Power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold

Abstract

The method comprises the following steps: obtaining a power quality signal containing noise; selecting permutation entropy as an adaptive function of genetic algorithm, calling variational mode decomposition through genetic algorithm, and iteratively optimizing a penalty factor α and a decomposition mode number k of the variational mode decomposition to determine optimal parameters; decomposing signal data into k mode components through the variational mode decomposition, and determining effective mode components and noise mode components through a correlation coefficient; for improved wavelet threshold, a parameter-adjustable threshold function is proposed, and the concept of wavelet energy entropy is introduced into the threshold function; the noise mode components are denoised through the improved wavelet threshold, and the effective mode components and the denoised noise mode components are reconstructed to obtain a denoised power quality disturbance signal. The method can effectively remove noise interference while retaining singular information of mutation points of the collected signal, and provides help for subsequent analysis and treatment of the power quality disturbance signal.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power quality disturbance signal denoising, and particularly relates to a power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold. BACKGROUND

[0002] Under the background of "double high", the power quality problem in the power system is increasingly prominent. In order to govern the power quality disturbance, the disturbance signal needs to be collected first. However, in actual application, the power quality signal collected in real time by the power system has certain noise interference, and the collected power quality disturbance signal cannot be directly subjected to feature extraction and analysis, and thus the disturbance signal cannot be governed. Therefore, a suitable method needs to be used to denoise the collected power quality signal.

[0003] Wavelet threshold denoising is one of wavelet denoising, and is widely used in signal denoising due to its advantages of simplicity, efficiency, stability and flexibility. In wavelet threshold denoising, the selection of threshold function and the estimation of threshold are the keys of the whole denoising process. The discontinuity of the traditional hard threshold function at the threshold will cause signal oscillation, and the transition smoothing of the soft threshold function will cause constant bias, thereby affecting the approximation degree of the reconstructed signal and the real signal, and the fixed general threshold cannot be adaptively changed according to the decomposition layer, affecting the denoising effect.

[0004] Variational mode decomposition is proposed on the basis of traditional Wiener filtering, and can decompose a signal into a series of intrinsic mode components. The mode component where the noise is located is selected for processing, so that the denoising effect can be achieved. However, the decomposition effect of variational mode decomposition depends on the selection of penalty factor alpha and decomposition mode number k. When the optimal alpha and k values are selected, the noise signal can be fully decomposed, which is very suitable for denoising of various signals.

[0005] At present, there is a denoising method for noisy power quality disturbance signal combining variational mode decomposition and mean filtering, which selects effective mode components for direct reconstruction and uses mean filtering to extract features of useless components, thereby improving the denoising effect. However, the singularity detection is not performed, and it cannot be determined whether the signal denoised by the algorithm can be positioned. A denoising method combining variational mode decomposition and wavelet threshold selects part of the mode components for denoising and reconstruction by observation, and achieves good denoising effect. However, it still selects the traditional hard threshold function and the general threshold, which may lead to a reduction in feature quantity, and the positioning effect needs to be considered. SUMMARY

[0006] To solve the above technical problems, the application provides a power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold, which comprises three parts of genetic algorithm, variational mode decomposition and improved wavelet threshold denoising.

[0007] The technical scheme adopted by the application is as follows:

[0008] The power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold comprises the following steps:

[0009] Step 1: obtaining a one-dimensional noisy power quality signal and storing the one-dimensional noisy power quality signal in variational mode decomposition;

[0010] Step 2: selecting permutation entropy as an adaptive function of genetic algorithm, calling variational mode decomposition through genetic algorithm, and iteratively optimizing a penalty factor α and a decomposition mode number k of the variational mode decomposition to determine optimal parameters;

[0011] Step 3: according to the optimization result of step 2, decomposing the signal data into k mode components by using variational mode decomposition, and determining effective mode components and noise mode components by using a correlation coefficient;

[0012] Step 4: to improve the shortcomings of the traditional wavelet threshold and improve the denoising effect on the noise mode components, for the improved wavelet threshold, a parameter-adjustable threshold function is proposed, which can take into account the advantages of soft and hard threshold functions, and the concept of wavelet energy entropy is introduced into the threshold function, and an adaptive threshold that can adaptively change according to the noise content is proposed;

[0013] Step 5: using the improved wavelet threshold of step 4 to denoise the noise mode components of step 3, and selecting effective mode components and noise mode components after denoising to reconstruct to obtain a denoised power quality disturbance signal.

[0014] In step 1, the one-dimensional noisy power quality signal is inputted, and:

[0015] x(t)=f(t)

[0016] In the formula, x(t) is a one-dimensional noisy power quality signal, and f(t) is an input signal of variational mode decomposition.

[0017] In step 2, the calculation process of permutation entropy is as follows:

[0018] A time series S contains N signals {x(k), k=1, 2, …, N}, and spatial reconstruction is performed on the time series S to obtain the following matrix:

[0019]

[0020] In the formula: each line represents a segment of signal; r=N-(m-1)τ; m represents the dimension; τ represents the delay time; r represents the number of segments after the reconstruction and decomposition of sequence S; N represents the total number of signals in each segment; j represents the jth segment of signal.

