Harmonic detection method and device based on improved SVD and parameter optimization VMD

Abstract

The invention provides a harmonic detection method and device based on improved SVD and parameter optimization VMD. The method comprises the following steps: carrying out improved noise reduction preprocessing on a noisy harmonic signal, and determining an effective rank by adopting singular value shrinkage to realize noise separation; an improved tornado optimization algorithm is adopted to optimize a preset modal number and a penalty factor of variational modal decomposition, the improved tornado optimization algorithm introduces a thunderstorm number adaptive adjustment strategy, and the thunderstorm number is dynamically adjusted according to population diversity to balance global exploration and local development capabilities; constructing a fitness function, and according to the improved tornado optimization algorithm TOC algorithm, minimizing the fitness function to obtain an optimal preset modal number and a penalty factor; decomposing the denoised signal by using an optimal preset modal number and a penalty factor to obtain each harmonic modal component; and modulating each modal component based on a second-order central difference Teager energy operator, and extracting instantaneous amplitude and frequency information of harmonic waves.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of power system operation and maintenance technology, and in particular to a harmonic detection method and device based on improved SVD and parameter-optimized VMD. Background Technology

[0002] With the large-scale grid connection of power systems and the widespread integration of nonlinear loads, the impact of harmonics on the stability of power equipment and power quality is becoming increasingly significant. Transient harmonics, as harmonic components with non-stationary characteristics, are far more difficult to detect than stationary harmonics, necessitating efficient detection methods. Among existing transient harmonic detection methods, the Short-Time Fourier Transform (STFT) is limited by window length, resulting in spectral leakage and the picket-fence effect; the wavelet transform (WT) accuracy depends on the wavelet basis selection and has insufficient high-frequency decomposition capability; the Synchronous Squeezed Wavelet Transform (SST), while improving frequency resolution, is computationally complex; and the Hilbert-Huang Transform (HHT) is prone to mode aliasing and exhibits negative frequencies during analysis. Variational Mode Decomposition (VMD) has significant advantages in non-stationary signal processing, but its decomposition effect is significantly affected by the preset number of modes K and the penalty factor α. Existing VMD parameter optimization methods either rely on manual intervention or use a single fitness function, leading to unstable parameter selection. Furthermore, traditional noise reduction methods lack robustness in complex noise environments, affecting detection accuracy. Therefore, developing a harmonic detection method and device based on improved SVD and parameter-optimized VMD can effectively overcome the shortcomings of the above-mentioned related technologies, which has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0003] To address the aforementioned problems in the existing technology, embodiments of the present invention provide a harmonic detection method and device based on improved SVD and parameter-optimized VMD.

[0004] In a first aspect, embodiments of the present invention provide a harmonic detection method based on improved SVD and parameter-optimized VMD, comprising: performing improved SVD denoising preprocessing on noisy harmonic signals; using singular value shrinkage to determine the effective rank to achieve noise separation; using an improved tornado optimization algorithm TOC to optimize the preset mode number K and penalty factor α of variational mode decomposition VMD, wherein the improved tornado optimization algorithm TOC introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms according to population diversity to balance global exploration and local exploitation capabilities; and constructing a fitness function Fit(K,α)=fre_un The algorithm is defined as follows: fre_uniform + Ort + MaxSe, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The fitness function is minimized according to the improved Tornado Optimization Algorithm (TOC) to obtain the optimal preset mode number K and penalty factor α. The denoised signal is then subjected to VMD decomposition using the optimal preset mode number K and penalty factor α to obtain the harmonic mode components. Each mode component is then regulated based on the second-order central difference Teager energy operator to extract the instantaneous amplitude and frequency information of the harmonics.

[0005] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the following improved SVD denoising preprocessing: constructing the Toeplitz trajectory matrix of the signal according to the phase space reconstruction, performing singular value decomposition on the Toeplitz trajectory matrix to obtain a singular value sequence; determining the maximum threshold τ that satisfies the constraint conditions using the matrix rank minimization method and binary search, shrinking the singular values, reconstructing the signal matrix and diagonally averaging it to obtain the denoised signal.

[0006] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes a thunderstorm number adaptive adjustment strategy, comprising: setting an upper bound of thunderstorm number nt_max and a lower bound of thunderstorm number nt_min; calculating initial population diversity and setting an upper bound of diversity threshold diversity_h and a lower bound of diversity threshold diversity_l; during the iteration process, if the population diversity is greater than the upper bound of diversity threshold diversity_h, then the thunderstorm number nt is increased; if the population diversity is less than the lower bound of diversity threshold diversity_l, then the thunderstorm number nt is decreased, ensuring that the thunderstorm number nt is within the range of the lower bound of thunderstorm number nt_min and the upper bound of thunderstorm number nt_max, wherein the population diversity is the average distance between individuals.

[0007] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the orthogonality index Ort, which includes:

[0008]

[0009] Among them, u k The first harmonic mode component; u l The second harmonic mode component; || is the norm sign; || is the absolute value sign; <> is the mean operator; the uniformity of the center frequency spacing fre_uniform is the standard deviation of the difference between adjacent frequencies after sorting the center frequencies of the decomposed modes; the maximum sample entropy MaxSe is the maximum value of the sample entropy of each mode.

