A broadband oscillation signal parameter identification method based on CEEMDAN-ESPRIT algorithm

Abstract

A method for identifying parameters of broadband oscillation signals based on the CEEMDAN-ESPRIT algorithm belongs to the field of broadband oscillation parameter identification technology in novel power systems. First, the CEEMDAN algorithm is used to denoise and reconstruct the noisy broadband oscillation signal, obtaining the reconstructed broadband oscillation waveform. Second, the ESPRIT algorithm is used to identify the frequency and amplitude of the reconstructed broadband oscillation waveform. The effectiveness of the method proposed in this invention is verified using the ADPSS platform, demonstrating that this invention can effectively solve the problem of parameter identification of noisy broadband oscillation signals, opening a new path for the accurate identification of broadband electromagnetic oscillation mode parameters in novel power systems, and effectively obtaining the core parameters such as the oscillation frequency and amplitude of each mode signal.

Description

Technical Field

[0001] This invention belongs to the field of novel power system broadband oscillation parameter identification technology, and in particular relates to a broadband oscillation signal parameter identification method based on the CEEMDAN-ESPRIT algorithm. Background Technology

[0002] With the deepening construction of high-voltage and high-efficiency power systems, the inertia of the original power systems is gradually decreasing, making broadband oscillations in the power system more frequent. Data shows that in 2013, a subsynchronous / supersynchronous oscillation event with a frequency of 6 and 94 Hz coupled occurred in Guyuan County, Zhangjiakou City, Hebei Province, with the oscillation repeating more than 100 times, causing more than 1,000 wind turbine generators to disconnect from the grid. In 2015, a subsynchronous / supersynchronous oscillation accident with a frequency of 34 and 66 Hz coupled occurred in Hami Prefecture, Xinjiang Uygur Autonomous Region, causing three 660MW thermal power units to trip and shut down. From these two typical accidents, it can be seen that the occurrence of subsynchronous / supersynchronous oscillations will cause abnormal fluctuations in the grid frequency, posing a great threat to the safety and stability of grid operation, and causing significant direct and indirect economic losses to the local area. Therefore, reliable broadband oscillation parameter identification technology is urgently needed.

[0003] However, based on existing research findings, current research on parameter identification for broadband oscillations faces the following problems: 1. Given that the broadband oscillation signals to be identified often contain noise, it is necessary to perform necessary noise reduction and reconstruction on the noisy broadband oscillation signals before conducting formal parameter identification; 2. Existing literature on broadband oscillation parameter identification mainly focuses on the low-frequency band and subsynchronous frequency band, with little mention of oscillation parameter identification for higher frequency bands. Therefore, it is necessary to conduct research on the problem of oscillation parameter identification for higher frequency bands.

[0004] Therefore, existing technologies urgently need a new solution to address the aforementioned problems. Summary of the Invention

[0005] The technical problem this invention aims to solve is to provide a method for identifying parameters of broadband oscillation signals based on the CEEMDAN-ESPRIT algorithm. This method utilizes the CEEMDAN (Complete Ensemble Empirical Mode Decomposition) algorithm to perform denoising and reconstruction of noisy broadband oscillation signals, followed by the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm to complete signal reconstruction and parameter identification. The CEEMDAN-ESPRIT algorithm is designed to pave a new path for the accurate identification of broadband electromagnetic oscillation mode parameters in novel power systems, effectively obtaining core parameters such as the oscillation frequency and amplitude of each mode signal.

[0006] A method for identifying parameters of a broadband oscillation signal based on the CEEMDAN-ESPRIT algorithm includes the following steps, which are performed sequentially:

[0007] Step 1: Add white noise to the original broadband oscillation signal, and use the Empirical Mode Decomposition (EMD) algorithm to perform empirical mode decomposition on the noisy signal to obtain the reconstructed signal;

[0008] Step 2: Use the ESPRIT algorithm to identify the reconstructed signal, obtain the oscillation frequency, amplitude, and phase parameter information of each mode signal, and complete the parameter identification of the broadband oscillation signal.