[0021] x(1), x(j), x(r), x(1+τ), x(j+τ), x(r+τ), x(1+(m-1)τ), x(j+(m-1)τ), x(r+(m-1)τ) are all signals in the original sequence S.

[0022] The elements in each segment of signal are rearranged in ascending order to obtain the position of each element in the vector, forming a set of symbol sequences: S(l)=(j1,j2,…,j m ), l=1,2,…,r, r≤m!, m-dimensional space maps different symbol sequences, a total of m!.

[0023] j1,j2,…,j m are all signals in the original sequence S, r represents the number of segments after the reconstruction and decomposition of sequence S, and m! represents m! arrangement modes of m different symbols, corresponding to m! symbol sequences.

[0024] The number of each r symbol sequence is divided by m!, and then the total number of different symbol sequences is obtained. The probability of the appearance of different symbol sequences is S(l){P1,P2,…,P r}; S(l) represents different symbol sequences, and {P1,P2,…,P r} represents the probability of the appearance of different symbol sequences.

[0025] The permutation entropy of the time sequence {X(K)=1,2,…,N} is calculated as follows:

[0026]

[0027] P j represents the probability of the appearance of sequence j, r represents the total number of sequences, and j represents the jth sequence.

[0028] The maximum value of the permutation entropy is ln(m!), and the permutation entropy is normalized as follows:

[0029]

[0030] From the calculation process of the permutation entropy, it can be seen that the size of the permutation entropy is related to the signal noise amplitude. The smaller the value is, the simpler and more regular the sequence is; on the contrary, the larger the value is, the more complex and random the sequence is.

[0031] In step 2, the variational mode decomposition is called by the genetic algorithm, and the penalty factor alpha and the number of decomposition modes k of the variational mode decomposition are iteratively optimized to determine the optimal parameters; comprising the following steps:

[0032] Step 2.1: Set the optimization interval of k in the genetic algorithm as [3, 8];

[0033] Step 2.2: Set the optimization interval of alpha in the genetic algorithm as [100, 2200];

[0034] Step 2.3: Set the permutation entropy as the adaptive function of the genetic algorithm;

[0035] Step 2.4: Start the iterative optimization to determine the optimal values of alpha and k.

[0036] The step 3 comprises the following steps:

[0037] Step 3.1: Construct the objective constraint function for solving the variational mode decomposition problem, the formula is as follows:

[0038]

[0039] In the formula, u k is the decomposition component, ω k is the instantaneous frequency of the Kth component; delta(t) represents the Dirac distribution about time t, u k (t) represents the eigenmode component; represents the transformation factor, f(t) represents the original signal, k represents the number of modal components, j represents the complex number, represents the partial derivative with respect to time t.

[0040] Step 3.2: Construct the unconstrained variational problem, the formula is as follows:

[0041]

[0042] In the formula, alpha is the penalty factor, and lambda is the Lagrange multiplier operator.

[0043] {u k} represents the eigenmode component set; {omega k} represents the instantaneous frequency set; lambda(t) represents the Lagrange multiplier term about time t; represents the sum of modal components; represents the Lagrange multiplier term; < > represents a vector.

[0044] By the alternating direction multiplier algorithm, the component and the center frequency are obtained, the formula is as follows:

[0045]

[0046] Indicates the updated intrinsic mode components; u i λ(ω) represents the iterative value of the eigenmode component in the Fourier domain, λ(ω) represents the Lagrange multiplier operator in the frequency domain, and ω represents the frequency parameter.

[0047]

[0048] This represents the updated center frequency value.

[0049]

[0050] λ n+1 (ω) represents the updated frequency domain Lagrange multiplier operator value, λ n (ω) represents the iterative value of the Lagrange multiplier operator in the Fourier domain.

[0051] Step 3.3: Stop the loop decomposition when the decomposed function components satisfy the following formula; otherwise, repeat step 3.2.

[0052] Step 3.4: Calculate the cross-correlation coefficient between the modal components and the original signal using the Pearson correlation coefficient. For two random variables X = {x1, x2, ..., x...} n};x1,x2,…,x n Let Y = {y1, y2, ..., y3} represent the elements in variable X. n};y1,y2,…,y n These represent the elements of variable Y.

[0053] The calculation formula is as follows:

[0054]

[0055] In the formula, Let R represent the means of random variables X and Y, respectively. xy Represents the correlation coefficient; x i Represents the i-th element in variable X; y i Let represent the i-th element in variable Y; n represents the total number of elements in variables X and Y.

[0056] Step 3.5: Use the boundary formula to distinguish the correlation coefficients to determine the noise mode component and the effective mode component. The boundary formula is as follows:

[0057] μ = max(R) xy ) / [10max(R xy )-3]

[0058] In the formula, μ represents the boundary value, and max(R) xy) represents the maximum value of the correlation coefficient.

[0059] The modal component with the correlation coefficient greater than or equal to the threshold value is defined as an effective component, and the modal component with the correlation coefficient less than or equal to the threshold value is defined as a noise modal component.

