Wideband measurement method and system for power system based on wavelet packet and SVMD

Abstract

The invention relates to an electric power system broadband measurement method and system based on a wavelet packet and SVMD, and belongs to the technical field of electronic measurement. The method comprises the following steps: acquiring frequency information corresponding to a circuit signal of each measurement point in a circuit system; performing wavelet packet decomposition on the frequency information, and determining an optimal wavelet basis for broadband measurement of the power system; performing multilayer decomposition on the frequency information according to the optimal wavelet basis to obtain a plurality of wavelet frequency bands; performing component extraction on the wavelet frequency band to obtain a harmonic component corresponding to the wavelet frequency band; de-noising the harmonic components by using a wavelet coefficient correlation algorithm to obtain de-noised harmonics; decomposing the noise reduction harmonic wave according to an EMD algorithm to obtain a signal residual error meeting a preset stop condition; and calculating to obtain measurement and calculation data corresponding to each harmonic waveform according to the signal residual error. According to the technical scheme, the time-frequency characteristics of the signals can be captured more accurately, and the method has better performance on non-stationary signals and signals with complex frequency structures.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic measurement of power systems, and in particular to a method and system for broadband measurement of power systems based on the combination of wavelet packets and SVMD. Background Art

[0002] For an ideal three-phase power system, the basic parameters that the measuring device needs to measure are the amplitude and phase angle of the power frequency voltage. Usually, the voltage and current waveforms obtained at each measuring point in the power grid are not three-phase symmetrical sine waves, which is related to the equipment connected to it. If the power supply is connected by a power electronic device and the load is nonlinear, a large amount of harmonics will be injected into the system, causing the voltage and current waveforms to be distorted. With the widespread application of nonlinear loads and power electronic devices, the monitoring of high-order harmonic information of broadband signals has become an important direction in the current research of new power systems. Compared with traditional wavelet transforms, wavelet packet transform can more comprehensively describe the time-frequency characteristics of signals. Although the wavelet decomposition algorithm can effectively divide the frequency band of broadband signals, the algorithm cannot complete the extraction and detection of harmonics of specific frequencies, thus affecting the accuracy and reliability of the measurement results.

[0003] The present invention introduces SVMD (Successive Variational Mode Decomposition, SVMD) algorithm to further process the wavelet decomposition frequency band, and fully extracts each frequency component by combining the adaptive extraction characteristics of the introduced algorithm with the frequency band decomposition characteristics of the wavelet algorithm, thereby realizing effective measurement of broadband signals. Summary of the invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art or related art.

[0005] To this end, the purpose of the present invention is to provide a wideband measurement method and system for power systems based on a combination of wavelet packets and SVMD, which can more accurately capture the time-frequency characteristics of signals and have better performance for non-stationary signals and signals with complex frequency structures.

[0006] To achieve the above object, the technical solution of the first aspect of the present invention provides a power system broadband measurement method based on the combination of wavelet packets and SVMD, comprising the following steps: Obtaining frequency information corresponding to circuit signals at various measurement points in the circuit system; Perform wavelet packet decomposition on frequency information to determine the best wavelet basis for broadband measurement of power system; Perform multi-layer decomposition of frequency information according to the optimal wavelet basis to obtain multiple wavelet frequency bands; Extract components of the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; The harmonic components are denoised using the wavelet coefficient correlation algorithm to obtain the de-noised harmonics; Decompose the noise reduction harmonics according to the EMD algorithm to obtain the signal residual that meets the preset stop condition; The measured data corresponding to each harmonic waveform is obtained based on the signal residual calculation.

[0007] In the above technical solution, preferably, determining the optimal wavelet basis for broadband measurement of the power system includes: Using the Mallat decomposition algorithm, determine the decomposition relationship between standard orthogonal bases and the decomposition and synthesis relationship of the subspace coordinates corresponding to the decomposition relationship between standard orthogonal bases; (1); (2); (1)-(2) Where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {g m ; m∈Z} are called low-pass filters and high-pass filters.

[0008] According to the preset conditions, the decomposition relationship between the standard orthogonal bases is decomposed into a transformation space to obtain a standard orthogonal base of a closed subspace on the finite function space; (3); (4); In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, d j,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0009] According to the nature of the filter itself: , derive the standard orthogonal basis After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship of the corresponding standard orthogonal systems are formed; (5); (6); (7); In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter.

[0010] According to the standard orthogonal system and its subspace relationship, the decomposition result and the best wavelet basis of the corresponding wavelet packet are obtained; The decomposition result is expressed as: (8) The optimal wavelet basis is expressed as: (9) In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0011] In the above technical solution, preferably, the frequency information is decomposed in multiple layers according to the optimal wavelet basis, including: Perform wavelet transform on the optimal wavelet basis to obtain a single periodic function representation of one period of the harmonic waveform: (10) Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The coordinate sequence in .

[0012] The function representation of the entire harmonic waveform is obtained based on the single period function representation: (11); In the formula, G (t o, w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, is the basis function. According to the dynamic window characteristics, the function representation of the entire harmonic waveform is transformed into a continuous wavelet, and a continuous wavelet dependent on the scale parameter and a function representation corresponding to the continuous wavelet are obtained; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) (12); (13); The continuous wavelet representation that depends on the scale parameter is: (14); In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function, corresponding to the continuous wavelet function representation: (15); The wavelet transform window is centered at the coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a. In the formula, a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t).

[0013] Perform an inverse transform on the continuous wavelet and its corresponding function representation to obtain the inverse function representation of the corresponding continuous wavelet: (16); In the formula To invert the wavelet packet energy, the wavelet transform shows the changes of the signal f(t) around the time point b as the scale parameter a changes continuously; the inverse function is discretized to obtain multiple wavelet frequency bands.