[0009] The original wideband oscillation signal X (t), with standard deviation as α White noise n After (t), the signal X n The expression for (t) is:

[0010] (1)

[0011] The EMD method is used to decompose equation (1) and calculate the average value of the obtained components to obtain several IMFs (Intrinsic Mode Functions):

[0012] (2)

[0013] Subtracting equation (2) from the first term in equation (1) yields the residual components:

[0014] (3)

[0015] The signal is further decomposed using the EMD method to obtain the second-order IMF components:

[0016] (4)

[0017] In the formula, EMD(·) represents the first decomposition obtained after EMD method. m The second-order IMF component has the following residuals:

[0018] (5)

[0019] No. p The residuals of the stage and the ( p The relationship between the +1) order components is:

[0020] (6)

[0021] In the formula, IMF p+1 ( t ) is the ( p +1) IMF components, repeating the operation of formula (6) until the residual components are obtained. R p ( t The criterion formula is: (The convergence continues until the convergence is achieved.)

[0022] (7)

[0023] In the formula, T For signal X ( t ) length, SD p It is numerically equal to 0.2.

[0024] At this point, the original broadband oscillation signal X ( t Decomposed into using the CEEMDAN method p One IMF component and one residual component R p ( t ).

[0025] The ESPRIT algorithm identifies the reconstructed signal using the following method:

[0026] The reconstructed signal is preprocessed to obtain the processed measurement data sequence. x 0, x 1, ..., x N-1 This forms the Hankel matrix. X :

[0027] (8)

[0028] In the formula, L, M, and N satisfy the relationship M + L - 1 = N;

[0029] For the Hankel matrix X Perform singular value decomposition to obtain the signal subspace. V s and noise subspace V n :

[0030] (9)

[0031] In the formula, V H yes V The conjugate transpose; ∑ is the matrix X A diagonal matrix consisting of singular values ​​arranged from highest to lowest; U S Let U be the left singular vector matrix of the signal subspace. N Let ε be the left singular vector matrix of the noise subspace. S Let be a singular value diagonal matrix in the signal subspace.

[0032] For signal subspace V s Construct two dimension-reduced subspaces: remove the first row to obtain V 1. Obtain by removing the tail line. V 2; There exists a unique invertible matrix in each of the two subspaces. T , making V 1 = V 2· T For the signal reconstructed by CEEMDAN U Using the same dimensionality reduction operation, the first row is removed to obtain... U 1. Obtain by removing the tail line. U 2. The two satisfy the following relationship:

[0033] (10)

[0034] In the formula, Ψ , U 1. U The quantitative relationship between 2 satisfies:

[0035] (11)

[0036] Ψ It is a transformation matrix constructed from the dimension-reduced signal subspace matrix;

[0037] For equation (11), the eigenvalues ​​are obtained, and for each modal component...f p The estimation is expressed as follows:

[0038] (12)

[0039] f p To estimate the frequency of each periodic component in the signal, λ p To obtain the eigenvalues ​​of Ψ, T s The sampling period.

[0040] get f p Afterwards, for those with N The process of calculating the amplitude of each mode for a signal with 1 sampling point is as follows:

[0041] (13)

[0042] In the formula, λ The Vandermonde matrix is ​​the matrix of eigenvalues. c The matrix obtained by solving the modal components using the least squares method is... α p For amplitude, φ p For phase.

[0043] Through the above design scheme, the present invention can bring the following beneficial effects: a method for identifying parameters of broadband oscillation signals based on the CEEMDAN-ESPRIT algorithm, firstly, using the CEEMDAN algorithm to complete the denoising and reconstruction of the noisy broadband oscillation signal to obtain the reconstructed broadband oscillation waveform; secondly, using the ESPRIT algorithm to identify the frequency and amplitude of the reconstructed broadband oscillation signal waveform; by using the ADPSS platform to verify the effectiveness of the method proposed in this invention, it is proved that the present invention can effectively solve the problem of parameter identification of noisy broadband oscillation signals. Attached Figure Description

[0044] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0045] Figure 1 The diagram shows the ideal signal and the signal after adding Gaussian white noise in a specific embodiment of the present invention, where a is the ideal signal and b is the signal after adding Gaussian white noise.