[0060] The step 4 includes the following steps:

[0061] Step 4.1: decompose the one-dimensional noisy signal x(t) by using the discrete wavelet transform, and the following formula can be obtained:

[0062]

[0063] In the formula, Z represents an integer; m J,k is an approximation coefficient, representing a low-frequency component in the noisy signal; n J,k is a detail coefficient, representing a high-frequency component in the noisy signal; φ J,k (t) represents a scaling function; ψ J,k (t) represents a wavelet basis function; J represents the number of decomposition layers, j represents the layer number, and k represents the element number in the layer.

[0064] Noise is a high-frequency component existing in the detail sequence, and useful signal is generally a low-frequency component existing in the approximation sequence. The detail sequence is processed by a threshold function, and the formula of the adjustable threshold function is as follows:

[0065]

[0066] In the formula, b is a variable parameter, λ j is an improved adaptive threshold; d j,k represents a wavelet detail coefficient, d j ′ ,k represents a wavelet coefficient after threshold quantization, sgn(d j,k ) represents the positive and negative of the wavelet detail coefficient, represents a variable factor.

[0067] Different values of b will affect the trend of the improved threshold function. The threshold functions under different b values are shown in Figure 2 As can be seen from Figure 2 , by changing the size of the variable parameter b, different function effects can be obtained. When a suitable b value is selected, the advantages of soft and hard threshold functions can be considered, and effective denoising can be achieved.

[0068] Step 4.2: for the improved adaptive threshold λ j of step 4.1, the determination method is as follows:

[0069] The detail coefficient sequence of the i-th layer is divided into several subintervals, the subinterval with the maximum wavelet energy entropy is taken as a characteristic interval, the mean value of the wavelet coefficient in the interval is taken as the noise standard deviation of the signal of the layer, and the new threshold value formula is as follows:

[0070]

[0071] In the formula, is the noise standard deviation on the decomposition scale j, N is the signal length, and j is the number of wavelet decomposition.

[0072] Therefore, the wavelet threshold value algorithm is improved.

[0073] The technical effects of the power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold value are as follows:

[0074] 1) In step 2 of the present application, the permutation entropy is taken as an adaptive function of the genetic algorithm, the variational mode decomposition algorithm is iteratively optimized, the optimal alpha and k values can be selected, and the over-decomposition and under-decomposition phenomena of the variational mode decomposition when decomposing the noisy power quality signal are avoided.

[0075] 2) In step 3 of the present application, the threshold value boundary formula can accurately distinguish the effective modal component and the noise modal component, and provides effective help for denoising of the noisy power quality disturbance signal.

[0076] 3) In step 4 of the present application, the variable threshold function of the improved wavelet threshold denoising algorithm can take into account the advantages of the soft and hard threshold functions, and overcome the disadvantages of the soft and hard threshold functions, such as discontinuity, easy oscillation and large deviation; the threshold value selection method based on wavelet energy entropy can further modify the threshold value formula according to the noise content in each layer, accurately evaluate the noise content, and improve the threshold accuracy.

[0077] 4) In step 5 of the present application, on the basis of distinguishing the effective modal component and the noise modal component, the improved wavelet threshold denoising algorithm is used to only denoise the noise modal component, so that significant denoising effect can be obtained in a strong noise environment, the singular information of the disturbance point is retained, and help can be provided for subsequent analysis and treatment of the power quality disturbance signal. DETAILED DESCRIPTION

[0078] The present application will be further described below in combination with the drawings and examples:

[0079] Figure 1 The signal denoising flowchart of the present application.

[0080] Figure 2 The threshold value function comparison diagram under different values.

[0081] Figure 3The figure is the denoising effect diagram of the 20 dB interruption + harmonic signal.

[0082] Figure 4 The figure is the denoising effect diagram of the interruption + harmonic signal.

[0083] Figure 5 The figure is the oscillation SNR comparison diagram.

[0084] Figure 6 The figure is the oscillation MSE comparison diagram.

[0085] Figure 7 The figure is the interruption + harmonic SNR comparison diagram.

[0086] Figure 8 The figure is the interruption + harmonic MSE comparison diagram.

[0087] Figure 9 The figure is the third layer component signal diagram of the three signals without denoising.

[0088] Figure 10 The figure is the transient oscillation signal start and end point positioning diagram.

[0089] Figure 11 The figure is the transient drop signal start and end point positioning diagram.

[0090] Figure 12 The figure is the interruption signal start and end point positioning diagram. DETAILED DESCRIPTION

[0091] The power quality disturbance denoising method based on variational mode decomposition and improved wavelet threshold includes the following steps:

[0092] Step one: obtain a one-dimensional noisy power quality signal, and store the one-dimensional noisy power quality signal in the variational mode decomposition; step two: select permutation entropy as the fitness function of genetic algorithm, call the variational mode decomposition through the genetic algorithm, and iteratively optimize the penalty factor α and the decomposition mode number k of the variational mode decomposition to determine the optimal parameters;

[0093] Step three: according to the optimization result of step two, decompose the signal data into k modal components by using the variational mode decomposition, and determine the effective modal component and the noise modal component by using the correlation coefficient;

[0094] Step four: in order to improve the shortcomings of the traditional wavelet threshold and improve the denoising effect of the noise modal component, for the improved wavelet threshold, a parameter-adjustable threshold function is proposed, which can take into account the advantages of soft and hard threshold functions, and the concept of wavelet energy entropy is introduced into the threshold function, and an adaptive threshold is proposed which can adaptively change according to the noise content;

[0095] Step five: using the improved wavelet threshold in step four to denoise the noise modal component in step three, and selecting the effective modal component and the noise modal component after denoising to reconstruct, to obtain the denoised power quality disturbance signal.

