CN111308199A - Double spectral line interpolation DFT harmonic wave analysis method, system and medium based on spectrum resolution self-adaption - Google Patents

Double spectral line interpolation DFT harmonic wave analysis method, system and medium based on spectrum resolution self-adaption Download PDF

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CN111308199A
CN111308199A CN202010171040.8A CN202010171040A CN111308199A CN 111308199 A CN111308199 A CN 111308199A CN 202010171040 A CN202010171040 A CN 202010171040A CN 111308199 A CN111308199 A CN 111308199A
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harmonic
frequency
fundamental wave
fundamental
spectral
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李恺
卜文彬
陈向群
谭海波
解玉满
黄红桥
谈丛
王海元
周宇烨
杨茂涛
黄瑞
陈浩
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
Metering Center of State Grid Hunan Electric Power Co Ltd
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State Grid Hunan Electric Power Co Ltd
Metering Center of State Grid Hunan Electric Power Co Ltd
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Abstract

本发明公开了一种基于频谱分辨率自适应的双谱线插值DFT谐波分析方法、系统及介质,本发明方法包括针对输入的M点采样值序列对前N点进行加窗计算谐波信号的基波粗糙频率f并计算采样点数Ni;对采样点数Ni点采样序列进行加窗双谱线插值DFT计算获得频率修正系数;求解基波特征参量,针对k次谐波:对基波频率进行k倍倍频得到k次谐波频率;根据k次谐波频率逆推频率修正系数;在基波频率和基波相位的基础上,根据频率修正系数修正得到k次谐波频率和k次谐波相位。本发明通过频谱分辨率自适应抑制基波对谐波计算的频谱干扰,并通过倍频逆推求取整次谐波,能够避免插值计算谐波带来的误差。

Figure 202010171040

The invention discloses a dual spectral line interpolation DFT harmonic analysis method, system and medium based on adaptive spectral resolution. The method of the invention includes windowing the first N points for the input sampling value sequence of M points to calculate harmonic signals the rough frequency f of the fundamental wave and calculate the number of sampling points N i ; perform windowed bispectral interpolation DFT calculation on the sampling sequence of the number of sampling points N i to obtain the frequency correction coefficient; solve the characteristic parameters of the fundamental wave, for the kth harmonic: The frequency is multiplied by k times to obtain the k-th harmonic frequency; the frequency correction coefficient is reversed according to the k-th harmonic frequency; on the basis of the fundamental wave frequency and the fundamental wave phase, the k-th harmonic frequency and k are obtained by correcting the frequency correction coefficient. subharmonic phase. The invention adaptively suppresses the spectral interference of the fundamental wave to the harmonic calculation through the spectral resolution, and obtains the integer harmonics through frequency multiplication inverse, so as to avoid the error caused by the interpolation calculation of the harmonics.

Figure 202010171040

Description

基于频谱分辨率自适应的双谱线插值DFT谐波分析方法、系统 及介质Dual spectral line interpolation DFT harmonic analysis method and system based on adaptive spectral resolution and medium

技术领域technical field

本发明涉及电力系统谐波信号分析领域,具体涉及一种基于频谱分辨率自适应的双谱线插值DFT谐波分析方法、系统及介质,用于分析电力系统谐波信号提取其中的特征信息。The invention relates to the field of power system harmonic signal analysis, in particular to a spectral resolution adaptive bispectral line interpolation DFT harmonic analysis method, system and medium, which are used for analyzing power system harmonic signals to extract characteristic information therein.

背景技术Background technique

电力系统中电力电子设备的广泛应用,产生大量的谐波,极大地威胁到电力系统的安全稳定运行。因此,对电力系统中存在的电力系统谐波信号进行检测并分析,以防治谐波危害,是十分必要的。由于电力系统的时域信号存在多种谐波及宽带随机噪声,因此很难进行信号特征信息的直接测量。The wide application of power electronic equipment in the power system produces a large number of harmonics, which greatly threatens the safe and stable operation of the power system. Therefore, it is very necessary to detect and analyze the harmonic signals of the power system in the power system in order to prevent the harm of harmonics. Due to the existence of various harmonics and broadband random noise in the time domain signal of the power system, it is difficult to directly measure the signal characteristic information.

离散傅里叶变换(Discrete Fourier Transform,DFT)作为一种经典的频谱分析方法,实现频谱分离的同时,具有较高的信噪比增益,常被应用于电力系统基波、谐波特征信息的检测。通常采用时域加窗函数、频域谱线插值的方法来提高DFT算法精度。多年来,窗函数经历了从Hannning窗到Nuttull窗的演变,插值方法的加权谱线数量也从一根增加到两根、乃至三根。因此,窗函数旁瓣电平不断减小、插值谱线数量不断增多,算法的频谱泄露和栅栏效益得到抑制,算法精度得到提升。但是现有算法仍存在谱间干扰下相位误差偏大、噪声背景下相位估计方差偏大等不足。Discrete Fourier Transform (DFT), as a classical spectrum analysis method, realizes spectrum separation and has high signal-to-noise ratio gain. detection. Usually, the time-domain windowing function and the frequency-domain spectral line interpolation are used to improve the accuracy of the DFT algorithm. Over the years, window functions have evolved from Hannning windows to Nuttull windows, and the number of weighted spectral lines for interpolation methods has increased from one to two, or even three. Therefore, the side lobe level of the window function is continuously reduced, the number of interpolated spectral lines is continuously increased, the spectral leakage and the fence benefit of the algorithm are suppressed, and the algorithm accuracy is improved. However, the existing algorithms still have some shortcomings, such as large phase error under inter-spectral interference and large phase estimation variance under noise background.