[0014] In the above technical solution, preferably, discretizing the inverse function includes: Define the preset function representation that constitutes the standard orthogonal basis for the corresponding wavelet band: (17); According to the preset function representation, the linear representation of the corresponding wavelet band and the inverse function after discretization is obtained: (18); Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; According to the coefficient sequence of the preset standard orthogonal basis, the wavelet band is obtained: (19); In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0.

[0015] In the above technical solution, preferably, extracting components from the wavelet frequency band includes: The NRBO optimization algorithm is used to remove harmonic aliasing in the wavelet frequency band and obtain the coefficient optimization sequence: (20); In the formula, p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2... According to the coefficient optimization sequence, each harmonic component is obtained, and the wavelet frequency band is extracted according to each harmonic component.

[0016] The technical solution of the second aspect of the present invention provides a power system broadband measurement system based on the combination of wavelet packets and SVMD, comprising: An acquisition module is configured to acquire frequency information corresponding to circuit signals at various measurement points in the circuit system; A wavelet decomposition module is configured to perform wavelet packet decomposition on the frequency information to determine an optimal wavelet basis for broadband measurement of the power system; A multi-layer decomposition module is configured to perform multi-layer decomposition on the frequency information according to an optimal wavelet basis to obtain a plurality of wavelet frequency bands; A component extraction module is configured to extract components from the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; A noise reduction module is configured to perform noise reduction processing on harmonic components using a wavelet coefficient correlation algorithm to obtain noise-reduced harmonics; A harmonic decomposition module is configured to decompose the noise reduction harmonics according to an EMD algorithm to obtain a signal residual that meets a preset stop condition; The calculation module is configured to calculate the measurement data corresponding to each harmonic waveform based on the signal residual.

[0017] In the above technical solution, preferably, the wavelet decomposition module includes: An orthogonal basis decomposition unit is configured to determine a decomposition relationship between standard orthogonal bases and a decomposition and synthesis relationship of subspace coordinates corresponding to the decomposition relationship between the standard orthogonal bases using a Mallat decomposition algorithm; (1); (2); (1)-(2) Where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {g m ; m∈Z} are called low-pass filters and high-pass filters.

[0018] A space transformation unit is configured to transform the decomposition relationship between the standard orthogonal bases according to a preset condition to obtain a standard orthogonal base of a closed subspace on the finite function space; (3); (4); In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, d j,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0019] The subspace decomposition unit is set to be used according to the properties of the filter itself: , derive the standard orthogonal basis After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship of the corresponding standard orthogonal systems are formed; (5); (6); (7); In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter.

[0020] The optimal wavelet basis generating unit is configured to obtain the decomposition result and the optimal wavelet basis of the corresponding wavelet packet according to the standard orthogonal system and its subspace relationship; The decomposition result is expressed as: (8); The optimal wavelet basis is expressed as: (9).

[0021] In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0022] In the above technical solution, preferably, the multi-layer decomposition module includes: The wavelet transform unit is configured to perform wavelet transform on the optimal wavelet basis to obtain a single periodic function representation of one period of the harmonic waveform: (10); Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The waveform generation unit is configured to obtain the function representation of the entire harmonic waveform according to the single period function representation: (11); In the formula, G (t o , w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, is the basis function.

[0023] A continuous wavelet generation unit is configured to perform a continuous wavelet transform on the function representation of the entire harmonic waveform according to the dynamic window characteristic to obtain a scale-parameter-dependent continuous wavelet and a function representation corresponding to the continuous wavelet; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) (12); (13); The continuous wavelet representation that depends on the scale parameter is: (14); In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function. The corresponding continuous wavelet function is expressed as: (15); The wavelet transform window is a rectangular window centered at the coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a.

[0024] Where a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t).

[0025] The inverse transform unit is configured to perform an inverse transform on the continuous wavelet and its corresponding function representation to obtain an inverse function representation of the corresponding continuous wavelet: (16); In the formula To invert the wavelet packet energy, the wavelet transform represents the change of the signal f(t) around the time point b as the scale parameter a changes continuously; the discrete processing unit is configured to discretize the inverse function to obtain multiple wavelet frequency bands.

[0026] In the above technical solution, preferably, the discrete processing unit includes: The wavelet frequency band generation subunit is configured to define a preset function representation of a standard orthogonal basis constituting a corresponding wavelet frequency band: (17); The frequency band linear function generating subunit is configured to obtain the linear representation of the corresponding wavelet frequency band and the inverse function after discretization according to the preset function representation: (18); Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; The orthogonal coefficient generating subunit is configured to obtain the wavelet frequency band according to the coefficient sequence of the preset standard orthogonal basis: (19); In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0.

[0027] In the above technical solution, preferably, the component extraction module includes: The coefficient optimization unit is set to remove harmonic aliasing in the wavelet frequency band using the NRBO optimization algorithm to obtain the coefficient optimization sequence: (20); In the formula, p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2... The component extraction unit is configured to obtain each harmonic component according to the coefficient optimization sequence, and extract components of the wavelet frequency band according to each harmonic component.

[0028] Compared with the prior art, the advantages of the power system broadband measurement method and system based on the combination of wavelet packet and SVMD provided by the present invention are: the wavelet packet transform has higher resolution and richer frequency information, can more accurately capture the time-frequency characteristics of the signal, and has better performance for non-stationary signals and signals with complex frequency structures. At the same time, it has greater flexibility and adjustability, and can decompose the signal more deeply or more roughly as needed, so as to obtain time-frequency representations of different scales.

[0029] The basic wavelet packet decomposition algorithm can only complete the frequency band division, but cannot decompose each component in detail. By combining the frequency band decomposition function of the wavelet packet algorithm and the adaptive extraction function of SVMD, the problem of wavelet basis and decomposition layer selection can be effectively solved.

