Rapid compressed sensing method and system for broadband static and dynamic signals of power system, computer program product and storage medium

Abstract

The invention discloses a rapid compressed sensing method and system for broadband static and dynamic signals of a power system, a computer program product and a storage medium. The method comprises the following steps: acquiring the broadband static and dynamic signals; performing high-order polynomial fitting on the broadband static and dynamic signals, and constructing a sparse representation model of the broadband static and dynamic signals; based on the sparse representation model of the broadband static and dynamic signals, the broadband static and dynamic signals are compressed through a Gaussian random measurement matrix, and compressed signals are obtained and stored; and reconstructing the compressed signal by using a least square method, and outputting a reconstructed signal. According to the method, under the condition that signal parameters are unknown, efficient compressed sensing can be carried out on broadband static and dynamic signals of a power system, and meanwhile, the signals can be accurately reconstructed under the condition of a high compression ratio.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to a fast compressed sensing method, system, computer program product, and storage medium for broadband static and dynamic signals in power systems. Background Technology

[0002] As power system operation evolves towards a wider frequency domain, power quality problems caused by higher harmonics are becoming increasingly prominent. Wideband oscillations occur frequently, with frequencies ranging from a few Hz to several kHz, accompanied by multi-mode and dynamic characteristics. Wideband measurement, as an improvement over existing measurement technologies, holds promise for rapid sensing of wideband operating conditions due to its defined measurement bandwidth. However, wideband measurement is based on sampling frequencies of at least 12.8 kHz. This high frequency necessitates substantial storage and data transmission for data sampled using existing Nyquist methods, potentially limiting real-time performance. Therefore, reducing data storage and transmission burdens is crucial for the development and application of wideband data.

[0003] Compressed sensing, as a novel data acquisition and reconstruction approach, enables the projection of signals with sparse characteristics from a high-dimensional space to a low-dimensional space, and then accurately reconstructs the original signal using reconstruction algorithms. Compressed sensing overcomes the limitations of the Nyquist sampling theorem and has been widely applied in information theory, image processing, communications, and medicine.

[0004] Currently, compressed sensing of broadband signals mainly suffers from high computational complexity, low compression ratio, low compression efficiency, and reconstruction methods that are susceptible to noise and have low reconstruction efficiency. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a fast compressed sensing method, system, computer program product, and storage medium for broadband static and dynamic signals in power systems. It can perform high-order polynomial fitting on broadband static and dynamic signals even when signal parameters are unknown, obtaining a sparse representation model of the broadband signal. Then, through compressed sensing technology based on Fast Fourier Transform, it efficiently compresses and accurately reconstructs the broadband static and dynamic signals under high compression ratio conditions. Furthermore, it features low computational complexity and minimal susceptibility to noise.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, a fast compressed sensing method for broadband static and dynamic signals in power systems is provided, comprising: acquiring broadband static and dynamic signals; performing polynomial fitting on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals; compressing the broadband static and dynamic signals using a Gaussian random measurement matrix based on the sparse representation model of the broadband static and dynamic signals to obtain a compressed signal and storing it; and reconstructing the compressed signal using the least squares method to output a reconstructed signal.

[0008] In conjunction with the first aspect, a polynomial fitting is performed on the broadband static / dynamic signal to construct a sparse representation model of the broadband static / dynamic signal, including: For a broadband static / dynamic signal containing multiple frequency components, its signal model x(t) is expressed as:

[0009] (1)

[0010] Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. For interference components, K is the total number of non-fundamental frequency components;

[0011] The sparse representation model of wideband static and dynamic signals is expressed as:

[0012] (4)

[0013] The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows:

[0014] (5)

[0015] (6)

[0016] I is the degree of the polynomial, M 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal, T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

[0017] Combining the first aspect, when the frequency of each component in equation (4) is given, first calculate the transformation basis C(t) according to the frequency of each component in equation (4), and then solve for the polynomial coefficient matrix D by the least squares method:

[0018] (7)

[0019] The polynomial coefficient matrix D is a sparse vector.

[0020] Combining the first aspect, for a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, then:

[0021] (8)

[0022] in, It is a sparse vector of dimension N;

[0023] The compressed signal y is:

[0024] (11)

[0025] Where A is the sensing matrix, Let M be an M×N order measurement matrix, where M is the dimension of the observation vector, and M < <N。

[0026] In conjunction with the first aspect, the compressed signal is reconstructed using the least squares method, including: solving for the sparse vector using the least squares method. Specifically:

[0027] (14).