发明内容SUMMARY OF THE INVENTION

本发明要解决的技术问题:针对现有算法在频谱干扰、宽带噪声存在时计算精度上的不足,提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析方法、系统及介质,本发明通过频谱分辨率自适应抑制基波对谐波计算的频谱干扰,并通过倍频逆推求取整次谐波,能够避免插值计算谐波带来的误差。The technical problem to be solved by the present invention: aiming at the deficiencies in the calculation accuracy of the existing algorithms in the presence of spectral interference and broadband noise, a dual spectral line interpolation DFT harmonic analysis method, system and medium based on adaptive spectral resolution are provided, The invention adaptively suppresses the spectral interference of the fundamental wave to the harmonic calculation through the spectral resolution, and obtains the integer harmonics through frequency multiplication inverse, so as to avoid the error caused by the interpolation calculation of the harmonics.

为了解决上述技术问题,本发明采用的技术方案为:In order to solve the above-mentioned technical problems, the technical scheme adopted in the present invention is:

一种基于频谱分辨率自适应的双谱线插值DFT谐波分析方法,步骤包括:A dual spectral line interpolation DFT harmonic analysis method based on spectral resolution adaptation, the steps include:

1)输入M点采样值序列;1) Input the M point sample value sequence;

2)针对M点采样值序列对前N点进行加窗,基于FFT变换计算谐波信号的基波粗糙频率f,其中N为2的整数次方;2) windowing the first N points for the M-point sample value sequence, and calculating the fundamental rough frequency f of the harmonic signal based on the FFT transformation, where N is an integer power of 2;

3)根据谐波信号的基波粗糙频率f,计算满足频率分辨率自适应要求的采样点数Ni3) According to the fundamental rough frequency f of the harmonic signal, calculate the number of sampling points N i that meets the frequency resolution self-adaptation requirement;

4)对采样点数Ni点采样序列进行加窗双谱线插值DFT计算,获得频率修正系数δ(2)4) carry out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N i , obtain frequency correction coefficient δ (2) ;

5)采用插值方法求解基波特征参量,包括基波幅值A1、基波频率f1和基波相位

Figure BDA0002409188360000011
5) Use the interpolation method to solve the fundamental wave characteristic parameters, including the fundamental wave amplitude A 1 , the fundamental wave frequency f 1 and the fundamental wave phase
Figure BDA0002409188360000011

6)针对任意指定的k次谐波:通过对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波幅值A1和基波相位

Figure BDA0002409188360000021
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000022
6) For the arbitrarily specified k-th harmonic: obtain the k-th harmonic frequency f k by multiplying the fundamental frequency f 1 by k; according to the k-th harmonic frequency f k , reverse the frequency correction coefficient δ k (2) ; at fundamental amplitude A 1 and fundamental phase
Figure BDA0002409188360000021
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000022

可选地,步骤6)的详细步骤包括:Optionally, the detailed steps of step 6) include:

6.1)指定待修正的k次谐波;6.1) Specify the k-th harmonic to be corrected;

6.2)对基波频率f1进行k倍倍频得到k次谐波频率fk6.2) Perform k-fold frequency multiplication on the fundamental frequency f 1 to obtain the k-th harmonic frequency f k ;

6.3)根据k次谐波频率fk逆推频率修正系数δk(2)6.3) Inversely push the frequency correction coefficient δk (2) according to the k -th harmonic frequency fk;

6.4)在基波幅值A1和基波相位

Figure BDA0002409188360000023
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000024
6.4 ) At fundamental amplitude A1 and fundamental phase
Figure BDA0002409188360000023
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000024

6.5)判断谐波计算是否完成,如果尚未完成则指定新的待修正的k次谐波,跳转执行步骤6.2);否则结束。6.5) Determine whether the harmonic calculation is completed, if not, specify a new k-th harmonic to be corrected, and skip to step 6.2); otherwise, end.

可选地,步骤3)中采样点数Ni的计算函数表达式为:Optionally, the calculation function expression of the number of sampling points N i in step 3) is:

Figure BDA0002409188360000025
Figure BDA0002409188360000025

上式中,round为四舍五入取整函数,f为谐波信号的基波粗糙频率,fs为采样频率,N为步骤2)中针对M点采样值序列进行加窗的采样值数量。In the above formula, round is the rounding function, f is the fundamental rough frequency of the harmonic signal, fs is the sampling frequency, and N is the number of sampled values that are windowed for the M-point sampled value sequence in step 2).

可选地,所述逆推频率修正系数δk(2)的计算函数表达式为:Optionally, the calculation function expression of the inverse frequency correction coefficient δk (2) is:

Figure BDA0002409188360000026
Figure BDA0002409188360000026

上式中,fk为k次谐波频率,Ni为满足频率分辨率自适应要求的采样点数Ni,fs为采样频率,floor为向下取整函数。In the above formula, f k is the k -th harmonic frequency, Ni is the number of sampling points Ni that meets the frequency resolution adaptive requirement, f s is the sampling frequency, and floor is a round-down function.

此外,本发明还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括:In addition, the present invention also provides a dual spectral line interpolation DFT harmonic analysis system based on spectral resolution adaptation, including:

采样值输入程序单元,用于输入M点采样值序列;The sampled value input program unit is used to input the M-point sampled value sequence;

基波粗糙频率计算程序单元,用于针对M点采样值序列对前N点进行加窗,基于FFT变换计算谐波信号的基波粗糙频率f,其中N为2的整数次方;The fundamental wave rough frequency calculation program unit is used to add a window to the first N points for the M point sample value sequence, and calculate the fundamental wave rough frequency f of the harmonic signal based on FFT transformation, where N is an integer power of 2;

分辨率计算程序单元,用于根据谐波信号的基波粗糙频率f,计算满足频率分辨率自适应要求的采样点数Nia resolution calculation program unit, used for calculating the number of sampling points N i that satisfies the frequency resolution self-adaptation requirement according to the fundamental rough frequency f of the harmonic signal;

频率修正系数计算程序单元,用于对采样点数Ni点采样序列进行加窗双谱线插值DFT计算,获得频率修正系数δ(2)Frequency correction coefficient calculation program unit, for carrying out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N i , to obtain frequency correction coefficient δ (2) ;

