Ultra-harmonic detection method based on Nuttall window compressed sampling and reconstruction estimation

Abstract

The invention discloses an ultra-harmonic detection method based on Nuttall window compression sampling and reconstruction estimation, which comprises the following steps of: firstly, on the basis of a 32-equal-time-interval data window detection method, constructing a window sparse measurement matrix at a sampling end by combining a Gaussian random measurement matrix and a four-item 3-order Nuttall window function to perform windowing compression sampling on an ultra-harmonic signal; and then, reconstructing and estimating a sparse vector s (n) by using an orthogonal matching pursuit reconstruction algorithm (OMP) on the data subjected to windowing compressed sampling at a reconstruction end, and finally correcting a peak frequency point of the estimated sparse vector s (n) by using a three-spectral-line interpolation technology to realize accurate detection of each parameter of the ultra-harmonic signal. According to the invention, on the premise of ensuring certain detection precision, the signal data volume required by super-harmonic detection is greatly reduced; and a basis and conditions are provided for analyzing the generation mechanism and propagation characteristics of the ultraharmonics and subsequent treatment.

Description

Technical Field

[0001] The invention relates to a superharmonic detection method, in particular to a superharmonic detection method based on Nuttall window compression sampling and reconstruction estimation. Background Art

[0002] In recent years, with the rapid rise of renewable energy generation, the widespread application of electric vehicle charging and discharging technology, and the continuous access of nonlinear loads to the power grid, the degree of power electronics in electrical equipment has shown a significant growth trend. The functional circuits of these power electronics electrical equipment perform switching operations at high frequencies, which has caused an increasingly serious power quality disturbance problem - superharmonics. Superharmonics appear as quasi-steady-state waveform distortion in the frequency range of 2 to 150kHz, which has a significant impact on the stable operation of the power grid and the efficiency of power equipment. Therefore, superharmonics are a very challenging new topic arising from the development trend of power electronics in distribution networks. Accurate detection of superharmonics is an important basis for studying their propagation characteristics and effective management.

[0003] The general superharmonic detection methods have defects in the detection process and cannot solve the contradiction between frequency resolution and data volume caused by the high frequency and wide spectrum characteristics of superharmonics. Finding a new superharmonic detection method that can reduce data storage and improve detection accuracy has become the current research focus. Summary of the invention

[0004] The purpose of the present invention is to provide a superharmonic detection method based on Nuttall window compressed sampling and reconstruction estimation, so as to solve the technical problems mentioned above.

[0005] The technical solution of the present invention is a superharmonic detection method based on Nuttall window compressed sampling and reconstruction estimation, and the superharmonic parameter detection method comprises the following steps:

[0006] S1: Filter the 200ms superharmonic disturbance signal to obtain the superharmonic components of 2 to 150kHz, and then extract 32 groups of data with a length of 0.5ms at equal time;

[0007] S2: Using the compressed sensing method, a windowed sparse measurement matrix is ​​constructed by combining a Gaussian random measurement matrix and a 4-term 3rd-order Nuttall window to perform windowed compressed sampling on each set of data;

[0008] S3: Use the orthogonal matching pursuit algorithm to reconstruct and estimate the data after windowed compressed sampling to obtain the estimated sparse vector s(n);

[0009] S4: The peak frequency of the estimated sparse vector s(n) is interpolated and corrected using the three-spectrum interpolation technique to achieve accurate detection of the parameters of the superharmonic signal.

[0010] In the aforementioned method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation, in step S1, it is assumed that the superharmonic power signal is:

[0011]

[0012] In the above formula, A h 、f h , are amplitude, frequency and phase respectively, and the superharmonic test signal is set to include a fundamental wave with a frequency of 50 Hz and 7 superharmonic components;

[0013] The 200 ms superharmonic signal sampling data shown in formula (1) is filtered, and 32 groups of 0.5 ms superharmonic signal data are equally spaced from the 200 ms data window according to the 32 equal time interval data window measurement method.