[0030] The method we proposed based on the combination of these two algorithms not only reduces the number of wavelet decomposition layers, but also significantly improves the detection efficiency of broadband signals and adaptively completes the extraction of principal components of each frequency band. The improved broadband measurement algorithm can effectively extract each harmonic component. After analysis and calculation, the maximum relative error of amplitude detection is 1.45%, and the maximum error of phase angle detection is about 0.1°, which verifies the rationality and accuracy of the algorithm in processing broadband and dynamic signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which: Figure 1 A flowchart of a method according to an embodiment of the present invention is shown; Figure 2 A flowchart of step S2 according to an embodiment of the present invention is shown; Figure 3 A flowchart of step S3 according to an embodiment of the present invention is shown; Figure 4 shows a flowchart of step S35 involved in an embodiment of the present invention; Figure 5 A flowchart of step S4 according to an embodiment of the present invention is shown; Figure 6 A structural block diagram of a system involved in an embodiment of the present invention is shown; Figure 7 The structure block diagram of the wavelet decomposition module involved in the embodiment of the present invention is shown; Figure 8 A structural block diagram of a multi-layer decomposition module involved in an embodiment of the present invention is shown; Fig. 9 A structural block diagram of a discrete processing unit involved in an embodiment of the present invention is shown; Fig.10 The structure block diagram of the component extraction module involved in the embodiment of the present invention is shown; Fig.11 A schematic diagram of a single operation decomposition involved in an embodiment of the present invention is shown; Fig.12 A schematic diagram of wavelet decomposition involved in an embodiment of the present invention is shown; Fig.13 A schematic diagram of wavelet packet tree decomposition involved in an embodiment of the present invention is shown; Fig.14 The wavelet packet decomposition diagram of the signal model involved in the embodiment of the present invention is shown; Fig.15 The figure shows the effect of extracting the main component of the decomposed frequency band involved in the embodiment of the present invention; Fig.16 A flowchart of correlation noise reduction processing involved in an embodiment of the present invention is shown; Fig.17 The adaptive EMD decomposition effect diagram involved in the embodiment of the present invention is shown; Fig.18 A curve diagram of the permutation entropy values ​​of various components involved in an embodiment of the present invention is shown; Fig.19 A comparison diagram of the noise reduction effects involved in the embodiments of the present invention is shown. DETAILED DESCRIPTION

[0032] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0033] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0034] like Figure 1 As shown, according to an embodiment of the present invention, a power system broadband measurement method based on the combination of wavelet packets and SVMD includes the following steps: S1, obtaining frequency information corresponding to circuit signals at each measurement point in the circuit system; S2, decomposing the frequency information by wavelet packets to determine the best wavelet basis for broadband measurement of the power system; S3, performing multi-layer decomposition of the frequency information according to the optimal wavelet basis to obtain multiple wavelet frequency bands; S4, extracting components of the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; S5, use the wavelet coefficient correlation algorithm to denoise the harmonic components and obtain the denoised harmonics: (twenty one); In the formula, c j ( k ) is the wavelet coefficient, j is the scale, k is The number of points, ∑ is the accumulation symbol, and N is a natural number. By comparing the correlation of wavelet coefficients with the set threshold, it is determined whether to retain the current wavelet coefficients, so as to achieve the noise reduction effect. Wavelet coefficient correlation denoising is more effective for non-stationary signals and signals containing non-local features. Compared with wavelet modulus maximum denoising, it can better retain the detailed characteristics of the signal. In the case where the correlation between noise and signal is weak, it may cause signal distortion.

[0035] However, this algorithm is prone to the loss of high-frequency parameters in application. To solve this problem, we introduced an improved EMD algorithm to perform preliminary decomposition of the signal and calculate its permutation entropy value. For the part with high noise, the correlation denoising method is used for processing. The denoised signal obtained after reconstruction retains the broadband information well, thereby improving the accuracy and reliability of signal processing.

[0036] First of all, the traditional EMD decomposition is a step-by-step decomposition process for different fluctuation trends in the time domain, which decomposes the overall non-stationary signal into stationary components. These decomposition results are called intrinsic mode functions (IMFs). The detailed decomposition process is as follows: first, the local extreme value of f(t) is determined by interpolation and the envelope is formed. The overall trend component c(t) of the waveform is obtained by averaging. After removing c(t) from the original signal, a convergence test is performed. The above decomposition process is repeated until the screening stop condition is reached and the final signal residual r(t) is left, completing the decomposition process.

[0037] Through this process, it can be clearly seen that the advantage of EMD is that it is an adaptive signal decomposition method that does not require the assumption of the signal model or basis function in advance, so it is suitable for various types of signals, especially nonlinear and non-stationary signals. In addition, EMD is completely based on the decomposition algorithm in the time domain, which makes its decomposition result complete. All components of the output can be directly restored by direct addition without losing the original signal, as shown in formula (22). Compared with the uncertainty of the inverse process of wavelet transform, it avoids the algorithm adaptation problem caused by the double decomposition process of the signal, so this processing process will not have any impact on the correlation denoising algorithm. In addition, this iterative decomposition and direct addition synthesis process is simple and easy to implement, and will not cause too much calculation and time pressure.

[0038] (twenty two); Where c(t) is the overall trend component of the waveform, r(t) is the signal residual, and k is 0, 1, 2, etc.

[0039] Secondly, similar to most decomposition algorithms, Fourier spectrum analysis of IMF shows that the frequency distribution of each component is different. This decomposition method is mutually adaptable to the characteristics of the waveform data, so it does not have a strict frequency band division like wavelet decomposition. This adaptive decomposition process is one of the features required by this article. However, the screening and stopping criteria of this adaptive decomposition process are difficult to determine. It is usually judged based on a given fixed value, but this often loses some of the adaptability of the decomposition algorithm, resulting in insufficient or excessive decomposition during the decomposition of different characteristic signals, which will introduce errors. Therefore, the adaptive stopping mechanism is the key to ensuring the stability of each component.