[0046] Figure 2 This is a schematic diagram comparing the ideal signal and the reconstructed signal in a specific embodiment of the present invention.

[0047] Figure 3This is a schematic diagram comparing the reconstructed signal and the fitted signal in a specific embodiment of the present invention.

[0048] Figure 4 This is a schematic diagram comparing the signal after decomposition and reconstruction using the VMD algorithm with the ideal signal in a specific embodiment of the present invention.

[0049] Figure 5 This is a schematic diagram comparing the signal after decomposition and reconstruction using the IVMD algorithm with the ideal signal in a specific embodiment of the present invention.

[0050] Figure 6 This is a schematic diagram of the ADPSS example wiring in a specific embodiment of the present invention.

[0051] Figure 7 This is a schematic diagram of the phase A voltage waveform of bus Bus_1-2197 in a specific embodiment of the present invention.

[0052] Figure 8 This is a schematic diagram of the FFT spectrum analysis results of a specific embodiment of the present invention.

[0053] Figure 9 This is a schematic diagram of the phase A voltage waveform of the noisy bus Bus_1-2197 according to a specific embodiment of the present invention.

[0054] Figure 10 This is a comparison diagram of the ideal signal and the reconstructed signal in a specific embodiment of the present invention.

[0055] Figure 11 This is a comparison diagram of the reconstructed signal and the fitted signal according to a specific embodiment of the present invention.

[0056] Figure 12 This is a schematic diagram of the flowchart of a broadband oscillation signal parameter identification method based on the CEEMDAN-ESPRIT algorithm of the present invention. Detailed Implementation

[0057] A method for identifying parameters of broadband oscillation signals based on the CEEMDAN-ESPRIT algorithm, such as... Figures 1-12 As shown,

[0058] First, the CEEMDAN algorithm is used to denoise and reconstruct a noisy broadband oscillating signal. Then, the ESPRIT algorithm is used to identify the frequency and amplitude parameters of the reconstructed broadband oscillating signal. Finally, the method proposed in this invention is verified using the simulation software ADPSS.

[0059] The decomposition steps of CEEMDAN are as follows:

[0060] (1) Let the original signal be X (t), with standard deviation as α White noisen (t), then the signal after adding white noise at this time X n The expression for (t) is shown below:

[0061] (1)

[0062] (2) At this point, the EMD method is used to decompose equation (1) and calculate the average value of the obtained components. Several IMFs can be obtained as shown in the following equation:

[0063] (2)

[0064] (3) Subtracting equation (2) from the first term in equation (1) yields the following residual components:

[0065] (3)

[0066] (4) The EMD method decomposes the signal in depth, and the second-order IMF component is obtained as shown in the following formula:

[0067] (4)

[0068] In equation (4), EMD(·) represents the first digit obtained after decomposition using the EMD method. m The residual expression for the second-order IMF component is shown in the following equation:

[0069] (5)

[0070] (5) No. p The residuals of the stage and the ( p The following relationship exists between the +1) order components:

[0071] (6)

[0072] In equation (6), IMF p+1 ( t ) is the ( p +1) IMF components, repeating the operation of formula (6) until the residual components are obtained. R p ( t The convergence occurs until the desired outcome is achieved, and the relevant criteria are shown in the following formula:

[0073] (7)

[0074] In equation (7), T For signal X ( t ) length, SDp Numerically, it is usually equal to 0.2.

