A Method for Analyzing the Components of Wideband Oscillation Signals Based on Non-Iterative Classification Interpolation

Abstract

The present application relates to a method for analyzing the components of a broadband oscillation signal based on non-iterative classification interpolation. The method includes: First, modeling and time-domain sampling are performed on a random broadband oscillation signal to obtain a sampled signal; Then, windowed Fourier transform and rotation factor correction are performed on the sampled signal; Then, a rough frequency estimation sequence is determined based on the corrected sampled signal; Then, oscillation frequency separation is performed based on the rough frequency estimation sequence, and the oscillation frequency and non-oscillation frequency are determined through a classification interpolation formula; Finally, the non-oscillation amplitude, oscillation amplitude, and damping factor are determined by using the least squares method based on the sampled signal, oscillation frequency, and non-oscillation frequency. That is to say, through non-iterative classification interpolation and the least squares method, signal component analysis and parameter calculation can be quickly performed when the number of components in the signal is unknown and the component models are different.

Description

Technical Field

[0001] The present application relates to the technical field of signal and data analysis, and particularly to a method for analyzing the components of broadband oscillation signals based on non-iterative classification interpolation. Background Art

[0002] With the large-scale integration of new energy into the power grid, the oscillation characteristics in the power system are no longer limited to being characterized by low-frequency or sub-synchronous oscillations within 100 Hz, but are developing towards a wider frequency range. This change has led to the occurrence frequency bands of broadband oscillations being similar to those of non-oscillation components such as harmonics and inter-harmonics, and the number of different types of components being random, increasing the detection difficulty. Therefore, when performing signal component analysis, not only the fundamental frequency spectrum leakage needs to be addressed, but also the energy coupling between oscillations and non-oscillations needs to be considered. In addition, the damping characteristics of the oscillation components are different from those of harmonics and inter-harmonics. It is necessary to model the oscillation components as an exponentially damped sine model and the non-oscillation components as a sine model, and distinguish them when solving the parameters.

[0003] In recent years, researchers at home and abroad have proposed many methods for analyzing the components of oscillation signals. The main ones are: Discrete Fourier Transform (DFT), Iterative Interpolation Fourier Transform, and Prony method (PRONY), etc. However, when analyzing broadband oscillation signals with random components, these methods often require additional iterative or matrix operation steps to obtain prior information such as the number of signal components. At the same time, the detection accuracy of these methods is not ideal enough.

[0004] Therefore, in the related art, there is an urgent need for a method that can quickly and accurately analyze random broadband oscillation signals. Summary of the Invention

[0005] Based on this, in view of the above technical problems, it is necessary to provide a method for analyzing the components of broadband oscillation signals based on non-iterative classification interpolation that can quickly and accurately analyze random broadband oscillation signals.

[0006] In a first aspect, the present application provides a method for analyzing the components of broadband oscillation signals based on non-iterative classification interpolation. The method includes:

[0007] Modeling and time-domain sampling of the random broadband oscillation signal to obtain a sampled signal;

[0008] Performing windowed Fourier transform and rotation factor correction on the sampled signal;

[0009] Determining a rough frequency estimation sequence based on the corrected sampled signal;

[0010] Performing oscillation frequency separation based on the rough frequency estimation sequence, and determining the oscillation frequency and non-oscillation frequency through a classification interpolation formula;

[0011] Determine the non-oscillating amplitude, oscillating amplitude, and damping factor using the least squares method based on the sampling signal, oscillation frequency, and non-oscillation frequency.

[0012] Optionally, in an embodiment of the present application, the sampling signal is as follows:

[0013]

[0014] where A, f, are the amplitude (V), frequency (Hz), and initial phase (°) of each component respectively, σ v is the damping factor of the oscillating component, is a constant, n = 0, 1, 2,..., N - 1, N is the total number of sampling points, t s = 1 / f s is the sampling period, f s is the sampling frequency, V is the number of oscillating components, and U is the number of non-oscillating components.