[0010] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the discrete form of the second-order central difference Teager energy operator, comprising:

[0011] ψ d (u(n))=u 2 (n)-u(n-1)u(n+1)

[0012] The instantaneous amplitude and frequency are obtained from the three-point second-order central difference sequence, including:

[0013]

[0014]

[0015] Where arccos is the inverse cosine sign; || is the absolute value sign; n is the discrete-time index; ψ d (u(n)) is the Teager energy of the original signal; u(n) is the input discrete-time sequence; y(n) is the first derivative of u(n) after center difference; A(n) is the instantaneous amplitude; ψ d (y(n)) represents the Teager energy of the differential signal; w(n) represents the instantaneous frequency.

[0016] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention, wherein the noise separation is achieved by determining the effective rank through singular value contraction, includes: determining the constraint conditions through binary search. The maximum threshold τ is used to shrink singular values, where δ is the noise level and σ is the maximum threshold τ. i These are the singular values ​​of the Hankle matrix formed by the noisy signals, estimated using the median deviation statistic.

[0017] Based on the above method embodiments, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention, wherein minimizing the fitness function according to the improved tornado optimization algorithm TOC algorithm to obtain the optimal preset mode number K and penalty factor α, includes: fre_uniform avoiding over-decomposition by measuring the uniformity of center frequency spacing; Ort avoiding modal redundancy by evaluating inter-modal orthogonality; MaxSe judging modal aliasing by the maximum sample entropy, and Fit(K,α) taking the minimum value corresponds to the optimal preset mode number K and penalty factor α.

[0018] Secondly, embodiments of the present invention provide a harmonic detection device based on improved SVD and parameter-optimized VMD, comprising: a first main module for performing improved SVD denoising preprocessing on noisy harmonic signals, and using singular value shrinkage to determine the effective rank to achieve noise separation; a second main module for optimizing the preset mode number K and penalty factor α of variational mode decomposition VMD using an improved tornado optimization algorithm TOC, wherein the improved tornado optimization algorithm TOC introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms according to population diversity to balance global exploration and local exploitation capabilities; and a third main module for constructing a fitness function Fit(K,α)=f The algorithm is defined as re_uniform+Ort+MaxSe, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The fitness function is minimized according to the improved Tornado Optimization Algorithm (TOC) to obtain the optimal preset number of modes K and penalty factor α. The fourth main module is used to perform VMD decomposition on the denoised signal using the optimal preset number of modes K and penalty factor α to obtain the harmonic mode components. The fifth main module is used to adjust each mode component based on the second-order central difference Teager energy operator to extract the instantaneous amplitude and frequency information of the harmonics.

[0019] Thirdly, embodiments of the present invention provide an electronic device, comprising:

[0020] At least one processor, at least one memory, and a communication interface; wherein,

[0021] The processor, memory, and communication interface communicate with each other;

[0022] The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the harmonic detection method based on improved SVD and parameter-optimized VMD provided by any of the various implementations of the first aspect.

[0023] Fourthly, embodiments of the present invention provide a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a harmonic detection method based on improved SVD and parameter-optimized VMD provided by any of the various implementations of the first aspect.

[0024] The harmonic detection method and device based on improved SVD and parameter-optimized VMD provided in this invention improves the SVD noise reduction technology and achieves accurate noise separation based on singular value contraction theory, significantly enhancing the robustness of signal preprocessing and achieving better noise reduction performance than traditional methods. The proposed adaptive adjustment TOC algorithm for thunderstorm numbers, combined with a comprehensive fitness function including center frequency uniformity, orthogonality, and maximum sample entropy, solves the sensitivity problem of VMD parameter selection, making mode decomposition more accurate and stable, and avoiding over-decomposition and mode aliasing. The second-order central difference Teager energy operator is used to analyze the signal, effectively improving the accuracy of instantaneous amplitude and frequency detection and reducing the impact of noise. It maintains high accuracy even in low signal-to-noise ratio environments, providing a robust and adaptable solution for transient harmonic detection in power systems, and has significant engineering application value. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the harmonic detection method based on improved SVD and parameter-optimized VMD provided in an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the structure of the harmonic detection device based on improved SVD and parameter-optimized VMD provided in an embodiment of the present invention;

[0028] Figure 3 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention;

[0029] Figure 4 This is a schematic diagram showing the comparison between the denoised signal and the original signal provided in different embodiments of the present invention;

[0030] Figure 5 This is a schematic diagram of the convergence curve effect on the Sphere function provided in an embodiment of the present invention;

[0031] Figure 6This is a schematic diagram of the convergence curve effect on the Rastrigin function provided in an embodiment of the present invention;

[0032] Figure 7 This is a schematic diagram illustrating the effect of the fitness change curve provided in an embodiment of the present invention;

[0033] Figure 8 A schematic diagram of VMD decomposition results with K=3 and α=366 provided in an embodiment of the present invention;

[0034] Figure 9 This is a schematic diagram illustrating the short-time harmonic decomposition effect provided in an embodiment of the present invention;

[0035] Figure 10 A schematic diagram of the instantaneous amplitude and frequency of each component provided for embodiments of the present invention;

[0036] Figure 11 This is a schematic diagram illustrating the time-varying harmonic decomposition effect provided in an embodiment of the present invention;