[0075] In summary, the signals to be studied X ( t It can be decomposed into the following using the CEEMDAN method: p One IMF component and one residual component R p ( t )

[0076] 2. ESPRIT Algorithm

[0077] In the field of signal parameter estimation, ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) demonstrates superior high-resolution analysis performance in numerous scenarios due to its rotational invariance principle. Numerous studies have confirmed its application value; for example, researchers have successfully achieved accurate determination of harmonic and interharmonic parameters using TLS-ESPRIT technology; others have used the ESPRIT algorithm to effectively extract key parameters such as frequency and attenuation factor of multi-component attenuated sinusoidal signals under Gaussian colored noise environments. Given ESPRIT's powerful waveform parameter analysis capabilities, this invention integrates it with the CEEMDAN algorithm to construct the CEEMDAN-ESPRIT algorithm, aiming to pave a new path for the accurate identification of broadband electromagnetic oscillation mode parameters in new power systems. It can effectively obtain core parameters such as oscillation frequency and amplitude of each mode signal. Compared to traditional parameter identification methods such as Prony and Hilbert, the unique feature of the ESPRIT algorithm lies in its spectral peak search strategy, which eliminates the need to process the entire time-domain signal. This characteristic gives it significant advantages, including high tolerance to noise interference, low computational complexity, and relaxed parameter setting requirements. Its operation process is as follows:

[0078] (1) The input signal is preprocessed to obtain the processed measurement data sequence. x 0, x 1, ..., x N-1 The Hankel matrix is ​​formed according to the formula. X As shown in the following formula:

[0079] (8)

[0080] In equation (8), L, M, and N satisfy the condition M + L - 1 = N.

[0081] (2) In forming the Hankel matrix X Then, its signal subspace is obtained by performing singular value decomposition on it.V s and noise subspace V n As shown in the following formula:

[0082] (9)

[0083] In equation (9), V H yes V The conjugate transpose; ∑ is the matrix X A diagonal matrix consisting of singular values ​​arranged from highest to lowest.

[0084] (3) For the signal space V s Two reduced-dimensional subspaces can be constructed by removing the first and last rows: V 1 (remove the first line) and V 2 (Removing the trailing line). Theoretically, these two subspaces have a strict linear transformation relationship, that is, there exists a unique invertible matrix. T , making V 1 = V 2· T For the original signal U Using the same dimensionality reduction operation, we obtain U 1 (remove the first line) and U 2 (removing trailing lines), the two satisfy the following relationship:

[0085] (10)

[0086] In equation (10), Ψ , U 1. U The quantitative relationship between 2 and 2 satisfies the following formula:

[0087] (11)

[0088] (4) According to equation (11), obtain its eigenvalues, and then for each modal component... f p The estimation is performed, and the expression used for the estimation is shown in the following formula:

[0089] (12)

[0090] (5) Obtain the result using equation (12) f p Afterwards, for those with N The amplitude calculation process for each mode of the signal at each sampling point is shown in the following formula:

[0091] (13)

[0092] In the formula, λ The Vandermonde matrix is ​​the matrix of eigenvalues. c The matrix obtained by solving the modal components using the least squares method is... α p For amplitude, φ p For phase.

[0093] After the above ESPRIT identification process, the modal parameter information such as oscillation frequency, amplitude, and phase of each modal signal can be obtained, thus completing the identification of broadband oscillation multimode.

[0094] Simulation verification:

[0095] This invention patent primarily focuses on the supersynchronous oscillation band and the mid-to-high frequency oscillation band in wideband oscillation, and the self-synthesized signal model is shown in the following equation:

[0096] (14)

[0097] In equation (14), A Represented as amplitude, f Represented as frequency, α Represented as the attenuation factor, φ Represented as phase, sup Represented as supersynchronous components, med Represented as the intermediate frequency component, this invention mainly focuses on the supersynchronous frequency band and intermediate frequency band in broadband oscillations, and self-synthesizes their ideal signal model as shown in the following equation:

[0098] (15)

[0099] This broadband oscillation ideal signal contains two modes, and the frequencies and amplitudes of the two modes are shown in Table 1 below:

[0100] Table 1. Frequency and amplitude of each mode of an ideal signal

[0101] Modal Frequency (Hz) Amplitude 1 180 100 2 82 40

[0102] To ensure the authenticity of the signal under study, the amplitudes and frequencies of the two modes differ significantly, and Gaussian white noise with a signal-to-noise ratio of 20dB is added to the ideal signal in equation (15). The comparison effect between the ideal signal and the noisy signal is as follows: Figure 1 As shown.