基波特征获取程序单元,用于采用插值方法求解基波特征参量,包括基波幅值A1、基波频率f1和基波相位

Figure BDA0002409188360000027
Fundamental wave feature acquisition program unit, used to solve the fundamental wave characteristic parameters by interpolation method, including the fundamental wave amplitude A 1 , the fundamental wave frequency f 1 and the fundamental wave phase
Figure BDA0002409188360000027

谐波处理程序单元,用于针对任意指定的k次谐波:通过对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波幅值A1和基波相位

Figure BDA0002409188360000031
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000032
The harmonic processing program unit is used for any specified k-th harmonic: obtain the k-th harmonic frequency f k by multiplying the fundamental frequency f 1 by k times; according to the k-th harmonic frequency f k , the frequency is reversed and corrected Coefficient δ k(2) ; between fundamental amplitude A 1 and fundamental phase
Figure BDA0002409188360000031
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000032

可选地,所述谐波处理程序单元包括:Optionally, the harmonic processing program unit includes:

循环体初始化程序模块,用于指定待修正的k次谐波;The loop body initialization program module is used to specify the k-th harmonic to be corrected;

循环体执行程序模块,用于对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波频率f1和基波相位

Figure BDA0002409188360000033
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波频率fk和k次谐波相位
Figure BDA0002409188360000034
判断谐波计算是否完成,如果尚未完成则指定新的待修正的k次谐波,继续执行循环体执行程序模块;否则结束执行循环体程序单元。The loop body executes the program module, which is used to multiply the fundamental frequency f 1 by k times to obtain the k harmonic frequency f k ; inversely push the frequency correction coefficient δ k(2) according to the k harmonic frequency f k ; Frequency f1 and fundamental phase
Figure BDA0002409188360000033
On the basis of , the k-th harmonic frequency f k and the k-th harmonic phase are obtained by modifying according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000034
It is judged whether the harmonic calculation is completed, and if it has not been completed, a new k-th harmonic to be corrected is specified, and the execution of the loop body execution program module is continued; otherwise, the execution of the loop body program unit is ended.

此外,本发明还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括计算机设备,该计算机设备被编程或配置以执行所述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的步骤。In addition, the present invention also provides a spectral resolution adaptation based bispectral interpolation DFT harmonic analysis system, comprising a computer device programmed or configured to perform the spectral resolution adaptation based bispectrum Steps of the Interpolated DFT Harmonic Analysis Method.

此外,本发明还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括计算机设备,该计算机设备的存储器上存储有被编程或配置以执行所述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的计算机程序。In addition, the present invention also provides a spectral resolution-based adaptive bispectral line interpolation DFT harmonic analysis system, comprising a computer device, the computer device having a memory programmed or configured to perform the spectral resolution-based automatic analysis. A computer program adapted to the bispectral line interpolation DFT harmonic analysis method.

此外,本发明还提供一种计算机可读存储介质,该计算机可读存储介质上存储有被编程或配置以执行所述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的计算机程序。In addition, the present invention also provides a computer-readable storage medium, on which is stored a computer program programmed or configured to execute the spectral resolution adaptive-based bispectral interpolation DFT harmonic analysis method .

和现有技术相比,本发明具有下述优点:Compared with the prior art, the present invention has the following advantages:

1、本发明采用的算法简单,易于实现;1. The algorithm adopted in the present invention is simple and easy to implement;

2、本发明采用的算法和现有插值FFT算法相比,具有更高的噪声性能,在高斯噪声环境下相位误差更小。本发明采用了频谱分辨率自适应的方法以抑制频谱干扰。频谱分辨率自适应是指根据被测信号的频率范围自适应调整频率分辨率,一方面,能够使每次参数估计的方差都落于其参数估计的方差下限,以提高算法的噪声性能;另一方面,频谱分辨率自适应根据窗函数旁瓣特性合理自适应调整频率分辨率,使谐波计算时两根插值谱线幅值中的基波干扰分量大小基本一致,以抑制频谱干扰;2. Compared with the existing interpolation FFT algorithm, the algorithm adopted in the present invention has higher noise performance, and the phase error is smaller in the Gaussian noise environment. The present invention adopts a spectrum resolution adaptive method to suppress spectrum interference. Spectral resolution adaptation refers to adaptively adjusting the frequency resolution according to the frequency range of the measured signal. On the one hand, the variance of each parameter estimation can fall within the lower limit of the variance of its parameter estimation, so as to improve the noise performance of the algorithm; On the one hand, the spectral resolution adaptively adjusts the frequency resolution adaptively according to the side lobe characteristics of the window function, so that the magnitude of the fundamental interference component in the amplitudes of the two interpolated spectral lines is basically the same during the harmonic calculation, so as to suppress the spectral interference;

3、本发明采用的算法和现有插值FFT算法相比,在频率波动时相位误差更小。本发明采用了倍频逆推求取整次谐波的方法来避免谐波频率修正系数直接插值带来的噪声误差。倍频逆推求取整次谐波是指先通过基波频率倍频,估计k次谐波频率,逆推频率修正系数,在基波幅值A1和基波相位