[0037] Figure 12 This is a schematic diagram showing the amplitude and frequency of each component of a time-varying signal provided in an embodiment of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form feasible technical solutions. Such combinations are not constrained by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. If there are step numbers in the following embodiments, they are only set for ease of explanation and the order between steps is not limited. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0039] This invention provides a harmonic detection method based on improved SVD and parameter-optimized VMD. See [link to relevant documentation]. Figure 1The method includes: performing improved SVD denoising preprocessing on noisy harmonic signals, using singular value shrinkage to determine the effective rank to achieve noise separation; using an improved tornado optimization algorithm TOC to optimize the preset number of modes K and penalty factor α of variational mode decomposition VMD, wherein the improved tornado optimization algorithm TOC introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms according to population diversity to balance global exploration and local exploitation capabilities; and constructing a fitness function Fit(K,α)=fre_uniform+Ort+MaxSe, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The fitness function is minimized according to the improved tornado optimization algorithm TOC to obtain the optimal preset mode number K and penalty factor α. The denoised signal is then subjected to VMD decomposition using the optimal preset mode number K and penalty factor α to obtain the harmonic mode components. The second-order central difference Teager energy operator is used to adjust each mode component to extract the instantaneous amplitude and frequency information of the harmonics.

[0040] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the following improved SVD noise reduction preprocessing: constructing the Toeplitz trajectory matrix of the signal according to the phase space reconstruction, performing singular value decomposition on the Toeplitz trajectory matrix to obtain a singular value sequence; determining the maximum threshold τ that satisfies the constraint conditions using a binary search method based on the matrix rank minimization method, shrinking the singular values, reconstructing the signal matrix and diagonally averaging it to obtain the noise-reduced signal.

[0041] Given signal data X of length N N ={x0,x1,...,x N-1 According to the phase space reconstruction theory, its mapping trajectory matrix can be obtained as follows:

[0042]

[0043] From equation (1), it is easy to see that matrix X is a Toeplitz matrix of size N-L+1×L. Calculating the singular value decomposition of matrix X, we get:

[0044]

[0045] Where u i and v i Let X be the left and right singular vectors of X, respectively, and d represent the rank of matrix X, i.e., the number of non-zero singular values, and d ≤ min(L, N-L+1), σ1, σ2, ..., σ dThese are the singular values ​​of X arranged in descending order. By estimating the effective rank r of X, a clean signal is obtained: To separate the clean signal matrix S and the noise matrix N, we have X = S + N. Finally, the separated clean signal matrix S is diagonally averaged to obtain the following matrix:

[0046]

[0047] According to (3), the noise-reduced data S can be obtained. N ={s0,s1,...,s N-1 However, there are two issues to consider when using SVD denoising: first, the choice of the window length L when constructing the trajectory matrix; and second, the number of singular values ​​required to separate the signal matrix cleanly, i.e., the choice of the effective rank. Regarding the first issue, existing literature, through analysis and theoretical proof, suggests that taking the median of the sequence length (L = N / 2 if N is even) as L is the optimal choice. However, regarding the effective rank selection method in SVD denoising theory, based on the principle of matrix rank minimization and combined with singular value contraction theory, a new effective rank selection method is proposed to improve the robustness and adaptability of SVD denoising.

[0048] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes a thunderstorm quantity adaptive adjustment strategy, comprising: setting an upper bound of thunderstorm quantity nt_max and a lower bound of thunderstorm quantity nt_min; calculating the initial population diversity and setting an upper bound of diversity threshold diversity_h and a lower bound of diversity threshold diversity_l; during the iteration process, if the population diversity is greater than the upper bound of diversity threshold diversity_h, then the thunderstorm quantity nt is increased; if the population diversity is less than the lower bound of diversity threshold diversity_l, then the thunderstorm quantity nt is decreased, ensuring that the thunderstorm quantity nt is within the range of the lower bound of thunderstorm quantity nt_min and the upper bound of thunderstorm quantity nt_max, wherein the population diversity is the average distance between individuals.

[0049] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the orthogonality index Ort, which includes:

[0050]

[0051] Among them, u k The first harmonic mode component; u lThe second harmonic mode component; || is the norm sign; || is the absolute value sign; <> is the mean operator; the uniformity of the center frequency spacing fre_uniform is the standard deviation of the difference between adjacent frequencies after sorting the center frequencies of the decomposed modes; the maximum sample entropy MaxSe is the maximum value of the sample entropy of each mode.

[0052] In Virtual Mode Decomposition (VMD), the goal is to decompose a complex input signal into multiple modes, each corresponding to a specific frequency component of the signal. Ideally, these modes should be orthogonal, meaning that any two different modes u... k and u l The inner product of (k≠l) should be zero, but even in a non-ideal case, the inner product between different modes should be as small as possible. This orthogonality ensures that each mode captures unique information in the signal, avoiding redundancy or interference. The calculation of the orthogonality index, i.e., the sum of the inner products of each modal component after decomposition, is shown in Equation (4). It can be used to evaluate the independence between modes, and the smaller the value, the better the orthogonality.