[0040] In EMD, the number of screening iterations is directly determined by the screening stop criterion SSC. In both "underscreening" and "overscreening" cases, the number of iterations will affect the decomposition effect. If the number of iterations is not enough, the decomposition will be incomplete, and multiple single-component signals will be decomposed into one IMF, resulting in too many unrelated components. Too many iterations will result in the decomposition of single-component signals into multiple IMFs, resulting in a waste of computing resources and reduced decomposition accuracy, and will also affect the efficiency of the subsequent correlation denoising process. Therefore, it is crucial to reduce the amount of calculation to improve the denoising efficiency without sacrificing the decomposition accuracy. Liu, Zhiliang proposed the soft SSC (soft SSC is the improved screening stop criterion in this paper) in the paper Improved Hilbert-Huang transform based on soft screening stop criterion and its application in wheelset bearing fault diagnosis. It can monitor the screening process of EMD separation, and more importantly, it can select the optimal number of iterations. Based on the principle of successive decomposition of EMD, the sum of the absolute value of the root mean square value and kurtosis of each extracted component will always decrease compared with the previous extracted component, thereby defining a signal-related function: (twenty three); In the formula, n is the point value, k is the number of iterations, and N k The total number of iterations, E k is the kth iteration EMD decomposition component, c k (n) is the n-point value of the current k-th iteration component. When the αk generated by this iteration is smaller than that of the previous iteration, it can be considered as a stop condition, and the screening process is automatically stopped according to the value of the objective function, thereby obtaining better signal decomposition performance.

[0041] The idea of ​​soft SSC realizes the adaptability of the screening process. Due to the fixed screening conditions of traditional EMD, the decomposition process is often easily affected by noise and error values. The adaptive stop condition greatly improves the robustness of signal decomposition. Each screening will determine an optimal number of iterations, and no meaningless IMFs will be generated. The CPU time is proportional to the number of iterations and the number of IMFs. There will be no errors introduced due to under-screening, and no waste of computing resources and time due to over-screening.

[0042] In summary, the decomposition process of adaptive stop EMD can make up for the defects of correlation denoising and optimize its denoising effect. According to the principle of correlation denoising, signal denoising is performed in each decomposition domain of the signal, and the noise of each segment can be deeply denoised without waveform distortion. In order to reduce unnecessary calculation amount and loss of signal feature information, permutation entropy detection is performed on the components of the signal after adaptive EMD decomposition, and correlation denoising is performed only on the noise-dominated components. The specific algorithm flow chart is as follows: Fig.16 shown.

[0043] First, the noisy signal needs to be adaptively decomposed by EMD components to obtain components arranged from low frequency to high frequency. For parts with more Gaussian white noise, correlation denoising is required to remove them. Therefore, the entropy value of each component is calculated and arranged according to the entropy value. The components exceeding the noise limit are set to be processed by correlation denoising. Finally, the denoised signal is obtained by adding each component. Since each component has been adaptively decomposed once, the number of wavelet decomposition layers can be reduced when the noisy signal is subjected to correlation processing, thereby saving calculation amount and processing time, and better retaining real information.

[0044] In order to verify the effect of the modified correlation denoising algorithm, a denoising test was conducted on the signal containing 10dB Gaussian white noise. After experimental comparison, the db4 wavelet basis function was selected, and the 3-layer wavelet decomposition correlation denoising process was performed on the high noise signal. First, the adaptive preliminary decomposition of the signal is performed as follows Fig.17 shown.

[0045] The high-frequency components in the original waveform decomposition diagram usually contain more noise. After calculating the permutation entropy value of each component, a comparison diagram of all components can be obtained, such as the permutation entropy value curve of each component. Fig.18 As shown, it can be seen that wavelet correlation denoising processing is required for the IMF1-IMF2 component.

[0046] After the improved correlation algorithm is used for denoising, the signal-to-noise ratio is 23.485dB and the root mean square value is 0.43. Compared with the correlation denoising effect record of the traditional wavelet denoising algorithm in the previous article, the improved denoising algorithm retains more effective information and ensures the denoising effect. After denoising, each component is reconstructed to obtain the comparison chart of the improved correlation denoising effect of the low-noise signal and the original signal. Fig.19 As shown in the figure, the effect of the improved noise reduction algorithm is verified.

[0047] S6, decomposing the noise reduction harmonics according to the EMD algorithm to obtain a signal residual that meets a preset stop condition; S7, obtaining the measured data corresponding to each harmonic waveform according to the signal residual calculation.

[0048] In the above technical solution, preferably, Figure 2 As shown in Figure 2, S2 determines the optimal wavelet basis for broadband measurement of power systems, including: S21, using the Mallat decomposition algorithm, determining the decomposition relationship between standard orthogonal bases and the decomposition and synthesis relationship of the subspace coordinates corresponding to the decomposition relationship between the standard orthogonal bases; (1); (2); 1)-(2) where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is the sum of the nodes. m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {g m ; m∈Z} are called low-pass filters and high-pass filters.

[0049] From this, the decomposition relationship between its standard orthogonal bases is derived, and then the decomposition and composition relationship between coordinates can be obtained, that is, the Mallat decomposition algorithm and composition algorithm: S22, performing transformation space decomposition on the decomposition relationship between the standard orthogonal bases according to preset conditions to obtain a standard orthogonal base of a closed subspace on the finite function space; (3); (4); In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, dj,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0050] The Mallat algorithm can realize the decomposition operation of wavelet coefficients. This process is repeated until the preset decomposition level is reached, thereby constructing a wavelet transform decomposition tree, as shown in the wavelet decomposition diagram. Fig.12 As shown in Figure 1, each node represents the approximate or detailed component of the signal at different scales. The algorithm has good stability and locality, can accurately capture the local characteristics and time-frequency information of the signal, and is suitable for broadband and dynamic signal processing tasks.

[0051] Based on the idea of ​​the above algorithm, the standard orthogonal basis and coordinate sequence of the low-frequency part of this level are always used to decompose into high-frequency and low-frequency information of the next level. The decomposition tree obtained by repeating this process shows that the low-frequency part is continuously refined, and the high-frequency part is always maintained. If you want to get the high-frequency part information in the same way and improve the frequency resolution, you need to use the idea of ​​orthogonal wavelet packets.