[0096] In the step two, the permutation entropy is used as the adaptive function of the genetic algorithm, and the optimal parameters of the penalty factor a and the decomposition modal number k of the variational modal decomposition are determined by the genetic algorithm adaptive optimization, including the following steps:

[0097] Step S2.1: obtaining the noisy power quality disturbance signal by the signal acquisition device, and storing the noisy power quality disturbance signal into the variational modal decomposition as one-dimensional signal data.

[0098] The adaptive function of the genetic algorithm is selected, and the permutation entropy is an entropy for measuring the complexity of a time series. Compared with other time series complexity parameters (such as Lyapunov exponent, fractal dimension and approximate entropy), it is easier to calculate and has stronger anti-interference ability. In addition, it can accurately and conveniently locate the time of signal mutation, and quantitatively evaluate the random noise contained in the signal sequence; therefore, it is particularly suitable for signals containing dynamic and observation noise. Therefore, the permutation entropy is selected as the adaptive function of the algorithm, and the calculation process of the permutation entropy is as follows:

[0099] For a discrete sequence {X(K)=1,2,…,N} with length N, spatial reconstruction can be performed to obtain the following matrix:

[0100]

[0101] In the formula, j=1r, r=N-(m-1)τ, m is the dimension, and τ is the delay time.

[0102] The components are rearranged in ascending order to obtain the position of each element in the vector, and a set of symbol sequences S(l)=(j1,j2,…,j m ), l=1,2,…,r, r≤m!, m-dimensional space maps different symbol sequences, and there are m! kinds.

[0103] The number of each r symbol sequence is divided by m!, and the total number of different symbol sequences is the probability of different symbol sequences appearing S(l){P1,P2,…,P r}. The permutation entropy of the time series {X(K)=1,2,…,N} is calculated as:

[0104]

[0105] The maximum value of the permutation entropy is ln(m!), and the permutation entropy is normalized as follows:

[0106]

[0107] From the calculation process of permutation entropy, the size of permutation entropy is related to the signal noise amplitude, the smaller the value, the simpler and more regular the sequence, on the contrary, the larger the value, the more complex and random the sequence.

[0108] Step S2.2: calling variational mode decomposition by genetic algorithm, and iteratively optimizing the penalty factor a and the number of decomposition modes k.

[0109] In the third step, the signal is decomposed into k modal components by variational mode decomposition according to the optimization result, and the effective modal component and the noise modal component are determined by the correlation coefficient, including the following steps:

[0110] S3.1: constructing the objective constraint function for solving the variational problem, the formula is as follows:

[0111]

[0112] In the formula, u k is the decomposition component, ω k is the Kth instantaneous frequency.

[0113] S3.2: constructing an unconstrained variational problem, the formula is as follows:

[0114]

[0115] In the formula, a is the penalty factor, and λ is the Lagrange multiplier operator.

[0116] The component and the center frequency are obtained by the alternating direction multiplier algorithm, and the formula is as follows:

[0117]

[0118]

[0119]

[0120] S3.3: stopping the loop decomposition when the decomposed function component satisfies the following formula, if not, repeat S3.2.

[0121]

[0122] Taking the interrupted + harmonic signal with a signal-to-noise ratio of 20dB as an example, genetic algorithm and variational mode decomposition are used to decompose the noisy power quality disturbance signal. First, the two parameters of variational mode decomposition are adaptively iteratively optimized by genetic algorithm, and the optimal k, a value selected after genetic algorithm iterative optimization is 5, 584. The decomposition effect of variational mode decomposition on noisy power quality disturbance signal under the optimal value is as shown in Figure 3 .

[0123] S3.4: Calculate the cross-correlation coefficient of the decomposed k modal components and the original signal by using the Pearson correlation coefficient. For two random variables X = {x1, x2, …, xk} and Y = {y1, y2, …, yk}, the formula is as follows: n n

[0124]

[0125] wherein, and represent the mean of random variables X and Y.

[0126] S3.5: Determine the noise modal component and the effective modal component by distinguishing the correlation coefficient by the demarcation formula, which is as follows:

[0127] μ = max(R xy ) / [10max(R xy )-3];

[0128] For the modal component with a correlation coefficient greater than or equal to the demarcation value, it is defined as an effective component, and for the modal component with a correlation coefficient less than or equal to the demarcation value, it is defined as a noise modal component.