Figure BDA0002409188360000035
的基础上,根据频率修正系数进行修正得到k次谐波幅值和k次谐波相位从而求取整次谐波。传统的插值FFT算法会通过谐波频谱的插值来计算修正谐波参数。假设谐波信号含量为基波的m%,采用插值方法时,谐波特征参数的参数估计噪声方差将约是基波的10000/m2倍。为了改善这个问题,本实施例通过基波频率倍频估计k次谐波频率,倍频逆推求取整次谐波。这种方式的参数估计方差将约为基波的k2。对于通常需要检测的2-13次谐波,可知k2<<(10000/m2),本发明采用了倍频逆推求取整次谐波的方法避免了谐波频率修正系数直接插值带来的巨大噪声误差。3. Compared with the existing interpolation FFT algorithm, the algorithm adopted in the present invention has smaller phase error when the frequency fluctuates. The invention adopts the method of multiplying the frequency inversely to obtain the whole harmonic to avoid the noise error caused by the direct interpolation of the harmonic frequency correction coefficient. To obtain integer harmonics by inverse frequency doubling refers to first multiplying the fundamental frequency, estimating the frequency of the k-th harmonic, inversely deriving the frequency correction coefficient, and obtaining the harmonics between the fundamental amplitude A 1 and the fundamental phase.
Figure BDA0002409188360000035
On the basis of , the k-th harmonic amplitude and the k-th harmonic phase are obtained by modifying the frequency correction coefficient to obtain the integer harmonic. The traditional interpolation FFT algorithm calculates the modified harmonic parameters by interpolating the harmonic spectrum. Assuming that the harmonic signal content is m% of the fundamental wave, when the interpolation method is adopted, the parameter estimation noise variance of the harmonic characteristic parameters will be about 10000/m 2 times that of the fundamental wave. In order to improve this problem, in this embodiment, the frequency of the k-th harmonic is estimated by multiplying the frequency of the fundamental wave, and the integer harmonic is obtained by inversely multiplying the frequency. The variance of the parameter estimates in this way will be about k 2 of the fundamental. For the 2-13th harmonics that usually need to be detected, it can be known that k 2 <<(10000/m 2 ), and the present invention adopts the method of multiplying the frequency inversely to obtain the integer harmonics to avoid the direct interpolation band of the harmonic frequency correction coefficient. huge noise error.

附图说明Description of drawings

图1为本发明实施例方法的基本流程示意图。FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.

图2为本发明实施例方法的误差。FIG. 2 is the error of the method according to the embodiment of the present invention.

图3为本发明实施例中作为对比的采用现有双插值FFT方法的误差。FIG. 3 is the error of using the existing double-interpolation FFT method as a comparison in the embodiment of the present invention.

图4为本发明实施例中作为对比的采用现有三插值FFT方法的误差。FIG. 4 is the error of using the existing three-interpolation FFT method for comparison in the embodiment of the present invention.

图5为本发明实施例中三种方法的基波参数误差标准差对比。FIG. 5 is a comparison of standard deviations of fundamental wave parameter errors of three methods in an embodiment of the present invention.

图6为本发明实施例中三种方法的谐波参数误差标准差对比。FIG. 6 is a comparison of standard deviations of harmonic parameter errors of three methods in an embodiment of the present invention.

具体实施方式Detailed ways

下面对本发明作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案,而不能以此来限制本发明的保护范围。The present invention is further described below. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

如图1,本实施例基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的步骤包括:As shown in FIG. 1 , the steps of the dual spectral line interpolation DFT harmonic analysis method based on adaptive spectral resolution in this embodiment include:

1)输入M点采样值序列;1) Input the M point sample value sequence;

2)针对M点采样值序列对前N点进行加窗,基于FFT变换计算谐波信号的基波粗糙频率f,其中N为2的整数次方;2) windowing the first N points for the M-point sample value sequence, and calculating the fundamental rough frequency f of the harmonic signal based on the FFT transformation, where N is an integer power of 2;

3)根据谐波信号的基波粗糙频率f,计算满足频率分辨率自适应要求的采样点数Ni3) According to the fundamental rough frequency f of the harmonic signal, calculate the number of sampling points N i that meets the frequency resolution self-adaptation requirement;

4)对采样点数Ni点采样序列进行加窗双谱线插值DFT计算,获得频率修正系数δ(2)4) carry out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N i , obtain frequency correction coefficient δ (2) ;

5)采用插值方法求解基波特征参量,包括基波幅值A1、基波频率f1和基波相位

Figure BDA0002409188360000041
5) Use the interpolation method to solve the fundamental wave characteristic parameters, including the fundamental wave amplitude A 1 , the fundamental wave frequency f 1 and the fundamental wave phase
Figure BDA0002409188360000041

6)针对任意指定的k次谐波:通过对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波幅值A1和基波相位

Figure BDA0002409188360000042
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000043
6) For the arbitrarily specified k-th harmonic: obtain the k-th harmonic frequency f k by multiplying the fundamental frequency f 1 by k; according to the k-th harmonic frequency f k , reverse the frequency correction coefficient δ k (2) ; at fundamental amplitude A 1 and fundamental phase
Figure BDA0002409188360000042
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000043

作为一种特定的循环遍历实现方式,如图1,本实施例中步骤6)的详细步骤包括:As a specific implementation of loop traversal, as shown in Figure 1, the detailed steps of step 6) in this embodiment include:

6.1)指定待修正的k次谐波;6.1) Specify the k-th harmonic to be corrected;

6.2)对基波频率f1进行k倍倍频得到k次谐波频率fk6.2) Perform k-fold frequency multiplication on the fundamental frequency f 1 to obtain the k-th harmonic frequency f k ;

6.3)根据k次谐波频率fk逆推频率修正系数δk(2)6.3) Inversely push the frequency correction coefficient δk (2) according to the k -th harmonic frequency fk;

6.4)在基波幅值A1和基波相位

Figure BDA0002409188360000044
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000045
6.4 ) At fundamental amplitude A1 and fundamental phase
Figure BDA0002409188360000044
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000045

6.5)判断谐波计算是否完成,如果尚未完成则指定新的待修正的k次谐波,跳转执行步骤6.2);否则结束。6.5) Determine whether the harmonic calculation is completed, if not, specify a new k-th harmonic to be corrected, and skip to step 6.2); otherwise, end.