[0103] After obtaining the noisy signal, the CEEMDAN method is used to denoise and reconstruct the signal. The results of comparing the reconstructed signal with the ideal signal are shown below. Figure 2 As shown. From Figure 2It is easy to see that the reconstructed signal is basically consistent with the ideal signal, proving that the noise reduction effect is good, and further parameter identification can be carried out.

[0104] Then, the ESPRIT algorithm was used to identify the frequency and amplitude of the reconstructed signal. The comparison between the reconstructed signal and the fitted signal, and the identification results are as follows: Figure 3 As shown in Table 2:

[0105] Table 2. Frequency and amplitude identification results for each mode

[0106] Modal Frequency (Hz) Relative error (%) Amplitude (pu) Relative error (%) 1 180.0083 0.005 99.49 0.5 2 82.0017 0.002 39.13 2.2

[0107] The results above clearly show that the identification results of the ESPRIT algorithm are basically close to the frequency and amplitude values ​​in Table 1, which preliminarily proves the effectiveness of this invention patent. To further verify the effectiveness and superiority of the method proposed in this invention patent, VMD-Prony and IVMD-Prony methods were selected for comparative verification.

[0108] The figure below shows the waveform after noise reduction and reconstruction using the VMD method. Figure 4 It is readily apparent that the waveform reconstructed by the VMD method is almost entirely inconsistent with the ideal signal, let alone the parameter identification using the Prony algorithm. Figure 5 It is readily apparent that although the reconstruction effect of the IVMD algorithm is somewhat improved compared to the VMD algorithm, from the perspective of amplitude range and other aspects, the reconstruction effect of the IVMD algorithm is obviously inferior to the method proposed in this invention patent. Therefore, there is no need to use the Prony algorithm for further parameter identification.

[0109] In summary, the method proposed in this invention can effectively reduce noise and reconstruct noisy oscillation signals in higher frequency bands of broadband oscillations, and can accurately identify the corresponding frequency and amplitude.

[0110] Specifically, to further verify the method proposed in this invention patent, simulation verification of the method was conducted using a hybrid AC / DC circuit example on the ADPSS platform independently developed by the China Electric Power Research Institute. The simplified diagram of the example and some parameters are shown below. Figure 6 As shown in Table 3.

[0111] Table 3. Partial parameters of the example

[0112] parameter numerical values Short-circuit loss of a three-phase two-winding ordinary transformer 398.9kW No-load loss of a three-phase two-winding ordinary transformer 87.6kW Three-phase two-winding ordinary transformer rated operating frequency 50Hz RLC resistor R 0.9152Ω RLC inductor L 0.06H Three-phase time-controlled reference capacity 100MVA Three-phase time-controlled reference voltage 230kV

[0113] After generating a wideband oscillation, the instantaneous value of phase A voltage of bus Bus_1-2197 is arbitrarily selected, and the signal waveform is as follows: Figure 7 As shown.

[0114] Using the FFT method, the frequency and amplitude of the waveform were identified. The identification results show that the oscillation frequency of the waveform is 57Hz, which belongs to supersynchronous oscillation, and the amplitude is 0.4178. The FFT spectrum analysis results are as follows. Figure 8 As shown:

[0115] exist Figure 7 The waveform of the noisy signal obtained by adding Gaussian white noise with a signal-to-noise ratio of 5dB is as follows. Figure 9 As shown:

[0116] Then, using the method proposed in this invention, the CEEMDAN method is used to... Figure 9 The noisy waveform in the image is denoised and reconstructed, and the reconstructed signal is then compared with... Figure 7 The comparison results are as follows Figure 10 As shown:

[0117] from Figure 10 It can be observed that the signal waveform after denoising and reconstruction using the CEEMDAN method is basically consistent with the ideal signal waveform, proving that the denoising and reconstruction effect is good and can be used for further parameter identification. Subsequently, the ESPRIT method was used to perform parameter identification on the reconstructed signal waveform. The comparison between the reconstructed waveform and the fitted waveform, as well as the parameter identification results, are as follows. Figure 11 As shown in Table 4.