[0028] In conjunction with the first aspect, the transformation basis C(t) is solved, including: performing spectral analysis on the broadband signal x through fast Fourier transform, filtering out frequency components that exceed the set threshold of the fundamental frequency component, and obtaining the initial value of the frequency of each component.

[0029] Combining the first aspect, the difference between the compressed signal y and Aθ is defined as the residual r. n ,

[0030] (12)

[0031] in, It is a reconstructed signal obtained from the sensing matrix and sparse vectors.

[0032] Secondly, a fast compressed sensing system for broadband static and dynamic signals in power systems is provided, comprising: a signal acquisition module for acquiring broadband static and dynamic signals; a model building module for performing polynomial fitting on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals; a compression module for compressing the broadband static and dynamic signals based on the sparse representation model of the broadband static and dynamic signals using a Gaussian random measurement matrix to obtain and store the compressed signals; and a reconstruction module for reconstructing the compressed signals using the least squares method to output the reconstructed signals.

[0033] In conjunction with the second aspect, a polynomial fitting is performed on the broadband static / dynamic signal to construct a sparse representation model of the broadband static / dynamic signal, including: For a broadband static / dynamic signal containing multiple frequency components, its signal model x(t) is expressed as:

[0034] (1)

[0035] Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. For interference components, K is the total number of non-fundamental frequency components;

[0036] The sparse representation model of wideband static and dynamic signals is expressed as:

[0037] (4)

[0038] The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows:

[0039] (5)

[0040] (6)

[0041] I is the degree of the polynomial, M 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal, T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

[0042] In conjunction with the second aspect, when the frequency of each component in equation (4) is given, the transformation basis C(t) is first calculated based on the frequency of each component in equation (4), and then the polynomial coefficient matrix D is solved by the least squares method:

[0043] (7)

[0044] The polynomial coefficient matrix D is a sparse vector.

[0045] In conjunction with the second aspect, for a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, then:

[0046] (8)

[0047] in, It is a sparse vector of dimension N;

[0048] The compressed signal y is:

[0049] (11)

[0050] Where A is the sensing matrix, Let M be an M×N order measurement matrix, where M is the dimension of the observation vector, and M < <N。

[0051] In conjunction with the second aspect, the compressed signal is reconstructed using the least squares method, including: solving for the sparse vector using the least squares method. Specifically:

[0052] (14).

[0053] In conjunction with the second aspect, the transformation basis C(t) is solved, including: performing spectral analysis on the broadband signal x through fast Fourier transform, filtering out frequency components that exceed the set threshold of the fundamental frequency component, and obtaining the initial value of the frequency of each component.

[0054] Combining with the second aspect, the difference between the compressed signal y and Aθ is defined as the residual r. n ,

[0055] (12)

[0056] in, It is a reconstructed signal obtained from the sensing matrix and sparse vectors.

[0057] Thirdly, a computer program product is provided, including a computer program / instructions that, when executed by a processor, implement the steps of the fast compressed sensing method for broadband static and dynamic signals of a power system as described in the first aspect.

[0058] Fourthly, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the fast compressed sensing method for broadband static and dynamic signals of a power system as described in the first aspect.

[0059] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: the present invention can construct a sparse representation model of the wideband static and dynamic signal by performing polynomial fitting on the signal when the signal parameters are unknown; compress the sparse representation model of the wideband static and dynamic signal into a compressed signal and store it; reconstruct the compressed signal and output the reconstructed signal; through compressed sensing technology based on fast Fourier transform, the wideband static and dynamic signal can be efficiently compressed and accurately reconstructed under high compression ratio conditions, while having the characteristics of low computational complexity and low susceptibility to noise. Attached Figure Description

[0060] Figure 1 This is a schematic flowchart of the main process of a fast compressed sensing method for broadband static and dynamic signals in power systems provided by an embodiment of the present invention. Figure 1 ;

[0061] Figure 2 This is a flowchart illustrating a fast compressed sensing method for broadband static and dynamic signals in power systems, provided by an embodiment of the present invention. Figure 2 ;

[0062] Figure 3 This is a flowchart illustrating a fast compressed sensing method for broadband static and dynamic signals in power systems, provided by an embodiment of the present invention. Figure 3 ;