[0015] Optionally, in an embodiment of the present application, the frequency domain signal obtained by performing windowed Fourier transform and correction on the sampling signal and the frequency domain signal after rotation factor correction are as follows:

[0016]

[0017] where X w (k) is the frequency domain signal obtained by windowed Fourier transform, is the corrected frequency domain signal, M is the total number of components contained in the signal, W(·) is the spectral function of the Hanning window, Δf = 1 / (t s N) represents the frequency resolution, k = 0, 1, 2,..., K represents the spectral lines corresponding to each frequency in the frequency domain signal, K = ceil(f s / 2), and j is the imaginary unit.

[0018] Optionally, in an embodiment of the present application, after determining the rough frequency estimation sequence based on the corrected sampling signal, it includes:

[0019] Identify the difference spectrum corresponding to the oscillating component according to the damping characteristic of the oscillation.

[0020] Optionally, in an embodiment of the present application, the oscillation frequency and non-oscillation frequency are obtained according to the following formula:

[0021]

[0022] where k vi represents the peak spectral line corresponding to the oscillation frequency and k ui represents the non-oscillation frequency The corresponding peak spectral line. For the sake of auxiliary description, R is introduced. 1i and R 2i are used as intermediate variables, corresponding to the oscillatory component and the non-oscillatory component respectively. δ vi is the frequency correction coefficient corresponding to the oscillatory component, and δ ui is the frequency correction coefficient corresponding to the non-oscillatory component.

[0023] Optionally, in an embodiment of the present application, by using the least squares method, a parameter matrix P = [p(1) p(2) … p(N)] T and X = [x(1) x(2) … x(N)] are constructed, and the matrix U = (P T P) -1 P T X T is solved. The non-oscillatory amplitude, the oscillatory amplitude, and the damping factor are obtained according to the following formula:

[0024]

[0025] where p(n) gives the construction method of the nth term in the parameter matrix P, is the non-oscillatory amplitude, is the oscillatory amplitude, is the damping factor, and the auxiliary matrix I i (n) = [sin 2πf i T s n, cos 2πf i T s n]. For the oscillatory component, take For the non-oscillatory component, take is the number of oscillations, is the number of non-oscillations, and U(i) represents the value of the i-th column in the matrix U. U is order matrix.

[0026] The above-mentioned method for analyzing the components of a broadband oscillatory signal based on non-iterative classification interpolation. First, a random broadband oscillatory signal is modeled and sampled in the time domain to obtain a sampled signal; then, the sampled signal is subjected to windowed Fourier transform and rotation factor correction; then, a rough frequency estimation sequence is determined based on the corrected sampled signal; then, the oscillatory frequencies are separated based on the rough frequency estimation sequence, and the oscillatory frequencies and non-oscillatory frequencies are determined through the classification interpolation formula; finally, the non-oscillatory amplitude, the oscillatory amplitude, and the damping factor are determined based on the sampled signal, the oscillatory frequencies, and the non-oscillatory frequencies by using the least squares method. That is to say, through non-iterative classification interpolation and the least squares method, signal component analysis and parameter calculation can be quickly carried out when the number of components in the signal is unknown and the component models are different. Description of the Drawings

[0027] Figure 1 It is a schematic flow chart of a method for analyzing the components of a broadband oscillation signal based on non-iterative classification interpolation in an embodiment;

[0028] Figure 2 It is a schematic diagram of the analysis result of the components of a broadband oscillation signal in an embodiment. Specific embodiments

[0029] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0030] In one embodiment, as Figure 1 shown, a method for analyzing the components of a broadband oscillation signal based on non-iterative classification interpolation is provided, including the following steps:

[0031] S1: Model and perform time-domain sampling on a random broadband oscillation signal to obtain a sampled signal.