[0052] Compared with traditional wavelet transform, wavelet packet transform can more comprehensively describe the time-frequency characteristics of signals. Its basic principle is to decompose and reconstruct high-frequency and low-frequency signals simultaneously through a series of filter groups. When the preset number of decomposition layers or certain stop conditions are reached, a wavelet packet decomposition tree can be constructed, as shown in the diagram of wavelet packet tree decomposition. Fig.13 shown.

[0053] The root node of the tree represents the original signal, and each node represents the output of a filter. Different decomposition layers or stop conditions can be selected as needed to obtain a decomposition result suitable for a specific application.

[0054] S23, according to the nature of the filter itself: , derive the standard orthogonal basis After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship of the corresponding standard orthogonal systems are formed; (5); Correspondingly, from a spatial perspective, in order to facilitate the analysis of the spatial decomposition relationship of wavelet packet transform, the energy finite function space L 2 A closed subspace on (R) is represented by a new symbol Sij if: (6); The standard orthogonal basis of Sij can be deduced based on the properties of the high-pass filter and the low-pass filter: s2i(t) and s2i+1(t) can form two mutually orthogonal standard orthogonal systems after integer translation, and the corresponding subspace relationship is: (7); In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter.

[0055] S24, obtaining the decomposition result and the best wavelet basis of the corresponding wavelet packet according to the standard orthogonal system and its subspace relationship; The decomposition result is expressed as: (8); The optimal wavelet basis is expressed as: (9).

[0056] In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0057] Wavelet packet transform has higher resolution and richer frequency information, can capture the time-frequency characteristics of the signal more accurately, and has better performance for non-stationary signals and signals with complex frequency structures.

[0058] From the perspective of qualitative analysis, a more suitable wavelet basis function was selected, and the application of wavelet analysis in signal analysis was realized using MATLAB programming, verifying the feasibility of signal decomposition.

[0059] like Figure 3 As shown, in the above technical solution, preferably, S3, performing multi-layer decomposition of frequency information according to the optimal wavelet basis, includes: S31, perform wavelet transform on the optimal wavelet basis to obtain a single periodic function representation of one period of the harmonic waveform: (10); Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The coordinate sequence in . S32, obtain the function representation of the entire harmonic waveform according to the single period function representation: (11); In the formula, G (t o , w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, S33, performing continuous wavelet transform on the function representation of the entire harmonic waveform according to the dynamic window characteristic, to obtain a continuous wavelet dependent on the scale parameter and a function representation corresponding to the continuous wavelet; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) (12); (13); The continuous wavelet representation that depends on the scale parameter is: (14); In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function. The corresponding continuous wavelet function is expressed as: (15); The wavelet transform window is a rectangular window centered at the coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a.

[0061] Where a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t).

[0062] S34, performing an inverse transformation on the continuous wavelet and its corresponding function representation to obtain an inverse function representation of the corresponding continuous wavelet: (16); In the formula The wavelet transform is to invert the wavelet packet energy. The wavelet transform shows the change of the signal f(t) around the time point b as the scale parameter a changes continuously. S35, discretize the inverse function to obtain multiple wavelet frequency bands.

[0063] like Figure 4 As shown, in the above technical solution, preferably, S35, discretizing the inverse function includes: S351, defining a preset function representation of a standard orthogonal basis constituting a corresponding wavelet frequency band: (17); S352, obtaining a linear representation of the corresponding wavelet frequency band and the inverse function after discretization according to the preset function representation: (18); Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; S353, obtaining the wavelet frequency band according to the coefficient sequence of the preset standard orthogonal basis: (19); In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0.

[0064] like Figure 5 As shown, in the above technical solution, preferably, S4, extracting components from the wavelet frequency band includes: S41, using the NRBO optimization algorithm to remove harmonic aliasing in the wavelet frequency band, the coefficient optimization sequence is obtained: (20); In the formula, p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2... The entropy value can measure the degree of chaos of a one-dimensional discrete sequence. In order to ensure that the components extracted from the principal component contain only single-frequency components, this paper uses the envelope entropy minimum function as the optimization fitness function. This choice aims to effectively reduce harmonic aliasing within the component by minimizing the envelope entropy value, thereby improving the accuracy and purity of principal component extraction.

[0065] S42, obtaining each harmonic component according to the coefficient optimization sequence, and extracting components of the wavelet frequency band according to each harmonic component.

[0066] In order to verify the detection accuracy and efficiency of the improved algorithm for broadband signals, a simulation analysis is performed through the constructed signal model. First, the waveform sampling frequency is set to 12.8kHz, and extraction is performed every 10 fundamental cycles. Therefore, 2560 sampling points need to be processed. After wavelet packet decomposition, it can be obtained that the harmonics within 64 times have a total of 8 frequency bands. The waveform and spectrum diagram are as shown in the signal model wavelet packet decomposition Fig.14 shown.

[0067] The harmonics of the experimental signal model are evenly distributed in the 1st, 2nd, 4th and 7th frequency bands, and there is a slight frequency band aliasing phenomenon between the frequency bands. By extracting the main components of the four frequency bands respectively, all the harmonic components can be obtained, such as Fig.15 As shown in (a), 15 (b), 15 (c), and 15 (d).

[0068] The optimization results of the penalty parameter α based on NRBO are: 6949, 12866, 18764, 20480. After decomposition, the harmonic waveforms of the 10 fundamental wave periods can be obtained. However, due to the end effect at both ends, distortion occurs. The extraction results are corrected by removing the first and last two fundamental wave periods, and the amplitude and phase angle of each waveform are analyzed and calculated. The test result statistics are shown in the table.

[0069] Broadband algorithm test results statistics table

[0070] The simulation results show that the improved broadband measurement algorithm can effectively extract the harmonic components. After analysis and calculation, the maximum relative error of amplitude detection is 1.45%, and the maximum error of phase angle detection is about 0.1°, which verifies the rationality and accuracy of the algorithm in processing broadband and dynamic signals.