[0129] Use the S3.4 and S3.5 to calculate the cross-correlation coefficient of the five modal components in Table 1, and the calculation results are shown in Table 1. The noise modal components are modal 3 to modal 5 by the demarcation value μ in Table 1. Figure 3

[0130] Table 1 Correlation coefficient of different modal

[0131]

[0132]

[0133] In step four, for the improved wavelet threshold, a parameter-adjustable threshold function is proposed, which can take into account the advantages of soft and hard threshold functions, and the concept of wavelet energy entropy is introduced into the threshold. An adaptive threshold is proposed which can change adaptively according to the noise content, including the following steps:

[0134] S4.1: Decompose the one-dimensional noisy power quality disturbance signal x(t) by discrete wavelet transform, which can be obtained as follows:

[0135]

[0136] wherein, Z is an integer, m J,k is the approximation coefficient, representing the low-frequency component in the noisy signal. n J,k ​​​The detail coefficient represents the high frequency component in the noisy signal. J,k (t) is a scaling function, ψ J,k (t) is a wavelet basis function.

[0137] For a certain decomposition level, the power quality disturbance signal can be decomposed into approximation coefficients and detail coefficients by using the discrete wavelet transform. The noise signal belongs to the high frequency component, so it is distributed in the detail coefficient sequence. After the disturbance signal is decomposed by the discrete wavelet transform, the wavelet coefficient amplitude of the useful signal component is much larger than that of the noise signal component. This feature ensures that we can construct a threshold and a threshold function to process the decomposed detail coefficient sequence, so as to achieve the purpose of denoising. Finally, the processed wavelet coefficients are reconstructed by using the inverse wavelet transform, so that the denoised power quality disturbance signal can be obtained.

[0138] In short, the wavelet threshold denoising process includes multi-level wavelet decomposition, wavelet coefficient threshold shrinkage process, and wavelet reconstruction. In this process, the focus is on selecting a suitable threshold and threshold function. The traditional soft, hard threshold function and general threshold formula are as follows:

[0139] Soft threshold function:

[0140]

[0141] Hard threshold function:

[0142]

[0143] General threshold:

[0144]

[0145] In the formula, N is the length of the processed signal, is the standard deviation of the noise in the signal.

[0146] The traditional soft and hard threshold functions have the disadvantages of constant deviation, discontinuity and easy oscillation, which will affect the denoising effect of the disturbance signal. Therefore, the invention improves the traditional threshold function and proposes a new threshold function, which can retain the advantages of the soft and hard threshold functions while improving their shortcomings. The improved threshold function is as follows:

[0147]

[0148] In the formula, b is a variable parameter, λ j is the improved adaptive threshold. Different values of b will affect the trend of the improved threshold function. The threshold function under different b values is as shown in Figure 2 .

[0149] Figure 2 ​It can be seen that by changing the size of the variable parameter b, different function effects can be obtained. When b approaches 0, the improved threshold function is equivalent to a hard threshold function; when b approaches infinity, the improved threshold function is equivalent to a soft threshold function; and when b is in the range of (0, +∞), the improved threshold function can switch between the soft threshold function and the hard threshold function, thereby increasing the flexibility thereof.

[0150] S4.2: Introduce the wavelet energy entropy into the threshold formula. The more concentrated the noise content in the sub-interval, the greater the value of the wavelet energy entropy. That is, the wavelet coefficients in the interval are mostly noise corresponding wavelet coefficients. At this time, the interval can be taken as a characteristic interval of noise for analysis and processing. Therefore, the interval with the maximum wavelet energy entropy value in each layer is selected, and the mean value of the wavelet coefficients in the interval is taken as the noise standard deviation of the layer. The improved threshold formula is as follows:

[0151]

[0152] In the formula, is the noise standard deviation on the decomposition scale j, N is the length of the processed signal, and j is the number of wavelet decomposition layers.

[0153] With the increase of the scale of wavelet decomposition, the wavelet coefficient amplitude of the useful signal changes little, and the wavelet coefficient amplitude of the noise signal decreases. The general threshold formula is as follows:

[0154]

[0155] In the formula, is the noise standard deviation, and N is the length of the processed signal.

[0156] As can be seen from the general threshold solving method, the threshold is a constant value in the entire decomposition process. As a standard for distinguishing useful signals from noise signals, the threshold should decrease adaptively with the increase of the number of decomposition layers, so as to prevent too much useful signal from being omitted.

[0157] As can be seen from the improved threshold formula solving method, under the action of 2ln(j+1), the threshold λ j decreases with the increase of the number of decomposition layers, which is consistent with the rule that the wavelet coefficient of the noise signal decreases with the increase of the number of decomposition layers. The redefined noise standard deviation can further correct the threshold formula according to the noise content in each layer, and compared with the original formula, it can more accurately evaluate the noise content and improve the accuracy of the threshold.

[0158] In step five, the improved wavelet threshold is used to denoise the noise modal component, and the effective modal component and the denoised noise modal component are selected for reconstruction to obtain a denoised power quality disturbance signal, including the following steps:

[0159] S5.1: Denoising the noise modal components using the improved wavelet threshold described in step four.

[0160] S5.2: Signal reconstruction of the denoised noise modal components and the effective modal components described in S3.5, and output the reconstructed signal to obtain the denoised acquisition signal.

