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 PDFInfo
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Abstract
The invention discloses a method, a system and a medium for double spectral line interpolation DFT harmonic analysis based on spectrum resolution self-adaptationi(ii) a Number of sampling points NiPerforming windowing double-spectral-line interpolation DFT calculation on the point sampling sequence to obtain a frequency correction coefficient; solving fundamental wave characteristic parameters, aiming at k-th harmonic: carrying out k times frequency multiplication on the fundamental frequency to obtain k times of harmonic frequency; reversely pushing a frequency correction coefficient according to the k-th harmonic frequency; and on the basis of the fundamental wave frequency and the fundamental wave phase, correcting according to the frequency correction coefficient to obtain the k-th harmonic frequency and the k-th harmonic phase. The invention can adaptively inhibit the spectrum interference of the fundamental wave on the harmonic calculation through the spectrum resolution, and can avoid the error caused by the interpolation calculation of the harmonic by calculating the integral harmonic through the frequency multiplication reverse deduction.
Description
Technical Field
The invention relates to the field of harmonic signal analysis of a power system, in particular to a double spectral line interpolation DFT harmonic analysis method, system and medium based on spectrum resolution self-adaption, which are used for analyzing harmonic signals of the power system and extracting characteristic information in the harmonic signals.
Background
The wide application of power electronic equipment in a power system generates a large amount of harmonic waves, and the safe and stable operation of the power system is greatly threatened. Therefore, it is necessary to detect and analyze harmonic signals of the power system in order to prevent harmonic damage. Because various harmonics and broadband random noise exist in a time domain signal of a power system, direct measurement of signal characteristic information is difficult to perform.
Discrete Fourier Transform (DFT) is used as a classical spectrum analysis method, has higher signal-to-noise ratio gain while realizing spectrum separation, and is often applied to detection of fundamental wave and harmonic characteristic information of a power system. The DFT algorithm precision is improved by adopting a time domain windowing function and a frequency domain spectral line interpolation method. For many years, the window function has undergone an evolution from the Hannning window to the Nuttll window, and the number of weighted spectral lines of the interpolation method has also increased from one to two, or even three. Therefore, the sidelobe level of the window function is continuously reduced, the number of the interpolation spectral lines is continuously increased, the frequency spectrum leakage and the fence benefit of the algorithm are inhibited, and the algorithm precision is improved. However, the existing algorithm still has the defects of large phase error under inter-spectrum interference, large phase estimation variance under noise background and the like.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: aiming at the defects of the existing algorithm in the calculation accuracy in the presence of spectrum interference and broadband noise, the invention provides a spectrum resolution self-adaptive double-spectrum-line interpolation DFT harmonic analysis method, system and medium.
In order to solve the technical problems, the invention adopts the technical scheme that:
a double spectral line interpolation DFT harmonic analysis method based on spectrum resolution self-adaption comprises 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) By means of a socketSolving fundamental characteristic parameters including fundamental amplitude A by value method1Fundamental 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 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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
Optionally, the detailed steps of step 6) include:
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd 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.
Optionally, 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, fsAnd N is the sampling value number for windowing the M-point sampling value sequence in the step 2).
Optionally, the backward frequency correction factor δk(2)The formula of the calculation function is:
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.
In addition, the invention also provides a spectrum resolution self-adaptive dual-spectral line interpolation DFT harmonic analysis system, which comprises:
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
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 phase
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
Optionally, the harmonic processing program unit includes:
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic frequency fkAnd 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.
Furthermore, the present invention also provides a spectral resolution adaptation based bilinear interpolation DFT harmonic analysis system, comprising a computer device programmed or configured to perform the steps of the spectral resolution adaptation based bilinear interpolation DFT harmonic analysis method.
In addition, the invention also provides a spectral resolution adaptive-based double-spectral-line interpolation DFT harmonic analysis system, which comprises a computer device, wherein a memory of the computer device is stored with a computer program programmed or configured to execute the spectral resolution adaptive-based double-spectral-line interpolation DFT harmonic analysis method.