[0063] Figure 4 This is a schematic diagram of the step signal reconstruction result in an embodiment of the present invention. (a) shows that the FHPCS method can accurately reflect signal changes when there are multiple step components, and (b) shows that the reconstruction of the step signal will have a response process. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0065] Example 1

[0066] like Figure 1As shown, a fast compressed sensing method for broadband static and dynamic signals in power systems includes: acquiring broadband static and dynamic signals; performing polynomial fitting on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals; compressing the broadband static and dynamic signals using a Gaussian random measurement matrix based on the sparse representation model of the broadband static and dynamic signals to obtain a compressed signal and storing it; and reconstructing the compressed signal using the least squares method to output a reconstructed signal.

[0067] This invention mainly consists of a broadband static and dynamic signal sparse characterization method and compressed sensing technology, such as... Figure 2 As shown, firstly, a sparse representation model is constructed by fitting a high-order polynomial to a wideband static and dynamic signal containing multiple frequency components; secondly, the initial judgment of the wideband static and dynamic signal is achieved through the fast Fourier transform method; finally, efficient compression and signal reconstruction are achieved using compressed sensing.

[0068] I. Sparse Representation Model of Wideband Static and Dynamic Signals.

[0069] For a wideband static-dynamic signal containing multiple frequency components, its signal model x(t) can be expressed as:

[0070] (1)

[0071] Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. K represents the interference component, and K represents the total number of non-fundamental frequency component signals.

[0072] By performing a trigonometric expansion on the signal part of equation (1), we can obtain equation (2):

[0073] (2)

[0074] Using a polynomial approximation of time t in equation (2) A n (t)cosφ n (t), A n (t)sinφ n (t), A k (t)cosφ k (t) and A k (t)sinφ k (t), thus obtaining the high-order polynomial fitting model for the wideband static and dynamic signals:

[0075] (3)

[0076] In the formula, I represents the degree of the polynomial, and M represents the degree of the polynomial. 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal. By extracting the polynomial coefficients of equation (3), equation (3) can be simplified to:

[0077] (4)

[0078] The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows:

[0079] (5)

[0080] (6)

[0081] T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

[0082] Equation (4) can be regarded as a sparse representation model of broadband signal x(t). x(t) is sparse under the transform basis C(t), and the polynomial coefficient matrix D is a sparse vector.

[0083] When the frequency of each component in equation (4) is determined, C(t) can be determined, and the polynomial coefficient matrix D can be solved by the least squares method, as shown in equation (4). .

[0084] (7).

[0085] II. Compressed sensing of wideband static and dynamic signals.

[0086] like Figure 3 As shown, for a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, it can be represented by equation (8):

[0087] (8)

[0088] in, It is a sparse vector of dimension N.

[0089] The signal x(t) can be compressed using equation (9):

[0090] (9)

[0091] in, is a measurement matrix of order M×N (M << N), where M is the dimension of the observation vector, y is the observation vector of compressive sampling, and it is the linear projection of the original signal x on The compression ratio CR is defined as:

[0092] (10)

[0093] Substituting Equation (8) into Equation (9), we get:

[0094] (11)

[0095] In the equation, A is the sensing matrix. The difference between y and Aθ is defined as the residual r n , that is:

[0096] (12)

[0097] In the equation, is the reconstructed signal obtained from the sensing matrix and the sparse vector.

[0098] After storing the observation vector y, a signal reconstruction algorithm is needed to recover the compressed signal. Solving the sparse vector θ from y and A in Equation (11) is usually transformed into a problem of minimizing the norm :

[0099] (13)

[0100] Solving Equation (13) is an NP-hard problem, and the algorithm complexity increases exponentially with the increase of the signal length N. Considering applying the least squares method in Equation (7) to solve the sparse vector θ, specifically:

[0101] (14)

[0102] Compared with methods such as convex optimization, the least squares method has a small computational amount, will not fall into local optimal solutions, and has good applicability.

[0103] To ensure the accuracy of compression and restoration, a Gaussian random matrix is taken as the measurement matrix , C(t) in Equation (4) is used as the transformation basis in Equation (11) , and D in Equation (4) is used as the sparse vector θ in Equation (11).

