Wideband oscillation characteristic identification method for access of new energy to AC power grid

Abstract

A broadband oscillation characteristic identification method for a new energy access AC power grid comprises the following steps: compressing an oscillation signal acquired by a PMU by using a Gaussian random matrix, uploading low-dimensional data to a master station, and reconstructing the signal at the master station through an orthogonal matching pursuit (OMP) algorithm; a VMD algorithm with the minimum energy loss as a threshold value is adopted to conduct self-adaptive decomposition on the reconstructed signals, and IMF components containing oscillation information are obtained; the purpose of blind source separation is achieved by maximizing the non-Gaussian property of the output signal through FastICA, independent components are extracted from the mixed signal, and noise is removed; and finally, calculating related information (frequency and amplitude) of oscillation by using FFT (Fast Fourier Transform). According to the method, the technical advantages of CS-OMP, VMD and FastICA are combined, different kinds of oscillation modes and complex working conditions can be dealt with, broadband oscillation in a power system can be better monitored and recognized, safe and stable operation of a power grid is guaranteed, and accurate characteristic parameters (frequency and amplitude) are provided for the oscillation suppression technology.

Description

Technical Field

[0001] The present invention relates to the technical field of power system stability, and in particular to a method for identifying broadband oscillation characteristics of new energy access to an AC power grid based on CS-OMP, adaptive VMD and FastICA. Background Art

[0002] By 2025, renewable energy is expected to account for 18% of total consumption. Gansu Province is actively building UHV DC and regional hub power grids. As of the end of April, the grid-connected capacity of new energy has reached 31.2228 million kilowatts, accounting for 48.95% of the total installed capacity, and new energy accounts for 50% of the power transmitted. The access of large-scale new energy and power electronic equipment has changed the dynamic characteristics of the power grid, resulting in coupling and multiple superposition characteristics in the system in time and frequency, which is easy to cause safety problems such as broadband oscillation. Traditional oscillations are mainly electromechanical oscillations, but now they have been transformed into electromagnetic transient oscillations dominated by power electronics, with the frequency range extending from several Hz to thousands of Hz. Especially in Gansu, the distance between the load center and the wind and photovoltaic base exceeds 1,000 kilometers, forming weak grid characteristics, which aggravates the risk of broadband oscillation. There are few analyses of broadband oscillations of large-scale diversified new energy cluster transmission systems connected to the AC power grid, and the mechanism is not clear enough. It is urgent to carry out broadband analysis of large-scale diversified new energy cluster transmission systems connected to the AC power grid to reveal the broadband oscillation mechanism of large-scale diversified new energy cluster transmission systems under the power grid.

[0003] At present, broadband oscillation identification has been relatively maturely applied in low-frequency / ultra-low-frequency bands, but the previous detection methods cannot be fully transferred to the detection and identification of high-frequency oscillations in the "double-high" system. The frequency range of this type of oscillation ranges from subsynchronous to supersynchronous frequencies, making it difficult to detect and identify, mainly due to the limitations of communication bandwidth and the requirements of the sampling theorem. The problems with existing oscillation detection methods include: low sampling rate, difficulty in identifying high-frequency oscillations; large amount of data, resulting in transmission and storage difficulties; inaccurate signal decomposition, resulting in mode aliasing or improper signal detection.

[0004] The stability problem of power systems is becoming increasingly prominent, which has led to a significant increase in the possibility of broadband oscillations. Traditional power system oscillation monitoring methods can no longer meet the needs of new power systems, while the rapid development of wide-area measurement systems and the widespread application of artificial intelligence in the power sector have provided new solutions to deal with the impact of multiple coupling factors on the safety and stability of power systems. Summary of the invention

[0005] The present invention provides a method for identifying broadband oscillation characteristics of a new energy source connected to an AC power grid, thereby realizing broadband oscillation characteristics identification of a new energy source connected to an AC power grid.

[0006] The technical solution adopted by the present invention is:

[0007] A method for identifying broadband oscillation characteristics of new energy access to AC power grid collects real-time current and voltage signals from the synchronous vector measurement unit (PMU) in the power grid and performs data preprocessing; compresses and samples the preprocessed signals through the compressed sensing CS technology; reconstructs the original signal using the orthogonal matching pursuit OMP algorithm, and gradually selects the basis vectors most relevant to the current residual to gradually build a sparse representation of the signal; the reconstructed signal is decomposed using adaptive variational mode decomposition VMD to decompose the input signal into multiple sub-signals with specific center frequencies and narrow bandwidths. Through iterative optimization, accurate separation of different frequency components is achieved, thereby obtaining a series of modal functions. By analyzing these modal functions, features related to broadband oscillations are extracted, including oscillation frequency, amplitude, and phase information; each mode obtained by VMD decomposition is then subjected to fast independent component analysis FastICA to extract independent components; finally, the frequency and amplitude of the oscillation are identified from the extracted independent components using fast Fourier transform FFT to detect oscillation modes within different frequency ranges.