[0053] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention includes the discrete form of the second-order central difference Teager energy operator, comprising:

[0054] ψ d (u(n))=u 2 (n)-u(n-1)u(n+1)(5)

[0055] The instantaneous amplitude and frequency are obtained from the three-point second-order central difference sequence, including:

[0056]

[0057] Where arccos is the inverse cosine sign; || is the absolute value sign; n is the discrete-time index; ψ d (u(n)) is the Teager energy of the original signal; u(n) is the input discrete-time sequence; y(n) is the first derivative of u(n) after center difference; A(n) is the instantaneous amplitude; ψ d (y(n)) represents the Teager energy of the differential signal; w(n) represents the instantaneous frequency.

[0058] Signal modulation involves extracting information such as the envelope, frequency, and phase of a signal from its time-domain data. Currently, the most commonly used signal modulation method is the Hilbert transform. Existing research indicates that the Hilbert transform is less effective than the Teager energy operator in analyzing signals. However, forward or backward differential energy operators are sensitive to noise, and the accuracy of signal analysis is easily affected by noise. Therefore, using a symmetric differential energy operator to analyze signals can compensate for the shortcomings of the traditional Teager energy operator and achieve higher accuracy. Thus, for IMFs obtained through VMD, this patent utilizes a second-order central difference Teager energy operator to analyze and obtain the instantaneous amplitude and frequency information of harmonics. The definition of the discrete Teager nonlinear energy operator is shown in equation (5). Here, u(n) is the actual IMF after VMD, and its expression is:

[0059] u(n)=A(n)cos(φ(n))=A(n)cos(w(n)n)(9)

[0060] Based on the properties of the intrinsic mode function, its rate of change of frequency and rate of change of amplitude are much smaller than the change of φ(n), so when substituting (9) into (5), we can obtain:

[0061] ψ d (u(n))=A 2 (n)sin 2 w(n)(10)

[0062] The differential sequence of u(n) is expressed by the three-point second-order central difference sequence y(n) as shown in equation (6). Considering the properties of the eigenmode functions, we have ψ d (y(n))A 2 (n)sin 4 w(n), combined with equation (9), we can finally obtain equations (7) and (8).

[0063] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention, wherein the noise separation is achieved by determining the effective rank through singular value contraction, includes: determining the constraint conditions through binary search. Maximum threshold τ The singular values ​​are shrunk, where δ is the noise level and σ is the noise level. i These are the singular values ​​of the Hankle matrix formed by the noisy signals, estimated using the median deviation statistic.

[0064] Based on the above method embodiments, as an optional embodiment, the harmonic detection method based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention, wherein minimizing the fitness function according to the improved tornado optimization algorithm TOC algorithm to obtain the optimal preset mode number K and penalty factor α, includes: fre_uniform avoiding over-decomposition by measuring the uniformity of the center frequency spacing; Ort avoiding modal redundancy by evaluating the orthogonality between modes; MaxSe judging modal aliasing by the maximum sample entropy, and Fit(K,α) taking the minimum value corresponds to the optimal preset mode number K and penalty factor α.

[0065] To ensure that the center frequency spacing of each mode remains uniform and clearly spaced, since the harmonic components of the power system are basically integer multiples of the fundamental frequency, when the VMD decomposition is appropriate, the center frequency spacing of each mode should be uniform and clearly spaced. The expression is as follows (11):

[0066] fre_uniform=σ(Δω)(11)

[0067] Where Δω represents the vector formed by the differences between adjacent center frequencies after sorting the center frequencies of each decomposed mode; σ represents the standard deviation. Therefore, it can be seen that when the center frequencies are evenly distributed and the intervals are obvious, the smaller the standard deviation of Δω, the smaller fre_uniform is.

[0068] Sample entropy (SampEn) is an indicator of the complexity of a time series, used to evaluate the regularity and predictability of a signal. It is often used in signal processing to distinguish between noise and effective components, and it is highly sensitive to noise; the sample entropy of a noisy signal is significantly higher than that of a clean signal. This paper finds that sample entropy also plays a role in judging mode aliasing. For a single harmonic signal and a signal formed by the superposition of multiple harmonics, the sample entropy of the latter, while not significantly greater than that of the former, is still larger. Therefore, sample entropy is used as an indicator to construct the fitness function, and the maximum value among the sample entropies of all modes after decomposition is used as the indicator, as shown in equation (12):

[0069] MaxSe = max(SampEn) i ), i = 1, 2, ..., K(12)SampEn i Represents the decomposed mode u i The sample entropy. When the preset number of modes K and the penalty factor α are too small, mode aliasing will occur, and the sample entropy of the aliased modes is the largest. When the parameters are appropriate, each mode component is single, and even the largest sample entropy is relatively small. However, when the preset number of modes K and the penalty factor α are too large, if noise components are introduced, the maximum sample entropy will increase significantly.

[0070] Analysis of the three signal indices reveals that utilizing the uniformity of center frequency spacing (fre_uniform) and the orthogonality index (Ort) primarily avoids excessively large preset mode number K and penalty factor α, taking into account the distribution of center frequencies after decomposition and preventing over-decomposition. The maximum sample entropy prevents mode aliasing from occurring when the preset mode number K and penalty factor α are too small. Therefore, the fitness function Fit(K,α) combining these three indices achieves its minimum value under appropriate preset mode number K and penalty factor α.