[0014] In the aforementioned method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation, in step S2, windowed compressed sampling is performed on each group of 0.5 ms superharmonic signal data, specifically including the following operations:

[0015] (1) Use the 4-term 3rd-order Nuttall window function {w(n)} of length N to calculate the discrete sequence of the superharmonic signal x(t) Windowing and truncation to obtain the windowed superharmonic signal x w (n),

[0016]

[0017] in, is the sampling sequence of x(t), n=0,1...N-1, f s is the sampling frequency;

[0018] (2) Construct a window sparse measurement matrix to realize the compressed sampling of the signal. When the ultra-harmonic signal x(n) is a sparse signal, the windowed ultra-harmonic signal x in formula (2) is w (n) Available Gaussian random measurement matrix Φ∈R M×N (M<<N) for x w (n) Perform linear measurement to obtain the observation vector y(m)∈R M×1 The expression is:

[0019] y(m)=Φx w (n) (3)

[0020] Formula (3) can be further expressed as:

[0021]

[0022] In the above formula, represents the Hadamard product; Φ W is a window sparse measurement matrix of M×N dimensions;

[0023] (3) Construct the perception matrix A. If the superharmonic signal x(n) in the first step is not sparse, it is generally possible to find a specific transformation basis Ψ so that the windowed superharmonic signal x(n) exhibits the required sparsity under the projection of the transformation basis, that is:

[0024] x(n)=Ψs(n) (5)

[0025] Where Ψ is the Fourier orthogonal transform matrix that is uncorrelated with the Gaussian random measurement matrix Φ; s(n) is the sparse representation of the superharmonic signal x(n);

[0026] According to formula (4) and formula (5), it can be deduced that:

[0027] y(m)=Φ W x(n)=Φ W Ψs(n)=As(n) (6)

[0028] In the above formula, A = Φ W Ψ is called the perception matrix.

[0029] In the aforementioned method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation, in step S3, an orthogonal matching pursuit reconstruction algorithm is used to accurately reconstruct and estimate the sparse vector s(n) using the observation value y(m), the sensing matrix A and the sparsity K as input parameters;

[0030] Specifically include:

[0031] Writing formula (6) in matrix form, we get:

[0032]

[0033] Write formula (7) in column vector form, that is:

[0034]

[0035] In the above formula, δ i (i = [1, N]) is the column vector corresponding to the perception matrix. Since the sparse vector s(n) is K sparse, that is, s i There are K non-zero numbers in (i=[1, N]), and these K non-zero values ​​s are obtained by OMP algorithm. i (i=[1, N]), the specific steps of iteration are as follows:

[0036] (1) Input parameters: sensor matrix A∈R M×N , observation vector y∈R M , signal sparsity K;

[0037] (2) Parameter initialization: The initial value of the residual is set to the observation vector r0 = y; the support set Represents the index set of each iteration, the sub-matrix of the sensor matrix A represents the set of columns of matrix A selected by index Λ0, with the number of iterations t = 1;

[0038] (3) Calculate the inner product of the current residual and the column vector of the sensor matrix A, and find the position index λ of the column vector of the sensor matrix A when the inner product is maximum. t , Under this condition, the current residual and the λ of the sensor matrix A t The column vector has the greatest correlation;

[0039] (4) Let Λ t =Λ t-1 ∪{λ t},

[0040] (5) Find an estimated value of the sparse vector s(n) According to the principle of least squares method, find y = A t s t The least squares solution of :

[0041] (6) Update residual

[0042] (7) Iteration loop: t = t + 1, if t ≤ K, return to step (3), otherwise stop iteration and go to step (8);

[0043] (8) The reconstructed s(n) is in Λ t There are non-zero entries at the last iteration.

[0044] In the aforementioned method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation, in step S4, the correction formulas for the frequency, amplitude and phase of the superharmonic component using the three-line interpolation technology are respectively:

[0045]

[0046] In the formula, f s is the sampling frequency; f i , A i , are the required frequency, amplitude and phase respectively; α is the offset, and α∈[-0.5, 0.5]; the amplitudes of the three spectral lines are

[0047] Through polynomial fitting, we get the approximate values ​​of the intermediate variables α and v(α) of the four-term third-order Nuttall window functions.

[0048] Similar expressions:

[0049] α=1.01467793b-0.08516755b 3 +0.01483490b 5 -0.00288839b 7 (12)

[0050] v(α)=1.724338592+0.430782702b 2 +0.057559982b 4 +0.005698372b 6 (13) Among them,

[0051] Beneficial effects of the present invention: Compared with the prior art, the present invention proposes a superharmonic detection method combining Nuttall window compressed sampling and reconstruction estimation on the basis of the 32 equal time interval data window detection method recommended by standard IEC61000-4-30, which has the following advantages:

[0052] (1) Based on the advantages of the 32 equidistant data window detection method and the compressed sensing technology, the present invention can detect the superharmonic signal with only 4.8% of the data volume, which greatly facilitates the transmission and storage of data.