[0008] Further:

[0009] The measurement matrix Φ in the compressed sensing CS technology adopts a Gaussian matrix.

[0010] The adaptive variational mode decomposition (VMD) is an adaptive VMD algorithm based on energy loss. In order to enable the algorithm to adaptively decompose the signal, the decomposition process is as follows:

[0011] (1) For each modal function u k The analytical signal of (t) is Hilbert transformed, and finally its one-sided spectrum can be obtained:

[0012]

[0013]

[0014] (2) Estimated center frequency of each mode using the mixed -jωt As a reference, the corresponding modal frequency is modulated to the corresponding baseband:

[0015]

[0016] Among them, e -jωt is the phasor description of the center frequency on the complex plane, and ω is the center frequency.

[0017] (3) A multimodal oscillation signal f(t) is decomposed into k bandwidth-limited IMFs. The constrained variational model in the VMD decomposition process is constructed with the bandwidth and estimated minimum value of each component as the target:

[0018]

[0019] Where K is the number of modes to be decomposed; u k represents the kth IMF component after signal decomposition, represents the kth IMF central angular frequency; To find the partial derivative, f(t) represents the original signal and δ(t) represents the impulse function.

[0020] (4) To solve the constrained variational model of equation (1.11), the constrained variational model is transformed into an unconstrained variational problem through the augmented Lagrangian function, and the expression of the augmented Lagrangian function is obtained as follows:

[0021]

[0022] Where α is a quadratic penalty factor used to ensure the reconstruction accuracy of the signal under noise conditions; λ(t) is a Lagrange multiplier used to ensure the most stringent constraints.

[0023] (5) The Lagrangian function points of formula (1.12) are calculated alternately and iteratively by the alternating direction multiplier ADMM algorithm, that is, by iteratively updating and Find the "saddle point" of the augmented Lagrangian expression to obtain the optimal solution of the constrained variational model. It can be calculated by the following formula:

[0024]

[0025] (6) According to Plancherel Fourier isometry transformation, The iterative update formula of is transformed into the frequency domain, and the exponential term can be eliminated. The expression is:

[0026]

[0027] Where X is u k is the total possible set of , ω is the random frequency.

[0028] Now replace the first term ω with ω-ω k Replace, since the frequency band is shifted when the bandwidth of the sub-signal is obtained in (1.15), it is now restored to the original frequency band, and the formula is as follows:

[0029]

[0030] Then convert the above formula (1.16) into the form of non-negative frequency interval integral:

[0031]

[0032] Expand the above formula (1.17) into a functional and find its minimum value. The solution to the quadratic optimization problem is as follows:

[0033]

[0034] In the formula, the number of VMD decompositions K is determined starting from the spectrum. The intrinsic mode function is regarded as a compact structure around the center frequency ω from the spectrum. k The crest of the wave, is the Wiener filter of the boundary in n+1 iterations;

[0035] (7) Similarly, in order to solve the minimum The updated solution of the mid-corner frequency is transferred to the frequency domain as follows:

[0036]

[0037] In the formula, is the current IMF center angular frequency.

[0038] (8) The iterative formula for the center angular frequency is as follows:

[0039]

[0040] (9) Update the Lagrange multiplier according to the following formula:

[0041]

[0042] Where τ is the noise tolerance coefficient. When there is strong noise in the signal, τ can be set to 0 to achieve the effect of filtering noise.

[0043] (10) Set the convergence criterion and stop the iteration when the alternating iteration process satisfies formula (1.22):

[0044]

[0045] In the formula, ε represents the convergence accuracy;

[0046] (11) The optimal modal number k is determined from the energy perspective to achieve the purpose of adaptively determining the number of decomposition layers.

