An adaptive threshold SAMP reconstruction method of power quality disturbance signal

Abstract

The application discloses an adaptive threshold SAMP reconstruction method of power quality disturbance signals. The method obtains compressed observation values by constructing a random Gaussian observation matrix, and uses a discrete Fourier transform to perform sparse representation on an original signal. In the iterative reconstruction process, the application first introduces the spectral amplitude difference as an adaptive termination basis, and combines a dynamic threshold updating function to realize automatic adaptation to different noise levels and different disturbance characteristics. The method effectively avoids the problems of high estimation of traditional SAMP sparsity and redundant iteration, and significantly reduces the calculation load. Compared with the OMP, original SAMP and other methods, the application method can reduce the iteration number by 30% to 60%, the reconstruction signal-to-noise ratio is increased by 2 to 5 dB, the root mean square error is reduced by 10% to 25%, and the application method has higher robustness and real-time performance in the reconstruction of power quality disturbance signals, and is very suitable for compressed sampling, edge computing and high-speed signal reconstruction scenes in a power quality monitoring system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing and compressive sensing, and particularly relates to a sparse signal reconstruction method based on adaptive threshold SAMP, which is particularly suitable for fast reconstruction and edge computing of power quality disturbance signals in power systems. BACKGROUND

[0002] With the continuous expansion of the scale of the power system and the wide access of power electronic equipment and renewable energy devices, the power quality disturbance problems such as harmonics, interharmonics, voltage sag, voltage swell, voltage interruption, and voltage flicker in the power grid are increasingly prominent. Such disturbance signals are diverse, non-stationary, and transient, and put forward higher requirements on the data acquisition, transmission, and signal reconstruction capabilities of the power quality monitoring system. The traditional power quality monitoring method usually performs high-frequency sampling based on the Nyquist sampling theorem. In the context of the continuous expansion of the disturbance frequency spectrum range, the amount of sampled data is large, and the calculation and storage overhead is high, which makes it difficult to meet the application requirements of distributed monitoring, edge devices, and wireless sensing systems. Compressive sensing technology utilizes the sparsity of signals in the transform domain and can complete signal acquisition and reconstruction under the condition of lower than the Nyquist sampling rate, and has gradually been applied to the field of power quality disturbance signal processing.

[0003] In existing compressive sensing reconstruction algorithms, the orthogonal matching pursuit (OMP) and its improved algorithms generally rely on the prior information of the sparsity of the signal. However, the sparsity of the power quality disturbance signal varies with the type of disturbance and the operating condition, and it is difficult to accurately obtain the prior information. The sparsity adaptive matching pursuit (SAMP) algorithm avoids the dependence on the sparsity prior by gradually increasing the sparsity in stages, which improves the applicability of the algorithm to a certain extent. However, when this type of algorithm is applied to power quality disturbance signals with sudden characteristics, due to the influence of spectral leakage, the iteration termination method based on residual cannot converge below the conventional preset threshold, resulting in that even if the main frequency components have been accurately extracted, the residual cannot be effectively converged. Therefore, SAMP will mistakenly continue to expand the support set and repeatedly perform iteration operations, causing the sparsity estimation to be significantly overestimated. As the number of candidate atoms increases, the matrix operation complexity increases significantly, and the calculation time is forced to be prolonged. At the same time, the redundant atoms will cause overfitting of the algorithm in a noisy environment, and the quality of the reconstructed signal will decrease, especially when recovering key characteristic quantities such as phase jumps or sag depths. The existing technology uses a fixed number of iterations or manually sets an upper limit for the sparsity to terminate, but this method cannot be adaptive and cannot take into account the varying characteristics of different types of disturbance signals, which lacks stability and cannot guarantee the reconstruction accuracy.

[0004] Therefore, the prior art urgently needs a compressed sensing reconstruction method capable of realizing reliable reconstruction termination judgment in a spectrum leakage and noise interference environment without relying on sparsity prior conditions, so as to improve the stability and practicability of power quality disturbance signal reconstruction. SUMMARY

[0005] The technical problem to be solved by the present application is that the prior art method cannot accurately determine whether the power quality disturbance signal reconstruction converges or not, is prone to overestimate the sparsity under the condition of spectrum leakage, has too many iterations, and lacks robustness in a noise environment, and the like. The present application proposes a power quality disturbance reconstruction method capable of adaptively determining whether the reconstruction process is ended without relying on sparsity prior, and effectively suppressing the influence of spectrum leakage, reducing the number of iterations, improving the reconstruction accuracy and noise robustness.