[0053] (2) The present invention uses a Gaussian random measurement matrix and four third-order Nuttall window functions to construct a window sparse measurement matrix to perform windowed compressed sampling on the ultraharmonic signal, thereby effectively suppressing the influence of spectrum leakage in the detection process; at the same time, the three-line interpolation technology is used to reduce the measurement error caused by the fence effect and the low frequency resolution, so as to achieve accurate and rapid measurement of ultraharmonic disturbance parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the process of the present invention;

[0055] Figure 2 It is a schematic diagram of the implementation flow of the orthogonal matching pursuit (OMP) reconstruction algorithm of the present invention;

[0056] Figure 3 It is the three-spectrum interpolation principle diagram of the present invention;

[0057] Figure 4 is the relative error of amplitude under different compression ratios;

[0058] Figure 5 is the relative frequency error under different compression ratios;

[0059] Figure 6 is the relative phase error under different compression ratios. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but they are not intended to limit the present invention.

[0061] Embodiments of the present invention: Figure 1 As shown, the present invention provides a superharmonic detection method based on Nuttall window compressed sampling and reconstruction estimation, which specifically includes the following steps:

[0062] Step S1: Filter the 200ms superharmonic disturbance signal to obtain the superharmonic component of 2 to 150kHz, and then extract 32 groups of data with a length of 0.5ms from the same time;

[0063] Specifically, it is assumed that the superharmonic power signal is:

[0064]

[0065] In the above formula, A h 、f h , are amplitude, frequency and phase respectively, and the superharmonic test signal is set to include a fundamental wave with a frequency of 50 Hz and 7 superharmonic components.

[0066] Furthermore, a Chebyshev II digital bandpass filter is used to filter the 200 ms superharmonic signal sampling data shown in formula (1), and the fundamental and harmonic waves below 2 kHz and the frequency components above 150 kHz are filtered out, and only the superharmonic components within the frequency range of 2 to 150 kHz are retained. Then, 32 groups of 0.5 ms data are equally spaced from the 200 ms data window according to the 32 equal-time data window measurement method; in the subsequent steps, the frequency, amplitude and phase of the superharmonic component of each group of data are detected respectively through steps S2 to S4, and finally the 32 groups of data obtained are averaged to obtain the final detection value.

[0067] Step S2: Using the compressed sensing method, a windowed sparse measurement matrix is ​​constructed by combining a Gaussian random measurement matrix and a 4-term 3rd-order Nuttall window to perform windowed compressed sampling on each set of data;

[0068] Specifically, a window sparse measurement matrix is ​​constructed by combining the Gaussian random measurement matrix and four third-order Nuttall window functions using the compressed sensing method, and the 0.5ms ultraharmonic signal data in the observation time window is subjected to windowed compressed sampling. Specifically, the matrix includes:

[0069] (1) Use the 4-term 3rd-order Nuttall window function {w(n)} of length N to calculate the discrete sequence of the superharmonic signal x(t) Windowing and truncation:

[0070]

[0071] in, is the sampling sequence of x(t), n=0, 1...N-1, f s is the sampling frequency, x w (n) is the windowed superharmonic signal.

[0072] (2) Construct a window sparse measurement matrix to achieve compressed sampling of the signal. When the superharmonic signal x(n) is a sparse signal, the windowed superharmonic signal x in formula (2) is w (n) Available Gaussian random measurement matrix Φ∈R M×N (M<<N) for x w (n) performs linear measurement to obtain the observation vector y(m)∈R M×1 The expression is:

[0073] y(m)=Φx w (n) (3)

[0074] Formula (3) can be further expressed as:

[0075]

[0076] In the above formula, represents the Hadamard product; Φ W is a window sparse measurement matrix of M×N dimensions. Formula (4) combines the windowing information with the Gaussian random measurement matrix to improve the compressed sensing algorithm on the measurement matrix, thereby reducing the spectrum leakage of the superharmonic signal under the Fourier transform basis.

[0077] (3) Construct the perception matrix A. If the superharmonic signal x(n) in the first step is not sparse, it is generally possible to find a specific transformation basis Ψ so that the windowed superharmonic signal x(n) exhibits the required sparsity under the projection of the transformation basis, that is:

[0078] x(n)=Ψs(n) (5)

[0079] Wherein, Ψ is the Fourier orthogonal transform matrix that is uncorrelated with the Gaussian random measurement matrix Φ; s(n) is the sparse representation of the superharmonic signal x(n).