[0032] In the embodiment of the present application, let the random broadband oscillation signal be x(t), the total number of components contained in the signal be M, the frequency of the oscillation component be denoted as f v , the number of oscillation components be denoted as V, the frequency of the non-oscillation component be denoted as f u , and the number of non-oscillation components be denoted as U. In an embodiment of the present application, the sampled signal obtained by sampling x(t) is as follows:

[0033]

[0034] where A, f, are the amplitudes (V), frequencies (Hz), and initial phases (°) of each component respectively, σ v is the damping factor of the oscillation component, which is a constant, n = 0, 1, 2,..., N - 1, N is the total number of sampling points, t s = 1 / f s is the sampling period, f s is the sampling frequency, V is the number of oscillation components, and U is the number of non-oscillation components.

[0035] S2: Perform windowed Fourier transform and rotation factor correction on the sampled signal.

[0036] In the embodiment of the present application, perform windowed Fourier transform on the signal x(n) to obtain the frequency-domain signal X w (k), and the window function is selected as the Hanning window. Correct X w (k) through the rotation factor to obtain

[0037] In one embodiment of the present application, the frequency-domain signal obtained by performing windowed Fourier transform and correction on the sampled signal and the frequency-domain signal after rotation factor correction are as follows:

[0038]

[0039] where X w (k) is the frequency-domain signal obtained by windowed Fourier transform, is the corrected frequency-domain signal, M is the total number of components contained in the signal, W(·) is the spectral function of the Hanning window, Δf = 1 / (t s N) represents the frequency resolution, k = 0, 1, 2,..., K represents the spectral lines corresponding to each frequency in the frequency-domain signal, K = ceil(f s / 2), and d is the imaginary unit.

[0040] S3: Determine the rough frequency estimation sequence based on the corrected sampled signal.

[0041] In the embodiment of the present application, the number of quasi-peaks in the spectrum is taken as the estimated number of signal components The rough frequency estimation sequence of the signal components is where f ri = k ri Δf, representing the spectrum corresponding to each quasi-peak in

[0042] In one embodiment of the present application, after determining the rough frequency estimation sequence based on the corrected sampled signal, it includes:

[0043] Identify the difference spectrum corresponding to the oscillatory component according to the damping characteristic of the oscillation.

[0044] In one embodiment of the present application, take the first or last τ points of x(n), denoted as x'(n), x''(n), and the corresponding corrected spectra are denoted as Select the spectral quasi-peak of the difference spectrum as the oscillatory spectrum candidate. According to the damping characteristic of the oscillation, the difference spectrum corresponding to the oscillation should satisfy: 1) The ratio of the amplitude of the maximum difference spectrum to the amplitudes of other difference spectra corresponding to the oscillation is within a certain range; 2) The difference spectrum corresponding to the oscillation has opposite monotonicity in the neighborhoods on its left and right sides, that is:

[0045]

[0046] where λ represents the proportionality coefficient, k vi represents the difference spectrum corresponding to the oscillation, k v0Denote the maximum difference spectrum. Let m take 0, 1, 2. Denote the spectrum that meets the above characteristics among the oscillation spectrum alternatives as k v , and denote the number thereof as

[0047] S4: Based on the frequency rough estimation sequence, perform oscillation frequency separation, and determine the oscillation frequency and non-oscillation frequency through the classification interpolation formula.

[0048] In the embodiment of the present application, according to the principle of the minimum Euclidean distance, find within the search range points that are close to k v Δf, and denote the set composed of the similar points as At this time, is the data set with the minimum distance from k 2 in the l v norm, and its meaning is the set of rough estimations of the oscillation frequency. Among them, the principle of the minimum Euclidean distance is that for any x, y, let be the minimum, denotes the l 2 norm. Take in the complement set of , and denote it as as the set of rough estimations of the non-oscillation frequency, and denote the corresponding number of non-oscillation components as

[0049] Then the oscillation frequency and non-oscillation frequency are obtained according to the following formula:

[0050]

[0051] where k vi denotes the peak spectral line corresponding to the oscillation frequency , k ui denotes the peak spectral line corresponding to the non-oscillation frequency , To assist the description, introduce R 1i , R 2i as intermediate variables, corresponding to the oscillation component and non-oscillation component respectively, δ vi is the frequency correction coefficient corresponding to the oscillation component, and δ ui is the frequency correction coefficient corresponding to the non-oscillation component.