[0006] To solve the above technical problems, the present application proposes an adaptive threshold sparse adaptive matching pursuit (ATSAMP) reconstruction method for power quality disturbance signals. The method realizes adaptive sparse reconstruction of the disturbance signal by introducing a spectrum difference judgment and a dynamic threshold adjustment strategy, and solves the problems of fixed iteration stage, strong parameter dependence and noise sensitivity of the traditional SAMP. The method comprises the following steps:

[0007] S101, collecting original power quality disturbance signals containing harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike and voltage swell , and constructing a discrete time domain sampling sequence with a length of N;

[0008] S102, selecting a compressed sensing sparse transform base and a random Gaussian observation matrix ;

[0009] S103, starting reconstruction using ATSAMP, initializing the residual , the support set , the index set , the candidate set , the step size =S, the stage index stage=1, the number of iterations =1, and the iteration termination threshold ;

[0010] S104, calculating the index set : , merging the support set and the index set to obtain the candidate set : ; in performing final test to update support set : wherein, is the observation matrix corresponding to the candidate set the pseudo-inverse of the sub-matrix indexed by the support set : updating the residual : wherein is the observation matrix corresponding to the support set indexed by the support set, is the pseudo-inverse of ;

[0011] S105, calculating the spectral amplitude difference between the adjacent two iterations , i.e. the difference between the spectral amplitude sum of the reconstruction coefficients of the current iteration and the spectral amplitude sum of the reconstruction coefficients of the last iteration ;

[0012] S106, determining whether the iteration is terminated based on the spectral amplitude difference calculated in S105 , phase control and adaptive threshold update based on the residual, if , the iteration is determined to be terminated, and the algorithm flow jumps to S107; if , if , performing phase switching, stage = stage + 1, S*stage, adaptively updating the threshold , if , and M, then , ;

[0013] S107, outputting the final reconstruction coefficients .

[0014] Optionally, the detailed steps of S102 include:

[0015] Considering that the power quality disturbance has good sparsity under the discrete Fourier transform basis, the discrete Fourier transform basis is used as the sparse transform basis for the power quality disturbance , the power quality disturbance signal with a length of N is converted into a sparse coefficient vector , and then a random Gaussian observation matrix is used for compression observation to obtain the measurement value .

[0016] Optionally, the detailed steps of S103 include:

[0017] the iteration termination threshold The initial value is set to .

[0018] The ATSAMP method proposed in this application has the following advantages compared with traditional OMP and SAMP:

[0019] 1. Effectively avoid overestimation of sparsity: Since the spectral amplitude difference criterion is not sensitive to spectral leakage, this method can accurately reflect whether the reconstruction process is stable. It still achieves correct termination when spectral leakage leads to abnormal residuals, and it achieves automatic threshold adjustment without the need for manual determination of residual threshold, thereby effectively preventing the iteration out of control and overestimation of sparsity caused by spectral leakage in the SAMP algorithm.

[0020] 2. Significantly improve computational efficiency: By adaptively adjusting the threshold to terminate the iteration in time, this method effectively reduces a large amount of redundant calculation, significantly improves the computational efficiency of the algorithm, and shortens the overall time required for reconstruction.

[0021] 3. Improve reconstruction accuracy: This method effectively avoids the overfitting problem commonly existing in reconstruction algorithms and can more accurately reconstruct signals. Under different noise conditions, the signal-to-noise ratio (SNR) of the reconstructed signal is significantly improved, and the root mean square error (RMSE) is significantly reduced. The advantage is particularly obvious in the non-stationary disturbance and spectral leakage scenario.

[0022] 4. Stronger noise robustness: The dynamic adaptive threshold mechanism can automatically adjust according to the noise intensity, effectively avoid misjudgment, and make the algorithm applicable to high-noise application environments in actual power grids. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 The figure is a flow chart of the ATSAMP reconstruction method of a power quality disturbance signal according to an embodiment of the application.

[0024] Figure 2 The figure is a spectral leakage diagram of a power grid voltage interruption signal in an embodiment of the application.

[0025] Figure 3 The figure is a reconstruction process diagram of a power grid voltage interruption signal in an embodiment of the application, which includes the variation curves of the spectral amplitude sum and the spectral amplitude difference with the number of iterations in the iteration process.

[0026] Figure 4Figures for performance comparison of reconstruction of power grid harmonic signals in a noisy environment in the embodiments of the present application. Among them, (a) is a comparison figure of the reconstruction SNR performance of each algorithm for noisy harmonics under different compression lengths; (b) is a comparison figure of the reconstruction RMSE performance of each algorithm for noisy harmonics under different compression lengths.