[0047] For a signal f(t), convert it into a frequency domain signal F(f), and its spectrum energy expression is as follows:

[0048]

[0049] When the value of k is not appropriate, a certain frequency may be decomposed into multiple modal components, that is, when the value is not appropriate, the energy of the signal after decomposition will be reduced;

[0050] Assume that the broadband oscillation signal f(t) generates k IMF components after VMD decomposition, and the spectrum of the signal f(t) can be E total, the spectrum of each IMF component can be E k :

[0051]

[0052]

[0053] In the formula, i represents the sequence, N represents the spectrum length, and E total It represents the spectral energy of the original signal, and IMF represents the spectral energy of each IMF after the original signal is decomposed.

[0054] (12) According to the law of conservation of energy, the energy of the original signal in the frequency domain is equal to the sum of the energies of each frequency component, including:

[0055]

[0056] Where P is the number of IMFs after signal decomposition.

[0057] (13) The energy loss in the signal decomposition process is used to measure the mode number after VMD decomposition. The relationship between the correlation coefficient and the correlation is shown in Table 1. The expression of energy loss is:

[0058]

[0059] When the k value increases, η gradually decreases. When the η value is close to 0, the k value is the adaptive optimal mode number.

[0060] The present invention combines the advantages of CS-OMP, VMD and FastICA technologies, can cope with different types of oscillation modes and complex working conditions, can better monitor and identify broadband oscillations in power systems, ensure the safe and stable operation of power grids, and provide accurate characteristic parameters (frequency, amplitude) for oscillation suppression technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of the process of the present invention;

[0062] Figure 2 is a compressed sensing flow chart of the present invention;

[0063] Figure 3 This is a flow chart of OMP signal reconstruction of the present invention;

[0064] Figure 4 It is the VMD-FastICA-FFT monitoring flow chart of the present invention;

[0065] Figure 5 It is a model for connecting wind turbines to the grid;

[0066] Figure 6Comparison between the original signal and the reconstructed signal of broadband oscillation;

[0067] Figure 7 It is the result of FFT analysis on the original signal;

[0068] Figure 8 It is the result of VMD adaptation and FastICA denoising decomposition;

[0069] Fig. 9 is the FFT identification result. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below with reference to the accompanying drawings, specific derivations, and simulation experiments.

[0071] Reference Figure 1 A method for identifying broadband oscillation characteristics of renewable energy access to AC power grid collects real-time current and voltage signals from a synchronous vector measurement unit (PMU) in the power grid and performs data preprocessing; compresses and samples the preprocessed signals through compressed sensing (CS) technology, reduces the dimension of broadband oscillation signals and reduces the transmission volume of broadband oscillation data, thereby retaining important information of the original signal while achieving signal dimensionality reduction; reconstructs the original signal using the orthogonal matching pursuit (OMP) algorithm, and gradually selects the basis vectors most relevant to the current residual to gradually construct a sparse representation of the signal; and decomposes the reconstructed signal using adaptive variational mode decomposition (VMD) to decompose the input signal into multiple sub-signals with specific center frequencies and narrow bandwidths. Through iterative optimization, accurate separation of different frequency components is achieved, thus obtaining a series of modal functions. By analyzing these modal functions, features related to wide-band oscillations are extracted, including oscillation frequency, amplitude, and phase information. Fast independent component analysis FastICA is then performed on each mode obtained by VMD decomposition to extract independent components. Finally, fast Fourier transform FFT is used to identify the frequency and amplitude of the oscillation from the extracted independent components, and oscillation modes within different frequency ranges are detected.

[0072] The present invention will be described in detail below.

[0073] 1. Data Collection

[0074] In the power grid monitoring system of the present invention, synchronized phasor measurement units (PMUs) installed at different sites are connected to the power grid through voltage transformers (PTs) and current transformers (CTs), and electrical signals are monitored in real time to obtain key data such as the amplitude, phase, and frequency of voltage and current. The collected signals are converted into digital signals after analog-to-digital conversion (ADC), and time synchronization at the microsecond level is achieved through the built-in GPS synchronization system, thereby ensuring that PMU data from different geographical locations are synchronized and consistent, providing support for high-precision, time-space consistency identification of wide-band oscillation characteristics.

[0075] PMU has a high sampling rate of up to several thousand hertz, enabling it to capture broadband oscillation characteristics from subsynchronous to supersynchronous frequency bands, effectively supporting real-time monitoring of various oscillation modes in the system. The synchronous acquisition and high-frequency sampling characteristics of PMU ensure that the oscillation signal in the power grid system is not lost due to limited sampling bandwidth, thereby achieving rapid and accurate identification of broadband oscillation characteristics.

