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

Abstract

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.

Description

Dual spectral line interpolation DFT harmonic analysis method and system based on adaptive spectral resolution and medium

technical field

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.

Background technique

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.

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.

SUMMARY OF THE INVENTION

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.

In order to solve the above-mentioned technical problems, the technical scheme adopted in the present invention is:

A dual spectral line interpolation DFT harmonic analysis method based on spectral resolution adaptation, the steps include:

1) Input the M point sample value sequence;

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) 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) carry out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N _i , obtain frequency correction coefficient δ ₍₂₎ ;

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

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

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

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) .

Optionally, the detailed steps of step 6) include:

6.1) Specify the k-th harmonic to be corrected;

6.2) Perform k-fold frequency multiplication on the fundamental frequency f ₁ to obtain the k-th harmonic frequency f _k ;

6.3) Inversely push the frequency correction coefficient δk ₍₂₎ according to the _k -th harmonic frequency fk;

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

6.4 ₎ At fundamental amplitude A1 and fundamental phase

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) .

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.

Optionally, the calculation function expression of the number of sampling points N _i in step 3) is:

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).

Optionally, the calculation function expression of the inverse frequency correction coefficient δk ₍₂₎ is:

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.

In addition, the present invention also provides a dual spectral line interpolation DFT harmonic analysis system based on spectral resolution adaptation, including:

The sampled value input program unit is used to input the M-point sampled value sequence;

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;

a 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;

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₎ ;

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

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

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

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) .

Optionally, the harmonic processing program unit includes:

The loop body initialization program module is used to specify the k-th harmonic to be corrected;

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波频率f_k和k次谐波相位

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

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) .

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.

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.

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.

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 .

Compared with the prior art, the present invention has the following advantages:

1. The algorithm adopted in the present invention is simple and easy to implement;

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;

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.

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.

Description of drawings

FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.

FIG. 2 is the error of the method according to the embodiment of the present invention.

FIG. 3 is the error of using the existing double-interpolation FFT method as a comparison in the embodiment of the present invention.

FIG. 4 is the error of using the existing three-interpolation FFT method for comparison in the embodiment of the present invention.

FIG. 5 is a comparison of standard deviations of fundamental wave parameter errors of three methods in an embodiment of the present invention.

FIG. 6 is a comparison of standard deviations of harmonic parameter errors of three methods in an embodiment of the present invention.

Detailed ways

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.

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) Input the M point sample value sequence;

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) 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) carry out windowed bispectral interpolation DFT calculation to the sampling sequence of sampling point number N _i , obtain frequency correction coefficient δ ₍₂₎ ;

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

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

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

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) .

As a specific implementation of loop traversal, as shown in Figure 1, the detailed steps of step 6) in this embodiment include:

6.1) Specify the k-th harmonic to be corrected;

6.2) Perform k-fold frequency multiplication on the fundamental frequency f ₁ to obtain the k-th harmonic frequency f _k ;

6.3) Inversely push the frequency correction coefficient δk ₍₂₎ according to the _k -th harmonic frequency fk;

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

6.4 ₎ At fundamental amplitude A1 and fundamental phase

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) .

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.

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:

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).

In this embodiment, the calculation function expression of the inverse frequency correction coefficient δk ₍₂₎ is:

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.

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. Simulation of harmonic calculation accuracy without noise.

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.

Table 1: Table of simulation parameters.

The final simulation results are shown in Figure 2, Figure 3, Figure 4 and Table 2.

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. Simulation of harmonic error standard deviation under noise background.

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).

Table 3: Signal-to-noise ratio in the simulation.

harmonic order 1 2 3 4 5 6 7 A_i 100% 2% 5% 2% 5% 1% 1% SNR_i(dB) 83 49 57 49 57 43 43 harmonic order 8 9 10 11 12 13 - A_i 1% 1% 0.5% 0.5% 0.5% 0.5% - SNRi(dB) 43 43 37 37 37 37 -

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.

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.

In addition, this embodiment also provides a dual spectral line interpolation DFT harmonic analysis system based on spectral resolution adaptation, including:

The sampled value input program unit is used to input the M-point sampled value sequence;

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;

a 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;

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₎ ;

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

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波幅值A_k和k次谐波相位

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

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) .

As a specific implementation of loop traversal, the harmonic processing program unit in this embodiment includes:

The loop body initialization program module is used to specify the k-th harmonic to be corrected;

的基础上，根据频率修正系数δ_k(2)进行修正得到k次谐波频率f_k和k次谐波相位

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

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) .

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.

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.

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.

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.

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.

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 resolution_i；

4) Number of sampling points N_iPerforming 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

6) For any given k harmonics: by applying to the fundamental frequency f₁K times frequency multiplication is carried out to obtain k harmonic frequency f_k(ii) a According to the k harmonic frequency f_kInverse frequency correction factor delta_k(2)(ii) a At the fundamental amplitude A₁And fundamental wave phase

Based on the frequency correction factor delta_k(2)Corrected to obtain k-th harmonic amplitude A_kAnd phase of the k harmonic

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 f_k；

6.3) according to the k harmonic frequency f_kInverse frequency correction factor delta_k(2)；

6.4) at fundamental amplitude A₁And fundamental wave phase

Based on the frequency correction factor delta_k(2)Corrected to obtain k-th harmonic amplitude A_kAnd phase of the k harmonic

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:

in the above formula, round is a rounding function, f is the fundamental coarse frequency of the harmonic signal, f_sAnd 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 δ_k(2)The formula of the calculation function is:

in the above formula, f_kIs the k harmonic frequency, N_iNumber of sampling points N for satisfying frequency resolution self-adaptive requirement_i，f_sFor 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 signal_i；

A frequency correction coefficient calculation program unit for counting the number of sampling points N_iPerforming 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

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 f_k(ii) a According to the k harmonic frequency f_kInverse frequency correction factor delta_k(2)(ii) a At the fundamental amplitude A₁And fundamental wave phaseBit

Based on the frequency correction factor delta_k(2)Corrected to obtain k-th harmonic amplitude A_kAnd phase of the k harmonic

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 f_k(ii) a According to the k harmonic frequency f_kInverse frequency correction factor delta_k(2)(ii) a At the fundamental frequency f₁And fundamental wave phase

Based on the frequency correction factor delta_k(2)Corrected to obtain k-th harmonic frequency f_kAnd phase of the k harmonic

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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