[0118] Table 4. Frequency and amplitude identification results

[0119] Modal Frequency (Hz) Relative error (%) Amplitude (pu) Relative error (%) 1 57.3936 0.7 0.4111 1.6

[0120] Based on the above results, the method of the present invention can effectively reduce noise and reconstruct noisy simulation signal waveforms, accurately fit the reconstructed waveform, and accurately identify the frequency and amplitude of the reconstructed waveform.

Claims

1. A method for identifying parameters of a broadband oscillation signal based on the CEEMDAN-ESPRIT algorithm, characterized in that: Includes the following steps, And the following steps are performed in sequence: Step 1: Add white noise to the original broadband oscillation signal, and use the Empirical Mode Decomposition (EMD) algorithm to perform empirical mode decomposition on the noisy signal to obtain the reconstructed signal; Step 2: Use the ESPRIT algorithm to identify the reconstructed signal, obtain the oscillation frequency, amplitude, and phase parameter information of each mode signal, and complete the parameter identification of the broadband oscillation signal; The original wideband oscillation signal X (t), with standard deviation as α White noise n After (t), the signal X n The expression for (t) is: （1） Using the EMD method, equation (1) is decomposed, and the average value of the obtained components is calculated to obtain several IMF eigenmode functions: （2） In the formula, IMF i ( t ) represents the i-th IMF component. Subtracting equation (2) from the first term in equation (1) yields the residual components: （3） The signal is further decomposed using the EMD method to obtain the second-order IMF components: （4） In the formula, EMD(·) represents the first decomposition obtained after EMD method. m The second-order IMF component has the following residuals: （5） No. p The residuals of the stage and the ( p The relationship between the +1) order components is: （6） In the formula, IMF p+1 ( t ) is the ( p +1) IMF components, repeating the operation of formula (6) until the residual components are obtained. R p ( t The criterion formula is: (The convergence continues until the convergence is achieved.) （7） In the formula, T For signal X ( t ) length, SD p Numerically equal to 0.2; At this point, the original broadband oscillation signal X ( t Decomposed into using the CEEMDAN method p One IMF component and one residual component R p ( t ).

2. The method for identifying parameters of a broadband oscillation signal based on the CEEMDAN-ESPRIT algorithm according to claim 1, characterized in that: The ESPRIT algorithm identifies the reconstructed signal using the following method: The reconstructed signal is preprocessed to obtain the processed measurement data sequence. x 0, x 1, ..., x N-1 This forms the Hankel matrix. X : （8） In the formula, L, M, and N satisfy the relationship M + L - 1 = N; For the Hankel matrix X Perform singular value decomposition to obtain the signal subspace. V s and noise subspace V n : （9） In the formula, V H yes V The conjugate transpose of; ∑ is a matrix X A diagonal matrix consisting of singular values ​​arranged from highest to lowest; U S Let U be the left singular vector matrix of the signal subspace. N Let ε be the left singular vector matrix of the noise subspace. S Let be a singular value diagonal matrix in the signal subspace; For signal subspace V s Construct two dimension-reduced subspaces: remove the first row to obtain V 1 Remove tails to obtain V 2 The two subspaces contain a unique invertible matrix. T , making V 1 = V 2 · T For the signal U reconstructed by CEEMDAN, the same dimensionality reduction operation is applied: the first row is removed to obtain U1, and the last row is removed to obtain U2. The two satisfy the following relationship: （10） In the formula, Ψ , U 1. U The quantitative relationship between 2 satisfies: （11） Ψ It is a transformation matrix constructed from the dimension-reduced signal subspace matrix; For equation (11), the eigenvalues ​​are obtained, and for each modal component... f p The estimation is expressed as follows: （12） f p To estimate the frequency of each periodic component in the signal, λ p To obtain the eigenvalues ​​of Ψ, T s The sampling period; get f p Afterwards, for those with N The process of calculating the amplitude of each mode for a signal with 1 sampling point is as follows: （13） In the formula, λ The Vandermonde matrix is ​​the matrix of eigenvalues. c The matrix obtained by solving the modal components using the least squares method is... α p For amplitude, φ p For phase.

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