[0076] 2. Data compression based on compressed sensing

[0077] In order to reduce the communication bandwidth requirements, the present invention combines compressed sensing technology (CS) to compress the collected signals and transmit key features to the master station. The master station receives compressed phasor data from multiple PMUs and reconstructs the signal through the OMP algorithm to ensure that the phase and amplitude information of the signal are fully restored, thereby accurately identifying the amplitude, frequency and other characteristics of the oscillation.

[0078] (1) The wideband oscillation signals collected from synchronized phasor measurement units (PMUs) are usually high-dimensional signals with huge data volumes, and traditional communication networks are difficult to meet the needs of real-time transmission. To solve this problem, the present invention adopts compressed sensing (CS) technology to collect and compress signals at a rate far lower than the Nyquist sampling frequency. By introducing compressed sensing, the present invention can achieve low-dimensional representation of key signal features while ensuring data integrity, thereby significantly reducing transmission bandwidth requirements. Compressed sensing technology projects high-dimensional signals into low-dimensional space through random projection, effectively retaining the important features of wideband oscillation signals and achieving simultaneous data acquisition and compression. This technology ensures that even under low sampling rate conditions, the system can still accurately reconstruct the original signal, thereby achieving accurate identification of wideband oscillation features. The compressed sensing process is as follows Figure 2 shown.

[0079] For broadband oscillation signals, their sparse characteristics are used for data compression. Assuming that the broadband signal x with a length of N is compressible, the signal can be expressed as a coefficient vector θ under a sparse basis:

[0080]

[0081] Wherein, θ represents the sparse domain coefficient under the sparse basis, and has sparseness (that is, most components are zero or close to zero), and Ψ represents the sparse basis matrix.

[0082] (2) In order to reduce the amount of data transmission, a random measurement matrix Φ is constructed to achieve dimensionality reduction of high-dimensional signals. The measurement matrix satisfies the restricted isometry property (RIP), that is, it can retain important information of high-dimensional signals in low-dimensional space. Projecting the signal x into the low-dimensional space, the compressed signal y is expressed as:

[0083] y=Φx(1.2)In the formula, y is the compressed low-dimensional signal with a signal length of N×1, which contains the key information of the signal; Φ is a low-dimensional measurement matrix with a signal length of M×N (MN); x represents the original high-dimensional signal. This process greatly reduces the demand for data transmission while retaining important information of the oscillation signal.

[0084] (3) Calculate the perception matrix Θ. Substituting equation (1.1) into equation (1.2), we get:

[0085] y=Φ·Ψ·θ=Θ·θ(1.3)

[0086] According to formula (1.3), y, Φ, and Ψ are all known. Since formula (1.3) is an underdetermined matrix, the original signal x cannot be directly solved from y. However, since θ is sparse, the known perception matrix Θ can be used to reconstruct θ through a reconstruction algorithm, and then the original signal x can be obtained from formula (1.2), thereby realizing signal reconstruction. The frequency domain coefficients of a wideband oscillation signal are not only 0 at the oscillation point, so they have a certain sparsity in the frequency domain. Compared with the discrete Fourier transform, the discrete cosine transform only involves the real number part in its input, which can obtain better reconstruction effects. The discrete data points are transformed to the frequency domain using the discrete cosine transform (DCT). The representation of DCT is:

[0087]

[0088] According to compression theory, in order to achieve signal dimensionality reduction while retaining important information of the original signal, the measurement matrix Φ should be uncorrelated with the sparse matrix Ψ, such as the Gaussian matrix or the Bernoulli matrix. Since the Gaussian matrix is ​​uncorrelated with the sparse matrix composed of fixed orthogonal bases such as DCT, it is more appropriate to choose a Gaussian random matrix as the measurement matrix, which obeys the Gaussian normal distribution.

[0089] (4) Orthogonal Matching Pursuit (OMP) is a greedy algorithm for sparse signal reconstruction. Its core idea is to gradually construct a sparse signal in an iterative process. In each iteration, the algorithm selects the atom that best matches the current residual from the perception matrix Θ (that is, the column that is most correlated with the residual vector). After selecting an atom, the algorithm calculates an updated residual to reflect the difference between the signal and the selected atom. To ensure that the selected atom is almost orthogonal to the new residual, the selected atom is deleted from the perception matrix. Next, the algorithm will continue to select the column that best matches the new residual from the updated perception matrix. This process will be repeated until the residual meets the preset stopping condition, that is, the required accuracy is achieved or the maximum number of iterations is reached. Through this iterative selection method, OMP can effectively approximate high-dimensional sparse signals while ensuring the orthogonality between the selected atoms, thereby improving the efficiency and accuracy of signal recovery. The OMP signal reconstruction process is as follows: Figure 3 shown.