[0071] Through simulation verification, the algorithm has shown good dynamic extraction capabilities in broadband measurement. Based on the algorithm programming simulation, the processing of measured data is realized, the actual processing capability of the algorithm is verified, and a solid foundation is laid for the further application of subsequent detection algorithms. Subsequently, three algorithms for wavelet denoising technology were learned. After in-depth analysis and comparison, the correlation denoising algorithm was finally selected.

[0072] like Figure 6 As shown, according to another embodiment of the present invention, a power system broadband measurement system 100 based on the combination of wavelet packets and SVMD includes: An acquisition module 10 is configured to acquire frequency information corresponding to a circuit signal at each measurement point in the circuit system; The wavelet decomposition module 20 is configured to perform wavelet packet decomposition on the frequency information to determine the best wavelet basis for broadband measurement of the power system; A multi-layer decomposition module 30 is configured to perform multi-layer decomposition on the frequency information according to the optimal wavelet basis to obtain a plurality of wavelet frequency bands; The component extraction module 40 is configured to extract components of the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; The noise reduction module 50 is configured to perform noise reduction processing on the harmonic components using a wavelet coefficient correlation algorithm to obtain noise-reduced harmonics; The harmonic decomposition module 60 is configured to decompose the noise reduction harmonics according to the EMD algorithm to obtain a signal residual that meets a preset stop condition; The calculation module 70 is configured to calculate the calculation data corresponding to each harmonic waveform according to the signal residual.

[0073] like Figure 7 As shown, in the above technical solution, preferably, the wavelet decomposition module 20 includes: An orthogonal basis decomposition unit 21 is configured to determine the decomposition relationship between standard orthogonal bases and the decomposition and synthesis relationship of subspace coordinates corresponding to the decomposition relationship between the standard orthogonal bases using a Mallat decomposition algorithm; (1); (2); (1)-(2) Where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {gm ; m∈Z} are called low-pass filters and high-pass filters.

[0074] The space transformation unit 22 is configured to perform transformation space decomposition on the decomposition relationship between the standard orthogonal bases according to a preset condition to obtain a standard orthogonal base of a closed subspace on the finite function space; (3); (4); In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, d j,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0075] The subspace decomposition unit 23 is configured to: , derive the standard orthogonal basis After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship of the corresponding standard orthogonal systems are formed; (5); (6); (7); In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter.

[0076] The optimal wavelet basis generating unit 24 is configured to obtain the decomposition result and the optimal wavelet basis of the corresponding wavelet packet according to the standard orthogonal system and its subspace relationship; The decomposition result is expressed as: (8); The optimal wavelet basis is expressed as: (9).

[0077] In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

[0078] like Figure 8 As shown, in the above technical solution, preferably, the multi-layer decomposition module 30 includes: The wavelet transform unit 31 is configured to perform wavelet transform on the optimal wavelet basis to obtain a single periodic function representation of one period of the harmonic waveform: (10); Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The waveform generation unit 32 is configured to obtain a function representation of the entire harmonic waveform according to a single periodic function representation: (11); In the formula, G (t o , w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, The continuous wavelet generation unit 33 is configured to perform a continuous wavelet transform on the function representation of the entire harmonic waveform according to the dynamic window characteristic to obtain a continuous wavelet dependent on the scale parameter and a function representation corresponding to the continuous wavelet; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) (12); (13); The continuous wavelet representation that depends on the scale parameter is: (14); In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function. The corresponding continuous wavelet function is expressed as: (15); The wavelet transform window is a rectangular window centered at the coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a.

[0079] Where a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t).

[0080] The inverse transform unit 34 is configured to perform an inverse transform on the continuous wavelet and its corresponding function representation to obtain an inverse function representation of the corresponding continuous wavelet: (16); In the formula To invert the wavelet packet energy, the wavelet transform shows the changes of the signal f(t) around time point b as the scale parameter a changes continuously. The wavelet transform shows the changes of the signal f(t) around time point b as the scale parameter a changes continuously; The discrete processing unit 35 is configured to discretize the inverse function to obtain a plurality of wavelet frequency bands.

[0081] like Fig. 9 As shown, in the above technical solution, preferably, the discrete processing unit 35 includes: The wavelet frequency band generation subunit 351 is configured to define a preset function representation of a standard orthogonal basis constituting a corresponding wavelet frequency band: (17); The frequency band linear function generating subunit 352 is configured to obtain a linear representation of the corresponding wavelet frequency band and the inverse function after discretization according to a preset function representation: (18); Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; The orthogonal coefficient generating subunit 353 is configured to obtain the wavelet frequency band according to the coefficient sequence of the preset standard orthogonal basis: (19); In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0. Fig.10 As shown, in the above technical solution, preferably, the component extraction module 40 includes: The coefficient optimization unit 41 is configured to remove harmonic aliasing in the wavelet frequency band using the NRBO optimization algorithm to obtain a coefficient optimization sequence: (20); In the formula, p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2... The component extraction unit 42 is configured to obtain each harmonic component according to the coefficient optimization sequence, and extract components of the wavelet frequency band according to each harmonic component.

[0082] Based on the above Figure 5 and Figure 6 The method shown, accordingly, an embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the power system wide-band measurement method based on the combination of wavelet packets and SVMD in any of the above embodiments are implemented.

[0083] Based on this understanding, the technical solution of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, USB flash drive, mobile hard disk, etc.), including a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of the present application.

[0084] Based on the above Figure 5 and Figure 6 The method shown, and Figure 7The virtual device embodiment shown, in order to achieve the above-mentioned purpose, the embodiment of the present application also provides a computer device, including a storage medium and a processor; the storage medium is used to store computer programs; the processor is used to execute the computer program to implement the steps of the power system wideband measurement method based on the combination of wavelet packets and SVMD in any of the above-mentioned embodiments.