[0161] For the modal components in Figure 3 , the noise modal components determined by S3.4 and S3.5 are modal 3 to modal 5, and the improved wavelet threshold is used for denoising the three noise modal components, and the denoised noise modal components are reconstructed with the effective modal components, and the reconstruction result is as shown in Figure 4 , and by comparing the (a) subgraph and the (c) subgraph in Figure 4 , it can be seen that the present application can realize effective denoising.

[0162] To further evaluate the denoising effect of the present application, four types of power quality noise disturbance signals, voltage sag, harmonic signal, transient oscillation, and interruption + harmonic, are selected for analysis, and different noise intensities of 10 dB, 15 dB, 20 dB, 25 dB, and 30 dB are added to them, respectively. The background technology of variational mode decomposition plus wavelet hard threshold (literature [1]: Feng Yilin, Yu Ci, Wang Mian. Power disturbance signal denoising algorithm based on VMD and wavelet analysis [J]. Sensors and microsystems, 2021, 40(01): 144-6+50.), wavelet hard threshold, wavelet soft threshold, and the denoising algorithm of the present application are used to denoise the noisy power quality disturbance signals.

[0163] After denoising by the four algorithms, the signal-to-noise ratio (SNR) and the mean square error (MSE) of the voltage sag and the harmonic signal are as shown in Tables 2 and 3:

[0164] Table 2 Comparison of SNR values after denoising

[0165]

[0166] Table 3 Comparison of MSE values after denoising

[0167]

[0168] The greater the SNR value, the smaller the MSE value, and the better the denoising effect of the algorithm. From Table 2 and Table 3, for the simple single disturbance signal of sag, the SNR value of the algorithm is higher than that of the other three algorithms, and the MSE value is lower than that of the other three algorithms. For the more complex disturbance signal of harmonic, when the SNR of the input signal is 10dB-20dB, the denoising effect of the algorithm is close to that of the algorithm in document [1], but as the SNR of the input signal increases, the advantage of the algorithm is more obvious, but no matter how large the SNR of the input signal is, the SNR value of the algorithm is higher than that of the other three algorithms, and the MSE value is lower than that of the other three algorithms. It can be seen that for sag and harmonic signals, the algorithm can achieve more effective denoising.

[0169] The SNR and MSE values of the denoised transient oscillation and interruption+harmonic signals are shown in Figure 5 、 Figure 6 、 Figure 7 and Figure 8 . From Figure 5 、 Figure 6 、 Figure 7 and Figure 8 , for the two complex signals of transient oscillation and harmonic+interruption, the SNR value of the denoised algorithm is higher than that of the other three algorithms, and the MSE value is lower than that of the other three algorithms. Based on the above simulation analysis, the algorithm can achieve good denoising effect as the algorithm in document [1], and from the comparison of SNR and MSE values, it can be seen that the algorithm has more advantages.

[0170] The preservation of singular information at the mutation point is an important standard for measuring denoising effect. Taking the interruption, transient oscillation and interruption+harmonic signals with an SNR of 15dB as examples, after denoising using the algorithm, a one-dimensional denoised signal is constructed into a Hankel matrix, and then the matrix is subjected to four-layer singular value decomposition, and the third layer component signal is used to locate the start and end positions of the disturbance.

[0171] Figure 9 The third layer component signal of the singular value decomposition of the three signals without denoising is shown in Figure 10 、 Figure 11 、 Figure 12 , and the (c) subgraph of the third layer component of the transient oscillation denoised signal, the third layer component of the sag signal and the third layer component of the interruption signal are shown in (c) subgraph. It can be seen that the third layer component of the undenoised signal cannot reflect the disturbance information, and thus cannot locate the start and end points of the disturbance. The actual disturbance start and end points located by the (c) subgraph in Figure 10 、 Figure 11 、 Figure 12 are summarized in Table 4.

[0172] Table 4 Analysis of Disturbance Start and End Point Location Results

[0173]

[0174] As shown in Table 4, after the denoised transient oscillation signal is located by singular value decomposition, the starting point and ending point are 1600 and 1791, respectively. The theoretical values ​​are 1600 and 1790, respectively. The positioning error is only 1 sampling point at the ending point.

[0175] For the voltage sag signal and the voltage interruption signal, after the denoised signal is located by the singular value decomposition method, the starting point and ending point of the location disturbance are 639, 1921 and 640, 1922 respectively. The theoretical values ​​of both signals are 640 and 1920. The voltage sag signal has 1 sampling error at both the starting point and the ending point, while the voltage interruption signal has 2 sampling errors only at the ending point.

[0176] from Figure 10 , Figure 11 , Figure 12 As shown in subgraph (b) and the analysis of the start and end points, simulation results demonstrate that the new algorithm achieves significant denoising and accurate location of abrupt change points. The algorithm proposed in this invention can effectively reproduce the waveform of the original, undisturbed signal, preserving the abrupt change point information of the disturbed signal while maintaining good denoising performance. This can assist in the identification and management of disturbed signals.