Furthermore, the present invention also provides a computer readable storage medium having stored thereon a computer program programmed or configured to execute the spectral resolution adaptation based bilinear interpolation DFT harmonic analysis method.
Compared with the prior art, the invention has the following advantages:
1. the algorithm adopted by the invention is simple and easy to realize;
2. compared with the existing interpolation FFT algorithm, the algorithm adopted by the invention has higher noise performance and smaller phase error in Gaussian noise environment. The invention adopts a method of spectrum resolution self-adaption to restrain spectrum interference. The self-adaption of the frequency spectrum resolution refers to self-adaption adjustment of the frequency resolution according to the frequency range of a detected signal, on one hand, the variance of each parameter estimation can be enabled to fall on the lower limit of the variance of the parameter estimation, and the noise performance of the algorithm is improved; on the other hand, the frequency resolution is adaptively and reasonably adjusted according to the sidelobe characteristic of the window function in a self-adaptive manner, so that the fundamental wave interference components in the amplitudes of the two interpolation spectral lines are basically consistent during harmonic calculation, and the frequency spectrum interference is suppressed;
3. compared with the existing interpolation FFT algorithm, the algorithm adopted by the invention has smaller phase error when the frequency fluctuates. The invention adopts a method of frequency multiplication inverse deduction to obtain integral harmonic wave to avoid noise error caused by direct interpolation of harmonic wave frequency correction coefficient. The frequency multiplication inverse calculation for the integral harmonic wave means that the frequency multiplication is carried out through the fundamental wave frequency, the k harmonic wave frequency is estimated, the frequency correction coefficient is inversely deduced, and the amplitude A of the fundamental wave is obtained1And fundamental wave phase
On the basis ofAnd the frequency correction coefficient is corrected to obtain the amplitude and the phase of the k-th harmonic wave so as to obtain the integral harmonic wave. The conventional interpolation FFT algorithm calculates the modified harmonic parameters by interpolation of 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 is about 10000/m of the fundamental wave2And (4) doubling. To improve this problem, the present embodiment estimates the frequency of the k-th harmonic by frequency multiplication of the fundamental frequency, and the frequency multiplication is performed by inverse calculation to obtain the integral harmonic. The variance of the parameter estimate in this way will be about k for the fundamental2. For harmonics 2-13, which typically need to be detected, k is known2<<(10000/m2) The invention adopts a method of frequency multiplication inverse deduction to obtain the integral harmonic wave, and avoids huge noise errors caused by direct interpolation of harmonic wave frequency correction coefficients.
Drawings
FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
FIG. 2 shows the error of the method according to an embodiment of the present invention.
Fig. 3 shows the error of the conventional dual interpolation FFT method as a comparison in the embodiment of the present invention.
Fig. 4 shows an error of the conventional three-interpolation FFT method as a comparison in the embodiment of the present invention.
FIG. 5 is a comparison of standard deviation of fundamental parameter errors for three methods in an embodiment of the present invention.
FIG. 6 is a comparison of standard deviation of harmonic parameter errors for three methods in an embodiment of the present invention.
Detailed Description
The invention is further described below. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Referring to fig. 1, the steps of the method for analyzing DFT harmonics based on spectral resolution adaptation in this embodiment include:
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
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
As a specific implementation of loop traversal, the detailed steps of step 6) in the present embodiment, as shown in fig. 1, include:
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
Based on the frequency correction factor deltak(2)Corrected to obtain k harmonicsAmplitude of wave AkAnd 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.
The physical meaning of the frequency resolution of the double interpolation method can be known, and the number of sampling points N is calculated to make the frequency correction coefficient as small as possibleiShould be (integer +1/2) signal cycles. In this embodiment, the number of sampling points N in step 3) isiThe 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, fsAnd N is the sampling value number for windowing the M-point sampling value sequence in the step 2).
In this embodiment, the inverse frequency correction coefficient δk(2)The formula of the calculation function is:
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.