[0080] According to formula (4) and formula (5), it can be deduced that:

[0081] y(m)=Φ W x(n)=Φ W Ψs(n)=As(n) (6)

[0082] In the above formula, A = Φ W Ψ is called the perception matrix. The window sparse matrix Φ WS and the sensing matrix A need to satisfy the condition of constrained equidistance. On this basis, if K, M, and N satisfy the condition of M ≥ K × log (N), the designed signal reconstruction algorithm can be used to restore the original signal of length N through M observations. In the next step S3, the orthogonal matching pursuit (OMP) reconstruction algorithm is used to accurately reconstruct and estimate the sparse vector s (n) using the observation value y (m), the sensing matrix A, and the sparsity K as input parameters.

[0083] Step S3: Use the orthogonal matching pursuit algorithm to reconstruct and estimate the data after windowed compressed sampling to obtain an estimated sparse vector s(n).

[0084] Specifically, the orthogonal matching pursuit (OMP) reconstruction algorithm is used to accurately reconstruct and estimate the sparse vector s(n) using the observation value y(m), the perception matrix A and the sparsity K as input parameters. OMP is an algorithm that implements iterative approximation through the least squares method. The residual obtained in each iteration is orthogonal to all the selected column vectors, and has the advantages of fast operation speed and easy implementation.

[0085] Specifically include:

[0086] Writing formula (6) in matrix form, we get:

[0087]

[0088] Furthermore, formula (7) is written in column vector form, that is:

[0089]

[0090] In the above formula, δ i (i = [1, N]) is the column vector corresponding to the perception matrix. Since the sparse vector s(n) is K sparse, that is, s i There are K non-zero numbers in (i=[1,N]). Here, we use the OMP algorithm to find these K non-zero values ​​s i (i=[1,N]). The OMP algorithm flow chart is as follows Figure 2 As shown, the specific steps of the iteration are as follows:

[0091] (1) Input parameters: sensor matrix A∈R M×N , observation vector y∈R M , signal sparsity K;

[0092] (2) Parameter initialization: The initial value of the residual is set to the observation vector r0 = y; the support set Represents the index (column number) set of each iteration, the submatrix of the sensor matrix A represents the set of columns of the matrix A selected by index Λ0 (a matrix of size M×t), with the number of iterations t=1;

[0093] (3) Calculate the inner product of the current residual and the column vector of the sensor matrix A, and find the position index λ of the column vector of the sensor matrix A when the inner product is maximum. t , Under this condition, the current residual and the λ of the sensor matrix A t Column vectors have the highest correlation.

[0094] (4) Let Λ t =Λ t-1 ∪{λ t},

[0095] (5) Find an estimated value of the sparse vector s(n) According to the principle of least squares method, find y = A t s t The least squares solution of :

[0096] (6) Update residual

[0097] (7) Iteration loop: t = t + 1, if t ≤ K, return to step (3), otherwise stop iteration and go to step (8);

[0098] (8) The reconstructed s(n) is in Λ t There are non-zero entries at the last iteration.

[0099] Step S4: using the three-line interpolation technique to interpolate and correct the peak frequency of the estimated sparse vector s(n), so as to achieve accurate detection of various parameters of the superharmonic signal.

[0100] Specifically, the three-spectral-line interpolation technique is used to interpolate and correct the peak frequency of the sparse vector s(n) reconstructed and estimated by the OMP algorithm. This technique can effectively measure the frequency point information that is not on the spectral line.

[0101] The principle of three-line interpolation is as follows Figure 3 As shown, by using the ployfit function to perform polynomial approximation, the distance k from the actual peak frequency is selected. i The weighted average of the nearest three discrete spectral lines k1, k2 and k3 is interpolated and corrected. The amplitudes of the three spectral lines are Then, the correction formulas for the frequency, amplitude and phase of the superharmonic component are:

[0102]

[0103]

[0104] In the formula, f s is the sampling frequency; f i , A i , are the required frequency, amplitude and phase respectively; a is the offset, and a∈[-0.5, 0.5].