[0104] Since the frequency components of the signal need to be given first to solve the sparse vector D, the compressive sensing method needs to consider solving the initial frequency of the matrix C(t) first. Considering applying the fast Fourier transform FFT method to frequency solving. The flow chart of the proposed wideband static and dynamic signal compressive sensing is as Figure 2 shown, and the specific steps are as follows:

[0105] (1) By performing FFT spectrum analysis on the broadband signal x, frequency components exceeding 1% of the fundamental frequency are selected, and the initial frequency value f of each component is obtained. k ;

[0106] (2) Wideband signal x and measurement matrix Multiply to obtain the compressed observation vector y, and then store or transmit it;

[0107] (3) Based on time t and f k Construct matrix C(t);

[0108] (4) Reconstruct the signal using equation (14), solve for the coefficient matrix θ, and then solve for the amplitude, phase angle and frequency of each frequency component.

[0109] (5) Determine the residual r n Check if the iteration termination condition is met. If not, return to step (4). If it is met, terminate the iteration.

[0110] (6) Output results.

[0111] III. Validation.

[0112] This paper analyzes the reconstruction effect of the present invention under static and dynamic signals. For static signals, a test scenario is considered that includes multiple harmonics, interharmonics, frequency shifts, and noise. For dynamic signals, cases involving amplitude and phase modulation, frequency ramps, and step changes are considered. To reflect the signal reconstruction effect of the algorithm, three parameters are used as evaluation indicators: reconstruction signal-to-noise ratio (SNR), reconstruction error (ERR), and energy recovery coefficient (ERP). The corresponding expressions are as follows.

[0113] Reconstructed signal-to-noise ratio (SNR):

[0114] (15)

[0115] In the formula, It is the reconstruction result of substituting the sparse vector θ into equation (8).

[0116] Reconstruction Error ERR:

[0117] (16)

[0118] Energy Recovery Factor (ERP):

[0119] (17)

[0120] (1) Static signal.

[0121] Since real-world signals typically contain multiple harmonics and interharmonics, the parameters in Table 1 are used as the test signal. Based on this, the effects of frequency offset (-0.5~0.5Hz) and noise (30dB~60dB) on the reconstruction results are considered. In the simulation, the sampling rate f is taken as... s =12.8kHz, order n=2, compression ratio CR=50%, window length t=0.2s. The proposed method is compared with methods based on discrete Fourier transform basis (DFTB), particle swarm optimization (PSO), and imperialist competitive algorithm (ICA). The three compressed sensing methods—overcomplete dictionary, overcomplete dictionary, and comparability—are compared. The simulation results are shown in Table 2.

[0122] Table 1: Static Signal Test Parameters

[0123]

[0124] Table 2: Compressed Sensing Reconstruction Results of Static Signals

[0125]

[0126] It can be seen that the signal reconstruction accuracy of the method of the present invention is significantly better than the other three methods under conditions of multiple frequency components, frequency offset and noise. Although the signal reconstruction accuracy of the method of the present invention will decrease as the signal-to-noise ratio decreases, when the signal-to-noise ratio is higher than 40dB, its reconstruction error ERR can be more than an order of magnitude higher than the other methods.

[0127] (2) Dynamic signals.

[0128] When real-world systems experience disturbances or faults, signals exhibit dynamic phenomena such as modulation, frequency ramps, and steps. Therefore, it is necessary to verify the applicability of compressed sensing methods under dynamic signal conditions. Considering adding dynamic parameters such as wideband amplitude-phase modulation, frequency ramps, and amplitude-phase steps to the signal parameters in Table 1, the dynamic test conditions and compressed sensing reconstruction results are shown in Table 3.

[0129] Table 3: Compressed Sensing Reconstruction Results of Dynamic Signals

[0130]

[0131] Comparing the results in Table 3 with the results for multiple frequency components in Table 2 reveals that dynamic changes in the signal significantly impact the reconstruction accuracy of the four methods. Specifically, DFTB cannot effectively characterize dynamic signal changes, PSO and ICA yield results after averaging the dynamic signal, while the method of this invention effectively reflects the dynamic process of the signal through polynomial fitting. When the signal exhibits amplitude and phase modulation and frequency ramp changes, the reconstruction results of the method of this invention are significantly superior to the other three methods, reconstructing the original signal with an energy recovery coefficient of no less than 99.99%.

[0132] When the signal undergoes a step change, the reconstruction accuracy of the method of this invention is better than that of existing methods. A schematic diagram of step signal reconstruction is shown below. Figure 4 As shown. Figure 4 Figure (a) shows that the FHPCS method can accurately reflect signal changes when multiple step components are present. Figure 4 (b) reflects that the reconstruction of the step signal will have a response process.