[0090] The specific process of OMP is as follows:

[0091] ① Input: observation matrix y M×1 , perception matrix Θ, sparse transformation basis Ψ, sparsity K;

[0092] ②Output: Reconstructed original signal

[0093] ③ Initialization: The initial value of the residual r0 = y, the index set F0 = φ, the support set Iteration number i = 1;

[0094] ④ Calculate the inner product of the perception matrix Θ = ΦΨ and the current residual, and find the index λ of the item with the largest absolute value of the inner product t :

[0095]

[0096] ⑤Update index set:

[0097]

[0098] In the formula, F i represents the index selected in the i-th iteration, Θ i ={α j} indicates that from F i Select an M×i-dimensional matrix consisting of a set of corresponding columns of the perception matrix.

[0099] ⑥ Estimation of the signal to be reconstructed, the formula is as follows:

[0100]

[0101] ⑦Update residual:

[0102]

[0103] ⑧ Loop stop judgment: If i<K, then i=i+1, and go to step ④, then enter step ⑨;

[0104] ⑨Reconstruct the estimated value F i There are non-zero entries, whose values ​​are obtained from the last iteration

[0105] The orthogonal matching pursuit algorithm is a greedy algorithm that selects the most effective atom for the current residual each time, so it can quickly approximate the sparse solution. Since only one atom is selected each time and the coefficients of the existing atoms are re-optimized, the algorithm has a better reconstruction effect when the signal is sparse. In addition, OMP has lower computational complexity than many sparse solution algorithms and is suitable for handling larger-scale sparse reconstruction problems.

[0106] 3. Adaptive VMD algorithm based on energy loss

[0107] The reconstructed signal is modally decomposed by adaptive VMD to obtain a series of modal functions. Each modal function contains the oscillation characteristics of a specific frequency band, laying the foundation for further analysis of high-frequency oscillation modes. FastICA is used to remove interference noise, retain the oscillation characteristics in the power system, and then the frequency and phase information of the oscillation is obtained through FFT.

[0108] The VMD algorithm is a signal multi-mode decomposition method. When decomposing multi-oscillation modal signals, VMD does not require stationarity assumptions and the selection of decomposition bases, retaining the essential characteristics of the original signal. Compared with the EMD algorithm, it can separate two modes with similar frequencies, avoiding endpoint effects and modal aliasing problems, and has strong robustness to noise. Since the wide-band oscillation signal is a multi-mode signal, the decomposition number K of the wide-band oscillation signal is related to the number of modes. When the K value is incorrect, the signal will be over-decomposed or under-decomposed, and the decomposed mode cannot contain all the modes of the signal. Therefore, it is necessary to distinguish the number of modes generated after VMD decomposition so that the algorithm can adaptively decompose the signal. The decomposition process is as follows:

[0109] (1) For each modal function u k The analytical signal of (t) is Hilbert transformed, and finally its one-sided spectrum can be obtained:

[0110]

[0111]

[0112] (2) Estimated center frequency of each mode using the mixed -jωt As a reference, the corresponding modal frequency is modulated to the corresponding baseband:

[0113]

[0114] Among them, e -jωt is the phasor description of the center frequency on the complex plane, and ω is the center frequency.

[0115] (3) A multimodal oscillation signal f(t) is decomposed into k bandwidth-limited IMFs. The constrained variational model in the VMD decomposition process is constructed with the bandwidth and estimated minimum value of each component as the target:

[0116]

[0117] Where K is the number of modes to be decomposed; u k represents the kth IMF component after signal decomposition, represents the kth IMF central angular frequency; To find the partial derivative, f(t) represents the original signal and δ(t) represents the impulse function.

[0118] (4) To solve the constrained variational model of equation (1.11), the constrained variational model is transformed into an unconstrained variational problem through the augmented Lagrangian function, and the expression of the augmented Lagrangian function is obtained as follows:

[0119]

[0120] Where α is a quadratic penalty factor used to ensure the reconstruction accuracy of the signal under noise conditions; λ(t) is a Lagrange multiplier used to ensure the most stringent constraints.

[0121] (5) The Lagrangian function points of formula (1.12) are calculated alternately and iteratively by the alternating direction multiplier ADMM algorithm, that is, by iteratively updating and Find the "saddle point" of the augmented Lagrangian expression to obtain the optimal solution of the constrained variational model. It can be calculated by the following formula:

[0122]

[0123] (6) According to Plancherel Fourier isometry transformation, The iterative update formula of is transformed into the frequency domain, and the exponential term can be eliminated. The expression is:

[0124]

[0125] Where X is u kis the total possible set of , ω is the random frequency.