[0105] Through polynomial fitting, the approximate expressions of the intermediate variables α and v(α) of the four-term third-order Nuttall window function can be obtained:

[0106] α=1.01467793b-0.08516755b 3 +0.01483490b 5 -0.00288839b 7 (12)

[0107] v(α)=1.724338592+0.430782702b 2 +0.057559982b 4 +0.005698372b 6 (13) Among them,

[0108] By adopting the three-spectrum interpolation technology, we can improve the detection accuracy of superharmonics and ensure more accurate measurement of the frequency, amplitude and phase information of superharmonic disturbances.

[0109] Next, the Nuttall window compressed sampling and reconstruction estimation detection algorithm is used to test the super harmonic disturbance signal. Consider the following power grid super harmonic signal:

[0110]

[0111] In the above formula, A h 、f h , are amplitude, frequency and phase respectively. The superharmonic test signal is set to include a fundamental wave with a frequency of 50 Hz and 7 superharmonic components. The test signal parameters are shown in Table 1.

[0112] Let the sampling frequency be f s =500kHz, the number of sampling points N=250, and the compression ratio is 0.6; a total of 200ms sampling data of the simulation signal model shown in formula (1) and Table 1 are taken for analysis. Specifically, firstly, 200ms of superharmonic signal data are filtered to obtain superharmonic components in the frequency range of 2 to 150kHz; then the filtered data are processed according to the 32 equidistant data window detection method to obtain 32 groups of superharmonic signal data with a length of 0.5ms; then each group of signal data is subjected to windowed compressed sampling to achieve a significant reduction in the amount of data required for detection; then the sparse vector after windowed compressed sampling is processed by OMP algorithm reconstruction estimation and three-spectrum interpolation technology to achieve accurate measurement of superharmonic disturbance parameters, and finally the 32 groups of data detection results are averaged to obtain the frequency, amplitude and phase information of the superharmonic disturbance signal.

[0113] Table 1 Parameters of superharmonic signal to be measured

[0114]

[0115] Tables 2 to 4 show the superiority of the present invention in the field of ultra-harmonic detection by using four third-order Nuttall window functions by comparing different window functions. The test results show that when the window function uses a 4-term 3rd-order Nuttall window, the relative error of the amplitude of each superharmonic component does not exceed 3.83×10 -3 %, the relative frequency error does not exceed 5.84×10 -4 %, relative phase error does not exceed -8.45×10 -4 %; It can be seen that the detection accuracy of the amplitude, frequency and phase of the superharmonic is significantly better than that of the Hanning window and the Blackman window. Therefore, the four-term third-order Nuttall window used in the present invention can better suppress spectrum leakage and achieve accurate measurement of superharmonic parameter information.

[0116] Table 2 Relative amplitude error of interpolation compressed sensing algorithm with different windowing (%)

[0117] Superharmonic Component Hanning Window Blackman Window 4-term 3rd-order Nuttall window Serving size: 1 <![CDATA[1.09×10 -1 ]]> <![CDATA[9.26×10 -3 ]]> <![CDATA[6.96×10 -4 ]]> Servings: 2 <![CDATA[1.62×10 -1 ]]> <![CDATA[1.78×10 -1 ]]> <![CDATA[1.25×10 -3 ]]> Servings: 3 <![CDATA[8.22×10 -2 ]]> <![CDATA[6.16×10 -1 ]]> <![CDATA[1.43×10 -3 ]]> Servings: 4 <![CDATA[1.12×10 -1 ]]> <![CDATA[-5.15×10 -3 ]]> <![CDATA[-2.94×10 -3 ]]> Servings: 5 <![CDATA[-3.36×10 -2 ]]> <![CDATA[6.62×10 -2 ]]> <![CDATA[3.83×10 -3 ]]> Servings: 6 <![CDATA[-2.84×10 -3 ]]> <![CDATA[1.08×10 -1 ]]> <![CDATA[5.51×10 -4 ]]> Servings: 7 1.26 <![CDATA[5.74×10 -1 ]]> <![CDATA[1.45×10 -3 ]]>

[0118] Table 3 Frequency relative error of interpolation compressed sensing algorithm with different windowing (%)