Claims

1. A power quality disturbance denoising method based on variational mode decomposition and improved wavelet thresholding, characterized in that The method comprises the following steps: Step 1: obtaining a one-dimensional noisy power quality signal and storing the one-dimensional noisy power quality signal into a variational mode decomposition; Step 2: selecting permutation entropy as an adaptive function of a genetic algorithm, calling the variational mode decomposition through the genetic algorithm, and iteratively optimizing a penalty factor alpha and a decomposition mode number k of the variational mode decomposition to determine optimal parameters; Step 3: according to the optimization result of step 2, decomposing the signal data into k mode components by using the variational mode decomposition, and determining effective mode components and noise mode components by using a correlation coefficient; Step 4: for the improved wavelet threshold, a parameter-adjustable threshold function is proposed, and the concept of wavelet energy entropy is introduced into the threshold function, and an adaptive threshold that can be adaptively changed according to the noise content is proposed; Step 5: using the improved wavelet threshold of step 4 to denoise the noise mode components of step 3, and selecting the effective mode components and the noise mode components after denoising to reconstruct, to obtain the denoised power quality disturbance signal; In step 4, for the improved wavelet threshold, a parameter-adjustable threshold function is proposed, and the concept of wavelet energy entropy is introduced into the threshold, and an adaptive threshold that can be adaptively changed according to the noise content is proposed, comprising the following steps: S4.1: decomposing the one-dimensional noisy power quality disturbance signal x(t) by using discrete wavelet transform to obtain the following formula: where Z is an integer, m J,k is an approximation coefficient, representing low frequency components in the noisy signal; n J,k is a detail coefficient, representing high frequency components in the noisy signal; φ J,k (t) is a scaling function, ψJ,k (t) is a wavelet basis function; For a determined decomposition level, the power quality disturbance signal can be decomposed into an approximate coefficient and a detail coefficient sequence by using the discrete wavelet transform, and the noise signal belongs to a high-frequency component, so it is distributed in the detail coefficient sequence; after the disturbance signal is decomposed by the discrete wavelet transform, the wavelet coefficient amplitude of the useful signal component is much larger than that of the noise signal component, which ensures that a threshold and a threshold function can be constructed to process the decomposed detail coefficient sequence, so as to achieve the purpose of denoising; finally, the processed wavelet coefficient is reconstructed by using the inverse wavelet transform, so that the denoised power quality disturbance signal can be obtained; The wavelet threshold denoising process comprises multi-level wavelet decomposition, wavelet coefficient threshold shrinkage process and wavelet reconstruction; the traditional soft and hard threshold functions and the general threshold formula are as follows: Soft threshold function: Hard threshold function: General threshold: where N is the length of the processed signal, is the standard deviation of the noise in the signal; The traditional threshold function is improved, and a new threshold function is proposed, which can retain the advantages of the soft and hard threshold functions while improving the disadvantages; the improved threshold function is as follows: where b is a variable parameter, λ j The different values of b will affect the trend of the improved threshold function. By changing the value of the variable parameter b, different function effects can be obtained, when b → The improved threshold function is equivalent to the hard threshold function when b →∞ The improved threshold function is equivalent to the soft threshold function when b∈(0, +∞), and the improved threshold function can switch between the soft threshold function and the hard threshold function when b∈(0, +∞), increasing its flexibility. S4.2: introducing the wavelet energy entropy into the threshold formula, the more concentrated the noise content in the sub-interval, the larger the value of the wavelet energy entropy, that is, the wavelet coefficients in the interval are mostly noise corresponding wavelet coefficients, at this time, the interval can be analyzed and processed as a noise characteristic interval; therefore, the interval with the maximum wavelet energy entropy value in each layer is selected, and the mean value of the wavelet coefficients in the interval is taken as the noise standard deviation of the layer; the improved threshold formula is as follows: In the formula, N is the length of the processed signal, and j is the number of wavelet decomposition layers. With the increase of the scale of wavelet decomposition, the wavelet coefficient amplitude of the useful signal changes little, and the wavelet coefficient amplitude of the noise signal decreases, and the general threshold formula is as follows: wherein is the standard deviation of the noise, N is the length of the processed signal; It can be seen from the universal threshold solving method that the threshold is a constant value in the whole decomposition process, and the threshold as a standard for distinguishing useful signals from noise signals should be adaptively reduced with the increase of the decomposition layer number to prevent omitting too many useful signals; From the improved threshold formula solving method, it can be seen that the threshold λ j will decrease with the increase of the decomposition layer, which is consistent with the rule that the wavelet coefficient of the noise signal decreases with the increase of the decomposition layer; the redefined noise standard deviation can further correct the threshold formula according to the content of noise in each layer, and compared with the original formula, it can more accurately evaluate the noise content and improve the accuracy of the threshold.