[0126] Now replace the first term ω with ω-ω k Replace, since the frequency band is shifted when the bandwidth of the sub-signal is obtained in (1.15), it is now restored to the original frequency band, and the formula is as follows:

[0127]

[0128] Then convert the above formula (1.16) into the form of non-negative frequency interval integral:

[0129]

[0130] Expand the above formula (1.17) into a functional and find its minimum value. The solution to the quadratic optimization problem is as follows:

[0131]

[0132] In the formula, the number of VMD decompositions K is determined starting from the spectrum. The intrinsic mode function can be regarded as a compact structure around the center frequency ω from the spectrum. k The crest of the wave, is the Wiener filter of the boundary in n+1 iterations.

[0133] (7) Similarly, in order to solve the minimum The updated solution for the center angular frequency is transferred to the frequency domain as follows:

[0134]

[0135] In the formula, is the current IMF center angular frequency.

[0136] (8) The iterative formula for the center angular frequency is as follows:

[0137]

[0138] (9) Update the Lagrange multiplier according to the following formula:

[0139]

[0140] Where τ is the noise tolerance coefficient. When there is strong noise in the signal, τ can be set to 0 to achieve the effect of filtering noise.

[0141] (10) Set the convergence criterion and stop the iteration when the alternating iteration process satisfies formula (1.22):

[0142]

[0143] In the formula, ε represents the convergence accuracy.

[0144] (11) The optimal modal number k is determined from the energy perspective to achieve the purpose of adaptively determining the number of decomposition layers.

[0145] For a signal f(t), convert it into a frequency domain signal F(f), and its spectrum energy expression is as follows:

[0146]

[0147] When the value of k is not appropriate, a certain frequency may be decomposed into multiple modal components, that is, when the value is not appropriate, the energy of the signal after decomposition will be reduced;

[0148] Assume that the broadband oscillation signal f(t) generates k IMF components after VMD decomposition, and the spectrum of the signal f(t) can be E total , the spectrum of each IMF component can be E k :

[0149]

[0150]

[0151] In the formula, i represents the sequence, N represents the spectrum length, and E total It represents the spectral energy of the original signal, and IMF represents the spectral energy of each IMF after the original signal is decomposed.

[0152] (12) According to the law of conservation of energy, the energy of the original signal in the frequency domain is equal to the sum of the energies of each frequency component, including:

[0153]

[0154] Where P is the number of IMFs after signal decomposition.

[0155] (13) The energy loss in the signal decomposition process is used to measure the mode number after VMD decomposition. The relationship between the correlation coefficient and the correlation is shown in Table 1. The expression of energy loss is:

[0156]

[0157] When the k value increases, η gradually decreases. When the η value is close to 0, the k value is the adaptive optimal mode number.

[0158] Because a broadband oscillation signal may have multiple oscillation frequency components, the VMD algorithm itself has the problem that the modal number k is difficult to determine. When the k value is large or small, there will be corresponding problems. Therefore, the present invention determines the optimal modal number k from the energy perspective to achieve the purpose of adaptively determining the decomposition modal number of the IMF.

[0159] 4.FastICA denoising

[0160] (1) FastICA further extracts independent components of the signal based on VMD decomposition, and identifies different source signals by maximizing the non-Gaussianity of the signal. The FastICA algorithm requires that each weight vector be orthogonal to each other to ensure that the separated components are independent; when the updated weight vector change is lower than the set threshold or reaches the maximum number of iterations, it is considered to have converged, and the current weight is the direction of the independent component. Since noise components often have high Gaussianity, FastICA can effectively distinguish noise from target signals. Each modal signal obtained by VMD decomposition is centered and whitened, and the centralization processing formula is as follows:

[0161] X centered =XE[X](1.28)

[0162] Where X = [u1,u2,…,u k ], and then whiten it:

[0163]

[0164] Where E and D are the eigenvector and eigenvalue matrices of the covariance matrix.

[0165] (2) Iteratively update the weight matrix and initialize the random weight vector w k , the update formula is as follows:

[0166]

[0167] Among them, g is a nonlinear activation function.

