zhengyou,Zang Tianlei.A kind of hybrid convolution window and its application in harmonic analysis[J].Transactions of China Electrotechnical Society,2016,31(16):207-214.
[12]黄威威,蔡念,王晗,等.基于VSS窗的改进相位差电力谐波分析方法[J].电测与仪表,2014,51(22):76-81.Huang Weiwei,Cai Nian,Wang Han,et al.Improved Phase Difference Method Based on Variation Semi-Sinusoidal Window for Power Harmonic Analysis[J].Electrical Measurement&Instrumentation,2014,51(22):76-81.
[13]张鸿博,蔡晓峰,鲁改凤.基于全相位FFT改进相位差法的自动准同期并列参数测量[J].电力系统保护与控制,2016,44(4):76-83.Zhang Hongbo,Cai Xiaofeng,Lu Gaifeng.Generator quasi synchronization parameter measurement method based on improved phase difference method of all-phase fast Flourier transform[J].Power System Protection and Control,2016,44(4):76-83.
[14]GB/T 15945-2008,电能质量电力系统频率偏差[S].北京:中国标准出版社,2008.