由双插值方法频率分辨率的物理含义可知,为使频率修正系数尽可能小,采样点数Ni应为(整数+1/2)个信号周期。本实施例中,步骤3)中采样点数Ni的计算函数表达式为:From the physical meaning of the frequency resolution of the double interpolation method, it can be known that in order to make the frequency correction coefficient as small as possible, the number of sampling points N i should be (integer+1/2) signal period. In the present embodiment, the calculation function expression of the number of sampling points N i in step 3) is:

Figure BDA0002409188360000051
Figure BDA0002409188360000051

上式中,round为四舍五入取整函数,f为谐波信号的基波粗糙频率,fs为采样频率,N为步骤2)中针对M点采样值序列进行加窗的采样值数量。In the above formula, round is the rounding function, f is the fundamental rough frequency of the harmonic signal, fs is the sampling frequency, and N is the number of sampled values that are windowed for the M-point sampled value sequence in step 2).

本实施例中,所述逆推频率修正系数δk(2)的计算函数表达式为:In this embodiment, the calculation function expression of the inverse frequency correction coefficient δk (2) is:

Figure BDA0002409188360000052
Figure BDA0002409188360000052

上式中,fk为k次谐波频率,Ni为满足频率分辨率自适应要求的采样点数Ni,fs为采样频率,floor为向下取整函数。In the above formula, f k is the k -th harmonic frequency, Ni is the number of sampling points Ni that meets the frequency resolution adaptive requirement, f s is the sampling frequency, and floor is a round-down function.

为了对本实施例基于频谱分辨率自适应的双谱线插值DFT谐波分析方法进行验证,本实施例中采用了仿真对比的方法。In order to verify the dual spectral line interpolation DFT harmonic analysis method based on adaptive spectral resolution in this embodiment, a simulation comparison method is adopted in this embodiment.

1、无噪声下的谐波计算精度仿真。1. Simulation of harmonic calculation accuracy without noise.

在仿真过程中,保持各次谐波的幅值和相位不变,分析不同算法在信号频率45-55Hz变化时的误差情况(其他参数:基波幅值20000V,采样频率4kHz,参考算法采样点数1024,窗函数选择4项3阶窗)。仿真中在基波上叠加2-13次谐波,各次谐波相对含量如表1所示,对比使用的双插值FFT和三插值FFT算法作为本实施例基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的对比方法。In the simulation process, keep the amplitude and phase of each harmonic unchanged, and analyze the error of different algorithms when the signal frequency changes from 45 to 55 Hz (other parameters: fundamental wave amplitude 20000V, sampling frequency 4kHz, reference algorithm sampling points 1024, the window function selects 4 items of third-order window). In the simulation, the 2-13th harmonics are superimposed on the fundamental wave, and the relative content of each harmonic is shown in Table 1. The double-interpolation FFT and triple-interpolation FFT algorithms used in comparison are used as the bispectrum adaptive spectrum resolution based on this embodiment. Contrasting method of line interpolation DFT harmonic analysis method.

表1:仿真参数表。Table 1: Table of simulation parameters.

Figure BDA0002409188360000053
Figure BDA0002409188360000053

最终得到的仿真结果如图2、图3和图4所示以及表2所示。The final simulation results are shown in Figure 2, Figure 3, Figure 4 and Table 2.

Figure BDA0002409188360000054
Figure BDA0002409188360000054

Figure BDA0002409188360000061
Figure BDA0002409188360000061

仿真结果显示,2次谐波由于离基波最近,受到基波频谱干扰最大,因此检测误差最大,其中双插值FFT算法最大比差超过0.01%,最大角差接近±0.15%;三插值FFT最大比差接近±0.002%,最大角差接近±0.04%。而本文改进的算法最大比差±0.002%,最大角差-0.002%。总体而言,双插值FFT算法和三插值FFT算法虽然幅值计算精度很高,但是相位计算误差偏大,本实施例方法通过大范围提升相位计算精度,实现了算法谐波参数计算整体精度的提升。The simulation results show that the second harmonic is the closest to the fundamental wave and suffers the most interference from the fundamental wave spectrum, so the detection error is the largest. The maximum ratio difference of the double interpolation FFT algorithm exceeds 0.01%, and the maximum angle difference is close to ±0.15%; the triple interpolation FFT has the largest ratio difference. The ratio difference is close to ±0.002%, and the maximum angular difference is close to ±0.04%. The algorithm improved in this paper has a maximum ratio difference of ±0.002% and a maximum angle difference of -0.002%. In general, although the double-interpolation FFT algorithm and the triple-interpolation FFT algorithm have high amplitude calculation accuracy, the phase calculation error is relatively large. promote.

2、噪声背景下的谐波误差标准差仿真。2. Simulation of harmonic error standard deviation under noise background.

噪声背景下的谐波误差标准差仿真时,各次信号含量及其他参数如上无噪声下的谐波计算精度仿真,并在源信号的基础上方差为1的随机数模拟宽带噪声,此时基波信噪比约为83dB,各次谐波信号的信噪比分别如下表(表3)所示。When simulating the standard deviation of harmonic errors under the noise background, the signal content and other parameters of each order are as above the harmonic calculation accuracy simulation without noise, and based on the source signal, a random number with a variance of 1 simulates broadband noise. The signal-to-noise ratio of the wave is about 83dB, and the signal-to-noise ratio of each harmonic signal is shown in the following table (Table 3).

表3:仿真中信号噪声比。Table 3: Signal-to-noise ratio in the simulation.