[0168] (3) w k Normalize to ensure its length is 1:

[0169]

[0170] (4) For each w k Orthogonalization is performed to ensure that the newly obtained independent components are orthogonal to the previously obtained independent components. The orthogonalization formula is as follows:

[0171]

[0172] (5) Check the weight vector w before and after the update k Whether the change is less than the threshold, the dot product of the weight vector is used as the convergence criterion:

[0173]

[0174] (6) When all independent components converge, calculate the independent component matrix S = WXwhitened .

[0175] Through the above steps, the FastICA algorithm can effectively separate independent components from the observed data, thereby achieving the goal of independent component analysis. k (t) Perform FFT spectrum analysis to obtain the frequency information (frequency, amplitude) of the oscillation.

[0176] The adaptive VMD algorithm sets appropriate decomposition parameters according to the characteristics of the input signal. This step will adaptively determine the parameters by analyzing the signal spectrum characteristics, so that the decomposed mode has a clear physical meaning. After obtaining the appropriate parameters, the VMD algorithm is used to decompose the signal into multiple modes. VMD decomposes the signal into several narrowband eigenmodes through iterative optimization methods to ensure that each mode has a strong band limit, thereby achieving frequency band separation of complex signals. The modes decomposed by VMD may contain some useless or noise modes. Therefore, the effective modes containing the main information are selected through the energy distribution characteristics, and the irrelevant noise modes are removed, and the key modes are retained for subsequent processing. The FastICA algorithm is applied to the screened effective mode set for independent component analysis. FastICA processes each mode in the signal by maximizing the non-Gaussian method to obtain components with independent characteristics. It can enhance the independence of the characteristic components of the signal, which is conducive to further feature extraction and analysis. For each independent component, it is input into FFT for frequency domain analysis. FFT converts the time domain signal into a frequency domain signal and calculates the frequency and amplitude of the independent component. VMD-FastICA-FFT monitoring flow chart is as follows Figure 4 shown.

[0177] 5. Experimental verification

[0178] In order to prove the superiority and feasibility of the present invention, a wind farm model consisting of 6 wind turbines was established on the simulation platform MATLAB. Each wind turbine was connected to the 25kV distribution system through a corresponding transformer and output power to the 120kV grid through a 30km 25kV feeder. The simplified model is shown in Figure 5 shown.

[0179] Figure 5 The model shown is run in discrete mode with a sampling time of 1e -5 s, the running time is 0.2s, and the voltage waveform of wide-band oscillation 0.02-0.06s (a total of 12000 points) is collected. Then the compressed sensing theory is applied to the running data, and the Gaussian random matrix is ​​used for compression sampling. Finally, the compressed sampled data is reconstructed according to the OMP algorithm.

[0180] Figure 6The dotted line in the middle is the compressed and reconstructed signal, and the solid line is the original signal. The reconstructed signal basically restores the basic shape of the original signal, and the reconstruction error is 0.1263.

[0181] like Figure 7 ,According to FFT analysis, in addition to the fundamental frequency, the system has two main oscillation components, which are 149Hz and 199Hz.

[0182] The reconstructed data is subjected to adaptive VMD decomposition based on minimization of energy loss, and then denoised by FastICA. The oscillation frequency band information is obtained based on the IMF obtained by FFT calculation decomposition. The identification results are as follows: Figure 8 shown.

[0183] pass Figure 7 and Fig. 9 By comparison, it can be seen that through compressed sampling reconstruction, adaptive VMD decomposition and FastICA signal denoising, the oscillation information in the original signal can be obtained and a large amount of noise signals can be removed, which shows the accuracy and effectiveness of this method.

Claims

1. A method for identifying broadband oscillation characteristics of new energy access to an AC power grid, characterized in that: Collect real-time current and voltage signals from the synchronous vector measurement unit (PMU) in the power grid and perform data preprocessing; compressively sample the preprocessed signals using compressed sensing (CS) technology; The orthogonal matching pursuit (OMP) algorithm is used to reconstruct the original signal, and the basis vectors most relevant to the current residual are gradually selected to gradually construct a sparse representation of the signal; the adaptive variational mode decomposition (VMD) is used to decompose the reconstructed signal to decompose the input signal into multiple sub-signals with specific center frequencies and narrow bandwidths. Through iterative optimization, accurate separation of different frequency components is achieved to obtain a series of modal functions. By analyzing these modal functions, features related to broadband oscillations are extracted, including oscillation frequency, amplitude, and phase information; each mode obtained by VMD decomposition is then subjected to fast independent component analysis (FastICA) to extract independent components; finally, the fast Fourier transform (FFT) is used to identify the frequency and amplitude of the oscillation from the extracted independent components, and oscillation modes within different frequency ranges are detected.