In order to verify the spectrum resolution self-adaptive dual-spectral-line interpolation DFT harmonic analysis method of the embodiment, a simulation comparison method is adopted in the embodiment.
1. And (3) simulating harmonic calculation precision under the condition of no noise.
In the simulation process, the amplitude and the phase of each harmonic wave are kept unchanged, and the error conditions of different algorithms when the signal frequency is changed from 45 Hz to 55Hz are analyzed (other parameters are 20000V of fundamental amplitude, 4kHz of sampling frequency, 1024 of sampling points of reference algorithm, and 4-item 3-order window is selected by window function). In the simulation, 2-13 harmonics are superimposed on the fundamental wave, the relative content of each harmonic is shown in table 1, and the double-interpolation FFT and triple-interpolation FFT algorithms used for comparison are used as the comparison method of the spectral resolution adaptive-based double-spectral-line interpolation DFT harmonic analysis method in the embodiment.
Table 1: and (4) a simulation parameter table.
The simulation results obtained are shown in fig. 2, fig. 3 and fig. 4 and table 2.
Simulation results show that 2-order harmonic waves are closest to the fundamental wave and are subjected to the maximum interference of the frequency spectrum of the fundamental wave, so that the detection error is the maximum, wherein the maximum specific difference of a double-interpolation FFT algorithm exceeds 0.01%, and the maximum angular difference is close to +/-0.15%; the maximum specific difference of the three-interpolation FFT is close to +/-0.002 percent, and the maximum angular difference is close to +/-0.04 percent. While the algorithm improved herein has a maximum specific difference of + -0.002%, and a maximum angular difference of-0.002%. Generally speaking, although the amplitude calculation precision of the double-interpolation FFT algorithm and the three-interpolation FFT algorithm is very high, the phase calculation error is large, and the method of the embodiment improves the phase calculation precision in a large range, so that the integral precision of the harmonic parameter calculation of the algorithm is improved.
2. And (4) simulating harmonic error standard deviation under a noise background.
In the harmonic error standard deviation simulation under the noise background, the harmonic calculation accuracy simulation under the noise-free condition is performed on the content of each subharmonic signal and other parameters, the random number with the variance of 1 is used for simulating the broadband noise on the basis of the source signal, the signal-to-noise ratio of the fundamental wave is about 83dB, and the signal-to-noise ratio of each subharmonic signal is respectively shown in the following table (table 3).
Table 3: signal to noise ratio in the simulation.
| Number of |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Ai | 100％ | 2％ | 5％ | 2％ | 5％ | 1％ | 1％ |
| SNRi(dB) | 83 | 49 | 57 | 49 | 57 | 43 | 43 |
| Number of harmonics | 8 | 9 | 10 | 11 | 12 | 13 | - |
| |
1％ | 1％ | 0.5％ | 0.5％ | 0.5％ | 0.5％ | - |
| SNRi(dB) | 43 | 43 | 37 | 37 | 37 | 37 | - |
The simulation results of the specific difference standard deviation and the angular difference standard deviation extracted from the signal features of each algorithm under the background of noise are shown in fig. 5 and 6, wherein in the drawings, a broken line (improved double spectral lines) with circular points is the method of the embodiment, a broken line (double spectral lines) with star points is a double-interpolation FFT algorithm, and a broken line (triple spectral lines) with square points is a triple-interpolation FFT algorithm. From the results in fig. 5 and 6: (1) during fundamental wave calculation, the error standard deviation of the improved algorithm is always positioned below the error standard deviations of the double-interpolation FFT and the triple-interpolation FFT, the aim of enabling the variance of each parameter estimation to fall on the variance lower limit of the parameter estimation of the similar algorithm is achieved, and the parameter estimation variance under the noise background is reduced. (2) During harmonic calculation, the error of parameter estimation is obviously increased, wherein the standard deviation of the harmonic calculation ratio of the improved algorithm is about 0.06%, the standard deviation of the angular difference is about 2.3 ', the standard deviation is close to the standard deviation of the ratio deviation of the double interpolation FFT and the triple interpolation FFT, but compared with the standard deviation of the angular difference of about 8', the phase calculation precision is improved by about 4 times. (3) As shown in simulation, in a system with a broadband noise signal-to-noise ratio of 83dB, due to the fact that harmonic content is low, harmonic measurement noise errors are larger than spectrum interference errors, at the moment, algorithm noise errors become main components of the algorithm errors, and it is meaningless to further change the side lobe performance of a window function to inhibit spectrum leakage and spectrum interference. (4) It is foreseeable that when the harmonic content in the actual operation 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 conventional method of solving the harmonic parameter by interpolation; the method proposed herein avoids this problem, with errors independent of the harmonic content, only the fundamental signal-to-noise ratio and the harmonic order. From the simulation result, the double-interpolation FFT and triple-interpolation FFT algorithms also face the problem that the overall performance of the algorithms is affected due to the fact that the phase error is large in the noise background, and the method improves the phase estimation precision of the algorithms to a large extent, so that the overall precision of the algorithms is improved.