谐波次数harmonic order 11 22 33 44 55 66 77 A<sub>i</sub>A<sub>i</sub> 100%100% 2%2% 5%5% 2%2% 5%5% 1%1% 1%1% SNR<sub>i</sub>(dB)SNR<sub>i</sub>(dB) 8383 4949 5757 4949 5757 4343 4343 谐波次数harmonic order 88 99 1010 1111 1212 1313 -- A<sub>i</sub>A<sub>i</sub> 1%1% 1%1% 0.5%0.5% 0.5%0.5% 0.5%0.5% 0.5%0.5% -- SNRi(dB)SNRi(dB) 4343 4343 3737 3737 3737 3737 --

噪声背景下各算法信号特征提取比差标准差和角差标准差仿真结果如图5、图6所示,图中,带圆形点的折线(改进双谱线)为本实施例方法,带星形点的折线(双谱线)为双插值FFT算法,带方形点的折线(三谱线)为三插值FFT算法。从图5和图6中的结果来看:(1)基波计算时,改进算法的误差标准差一直位于双插值FFT和三插值FFT误差标准差的下方,达到了使每次参数估计的方差都落于类似算法参数估计的方差下限的目标,减小了噪声背景下参数估计方差。(2)谐波计算时,参数估计的误差明显增大,其中改进算法谐波计算比差标准差约为0.06%,角差标准差约为2.3′,与双插值FFT和三插值FFT比差标准差与此接近,但是相比后两者的约8′角差标准差,相位计算精度提升近4倍。(3)如仿真所示的一个宽带噪声信噪比83dB的系统,由于谐波含量较低,谐波测量噪声误差大于频谱干扰误差,此时算法噪声误差已成为算法误差的主要成分,进一步改变窗函数的旁瓣性能抑制频谱泄露和频谱干扰已没有意义。(4)可以预见的是,当实际运行状态中谐波含量更低时,其谐波信噪比将进一步降低,使用传统的插值求谐波参数的方法相位测量误差将进一步增大;而本文提出的方法避免了这一问题,其误差与谐波的含量无关,仅与基波信噪比和谐波次数有关。从仿真结果总体来看,双插值FFT和三插值FFT算法在噪声背景下也面临着相位误差偏大而影响算法整体性能的问题,本实施例方法较大程度的提升了算法的相位估计精度,从而提升了算法的整体精度。The simulation results of the ratio standard deviation and angular deviation standard deviation of each algorithm's signal feature extraction under the noise background are shown in Figure 5 and Figure 6. The broken line (double spectral line) with star-shaped points is the double interpolation FFT algorithm, and the broken line (triple spectrum) with square points is the triple interpolation FFT algorithm. From the results in Figure 5 and Figure 6: (1) During the fundamental wave calculation, the error standard deviation of the improved algorithm is always below the error standard deviation of the double-interpolation FFT and triple-interpolation FFT, and the variance of each parameter estimation is achieved. All fall within the target of the lower limit of the variance of the parameter estimation of the similar algorithm, which reduces the variance of the parameter estimation under the noise background. (2) During the harmonic calculation, the error of parameter estimation increases obviously. The standard deviation of the harmonic calculation ratio of the improved algorithm is about 0.06%, and the standard deviation of the angle deviation is about 2.3′, which is worse than the double interpolation FFT and triple interpolation FFT. The standard deviation is close to this, but compared with the standard deviation of about 8′ angular deviation of the latter two, the phase calculation accuracy is improved by nearly 4 times. (3) As shown in the simulation, for a system with a wideband noise signal-to-noise ratio of 83dB, due to the low harmonic content, the harmonic measurement noise error is greater than the spectral interference error. At this time, the algorithm noise error has become the main component of the algorithm error, and further changes The side lobe performance of the window function has no meaning to suppress spectral leakage and spectral interference. (4) It is foreseeable that when the harmonic content in the actual operating state is lower, the harmonic signal-to-noise ratio will be further reduced, and the phase measurement error will be further increased by using the traditional interpolation method to obtain harmonic parameters. The proposed method avoids this problem, and its error has nothing to do with the content of harmonics, but only with the fundamental signal-to-noise ratio and harmonic order. From the overall simulation results, the double-interpolation FFT and triple-interpolation FFT algorithms also face the problem that the phase error is too large under the noise background, which affects the overall performance of the algorithm. The method of this embodiment greatly improves the phase estimation accuracy of the algorithm. This improves the overall accuracy of the algorithm.

综上所述,利用常用的双插值FFT或三插值FFT进行谐波参数估计时,面临着谱间干扰致使相位误差偏大、宽带噪声干扰造成谐波参数估计值方差偏大等问题。本发明通过分析窗函数、插值方法对算法谱间干扰误差和宽带噪声误差的影响机理,提出了一种改进双插值DFT算法,本实施例方法通过频谱分辨率自适应抑制谱间干扰、降低参数估计方差,并通过倍频逆推求整次谐波避免了插值求谐波方法带来的误差增大。本实施例对双插值FFT、三插值FFT以及本实施例方法开展了仿真实验,结果表明,在相同信号条件下,本实施例方法提出的算法精度更高。因此,本实施例基于频谱分辨率自适应的双谱线插值DFT谐波分析方法通过频谱分辨率自适应抑制基波对谐波计算的频谱干扰,并通过倍频逆推求取整次谐波,避免插值计算谐波带来的误差。To sum up, when using the commonly used double-interpolation FFT or triple-interpolation FFT to estimate harmonic parameters, there are problems such as large phase error caused by inter-spectral interference and large variance of harmonic parameter estimates caused by broadband noise interference. The present invention proposes an improved double-interpolation DFT algorithm by analyzing the influence mechanism of the window function and the interpolation method on the inter-spectral interference error and the broadband noise error of the algorithm. The variance is estimated, and the integer harmonics are obtained by inverse frequency doubling to avoid the increase of errors caused by the interpolation method for obtaining harmonics. In this embodiment, a simulation experiment is carried out on the double-interpolation FFT, the triple-interpolation FFT and the method of this embodiment, and the results show that under the same signal conditions, the algorithm proposed by the method of this embodiment has higher precision. Therefore, the present embodiment based on the spectral resolution adaptive bispectral line interpolation DFT harmonic analysis method suppresses the spectral interference of the fundamental wave on the harmonic calculation through the spectral resolution adaptive, and obtains the integer harmonics through frequency doubling inverse. , to avoid the error caused by the interpolation calculation of harmonics.