[0071] The harmonic detection method based on improved SVD and parameter-optimized VMD provided in this invention improves the SVD noise reduction technology and achieves accurate noise separation based on singular value contraction theory, significantly enhancing the robustness of signal preprocessing and outperforming traditional methods in noise reduction. The proposed adaptive TOC algorithm for thunderstorm quantity adjustment, combined with a comprehensive fitness function incorporating center frequency uniformity, orthogonality, and maximum sample entropy, solves the sensitivity problem of VMD parameter selection, making mode decomposition more accurate and stable, and avoiding over-decomposition and mode aliasing. The second-order central difference Teager energy operator is used to analyze the signal, effectively improving the accuracy of instantaneous amplitude and frequency detection and reducing noise impact. Maintaining high accuracy even in low signal-to-noise ratio environments, this method provides a robust and adaptable solution for transient harmonic detection in power systems, possessing significant engineering application value.

[0072] The proposed denoising method is compared with three other methods—wavelet thresholding, sparse decomposition, and energy-based SVD denoising—to denoise the same noisy harmonic signal data. The signal-to-noise ratio (SNR) and mean square error (MSE) of the denoised data are compared. The definitions of the two metrics are as follows (13) and (14):

[0073]

[0074] in Let x(i) represent the denoised signal data, x(i) be the pure signal data, and N be the length of the signal. Assume the mathematical model of the noisy harmonic signal is as shown in equation (15):

[0075] s(t)=50sin(100πt)+10sin(300πt)+15sin(360πt)+5sin(568πt)+ε(t)(15)

[0076] Where ε(t) represents Gaussian white noise with a signal-to-noise ratio of 20dB. Using the above model, the sampling frequency is set to 2000Hz and the sampling time to 0.5s. The signal data shown in (15) is denoised using the denoising method, wavelet thresholding, sparse decomposition, and SVD denoising based on the energy criterion proposed in this paper. The results are as follows. Figure 4 See Table 1.

[0077] Table 1

[0078]

[0079] from Figure 4 As can be seen from the results in Table 1, the proposed improved SVD denoising effect is good and its performance is better than some existing denoising algorithms.

[0080] The TOC algorithm can be improved by adaptively adjusting the number of thunderstorms as described above. To demonstrate that the improved TOC algorithm further enhances its adaptability and improves its performance in escaping local optima in complex problems, simulation tests are conducted using two types of benchmark functions. One type is a unimodal function, representing simple problems, used to test the algorithm's convergence ability; the Sphere function is selected as the representative for testing. The other type is a multimodal function, representing complex problems; this type of function can be used to test the algorithm's ability to escape local optima; the Rastrigin function is selected as the test object, and its expression is: n is the dimension of x. To fairly compare the improved TOC algorithm and the original TOC algorithm, both were run under the same conditions: population size of 30; number of iterations of 1000; dimension of 30; and 30 runs, with the average value taken to reduce the impact of random behavior. The search range, Sphere and Rastrigin functions, were both set to [-5.12, 5.12]. Regarding the parameter settings for the improved TOC and original TOC algorithms, all parameters were the same except for the setting of the number of thunderstorms, nt. The improved TOC algorithm set nt_max and nt_min to [values ​​missing]. And 1; the upper and lower bounds of the population diversity threshold are taken as 80% and 20% of the initial diversity, respectively.

[0081] The TOC and the improved TOC were each run 30 times on two benchmark functions. The average of the best solutions from the 30 runs was used as the convergence error criterion, and the standard deviation of the best solutions from the 30 runs was used as the algorithm stability criterion. The results are shown in Table 1, and the fitness curves for a single run are shown in Table 2. Figure 5 , Figure 6 .

[0082] Table 2

[0083]

[0084] From Table 2 and Figure 5 The results show that the improved TOC algorithm is less accurate than the original TOC algorithm in terms of convergence accuracy for the Sphere function, but it is more stable and has a smaller standard deviation in convergence accuracy. However, for the Rastrigin function, the improved TOC algorithm outperforms the original TOC algorithm in both convergence accuracy and stability. Therefore, the improved TOC algorithm, by utilizing a strategy of adaptive adjustment of the number of thunderstorms, is more conducive to the optimization ability of the algorithm on complex problems, has better exploratory performance, and avoids getting trapped in local optima.

[0085] By using the improved TOC optimization algorithm and constructing an adaptive function Fit(K,α), the parameter values ​​are obtained by optimizing it.

[0086]

[0087] Taking the harmonic model of equation (16) as an example, the fitness function with respect to the preset number of modes K and the penalty factor α is obtained using Fit(K,α). The improved TOC algorithm is used to optimize and solve the above problem to find the minimum value. Considering the efficiency of the algorithm, the parameter population size n = 10, the maximum number of iterations T = 20, and the number of optimization parameters is 2, so the dimension is 2. The upper and lower bounds of parameter K are 10 and 2, and the upper and lower bounds of α are 10000 and 300. Then, the optimization result is rounded to the nearest integer as the parameter of VMD. The final result is K = 3, α = 366, and the minimum fitness value is 0.2419. The fitness change curve is as follows. Figure 7 Using the obtained parameters K=3 and α=366, VMD was performed, and the decomposition results are as follows. Figure 8 .