2. A method for identifying broadband oscillation characteristics of new energy access to an AC power grid according to claim 1, characterized in that: The measurement matrix Φ in the compressed sensing CS technology adopts a Gaussian matrix.

3. The method for identifying broadband oscillation characteristics of a new energy source connected to an AC power grid according to claim 1, characterized in that: The adaptive variational mode decomposition (VMD) is an adaptive VMD algorithm based on energy loss. In order to enable the algorithm to adaptively decompose the signal, the decomposition process is as follows: (1) For each modal function u k The analytical signal of (t) is Hilbert transformed, and finally its one-sided spectrum can be obtained: (2) The estimated center frequency of each mode is e -jωt As a reference, the corresponding modal frequency is modulated to the corresponding baseband: Among them, e -jωt is the phasor description of the center frequency on the complex plane, and ω is the center frequency. (3) A multimodal oscillation signal f(t) is decomposed into k bandwidth-limited IMFs. The constrained variational model in the VMD decomposition process is constructed with the bandwidth and estimated minimum value of each component as the target: Where K is the number of modes to be decomposed; u k represents the kth IMF component after signal decomposition, represents the kth IMF central angular frequency; To find the partial derivative, f(t) represents the original signal and δ(t) represents the impulse function. (4) To solve the constrained variational model of equation (1.11), the constrained variational model is transformed into an unconstrained variational problem through the augmented Lagrangian function, and the expression of the augmented Lagrangian function is obtained as follows: Where α is a quadratic penalty factor used to ensure the reconstruction accuracy of the signal under noise conditions; λ(t) is a Lagrange multiplier used to ensure the most stringent constraints. (5) The Lagrangian function points of formula (1.12) are calculated alternately and iteratively by the alternating direction multiplier ADMM algorithm, that is, by iteratively updating and Find the "saddle point" of the augmented Lagrangian expression to obtain the optimal solution of the constrained variational model. It can be calculated by the following formula: (6) According to Plancherel Fourier isometry transformation, The iterative update formula of is transformed into the frequency domain, and the exponential term can be eliminated. The expression is: Where X is u k is the total possible set of , ω is the random frequency. Now replace the first term ω with ω-ω k Replace, since the frequency band is shifted when the bandwidth of the sub-signal is obtained in (1.15), it is now restored to the original frequency band, and the formula is as follows: Then convert the above formula (1.16) into the form of non-negative frequency interval integral: Expand the above formula (1.17) into a functional and find its minimum value. The solution to the quadratic optimization problem is as follows: In the formula, the number of VMD decompositions K is determined starting from the spectrum. The intrinsic mode function is regarded as a compact structure around the center frequency ω from the spectrum. k The crest of the wave, is the Wiener filter of the boundary in n+1 iterations; (7) Similarly, in order to solve the minimum The updated solution of the mid-corner frequency is transferred to the frequency domain as follows: In the formula, is the current IMF center angular frequency. (8) The iterative formula for the center angular frequency is as follows: (9) Update the Lagrange multiplier according to the following formula: Where τ is the noise tolerance coefficient. When there is strong noise in the signal, τ can be set to 0 to achieve the effect of filtering noise. (10) Set the convergence criterion and stop the iteration when the alternating iteration process satisfies formula (1.22): In the formula, ε represents the convergence accuracy; (11) The optimal modal number k is determined from the energy perspective to achieve the purpose of adaptively determining the number of decomposition layers. For a signal f(t), convert it into a frequency domain signal F(f), and its spectrum energy expression is as follows: When the value of k is not appropriate, a certain frequency may be decomposed into multiple modal components, that is, when the value is not appropriate, the energy of the signal after decomposition will be reduced; Assume that the broadband oscillation signal f(t) generates k IMF components after VMD decomposition, and the spectrum of the signal f(t) can be E total , the spectrum of each IMF component can be E k : In the formula, i represents the sequence, N represents the spectrum length, and E total It represents the spectral energy of the original signal, and IMF represents the spectral energy of each IMF after the original signal is decomposed. (12) According to the law of conservation of energy, the energy of the original signal in the frequency domain is equal to the sum of the energies of each frequency component, including: Where P is the number of IMFs after signal decomposition. (13) The energy loss in the signal decomposition process is used to measure the mode number after VMD decomposition. The relationship between the correlation coefficient and the correlation is shown in Table 1. The expression of energy loss is: When the k value increases, η gradually decreases. When the η value is close to 0, the k value is the adaptive optimal mode number.

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