2. The power quality disturbance denoising method based on variational mode decomposition and improved wavelet thresholding according to claim 1, characterized in that: In step 1, a one-dimensional noisy power quality signal is input, and x(t) = f(t) is obtained. In the formula, x(t) is a one-dimensional noisy power quality signal, and f(t) is the input signal of the variational mode decomposition. In step 2, the calculation process of the permutation entropy is as follows:

3. The power quality disturbance denoising method based on variational mode decomposition and improved wavelet thresholding according to claim 1, characterized in that: A time series S contains N signals {x(k), k = 1, 2, …, N}, and spatial reconstruction can obtain the following matrix: In the formula, each row represents a signal; r = N-(m-1)τ; m represents the dimension; τ represents the delay time; r represents the number of segments after the reconstruction and decomposition of the sequence S; N represents the total number of signals in each segment; j represents the jth signal segment; x(1), x(j), x(r), x(1+τ), x(j+τ), x(r+τ), x(1+(m-1)τ), x(j+(m-1)τ), x(r+(m-1)τ) are all signals in the original sequence S; The permutation entropy of the time series {X(K) = 1, 2, …, N} is calculated as follows: The elements in each segment of signal are rearranged in ascending order to obtain the position of each element in the vector, forming a set of symbol sequences: S(l) = (j1, j2, …, j m ), l = 1, 2, …, r, r ≤ m!, m-dimensional space mapping different symbol sequences, m! kinds; j1, j2,..., j m are signals in the original sequence S, r represents the number of segments of the sequence S after reconstruction and decomposition, and m! represents m! permutation modes of m different symbols, corresponding to m! symbol sequences; The number of each r symbol sequence is divided by m!, and the total number of different symbol sequences is the probability S(l) of different symbol sequences appearing {P1, P2, …, P r}; S(l) represents different symbol sequences, and {P1, P2, …, P r} respectively represents the probability of different symbol sequences appearing. The maximum value of the permutation entropy is ln(m!), and the permutation entropy is normalized as follows: P j represents the probability of occurrence of sequence j, r represents the total number of sequences, and j represents the jth sequence. From the calculation process of the permutation entropy, it can be seen that the size of the permutation entropy is related to the signal noise amplitude, and the smaller the value is, the simpler and more regular the sequence is; on the contrary, the larger the value is, the more complex and random the sequence is. In step 2, the variational mode decomposition is called through the genetic algorithm to iteratively optimize the penalty factor α and the decomposition mode number k to determine the optimal parameters; including the following steps:

4. The power quality disturbance denoising method based on variational mode decomposition and improved wavelet thresholding according to claim 3, characterized in that: Step 2.1: Set the optimization interval of k in the genetic algorithm to [3, 8]; Step 2.2: Set the optimization interval of α in the genetic algorithm to [100, 2200]; Step 2.3: Set the permutation entropy as the adaptive function of the genetic algorithm; Step 2.4: Start the iterative optimization to determine the optimal values of α and k. The step 3 includes the following steps:

5. The power quality disturbance denoising method based on variational mode decomposition and improved wavelet thresholding according to claim 1, characterized in that: Step 3.1: Construct the objective constraint function for solving the variational mode decomposition problem, and the formula is as follows: Step 3.2: Construct the unconstrained variational problem, and the formula is as follows: where u k is the decomposition component, ω k is the instantaneous frequency of the Kth component; δ(t) represents the Dirac distribution with respect to time t, u k (t) represents the eigenmode component; represents the transform factor, f(t) represents the original signal, k represents the number of modal components, j represents the complex number, represents the partial derivative with respect to time t; In the formula, α is the penalty factor, and λ is the Lagrange multiplier operator; Through the alternating direction multiplier algorithm, the component and the center frequency are obtained, and the formula is as follows: {u k} denotes a set of eigenmode components; {ω k} denotes a set of instantaneous frequencies; λ(t) denotes a Lagrange multiplier term with respect to time t; denotes a sum of modal components; denotes a Lagrange multiplier term; < > denotes a vector; Step 3.3: When the function component after decomposition satisfies the following formula, stop the loop decomposition to complete, if not, repeat step 3.2; denotes the updated eigenmode component; u i (ω) denotes the iterative value of the eigenmode component in the Fourier domain, λ(ω) denotes the Lagrange multiplier operator in the frequency domain; ω denotes the frequency parameter; denotes the updated center frequency value; λ n+1 (ω) denotes the updated frequency domain Lagrange multiplier operator value, λ n (ω) denotes the iterative value of the Lagrange multiplier operator value in the Fourier domain; The calculation formula is as follows: Step 3.4: Calculation of cross-correlation coefficients between modal components and original signal using Pearson correlation coefficient, for two random variables X = {xl, x2,..., x n}; xl, x2,..., x n denote the elements in variable X, Y = {yl, y2,..., y n}; yl, y2,..., y n denote the elements in variable Y, respectively. Step 3.5: The correlation coefficients are distinguished through the boundary formula to determine the noise mode component and the effective mode component, and the boundary formula is as follows: wherein respectively denote the mean of the random variables X, Y; R xy denotes the correlation coefficient; x i denotes the i-th element in the variable X; y i denotes the i-th element in the variable Y; n denotes the total number of elements in the variables X, Y; For the mode component with a correlation coefficient greater than or equal to the boundary value, it is defined as an effective component, and for the mode component with a correlation coefficient less than or equal to the boundary value, it is defined as a noise mode component. μ = max(R xy ) / [10 max(R xy )-3] wherein μ denotes a threshold value, max(R xy ) denotes a maximum value of the correlation coefficient; ​

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