[0119] Superharmonic Component Hanning Window Blackman Window 4-term 3rd-order Nuttall window Serving size: 1 <![CDATA[1.01×10 -2 ]]> <![CDATA[7.34×10 -3 ]]> <![CDATA[5.84×10 -4 ]]> Servings: 2 <![CDATA[6.55×10 -3 ]]> <![CDATA[-5.63×10 -2 ]]> <![CDATA[-2.91×10 -6 ]]> Servings: 3 <![CDATA[1.12×10 -2 ]]> <![CDATA[8.91×10 -2 ]]> <![CDATA[7.67×10 -5 ]]> Servings: 4 <![CDATA[6.41×10 -3 ]]> <![CDATA[9.05×10 -4 ]]> <![CDATA[-1.33×10 -5 ]]> Servings: 5 <![CDATA[-7.46×10 -3 ]]> <![CDATA[1.17×10 -2 ]]> <![CDATA[-1.62×10 -5 ]]> Servings: 6 <![CDATA[3.70×10 -3 ]]> <![CDATA[1.02×10 -2 ]]> <![CDATA[-8.39×10 -6 ]]> Servings: 7 <![CDATA[1.86×10 -2 ]]> <![CDATA[3.57×10 -2 ]]> <![CDATA[3.17×10 -5 ]]>

[0120] Table 4 Phase relative error of interpolation compressed sensing algorithm with different windowing (%)

[0121] Superharmonic Component Hanning Window Blackman Window 4-term 3rd-order Nuttall window Serving size: 1 <![CDATA[-2.49×10 -1 ]]> <![CDATA[-1.02×10 -2 ]]> <![CDATA[-7.96×10 -3 ]]> Servings: 2 <![CDATA[-1.86×10 -1 ]]> 2.23 <![CDATA[4.45×10 -4 <!-- 8 -->]]> Servings: 3 <![CDATA[-5.68×10 -1 ]]> -4.53 <![CDATA[-4.45×10 -3 ]]> Servings: 4 <![CDATA[5.23×10 -1 ]]> <![CDATA[-5.73×10 -2 ]]> <![CDATA[1.67×10 -3 ]]> Servings: 5 <![CDATA[5.91×10 -1 ]]> <![CDATA[-7.31×10 -2 ]]> <![CDATA[-5.74×10 -5 ]]> Servings: 6 <![CDATA[5.52×10 -1 ]]> <![CDATA[-8.66×10 -1 ]]> <![CDATA[6.05×10 -4 ]]> Servings: 7 1.98 -5.35 <![CDATA[-8.45×10 -3 ]]>

[0122] Figures 4 to 6 The present invention shows the measurement and analysis of the degree of data reduction and detection accuracy of the superharmonic signal under different compression ratios. Specifically, different mapping dimensions M are taken to make the compression ratio M / N vary in the range of 50% to 70%, with a step size of 10%. It can be seen from the figure that, first, when the compression ratio M / N = 50%, the detection error of the superharmonic increases sharply, but the detection accuracy can still meet the detection requirements; secondly, when the compression ratio M / N = 60% and 70%, the relative error of the amplitude of the superharmonic does not exceed 5.83×10 -3 %, the relative frequency error does not exceed 9.24×10 -3 %, relative phase error does not exceed -9.97×10 -3 %, the detection accuracy of the parameter information of each component of the superharmonic is high, and the difference is not large. Since the 32 equal-time-interval data window detection method used in the present invention only requires 8% of the signal data, if the compression ratio is set to 0.6, it is possible to accurately detect the superharmonic signal using only 4.8% of the signal data. In summary, the present invention greatly reduces the amount of data required for superharmonic detection while ensuring a certain detection accuracy, greatly facilitating data transmission and storage.

Claims

1. A superharmonic detection method based on Nuttall window compressed sampling and reconstruction estimation, characterized in that: The superharmonic parameter detection method comprises the following steps: S1: Filter the 200ms superharmonic disturbance signal to obtain the superharmonic components of 2 to 150kHz, and then extract 32 groups of data with a length of 0.5ms at equal time; S2: Using the compressed sensing method, a windowed sparse measurement matrix is ​​constructed by combining a Gaussian random measurement matrix and a 4-term 3rd-order Nuttall window to perform windowed compressed sampling on each set of data; S3: Use the orthogonal matching pursuit algorithm to reconstruct and estimate the data after windowed compressed sampling to obtain the estimated sparse vector s(n); S4: The peak frequency of the estimated sparse vector s(n) is interpolated and corrected using the three-spectrum interpolation technique to achieve accurate detection of the parameters of the superharmonic signal.

2. The method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation according to claim 1, characterized in that: In step S1, it is assumed that the superharmonic power signal is: In the above formula, A h 、f h , are amplitude, frequency and phase respectively, and the superharmonic test signal is set to include a fundamental wave with a frequency of 50 Hz and 7 superharmonic components; The 200 ms superharmonic signal sampling data shown in formula (1) is filtered, and 32 groups of 0.5 ms superharmonic signal data are equally spaced from the 200 ms data window according to the 32 equal time interval data window measurement method.