In summary, when the harmonic parameter estimation is performed by using the commonly used dual-interpolation FFT or triple-interpolation FFT, the problems of large phase error caused by inter-spectrum interference, large variance of the harmonic parameter estimation value caused by broadband noise interference, and the like are faced. The invention provides an improved double-interpolation DFT algorithm by analyzing the influence mechanism of window functions and interpolation methods on inter-spectrum interference errors and broadband noise errors of the algorithm. In the embodiment, simulation experiments are carried out on the double-interpolation FFT, the three-interpolation FFT and the method, and the result shows that the algorithm provided by the method has higher precision under the same signal condition. Therefore, in the present embodiment, the spectrum resolution adaptive-based dual-spectral-line interpolation DFT harmonic analysis method adaptively suppresses the spectrum interference of the fundamental wave on the harmonic calculation through the spectrum resolution, and obtains the integral harmonic through frequency multiplication inverse estimation, thereby avoiding the error caused by the interpolation calculation harmonic.
In addition, this embodiment further provides a spectral resolution adaptive-based dual-spectral line interpolation DFT harmonic analysis system, including:
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
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 phase
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd phase of the k harmonic
As a specific loop traversal implementation, the harmonic processing program unit in this embodiment includes:
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic frequency fkAnd 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.
The present embodiment further provides a spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis system, which comprises a computer device programmed or configured to perform the steps of the spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis method.
The present embodiment further provides a spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis system, which includes a computer device, where a memory of the computer device stores a computer program programmed or configured to execute the spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis method.
The present embodiment further provides a computer readable storage medium having stored thereon a computer program programmed or configured to execute the foregoing spectral resolution adaptation-based bilinear interpolation DFT harmonic analysis method.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or 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, and the like) 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 application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the 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
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd 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 fk；
6.3) according to the k harmonic frequency fkInverse frequency correction factor deltak(2)；
6.4) at fundamental amplitude A1And fundamental wave phase
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd 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, 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:
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
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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic amplitude AkAnd 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 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
Based on the frequency correction factor deltak(2)Corrected to obtain k-th harmonic frequency fkAnd 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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Cited By (5)
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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 |
| CN113640579A (en) * | 2021-10-13 | 2021-11-12 | 四川大学 | Harmonic measurement method based on double spectral line transformation, electronic device and storage medium |
| 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 |
| 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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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN113640579A (en) * | 2021-10-13 | 2021-11-12 | 四川大学 | Harmonic measurement method based on double spectral line transformation, electronic device and storage medium |
| 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 |
| CN114838809B (en) * | 2022-03-22 | 2024-10-18 | 珠海市运泰利自动化设备有限公司 | Audio signal measuring method capable of adaptively improving frequency measurement precision |
| 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 |
| CN116359605B (en) * | 2023-04-21 | 2023-09-12 | 中国计量科学研究院 | Harmonic signal analysis method based on secondary weighting |
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