[0052] S5: Based on the sampling signal, oscillation frequency and non-oscillation frequency, use the least squares method to determine the non-oscillation amplitude, oscillation amplitude and damping factor.

[0053] In the embodiment of the present application, according to the sampling signal x(n) in S1 and the oscillation frequency obtained in S4 non-oscillation frequency Construct the parameter matrix \(P = [p(1)\ p(2)\ \cdots\ p(N)]\) by the least squares method T and \(X = [x(1)\ x(2)\ \cdots\ x(N)]\), and solve the matrix \(U=(P T P) -1 P T X T , then the parameters corresponding to each component can be obtained.

[0054] In an embodiment of the present application, construct the parameter matrix \(P = [p(1)\ p(2)\ \cdots\ p(N)]\) by the least squares method T and \(X = [x(1)\ x(2)\ \cdots\ x(N)]\), and solve the matrix \(U=(P T P) -1 P T X T , and the non - oscillating amplitude, oscillating amplitude, and damping factor are obtained according to the following formula:

[0055]

[0056] where \(p(n)\) gives the construction method of the \(n\)th term in the parameter matrix \(P\), is the non - oscillating amplitude, is the oscillating amplitude, is the damping factor, and the auxiliary matrix \(I i (n)=[\sin(2\pi f i T s n),\cos(2\pi f i T s n)], for the oscillating component, take For the non - oscillating component, take is the number of oscillations, is the number of non - oscillations, \(U(i)\) represents the value of the \(i\)th column in the matrix \(U\), and \(U\) is order matrix.

[0057] In an embodiment of the present application, select the discrete Fourier transform (DFT) and Prony algorithm (PRONY) as comparison algorithms. Take the sampling frequency \(f s as \(5kHz\), the sampling window length is taken as 10 power frequency periods, that is, \(0.2\) seconds, and the proportionality coefficient \(\lambda = 50\), represents rounding down. Use the frequency error (\(Hz\)) and amplitude error (\(\%\)) as test indicators to evaluate the algorithm performance. The selection of the broadband oscillation test signal is as follows:

[0058]

[0059] where \(t s = 1 / fs Let \(T\) be the sampling period, \(n = 0, 1, 2, \cdots, N - 1\), and \(N = 1000\) be the total number of sampling points. The number of oscillatory components \(V = 2\), and the number of non - oscillatory components \(U = 4\). The corresponding component parameters are shown in Table 1, where the damping factor is a constant with a unit of 1.

[0060]

[0061] Table 1 Component Parameter Table of Wide - band Oscillatory Signal

[0062] Set the noise \(s_{noise}\) to zero and test the analysis accuracy of the wide - band oscillatory signal components in the case of no noise. The results are shown in Table 2. The frequency estimation accuracy for each component is within \(10\) -2 , and among them, the frequency measurement accuracy of the oscillatory components can reach \(10\) -4 , and the estimation errors of the amplitude and damping factor are relatively small. The present invention can accurately analyze and estimate the components of a wide - band oscillatory signal with unknown component types and unknown numbers of components.

[0063]

[0064] Table 2 Analysis Results of Wide - band Oscillatory Signal Components of the Present Invention in the Case of No Noise

[0065] Set the noise \(s\) nosie to 70 dB, compare the analysis accuracy of the wide - band oscillatory signal components of the present invention and the comparative algorithm in the case of noise, and present the frequency error (Hz) and amplitude error (%) in Figure 2 . From Figure 2 , it can be seen that the present invention has a certain anti - noise ability and has relatively stable performance when estimating different components. At the same time, compared with the comparative algorithm, the present invention can basically improve the frequency and amplitude estimation accuracy by more than 20 times in a non - iterative manner with a smaller computational cost.