[0027] Figure 5 Figures for performance comparison of reconstruction of power grid voltage sag signals in a noisy environment in the embodiments of the present application. Among them, (a) is a comparison figure of the reconstruction SNR performance of each algorithm for noisy voltage sag signals under different compression lengths; (b) is a comparison figure of the reconstruction RMSE performance of each algorithm for noisy voltage sag signals under different compression lengths. DETAILED DESCRIPTION

[0028] An ATSAMP reconstruction method of power quality disturbance signals, the specific implementation includes:

[0029] S101, collecting original power quality disturbance signals including harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike and voltage swell , and constructing a discrete time domain sampling sequence with a length of N;

[0030] S102, selecting a compressive sensing sparse transform base and a random Gaussian observation matrix ;

[0031] S103, starting reconstruction using ATSAMP, initializing the residual , the support set , the index set , the candidate set , the step size =S, the stage index stage=1, the number of iterations =1, and the iteration termination threshold ;

[0032] S104, calculating the index set : , merging the support set and the index set to obtain the candidate set : ; performing a final test on to update the support set : , wherein is the pseudo-inverse of the submatrix of the observation matrix corresponding to the candidate set index; calculating the reconstruction coefficient of the current iteration : , update the residual : where is the observation matrix corresponding to the support set indexed sub-matrix, is the pseudo-inverse of ;

[0033] S105, calculate the spectral amplitude difference between the two adjacent iterations , i.e. the spectral amplitude sum of the reconstruction coefficients of the current iteration and the spectral amplitude sum of the reconstruction coefficients of the last iteration ;

[0034] S106, determine whether the iteration is terminated based on the spectral amplitude difference calculated in S105 , phase control and adaptive threshold update based on the residual, if , the iteration is determined to be terminated, and the algorithm flow jumps to S107; if , if , stage switching is performed, stage = stage + 1, S*stage, adaptive update of the threshold , if , and M, then , ;

[0035] S107, output the final reconstruction coefficients .

[0036] The core innovation of the present application is to use the "spectral amplitude difference" as the iteration termination criterion. Its rationality can be proved by Figure 2 and Figure 3 .

[0037] Figure 2 is a schematic diagram of spectral leakage of a power grid voltage interruption signal. For this voltage interruption signal, due to the existence of spectral leakage, when reconstructed by the SAMP algorithm, the estimated sparsity K is 106. At this time, the final residual two-norm is always higher than the conventional termination threshold, resulting in that the sparsity cannot be accurately estimated, thereby reducing the reconstruction accuracy and increasing the calculation time.

[0038] Figure 3The internal iteration process of the ATSAMP algorithm proposed in the present application in reconstructing a certain power grid voltage interruption signal is shown. As shown in the figure, the spectrum amplitude sum curve tends to be stable and no longer increases after about the 60th iteration; at the same time, the spectrum amplitude difference curve also rapidly approaches 0 at this point. This indicates that after the 60th iteration, the key information of the signal has been completely reconstructed, and continuing iteration has no practical significance. Therefore, the present application adopts the spectrum amplitude difference as the termination condition, which is both scientific and efficient, can directly reflect the convergence of the reconstruction process, and avoids the interference of residual artifacts caused by spectrum leakage.

[0039] In order to verify the effectiveness of the ATSAMP method proposed in the present application, simulation experiments were carried out in the MATLAB environment. The experimental settings are as follows: the fundamental frequency = 50 Hz, the sampling frequency = 6.4 kHz, the length of each sampling signal N = 1280, and the compression length is fixed at M = 256. The signal-to-noise ratio (SNR) and the root mean square error (RMSE) are used as two commonly used indicators to quantitatively evaluate the reconstruction performance, and the specific calculation formulas are as follows:

[0040]

[0041]

[0042] wherein and are the original signal and the estimated value of the denoised signal, respectively.

[0043] The present application compares the reconstruction performance of the OMP, SAMP and ATSAMP algorithms under the condition of no noise, and the evaluation indicators include the estimated sparsity K, SNR, RMSE and average calculation time, and the specific results are shown in Table 1.

[0044]

[0045] As can be seen from the data in Table 1, for the power grid harmonic signal without spectrum leakage, all algorithms can accurately estimate the sparsity K = 8, and achieve almost perfect signal reconstruction with extremely high SNR and negligible RMSE. The reconstruction SNR is between about 286 and 288 dB, and the RMSE is extremely low, and the difference between the SNR and the RMSE of each method is negligible. However, for power quality disturbances with spectrum leakage, such as interharmonics, voltage interruptions, voltage swell, voltage sag, voltage spikes, voltage oscillations, and voltage flicker, OMP and SAMP both have obvious sparsity overestimation. In contrast, the ATSAMP method proposed in this application, relying on the iterative termination criterion based on spectral amplitude difference and the adaptive threshold mechanism, can accurately estimate the sparsity, thereby effectively solving the core defect of SAMP algorithm sparsity overestimation. Because of avoiding sparsity overestimation, ATSAMP is superior to OMP and SAMP in terms of SNR and RMSE. For example, in the reconstruction of interharmonic signals, the SNR achieved by ATSAMP is 28.29 dB, while that of OMP and SAMP is 26.40 dB and 25.04 dB, respectively; at the same time, the RMSE of ATSAMP is the lowest, only 0.0388, which is significantly better than 0.0487 of OMP and 0.0557 of SAMP.