[0088] As can be seen, the modal components were correctly obtained under these parameters, further illustrating the rationality of the fitness function selection and the effect of improving the TOC-optimized VMD decomposition. Transient harmonic phenomena generally fall into two categories: short-time harmonics, which appear briefly and are stable for a short period before disappearing; and time-varying harmonics, whose amplitude changes over time. For both cases, simulations under noisy conditions will be used to illustrate the performance of the proposed harmonic detection method.

[0089] The short-time harmonic model is established as shown in equation (17):

[0090]

[0091] Where ε(t) is a Gaussian white noise term with a signal-to-noise ratio of 20dB, the sampling frequency is set to 4096Hz, and the sampling time lasts for 1s. It can be seen that in the harmonic signal model shown in equation (17), except for the fundamental wave which is in a stable state, all other harmonic components appear only briefly. For the short-time harmonic signal shown in equation (17), after denoising the signal using the proposed denoising method, the signal is then decomposed based on the improved TOC parameter-optimized VMD. The results of plotting the original noisy signal, the denoised signal, and the decomposed IMFs are shown below. Figure 9 As shown. From Figure 9 The results show that the VMD optimization based on the improved TOC parameters successfully decomposed the signal. Then, the second-order central difference energy operator was used to adjust each IMF component, and the instantaneous amplitude and frequency of each component were obtained as follows: Figure 10 .

[0092] Figure 10 The flatter part circled in red is where the short-time harmonics appear. The average value of this part can be used as the harmonic detection result for this component. The final harmonic detection results are shown in Table 3.

[0093] Table 3

[0094]

[0095] The results in the table show that even in a noisy background, the accuracy of harmonic detection for short-time harmonic components is high. For the simulation analysis of time-varying harmonics, a typical mathematical model of time-varying harmonics is generated as shown in Equation (18). The sampling frequency is set to 4 kHz and the sampling time is 0.4 s.

[0096]

[0097] It can be seen that the amplitudes of the fundamental and harmonic components in the signal changed at different time intervals. At 0.1s, a new harmonic component was added and the fundamental amplitude changed; at 0.3s, both the fundamental and harmonic amplitudes changed. After denoising the signal using the proposed denoising method, the signal was further decomposed using VMD based on the improved TOC parameters. The results of plotting the original noisy signal, the denoised signal, and the decomposed IMFs are shown below. Figure 11 As shown.

[0098] from Figure 11 As can be seen, all three components in the time-varying harmonics were correctly identified: IMF1 corresponds to the 250Hz component, IMF2 to the 150Hz component, and IMF3 to the fundamental component. Then, the second-order central difference energy operator was used to adjust each component, resulting in the instantaneous amplitude and frequency images shown below. Figure 12 .pass Figure 12 Considering the edge effect, the average value of the flat part is also used as the result of harmonic detection. The final results are shown in Table 4.

[0099] Table 4

[0100]

[0101] As shown in Table 4, the average error for amplitude detection is 0.678% and the average error for frequency detection is 0.062% for time-varying harmonics. This also verifies that the harmonic detection method proposed in this paper has high detection accuracy for time-varying harmonics in noisy environments.

[0102] The various embodiments of this invention are implemented through programmed processing using a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention can be encapsulated into various modules. Based on this reality, and building upon the above embodiments, this invention provides a harmonic detection device based on improved SVD and parameter-optimized VMD. This device is used to execute the harmonic detection method based on improved SVD and parameter-optimized VMD in the above method embodiments. See also... Figure 2 The device includes: a first main module for improving SVD denoising preprocessing of noisy harmonic signals, using singular value shrinkage to determine the effective rank for noise separation; a second main module for optimizing the preset number of modes K and penalty factor α of Variational Mode Decomposition (VMD) using an improved Tornado Optimization Algorithm (TOC), wherein the improved TOC introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms according to population diversity to balance global exploration and local exploitation capabilities; and a third main module for constructing the fitness function Fit(K,α)=fre_uniform+Ort+Max. Se, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The fitness function is minimized according to the improved tornado optimization algorithm TOC algorithm to obtain the optimal preset number of modes K and penalty factor α; the fourth main module is used to implement VMD decomposition of the denoised signal using the optimal preset number of modes K and penalty factor α to obtain the harmonic mode components; the fifth main module is used to implement the adjustment of each mode component based on the second-order central difference Teager energy operator to extract the instantaneous amplitude and frequency information of the harmonics.

[0103] The harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention employs... Figure 2Several modules in the system improve upon SVD noise reduction technology, achieving precise noise separation based on singular value contraction theory, significantly enhancing the robustness of signal preprocessing, and achieving noise reduction performance superior to traditional methods. The proposed adaptive adjustment TOC algorithm for thunderstorm quantity, combined with a comprehensive fitness function incorporating center frequency uniformity, orthogonality, and maximum sample entropy, solves the sensitivity problem of VMD parameter selection, making mode decomposition more accurate and stable, and avoiding over-decomposition and mode aliasing. The second-order central difference Teager energy operator is used to analyze the signal, effectively improving the accuracy of instantaneous amplitude and frequency detection and reducing the impact of noise. It maintains high accuracy even in low signal-to-noise ratio environments, providing a robust and adaptable solution for transient harmonic detection in power systems, and has significant engineering application value.