[0066] In the above - mentioned method for analyzing the components of a wide - band oscillatory signal based on non - iterative classification interpolation, first, model and perform time - domain sampling on a random wide - band oscillatory signal to obtain a sampling signal; then, perform windowed Fourier transform and rotation factor correction on the sampling signal; then, determine a rough frequency estimation sequence based on the corrected sampling signal; then, perform oscillatory frequency separation based on the rough frequency estimation sequence, and determine the oscillatory frequency and non - oscillatory frequency through a classification interpolation formula; finally, determine the non - oscillatory amplitude, oscillatory amplitude, and damping factor based on the sampling signal, oscillatory frequency, and non - oscillatory frequency using the least - squares method. That is to say, through non - iterative classification interpolation and the least - squares method, signal component analysis and parameter calculation can be quickly carried out when the number of components in the signal is unknown and the component models are different.

[0067] It should be understood that although the steps in the flowcharts involved in the above-described embodiments are shown in sequence according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-described embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or steps or stages in other steps.

[0068] Those of ordinary skill in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memories can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc. The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0069] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0070] The above-described embodiments merely represent several implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation to the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A method for analyzing the components of a broadband oscillation signal based on non-iterative classification interpolation, characterized in that The method includes: Modeling and time-domain sampling of a random broadband oscillation signal to obtain a sampled signal; Performing windowed Fourier transform and rotation factor correction on the sampled signal; Determining a rough frequency estimation sequence based on the corrected sampled signal; Performing oscillation frequency separation based on the rough frequency estimation sequence, and determining the oscillation frequency and non-oscillation frequency through a classification interpolation formula; Determining the non-oscillation amplitude, oscillation amplitude, and damping factor using the least squares method based on the sampled signal, oscillation frequency, and non-oscillation frequency; The oscillation frequency and non-oscillation frequency are obtained according to the following formula: Among them, , , , , , are the corrected frequency-domain signals, represents the peak spectral line corresponding to the oscillation frequency , represents the peak spectral line corresponding to the non-oscillation frequency . For the sake of auxiliary description, is introduced as an intermediate variable, corresponding to the oscillation component and the non-oscillation component respectively, is the frequency correction coefficient corresponding to the oscillation component, is the frequency correction coefficient corresponding to the non-oscillation component, represents the frequency resolution, is the sampling period, is the sampling frequency, is the total number of sampling points; Construct a parameter matrix by the least squares method and , solve the matrix , and the non-oscillating amplitude, oscillating amplitude, and damping factor are obtained according to the following formula: Among them, gives the construction method of the th term in the parameter matrix . is the non-oscillating amplitude, is the oscillating amplitude, is the damping factor, and the auxiliary matrix . For the oscillating component, take . For the non-oscillating component, take . is the number of oscillations, is the number of non-oscillations, represents the value of the th column in the matrix . is order matrix.

2. The broadband oscillation signal component analysis method based on non-iterative classification interpolation according to claim 1, wherein, The sampled signal is as follows: Among them, , , are the amplitudes (V), frequencies (Hz), and initial phases (°) of each component respectively, is the damping factor of the oscillatory component and is a constant, , is the total number of sampling points, is the sampling period, is the sampling frequency, is the number of oscillatory components, is the number of non-oscillatory components.

3. A method for analyzing the components of a broadband oscillation signal based on non-iterative classification interpolation according to claim 1, characterized in that The frequency-domain signal obtained by performing windowed Fourier transform and correction on the sampled signal and the frequency-domain signal after rotation factor correction are as follows: Among them, is the frequency-domain signal obtained by windowed Fourier transform, is the corrected frequency-domain signal, is the total number of components contained in the signal, is the spectral function of the Hanning window, represents the frequency resolution, represents the spectral lines corresponding to each frequency in the frequency-domain signal, , is the imaginary unit.

4. A wideband oscillation signal component analysis method based on non-iterative classification interpolation according to claim 1, characterized in that After determining the rough frequency estimation sequence based on the corrected sampled signal, it includes: Identifying the difference spectrum corresponding to the oscillation component according to the damping characteristic of the oscillation.

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