[0085] Optionally, the computer device may also include a user interface, a network interface, a camera, a radio frequency (RF) circuit, a sensor, an audio circuit, a WI-FI module, etc. The user interface may include a display, an input unit such as a keyboard, etc., and the optional user interface may also include a USB interface, a card reader interface, etc. The network interface may optionally include a standard wired interface, a wireless interface (such as a Bluetooth interface, a WI-FI interface), etc.

[0086] Those skilled in the art will appreciate that the computer device structure provided in this embodiment does not limit the computer device, and may include more or fewer components, or a combination of certain components, or different component arrangements.

[0087] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages and saves the hardware and software resources of the computer device, and supports the operation of information processing programs and other software and / or programs. The network communication module is used to realize communication between the components inside the storage medium, and communication with other hardware and software in the physical device.

[0088] In the description of this specification, the description of the terms "one embodiment", "some embodiments", "specific embodiments", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A broadband measurement method for power system based on the combination of wavelet packet and SVMD, characterized in that: The following steps are involved: Obtaining frequency information corresponding to circuit signals at various measurement points in the circuit system; Performing wavelet packet decomposition on the frequency information to determine an optimal wavelet basis for broadband measurement of the power system; Perform multi-layer decomposition on the frequency information according to the optimal wavelet basis to obtain multiple wavelet frequency bands; Extracting components from the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; De-noising the harmonic components using a wavelet coefficient correlation algorithm to obtain de-noised harmonics; Decomposing the noise reduction harmonics according to the EMD algorithm to obtain a signal residual that meets a preset stop condition; The measured data corresponding to each harmonic waveform is obtained according to the signal residual calculation.

2. The power system broadband measurement method according to claim 1, characterized in that: Determine the optimal wavelet basis for broadband measurements in power systems, including: Using the Mallat decomposition algorithm, determining the decomposition relationship between standard orthogonal bases and the decomposition and synthesis relationship of the subspace coordinates corresponding to the decomposition relationship between the standard orthogonal bases; （1）； （2）； (1)-(2) Where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {g m ; m∈Z} is called a low-pass filter and a high-pass filter; Performing transformation space decomposition on the decomposition relationship between the standard orthogonal bases according to preset conditions to obtain a standard orthogonal base of a closed subspace on the finite function space; (3)； （4）； In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, d j,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions; According to the nature of the filter itself: , derive the standard orthogonal basis and After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship corresponding to the standard orthogonal systems are formed; （5）； （6）； （7）； In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter; Obtaining the decomposition result and the best wavelet basis of the corresponding wavelet packet according to the standard orthogonal system and its subspace relationship; The decomposition result is expressed as: （8） The optimal wavelet basis is expressed as: （9） In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

3. The method for broadband measurement of electric power system according to claim 2, characterized in that: The optimal wavelet basis performs multi-layer decomposition on the frequency information, including: The optimal wavelet basis is subjected to wavelet transform to obtain a single periodic function representation of one period of the harmonic waveform: （10）； Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The coordinate sequence in ; The function representation of the entire harmonic waveform is obtained according to the single period function representation: （11）； In the formula, G (t o , w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, is the basis function; Performing a continuous wavelet transform on the function representation of the entire harmonic waveform according to the dynamic window characteristics to obtain a continuous wavelet that depends on a scale parameter and a function representation corresponding to the continuous wavelet; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) （12）； （13）； The continuous wavelet representation that depends on the scale parameter is: （14）； In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function; the function corresponding to the continuous wavelet is expressed as: （15）； The window of wavelet transform is a rectangular window centered at coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a; Where a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t); Perform an inverse transformation on the continuous wavelet and its corresponding function representation to obtain the inverse function representation corresponding to the continuous wavelet: （16）； In the formula To invert the wavelet packet energy, the wavelet transform shows the changes of the signal f(t) around the time point b as the scale parameter a changes continuously; The inverse function is discretized to obtain a plurality of wavelet frequency bands.

4. The method for broadband measurement of electric power system according to claim 3, characterized in that: Discretizing the inverse function includes: The preset function that constitutes the standard orthogonal basis corresponding to the wavelet frequency band is defined as: （17）； According to the preset function representation, a linear representation of the inverse function corresponding to the wavelet frequency band and the discretization processing is obtained: （18）； Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; According to the preset coefficient sequence of the standard orthogonal basis, the wavelet frequency band is obtained: （19）； In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0.

5. The method for broadband measurement of electric power system according to claim 4, characterized in that: Extracting components from the wavelet frequency band includes: The NRBO optimization algorithm is used to remove the harmonic aliasing in the wavelet frequency band, and the coefficient optimization sequence is obtained: （20）； In the formula, p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2...; Each harmonic component is obtained according to the coefficient optimization sequence, and components of the wavelet frequency band are extracted according to the each harmonic component.

6. A power system broadband measurement system based on the combination of wavelet packets and SVMD, characterized in that: include: An acquisition module is configured to acquire frequency information corresponding to circuit signals at various measurement points in the circuit system; A wavelet decomposition module is configured to perform wavelet packet decomposition on the frequency information to determine an optimal wavelet basis for broadband measurement of the power system; A multi-layer decomposition module is configured to perform multi-layer decomposition on the frequency information according to the optimal wavelet basis to obtain a plurality of wavelet frequency bands; A component extraction module is configured to extract components from the wavelet frequency band to obtain harmonic components corresponding to the wavelet frequency band; A noise reduction module is configured to perform noise reduction processing on the harmonic components using a wavelet coefficient correlation algorithm to obtain noise-reduced harmonics; A harmonic decomposition module is configured to decompose the noise reduction harmonics according to an EMD algorithm to obtain a signal residual that meets a preset stop condition; The calculation module is configured to calculate the measurement data corresponding to each harmonic waveform according to the signal residual.