3. The method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation according to claim 1, characterized in that: In step S2, windowing and compressing sampling is performed on each group of 0.5 ms superharmonic signal data, which specifically includes the following operations: (1) Use the 4-term 3rd-order Nuttall window function {w(n)} of length N to calculate the discrete sequence of the superharmonic signal x(t) Windowing and truncation to obtain the windowed superharmonic signal x w (n), in, is the sampling sequence of x(t), n=0,1…N-1, f s is the sampling frequency; (2) Construct a window sparse measurement matrix to realize the compressed sampling of the signal. When the ultra-harmonic signal x(n) is a sparse signal, the windowed ultra-harmonic signal x in formula (2) is w (n) Available Gaussian random measurement matrix Φ∈R M×N (M<<N) for x w (n) Perform linear measurement to obtain the observation vector y(m)∈R M×1 The expression is: y(m)=Φx w (n) (3) Formula (3) can be further expressed as: In the above formula, represents the Hadamard product; Φ W is a window sparse measurement matrix of M×N dimensions; (3) Construct the perception matrix A. If the superharmonic signal x(n) in the first step is not sparse, it is generally possible to find a specific transformation basis Ψ so that the windowed superharmonic signal x(n) exhibits the required sparsity under the projection of the transformation basis, that is: x(n)=Ψs(n) (5) Where Ψ is the Fourier orthogonal transform matrix that is uncorrelated with the Gaussian random measurement matrix Φ; s(n) is the sparse representation of the superharmonic signal x(n); According to formula (4) and formula (5), it can be deduced that: y(m)=Φ W x(n)=Φ W Ψs(n)=As(n) (6) In the above formula, A = Φ W Ψ is called the perception matrix.

4. The method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation according to claim 3 is characterized in that: In step S3, an orthogonal matching pursuit reconstruction algorithm is used to accurately reconstruct and estimate the sparse vector s(n) using the observation value y(m), the perception matrix A and the sparsity K as input parameters; Specifically include: Writing formula (6) in matrix form, we get: Write formula (7) in column vector form, that is: In the above formula, δ i (i=[1,N]) is the column vector corresponding to the perception matrix. Since the sparse vector s(n) is K-sparse, that is, s i There are K non-zero numbers in (i=[1,N]), and these K non-zero values ​​s are obtained by OMP algorithm. i (i=[1,N]), the specific steps of iteration are as follows: (1) Input parameters: sensor matrix A∈R M×N , observation vector y∈R M , signal sparsity K; (2) Parameter initialization: The initial value of the residual is set to the observation vector r0 = y; the support set Represents the index set of each iteration, the sub-matrix of the sensor matrix A represents the set of columns of matrix A selected by index Λ0, with the number of iterations t = 1; (3) Calculate the inner product of the current residual and the column vector of the sensor matrix A, and find the position index λ of the column vector of the sensor matrix A when the inner product is maximum. t , Under this condition, the current residual and the λ of the sensor matrix A t The column vector has the greatest correlation; (4) Let Λ t = Λ t-1 ∪{λ t}, (5) Find an estimated value of the sparse vector s(n) According to the principle of least squares method, find y = A t s t The least squares solution of : (6) Update residual (7) Iteration loop: t = t + 1, if t ≤ K, return to step (3), otherwise stop iteration and go to step (8); (8) The reconstructed s(n) is in Λ t There are non-zero entries at the last iteration.

5. The method for detecting superharmonic parameters based on Nuttall window compressed sampling and reconstruction estimation according to claim 1, characterized in that: In step S4, the correction formulas for the frequency, amplitude and phase of the superharmonic component using the three-line interpolation technology are: In the formula, f s is the sampling frequency; f i , A i , are the required frequency, amplitude and phase respectively; α is the offset, and α∈[-0.5, 0.5]; the amplitudes of the three spectral lines are Through polynomial fitting, the approximate expressions of the intermediate variables α and v(α) of the four-term third-order Nuttall window function are obtained: α=1.01467793b-0.08516755b 3 +0.01483490b 5 -0.00288839b 7 (12) v(α)=1.724338592+0.430782702b 2 +0.057559982b 4 +0.005698372b 6 (13) in,

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