[0046] Table 1 also lists the average running time of each algorithm, from which the difference in computing efficiency can be seen. ATSAMP has slightly higher computing time than OMP due to the use of adaptive iteration mechanism, but can significantly improve the reconstruction accuracy. Compared with SAMP, ATSAMP shortens the running time through the early termination strategy based on spectral amplitude difference, achieving a balance between reconstruction accuracy and computing efficiency. This makes ATSAMP have obvious advantages in practical applications that require accurate and efficient power quality disturbance reconstruction.

[0047] In order to further evaluate the anti-noise performance of the ATSAMP algorithm, the present application reconstructs the power grid harmonic signal and the voltage sag signal superimposed with 30 dB Gaussian white noise, and compares the performance of the three algorithms under different compression lengths (M from 128 to 512). The specific results are shown in Figure 4 and Figure 5 .

[0048] As shown in Figure 4 , noise significantly reduces the effective sparsity of the harmonic signal, which poses a challenge to SAMP which relies on residual as a termination condition and OMP which relies on fixed sparsity. In contrast, ATSAMP can adaptively adjust the threshold according to the noise, thereby maintaining excellent reconstruction accuracy and performance stability. Under all compression lengths, the SNR of ATSAMP is always higher than that of OMP and SAMP, and the RMSE is always lower than that of the two. Figure 5Further indicated that under the noise condition, the ATSAMP can still accurately estimate the sparsity of the power grid voltage sag signal, effectively alleviating the problem of SAMP algorithm caused by overestimation of sparsity, which leads to the decline of reconstruction accuracy and convergence.

[0049] In summary, the present application proposes an ATSAMP reconstruction method for power quality disturbance signals, which successfully solves the problems of overestimation of sparsity, low computational efficiency and poor noise immunity of the SAMP algorithm in the prior art by using the spectral amplitude difference as the iteration termination criterion and combining with the adaptive threshold mechanism. Multiple simulation examples prove that the method of the present application is superior to the prior art in terms of reconstruction accuracy, computational efficiency and noise immunity, providing an efficient and reliable signal compression and reconstruction scheme for power quality monitoring, which has significant practical value and broad application prospects.

Claims

1. An adaptive threshold sparsity adaptive matched pursuit reconstruction method for power quality disturbance signals, characterized in that, include: S101 collects raw power quality disturbance signals including harmonics, interharmonics, voltage flicker, voltage interruption, voltage oscillation, voltage sag, voltage spike, and voltage rise. And construct a discrete time-domain sampling sequence of length N; S102, Selecting the Compressed Sensing Sparse Transform Basis and random Gaussian observation matrix ; S103, Reconstruction begins using adaptive threshold sparsity adaptive matching pursuit; the algorithm initializes the residuals. Support set index set Candidate set Step length =S, stage index stage=1, number of iterations =1, iteration termination threshold ; S104, Calculate the index set : Merge support set With index set Obtain candidate set : ;exist Perform the final test to update the support set. : ,in, Observation matrix Corresponding to candidate set The pseudo-inverse of the indexed submatrix; Calculate the reconstruction coefficients of the current iteration : Update residuals : ,in Observation matrix Corresponding to the support set Indexed submatrix, for The false reversal; S105, Calculate the spectral amplitude difference between two adjacent iterations. That is, the reconstruction coefficient of the current iteration. The sum of the spectral amplitudes and the reconstruction coefficients of the previous iteration The difference between the sum of the spectral amplitudes; S106, the spectral amplitude difference calculated based on S105 To determine whether the iteration has terminated, stage control and adaptive threshold updates are based on residuals. If the iteration terminates, the algorithm jumps to S107; if ,if Then, the execution phase switches, stage = stage + 1. S*stage, adaptive threshold update ,if ,and M, then , ; S107, output the final reconstruction coefficients. .

2. The adaptive threshold sparsity adaptive matched pursuit reconstruction method for power quality disturbance signals according to claim 1, characterized in that, In step S102, considering that the power quality disturbance has good sparsity under the discrete Fourier transform basis, the discrete Fourier transform basis is used as the sparse transform basis for the power quality disturbance. The power quality disturbance signal of length N Convert to sparse coefficient vector Then, a random Gaussian observation matrix was used. Compressed observations yielded measured values. .

3. The adaptive threshold sparsity adaptive matched pursuit reconstruction method for power quality disturbance signals according to claim 1, characterized in that, In step S103, the iteration termination threshold The initial value is set to .

4. The adaptive threshold sparsity adaptive matched pursuit reconstruction method for power quality disturbance signals according to claim 1, characterized in that, This method is used for compressed sensing acquisition and rapid reconstruction of power quality disturbance signals.

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