7. The power system broadband measurement system according to claim 6, characterized in that: The wavelet decomposition module includes: An orthogonal basis decomposition unit is configured to determine a decomposition relationship between standard orthogonal bases and a decomposition and synthesis relationship of subspace coordinates corresponding to the decomposition relationship between the standard orthogonal bases using a Mallat decomposition algorithm; （1）； （2）； (1)-(2) Where t is time, φ(t) is the wavelet function, ψ(t) is the subspace coordinate wavelet function, i is the number of nodes, j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h is m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter, the coordinate sequence {h m ; m∈Z}, {g m ; m∈Z} is called a low-pass filter and a high-pass filter; A space transformation unit is configured to perform a transformation space decomposition on the decomposition relationship between the standard orthogonal bases according to a preset condition to obtain a standard orthogonal base of a closed subspace on a finite function space; （3）； （4）； In formulas (3)-(4), j is the number of decomposition levels, k is the number of points in each level, Z is an integer, m is an integer in Z, and α jk is the coefficient sequence, c j,k is the scale factor, d j,k is the wavelet coefficient, h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions; The subspace decomposition unit is set to be used according to the properties of the filter itself: , derive the standard orthogonal basis After integer translation, two mutually orthogonal standard orthogonal systems and the subspace relationship corresponding to the standard orthogonal systems are formed; （5）； （6）； （7）； In (5)-(7), S is the root node original signal representing the output of a filter, S i j represents a closed subspace on L2(R), i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m is the impulse response function of the low-pass filter, g m is the impulse response function of the high-pass filter; An optimal wavelet basis generating unit is configured to obtain a decomposition result and an optimal wavelet basis of a corresponding wavelet packet according to the standard orthogonal system and its subspace relationship; The decomposition result is expressed as: （8） The optimal wavelet basis is expressed as: （9） In formulas (8)-(9), α j，k is the coefficient sequence, d j,k is the wavelet coefficient, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, Z is an integer, m is an integer in Z, ‌∑ is the accumulation symbol, and h m-2k is the impulse response function of the low-pass filter, g m-2k is the impulse response function of the high-pass filter, and are the conjugate functions of their corresponding impulse response functions respectively.

8. The power system broadband measurement system according to claim 6, characterized in that: The multi-layer decomposition module includes: The wavelet transform unit is configured to perform wavelet transform on the optimal wavelet basis to obtain a single periodic function representation of one period of the harmonic waveform: （10）； Where f(t) is a periodic function, is the basis, k is the number of points in each layer, It can be expressed as a periodic function f(t) in the basis The coordinate sequence in ; A waveform generating unit is configured to obtain a function representation of the entire harmonic waveform according to the single period function representation: （11）； In the formula, G (t o , w ) represents short-time Fourier transform, t is time, w is the angular frequency, f(t) is the waveform signal to be analyzed; g(t) is the window function that limits the analysis time range, t0 is the specified time point, indicating that the signal f(t) is near the time point t0 and the range is determined by the function g(t) The size of the component with a frequency of ω, is a basis function; a continuous wavelet generating unit, configured to perform a continuous wavelet transform on the function representation of the entire harmonic waveform according to a dynamic window characteristic, to obtain a continuous wavelet dependent on a scale parameter and a function representation corresponding to the continuous wavelet; The dynamic window characteristic is expressed as: ψ ( t )∈ L 2 ( R ) （12）； （13）； The continuous wavelet representation that depends on the scale parameter is: （14）； In formulas (12)-(14), is the wavelet packet energy, ψ(t) is the wavelet basis function, is the Fourier transform of the wavelet basis function w is the angular frequency, R* represents all non-zero real numbers, R represents all real numbers, and at the same time, the scale parameter a and the displacement parameter b are set, and L is the entire signal space. is the basis function; the function corresponding to the continuous wavelet is expressed as: （15）； The window of wavelet transform is a rectangular window centered at coordinate (b, ±ω0 / a), with a time domain window width of aΔψ and a frequency domain window width of Δψ / a; Where a is the scale parameter and b is the displacement parameter. is the complex conjugate of ψ(t); The inverse transform unit is configured to perform an inverse transform on the continuous wavelet and its corresponding function representation to obtain an inverse function representation corresponding to the continuous wavelet: （16）； In the formula To invert the wavelet packet energy, the wavelet transform represents the change of the signal f(t) around the time point b as the scale parameter a changes continuously; the discrete processing unit is configured to discretize the inverse function to obtain multiple wavelet frequency bands.

9. The power system broadband measurement system according to claim 8, characterized in that: Discrete processing units include: The wavelet frequency band generating subunit is configured to define a preset function representation of the standard orthogonal basis constituting the corresponding wavelet frequency band: （17）； The frequency band linear function generating subunit is configured to obtain a linear representation of the inverse function corresponding to the wavelet frequency band and the discretization processing according to the preset function representation: （18）； Among them, the composition The standard orthogonal basis of is an orthogonal wavelet; The orthogonal coefficient generating subunit is configured to obtain the wavelet frequency band according to a preset coefficient sequence of the standard orthogonal basis: （19）； In formulas (17)-(19), the coefficient sequence Indicates that when the scale parameter , displacement parameter The continuous wavelet transform of f(t) is is the complex conjugate of ψ(t), ψ(t) is the wavelet basis function, i is the number of nodes, j is the number of decomposition layers, k is the number of points in each layer, W f is a function of continuous wavelet, Z represents the set of integers, that is, {…-2, -1, 0, 1, 2…}, where the ellipsis indicates that the set of integers is infinite, including all positive integers, negative integers and 0.

10. The power system broadband measurement system according to claim 6, characterized in that: The component extraction module includes: The coefficient optimization unit is configured to remove harmonic aliasing in the wavelet frequency band using the NRBO optimization algorithm to obtain a coefficient optimization sequence: （20）； p i is the probability of calculating the envelope amplitude distribution of discrete components, S(i) is the envelope entropy of each component, N is a natural number, i is 0, 1, 2...; The component extraction unit is configured to obtain each harmonic component according to the coefficient optimization sequence, and perform component extraction on the wavelet frequency band according to the each harmonic component.

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