此外本实施例还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括:In addition, this embodiment also provides a dual spectral line interpolation DFT harmonic analysis system based on spectral resolution adaptation, including:

采样值输入程序单元,用于输入M点采样值序列;The sampled value input program unit is used to input the M-point sampled value sequence;

基波粗糙频率计算程序单元,用于针对M点采样值序列对前N点进行加窗,基于FFT变换计算谐波信号的基波粗糙频率f,其中N为2的整数次方;The fundamental wave rough frequency calculation program unit is used to add a window to the first N points for the M point sample value sequence, and calculate the fundamental wave rough frequency f of the harmonic signal based on FFT transformation, where N is an integer power of 2;

分辨率计算程序单元,用于根据谐波信号的基波粗糙频率f,计算满足频率分辨率自适应要求的采样点数Nia resolution calculation program unit, used for calculating the number of sampling points N i that satisfies the frequency resolution self-adaptation requirement according to the fundamental rough frequency f of the harmonic signal;

频率修正系数计算程序单元,用于对采样点数Ni点采样序列进行加窗双谱线插值DFT计算,获得频率修正系数δ(2)Frequency correction coefficient calculation program unit, for carrying out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N i , to obtain frequency correction coefficient δ (2) ;

基波特征获取程序单元,用于采用插值方法求解基波特征参量,包括基波幅值A1、基波频率f1和基波相位

Figure BDA0002409188360000071
Fundamental wave feature acquisition program unit, used to solve the fundamental wave characteristic parameters by interpolation method, including the fundamental wave amplitude A 1 , the fundamental wave frequency f 1 and the fundamental wave phase
Figure BDA0002409188360000071

谐波处理程序单元,用于针对任意指定的k次谐波:通过对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波幅值A1和基波相位

Figure BDA0002409188360000072
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波幅值Ak和k次谐波相位
Figure BDA0002409188360000073
The harmonic processing program unit is used for any specified k-th harmonic: obtain the k-th harmonic frequency f k by multiplying the fundamental frequency f 1 by k times; according to the k-th harmonic frequency f k , the frequency is reversed and corrected Coefficient δ k(2) ; between fundamental amplitude A 1 and fundamental phase
Figure BDA0002409188360000072
On the basis of , the k-th harmonic amplitude A k and the k-th harmonic phase are obtained by modifying it according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000073

作为一种特定的循环遍历实现方式,本实施例中谐波处理程序单元包括:As a specific implementation of loop traversal, the harmonic processing program unit in this embodiment includes:

循环体初始化程序模块,用于指定待修正的k次谐波;The loop body initialization program module is used to specify the k-th harmonic to be corrected;

循环体执行程序模块,用于对基波频率f1进行k倍倍频得到k次谐波频率fk;根据k次谐波频率fk逆推频率修正系数δk(2);在基波频率f1和基波相位

Figure BDA0002409188360000074
的基础上,根据频率修正系数δk(2)进行修正得到k次谐波频率fk和k次谐波相位
Figure BDA0002409188360000075
判断谐波计算是否完成,如果尚未完成则指定新的待修正的k次谐波,继续执行循环体执行程序模块;否则结束执行循环体程序单元。The loop body executes the program module, which is used to multiply the fundamental frequency f 1 by k times to obtain the k harmonic frequency f k ; inversely push the frequency correction coefficient δ k(2) according to the k harmonic frequency f k ; Frequency f1 and fundamental phase
Figure BDA0002409188360000074
On the basis of , the k-th harmonic frequency f k and the k-th harmonic phase are obtained by modifying according to the frequency correction coefficient δ k(2) .
Figure BDA0002409188360000075
It is judged whether the harmonic calculation is completed, and if it has not been completed, a new k-th harmonic to be corrected is specified, and the execution of the loop body execution program module is continued; otherwise, the execution of the loop body program unit is ended.

此外本实施例还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括计算机设备,该计算机设备被编程或配置以执行前述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的步骤。In addition, the present embodiment also provides a spectral resolution adaptive based bispectral interpolation DFT harmonic analysis system, comprising a computer device programmed or configured to perform the aforementioned spectral resolution adaptive based bispectral interpolation Steps of the DFT harmonic analysis method.

此外本实施例还提供一种基于频谱分辨率自适应的双谱线插值DFT谐波分析系统,包括计算机设备,该计算机设备的存储器上存储有被编程或配置以执行前述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的计算机程序。In addition, this embodiment also provides a spectral resolution-based adaptive bispectral line interpolation DFT harmonic analysis system, including a computer device, and the computer device has a memory that is programmed or configured to perform the aforementioned spectral resolution-based adaptation. A computer program for the bispectral interpolation DFT harmonic analysis method.

此外本实施例还提供一种计算机可读存储介质,该计算机可读存储介质上存储有被编程或配置以执行前述基于频谱分辨率自适应的双谱线插值DFT谐波分析方法的计算机程序。In addition, the present embodiment also provides a computer-readable storage medium on which a computer program programmed or configured to execute the foregoing spectral resolution adaptation-based bispectral interpolation DFT harmonic analysis method is stored.

本领域内的技术人员应明白,本申请的实施例可提供为方法、系统、或计算机程序产品。因此,本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein. The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram. These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flows of the flowcharts and/or the block or blocks of the block diagrams. These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

以上所述仅是本发明的优选实施方式,本发明的保护范围并不仅局限于上述实施例,凡属于本发明思路下的技术方案均属于本发明的保护范围。应当指出,对于本技术领域的普通技术人员来说,在不脱离本发明原理前提下的若干改进和润饰,这些改进和润饰也应视为本发明的保护范围。The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims (9)