[0104] It should be noted that the apparatus in the device embodiments provided by the present invention can be used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The difference lies only in the setting of corresponding functional modules. Its principle is basically the same as that of the above device embodiments provided by the present invention. As long as those skilled in the art, based on the above device embodiments and referring to the specific technical solutions in other method embodiments, obtain corresponding technical means and technical solutions composed of these technical means by combining technical features, and improve the apparatus in the above device embodiments while ensuring the practicality of the technical solutions, they can obtain corresponding device-type embodiments for implementing the methods in other method-type embodiments. For example:

[0105] Based on the above-described device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a first submodule, used to implement the improved SVD noise reduction preprocessing, including: reconstructing the Toeplitz trajectory matrix of the signal according to the phase space reconstruction, performing singular value decomposition on the Toeplitz trajectory matrix to obtain a singular value sequence; determining the maximum threshold τ that satisfies the constraint conditions using a binary search method based on the matrix rank minimization method, shrinking the singular values, reconstructing the signal matrix and diagonally averaging it to obtain the noise-reduced signal.

[0106] Based on the above-described device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a second submodule, used to implement the adaptive adjustment strategy for the number of thunderstorms, including: setting an upper bound of the number of thunderstorms nt_max and a lower bound of the number of thunderstorms nt_min; calculating the initial population diversity and setting an upper bound of the diversity threshold diversity_h and a lower bound of the diversity threshold diversity_l; during the iteration process, if the population diversity diversity is greater than the upper bound of the diversity threshold diversity_h, then the number of thunderstorms nt is increased; if the population diversity diversity is less than the lower bound of the diversity threshold diversity_l, then the number of thunderstorms nt is decreased, ensuring that the number of thunderstorms nt is within the range of the lower bound of the number of thunderstorms nt_min and the upper bound of the number of thunderstorms nt_max, wherein the population diversity is the average distance between individuals.

[0107] Based on the above-described device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a third submodule, used to implement the orthogonality index Ort, including:

[0108]

[0109] Among them, u k The first harmonic mode component; u l The second harmonic mode component; || is the norm sign; || is the absolute value sign; <> is the mean operator; the uniformity of the center frequency spacing fre_uniform is the standard deviation of the difference between adjacent frequencies after sorting the center frequencies of the decomposed modes; the maximum sample entropy MaxSe is the maximum value of the sample entropy of each mode.

[0110] Based on the above-described device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a fourth submodule, used to implement the discrete form of the second-order central difference Teager energy operator, including:

[0111] ψ d (u(n))=u 2 (n)-u(n-1)u(n+1)

[0112] The instantaneous amplitude and frequency are obtained from the three-point second-order central difference sequence, including:

[0113]

[0114] Where arccos is the inverse cosine sign; || is the absolute value sign; n is the discrete-time index; ψ d (u(n)) is the Teager energy of the original signal; u(n) is the input discrete-time sequence; y(n) is the first derivative of u(n) after center difference; A(n) is the instantaneous amplitude; ψ d (y(n)) represents the Teager energy of the differential signal; w(n) represents the instantaneous frequency.

[0115] Based on the above device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a fifth submodule, used to implement the noise separation by determining the effective rank using singular value contraction, including: determining the constraint conditions through binary search. Maximum threshold τ The singular values ​​are shrunk, where δ is the noise level and σ is the noise level. i These are the singular values ​​of the Hankle matrix formed by the noisy signals, estimated using the median deviation statistic.

[0116] Based on the above device embodiments, as an optional embodiment, the harmonic detection device based on improved SVD and parameter-optimized VMD provided in this embodiment of the invention further includes: a sixth submodule, used to implement the minimization of the fitness function according to the improved tornado optimization algorithm TOC algorithm to obtain the optimal preset mode number K and penalty factor α, including: fre_uniform avoids over-decomposition by measuring the uniformity of the center frequency spacing; Ort avoids modal redundancy by evaluating the orthogonality between modes; MaxSe judges modal aliasing by the maximum sample entropy, and Fit(K,α) takes the minimum value corresponding to the optimal preset mode number K and penalty factor α.

[0117] The method in this embodiment of the invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. For this purpose, this embodiment of the invention provides an electronic device, such as... Figure 3 As shown, the electronic device includes at least one processor, a communications interface, at least one memory, and a communications bus, wherein the at least one processor, the communications interface, and the at least one memory communicate with each other via the communications bus. The at least one processor can invoke logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0118] Furthermore, when the logical instructions in at least one of the aforementioned memories can be implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0119] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0120] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0121] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Based on this understanding, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, or sometimes in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0122] It should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Any expressions such as "predetermined threshold," "preset threshold," etc., without specifying a particular value, can be determined by those skilled in the art through simple experimentation or appropriate adjustments.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A harmonic detection method based on improved SVD and parameter-optimized VMD, characterized in that, include: An improved SVD noise reduction preprocessing is performed on noisy harmonic signals, and singular value shrinkage is used to determine the effective rank to achieve noise separation; An improved Tornado Optimization Algorithm (TOC) is used to optimize the preset number of modes K and the penalty factor α in Variational Mode Decomposition (VMD). The improved TOC introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms based on population diversity to balance global exploration and local exploitation capabilities. A fitness function Fit(K,α) = fre_uniform + Ort + MaxSe is constructed, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The improved TOC algorithm minimizes this fitness function to obtain the optimal preset number of modes K and penalty factor α. The denoised signal is then subjected to VMD decomposition using the optimal preset number of modes K and penalty factor α to obtain the harmonic mode components. The second-order central difference Teager energy operator is used to adjust each modal component and extract the instantaneous amplitude and frequency information of the harmonics.

2. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 1, characterized in that, The improved SVD denoising preprocessing includes: reconstructing the Toeplitz trajectory matrix of the signal based on phase space reconstruction, performing singular value decomposition on the Toeplitz trajectory matrix to obtain a singular value sequence; using the matrix rank minimization method, employing binary search to determine the maximum threshold τ that satisfies the constraint conditions, shrinking the singular values, reconstructing the signal matrix and performing diagonal averaging to obtain the denoised signal.

3. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 2, characterized in that, The adaptive adjustment strategy for thunderstorm numbers includes: setting an upper bound of thunderstorm numbers nt_max and a lower bound of thunderstorm numbers nt_min; calculating the initial population diversity and setting an upper bound of diversity threshold diversity_h and a lower bound of diversity threshold diversity_l; during the iteration process, if the population diversity is greater than the upper bound of diversity threshold diversity_h, then the number of thunderstorms nt is increased; if the population diversity is less than the lower bound of diversity threshold diversity_l, then the number of thunderstorms nt is decreased, ensuring that the number of thunderstorms nt is within the range of the lower bound of thunderstorm numbers nt_min and the upper bound of thunderstorm numbers nt_max, where the population diversity is the average distance between individuals.

4. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 3, characterized in that, The orthogonality index Ort includes: Among them, u k The first harmonic mode component; u l The second harmonic mode component; |||| is the norm sign; || is the absolute value sign; <> is the mean operator; the uniformity of the center frequency spacing fre_uniform is the standard deviation of the difference between adjacent frequencies after sorting the center frequencies of the decomposed modes; the maximum sample entropy MaxSe is the maximum value of the sample entropy of each mode.

5. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 4, characterized in that, The discrete form of the second-order central difference Teager energy operator includes: ψ d (u(n))=u 2 (n)-u(n-1)u(n+1); The instantaneous amplitude and frequency are obtained from the three-point second-order central difference sequence, including: Where arccos is the inverse cosine sign; || is the absolute value sign; n is the discrete-time index; ψ d (u(n)) is the Teager energy of the original signal; u(n) is the input discrete-time sequence; y(n) is the first derivative of u(n) after center difference; A(n) is the instantaneous amplitude; ψ d (y(n)) represents the Teager energy of the differential signal; w(n) represents the instantaneous frequency.

6. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 5, characterized in that, The method of using singular value shrinkage to determine the effective rank for noise separation includes: determining the constraint conditions through binary search. The maximum threshold τ is used to shrink singular values, where δ is the noise level and σ is the maximum threshold τ. i These are the singular values ​​of the Hankle matrix formed by the noisy signals, estimated using the median deviation statistic.

7. The harmonic detection method based on improved SVD and parameter-optimized VMD according to claim 6, characterized in that, The step of minimizing the fitness function according to the improved tornado optimization algorithm TOC to obtain the optimal preset number of modes K and penalty factor α includes: fre_uniform avoids over-decomposition by measuring the uniformity of the center frequency spacing; Ort avoids modal redundancy by evaluating the orthogonality between modes; MaxSe judges mode aliasing by the maximum sample entropy; and Fit(K,α) takes the minimum value, which corresponds to the optimal preset number of modes K and penalty factor α.

8. A harmonic detection device based on improved SVD and parameter-optimized VMD, characterized in that, include: The first main module is used to implement SVD noise reduction preprocessing for noisy harmonic signals, and uses singular value shrinkage to determine the effective rank to achieve noise separation; The second main module is used to optimize the preset number of modes K and the penalty factor α of Variational Mode Decomposition (VMD) using the improved Tornado Optimization Algorithm (TOC). The improved Tornado Optimization Algorithm (TOC) introduces an adaptive adjustment strategy for the number of thunderstorms, dynamically adjusting the number of thunderstorms according to population diversity to balance global exploration and local exploitation capabilities. The third main module is used to construct the fitness function Fit(K,α)=fre_uniform+Ort+MaxSe, where fre_uniform is the standard deviation of the center frequency spacing of the decomposed modes, Ort is the orthogonality index between modes, and MaxSe is the maximum sample entropy of the decomposed modes. The fitness function is minimized according to the improved Tornado Optimization Algorithm (TOC) to obtain the optimal preset number of modes K and penalty factor α. The fourth main module is used to perform VMD decomposition on the denoised signal using the optimal preset number of modes K and penalty factor α to obtain the harmonic mode components. The fifth main module is used to adjust each modal component based on the second-order central difference Teager energy operator and extract the instantaneous amplitude and frequency information of the harmonics.

9. An electronic device, characterized in that, include: At least one processor, at least one memory, and a communication interface; wherein, The processor, memory, and communication interface communicate with each other; The memory stores program instructions that can be executed by the processor, which calls the program instructions to execute the harmonic detection method based on improved SVD and parameter-optimized VMD as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the harmonic detection method based on improved SVD and parameter-optimized VMD as described in any one of claims 1 to 7.

Images