[0133] In summary, under the static and dynamic signal testing conditions specified in this invention, the static and dynamic reconstruction results of the method presented in this invention are superior to those based on orthogonal bases and overcomplete dictionaries. The reconstruction error ERR is nearly an order of magnitude higher than other methods. Furthermore, it can accurately reconstruct dynamic signals such as modulated signals. Therefore, the method of this invention achieves both high-efficiency compression and accurate reconstruction. This invention obtains a sparse representation model of the wideband signal by performing high-order polynomial fitting on the wideband static and dynamic signals, and then uses the least squares method to achieve accurate signal reconstruction. Simultaneously, it can accurately reconstruct the signal under high compression ratio conditions.

[0134] Example 2

[0135] Based on the fast compressed sensing method for broadband static and dynamic signals of power systems described in Embodiment 1, this embodiment provides a fast compressed sensing system for broadband static and dynamic signals of power systems, comprising:

[0136] The signal acquisition module is used to acquire wideband static and dynamic signals;

[0137] The model building module is used to perform polynomial fitting on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals.

[0138] The compression module is used for a sparse representation model based on broadband static and dynamic signals. It compresses the broadband static and dynamic signals using a Gaussian random measurement matrix to obtain and store the compressed signals.

[0139] The reconstruction module is used to reconstruct the compressed signal using the least squares method and output the reconstructed signal.

[0140] Polynomial fitting is performed on the broadband static / dynamic signal to construct a sparse representation model of the broadband static / dynamic signal, including: For a broadband static / dynamic signal containing multiple frequency components, its signal model x(t) is expressed as:

[0141] (1)

[0142] Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. For interference components, K is the total number of non-fundamental frequency components;

[0143] The sparse representation model of wideband static and dynamic signals is expressed as:

[0144] (4)

[0145] The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows:

[0146] (5)

[0147] (6)

[0148] I is the degree of the polynomial, M 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal, T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

[0149] Given the frequency of each component in equation (4), first calculate the transformation basis C(t) based on the frequency of each component in equation (4), and then solve for the polynomial coefficient matrix D using the least squares method:

[0150] (7)

[0151] The polynomial coefficient matrix D is a sparse vector.

[0152] For a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, then:

[0153] (8)

[0154] in, It is a sparse vector of dimension N;

[0155] The compressed signal y is:

[0156] (11)

[0157] Where A is the sensing matrix, Let M be an M×N order measurement matrix, where M is the dimension of the observation vector, and M < <N。

[0158] Reconstructing the compressed signal using the least squares method includes: solving for the sparse vector using the least squares method. Specifically:

[0159] (14).

[0160] Solving for the transform basis C(t) involves: performing spectral analysis on the broadband signal x using the Fast Fourier Transform, filtering out frequency components that exceed a set threshold for the fundamental frequency component, and obtaining the initial value of the frequency of each component.

[0161] Define the difference between the compressed signal y and Aθ as the residual r. n ,

[0162] (12)

[0163] in, It is a reconstructed signal obtained from the sensing matrix and sparse vectors.

[0164] Example 3

[0165] Based on the fast compressed sensing method for broadband static and dynamic signals of power systems described in Embodiment 1, this embodiment provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the fast compressed sensing method for broadband static and dynamic signals of power systems described in Embodiment 1.

[0166] Example 4

[0167] Based on the fast compressed sensing method for broadband static and dynamic signals of power systems described in Embodiment 1, this embodiment provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the fast compressed sensing method for broadband static and dynamic signals of power systems as described in Embodiment 1.

[0168] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0169] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0170] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0171] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0172] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A fast compressed sensing method for broadband static and dynamic signals in power systems, characterized in that, include: Acquire wideband static and dynamic signals; Polynomial fitting is performed on the wideband static and dynamic signals to construct a sparse representation model of the wideband static and dynamic signals; Based on the sparse representation model of broadband static and dynamic signals, the broadband static and dynamic signals are compressed by Gaussian random measurement matrix to obtain compressed signals and store them. The compressed signal is reconstructed using the least squares method, and the reconstructed signal is output.

2. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 1, characterized in that, Polynomial fitting is performed on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals, including: For a wideband static-dynamic signal containing multiple frequency components, its signal model x(t) is expressed as: （1） Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. For interference components, K is the total number of non-fundamental frequency components; The sparse representation model of wideband static and dynamic signals is expressed as: （4） The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows: （5） （6） I is the degree of the polynomial, M 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal, T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

3. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 2, characterized in that, Given the frequency of each component in equation (4), first calculate the transformation basis C(t) based on the frequency of each component in equation (4), and then solve for the polynomial coefficient matrix D using the least squares method: （7） The polynomial coefficient matrix D is a sparse vector.

4. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 3, characterized in that, For a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, then: （8） in, It is a sparse vector of dimension N; The compressed signal y is: （11） Where A is the sensing matrix, Let M be an M×N order measurement matrix, where M is the dimension of the observation vector, and M < <N。 5. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 4, characterized in that, The compressed signal is reconstructed using the least squares method, including: Solving sparse vectors using the least squares method Specifically: （14）。 6. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 5, characterized in that, Solving for the transformation basis C(t) includes: By performing spectral analysis on the broadband signal x using Fast Fourier Transform, frequency components exceeding a set threshold of the fundamental frequency are selected, and the initial value of the frequency of each component is obtained.

7. The fast compressed sensing method for broadband static and dynamic signals in power systems according to claim 5, characterized in that, Define the difference between the compressed signal y and Aθ as the residual r. n , （12） in, It is a reconstructed signal obtained from the sensing matrix and sparse vectors.

8. A fast compressed sensing system for broadband static and dynamic signals in power systems, characterized in that, include: The signal acquisition module is used to acquire wideband static and dynamic signals; The model building module is used to perform polynomial fitting on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals. The compression module is used for a sparse representation model based on broadband static and dynamic signals. It compresses the broadband static and dynamic signals using a Gaussian random measurement matrix to obtain and store the compressed signals. The reconstruction module is used to reconstruct the compressed signal using the least squares method and output the reconstructed signal.

9. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 8, characterized in that, Polynomial fitting is performed on the broadband static and dynamic signals to construct a sparse representation model of the broadband static and dynamic signals, including: For a wideband static-dynamic signal containing multiple frequency components, its signal model x(t) is expressed as: （1） Among them, A n (t), f n and A corresponds to the time-varying amplitude, frequency, and phase of the fundamental frequency component, respectively. k (t), f k and These correspond to the time-varying amplitude, frequency, and phase of the k-th frequency component, respectively, where t is time. For interference components, K is the total number of non-fundamental frequency components; The sparse representation model of wideband static and dynamic signals is expressed as: （4） The transformation basis C(t) and the polynomial coefficient matrix D are expressed as follows: （5） （6） I is the degree of the polynomial, M 0I and N 0I To fit the coefficients of the I-th degree polynomial of the fundamental frequency signal, M kI and N kI To fit the coefficients of the I-th degree polynomial of the k-th frequency component signal, T denotes matrix transpose, f K Let be the frequency value of the Kth frequency component.

10. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 9, characterized in that, Given the frequency of each component in equation (4), first calculate the transformation basis C(t) based on the frequency of each component in equation (4), and then solve for the polynomial coefficient matrix D using the least squares method: （7） The polynomial coefficient matrix D is a sparse vector.

11. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 10, characterized in that, For a wideband static / dynamic signal x of length N, if its transform basis... If the following is sparse, then: （8） in, It is a sparse vector of dimension N; The compressed signal y is: （11） Where A is the sensing matrix, Let M be an M×N order measurement matrix, where M is the dimension of the observation vector, and M < <N。 12. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 11, characterized in that, The compressed signal is reconstructed using the least squares method, including: Solving sparse vectors using the least squares method Specifically: （14）。 13. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 12, characterized in that, Solving for the transformation basis C(t) includes: By performing spectral analysis on the broadband signal x using Fast Fourier Transform, frequency components exceeding a set threshold of the fundamental frequency are selected, and the initial value of the frequency of each component is obtained.

14. The fast compressed sensing system for broadband static and dynamic signals in power systems according to claim 13, characterized in that, Define the difference between the compressed signal y and Aθ as the residual r. n , （12） in, It is a reconstructed signal obtained from the sensing matrix and sparse vectors.

15. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the fast compressed sensing method for broadband static and dynamic signals of power systems as described in any one of claims 1 to 7.

16. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the fast compressed sensing method for broadband static and dynamic signals in power systems as described in any one of claims 1 to 7.

Images