1. A double spectral line interpolation DFT harmonic analysis method based on spectrum resolution self-adaption is characterized by comprising the following steps:
1) inputting an M-point sampling value sequence;
2) windowing is carried out on the first N points aiming at the M point sampling value sequence, and the fundamental wave rough frequency f of the harmonic signal is calculated based on FFT transformation, wherein N is an integer power of 2;
3) according to the fundamental wave rough frequency f of the harmonic signal, calculating the number N of sampling points meeting the self-adaptive requirement of frequency resolutioni
4) Number of sampling points NiPerforming windowing double-spectral-line interpolation DFT calculation on the point sampling sequence to obtain a frequency correction coefficient delta(2)
5) The interpolation method is adopted to solve the fundamental wave characteristic parameters including the fundamental wave amplitude A1Fundamental frequency f1And fundamental wave phase
Figure FDA0002409188350000018
6) For any given k harmonics: by applying to the fundamental frequency f1K times frequency multiplication is carried out to obtain k harmonic frequency fk(ii) a According to the k harmonic frequency fkInverse frequency correction factor deltak(2)(ii) a At the fundamental amplitude A1And fundamental wave phase
Figure FDA0002409188350000014
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
Figure FDA0002409188350000015
2. The spectral resolution adaptation-based doublet line interpolation DFT harmonic analysis method according to claim 1, wherein the detailed step of step 6) comprises:
6.1) specifying a k-th harmonic to be corrected;
6.2) vs. fundamental frequency f1K times frequency multiplication is carried out to obtain k harmonic frequency fk
6.3) according to the k harmonic frequency fkInverse frequency correction factor deltak(2)
6.4) at fundamental amplitude A1And fundamental wave phase
Figure FDA0002409188350000016
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
Figure FDA0002409188350000017
6.5) judging whether the harmonic calculation is finished, if not, appointing a new k-th harmonic to be corrected, and skipping to execute the step 6.2); otherwise, ending.
3. The spectral resolution adaptive-based double-spectral-line interpolation DFT harmonic analysis method according to claim 1, wherein the number of sampling points N in step 3)iThe formula of the calculation function is:
Figure FDA0002409188350000011
in the above formula, round is a rounding function, f is the fundamental coarse frequency of the harmonic signal, fsAnd N is the sampling value number for windowing the M-point sampling value sequence in the step 2).
4. Spectral resolution adaptation based bilinear interpolation DFT harmonic in accordance with claim 1Analysis method characterized in that said inverse frequency correction factor δk(2)The formula of the calculation function is:
Figure FDA0002409188350000012
in the above formula, fkIs the k harmonic frequency, NiNumber of sampling points N for satisfying frequency resolution self-adaptive requirementi,fsFor sampling frequency, floor is a floor rounding function.
5. A double-spectral-line interpolation DFT harmonic analysis system based on spectrum resolution self-adaptation is characterized by comprising:
the sampling value input program unit is used for inputting M-point sampling value sequences;
a fundamental wave rough frequency calculation program unit, which is used for windowing the first N points aiming at the M point sampling value sequence and calculating the fundamental wave rough frequency f of the harmonic signal based on FFT transformation, wherein N is an integer power of 2;
a resolution calculation program unit for calculating the number N of sampling points satisfying the frequency resolution adaptive requirement according to the fundamental wave rough frequency f of the harmonic signali
A frequency correction coefficient calculation program unit for counting the number of sampling points NiPerforming windowing double-spectral-line interpolation DFT calculation on the point sampling sequence to obtain a frequency correction coefficient delta(2)
A fundamental wave characteristic acquisition program unit for solving fundamental wave characteristic parameters including fundamental wave amplitude A by interpolation method1Fundamental frequency f1And fundamental wave phase
Figure FDA0002409188350000021
A harmonic processing program unit for, for an arbitrarily specified k-th harmonic: by applying to the fundamental frequency f1K times frequency multiplication is carried out to obtain k harmonic frequency fk(ii) a According to the k harmonic frequency fkInverse frequency correction factor deltak(2)(ii) a At the fundamental amplitude A1And fundamental wave phaseBit
Figure FDA0002409188350000024
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
Figure FDA0002409188350000025
6. The spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis system of claim 5, wherein the harmonic processing program unit comprises:
the loop body initialization program module is used for appointing k-th harmonic waves to be corrected;
a program module is executed by the loop body for the fundamental frequency f1K times frequency multiplication is carried out to obtain k harmonic frequency fk(ii) a According to the k harmonic frequency fkInverse frequency correction factor deltak(2)(ii) a At the fundamental frequency f1And fundamental wave phase
Figure FDA0002409188350000022
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic frequency fkAnd phase of the k harmonic
Figure FDA0002409188350000023
Judging whether the harmonic calculation is finished or not, if not, designating a new k-th harmonic to be corrected, and continuing to execute the loop body execution program module; otherwise, ending executing the loop body program unit.
7. A spectral resolution adaptation based dual-line interpolation DFT harmonic analysis system comprising a computer device, characterized in that the computer device is programmed or configured to perform the steps of the spectral resolution adaptation based dual-line interpolation DFT harmonic analysis method according to any of claims 1 to 4.
8. A spectral resolution adaptation based dual-line interpolation DFT harmonic analysis system comprising a computer device, characterized in that a computer program programmed or configured to perform the spectral resolution adaptation based dual-line interpolation DFT harmonic analysis method according to any of claims 1 to 4 is stored on a memory of the computer device.
9. A computer readable storage medium having stored thereon a computer program programmed or configured to perform the spectral resolution adaptation based bilinear interpolation DFT harmonic analysis method according to any of claims 1 to 4.
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CN112462138A (en) * 2020-10-23 2021-03-09 南京国电南自电网自动化有限公司 Harmonic measurement method and system
CN112781723A (en) * 2021-01-27 2021-05-11 南京微动智测信息技术有限公司 Harmonic component detection method based on frequency spectrum variance
CN112781723B (en) * 2021-01-27 2023-09-12 南京微动智测信息技术有限公司 Harmonic component detection method based on frequency spectrum variance
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CN114838809A (en) * 2022-03-22 2022-08-02 珠海市运泰利自动化设备有限公司 Audio signal measuring method for self-adaptively improving frequency measurement precision
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CN116359605A (en) * 2023-04-21 2023-06-30 中国计量科学研究院 Harmonic signal analysis method based on secondary weighting
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