Wind farm subsynchronous oscillation source positioning method based on multivariate complex modulation model decomposition

Abstract

The application discloses a wind farm subsynchronous oscillation source positioning method based on a multi-element complex modulation model decomposition, and belongs to the technical field of power system subsynchronous oscillation monitoring and tracing. The method firstly converts three-phase voltage and current instantaneous values collected by a PMU from an abc coordinate system to an xy coordinate system, weakens the interference of a power frequency component on a weak subsynchronous mode, and reduces a fundamental error; then constructs a multi-element measurement matrix, and adopts MCMMD to adaptively decouple a multi-channel coupled oscillation signal, so as to improve mode aliasing and an end effect; the method selects effective subsynchronous modes through FFT frequency spectrum analysis combined with a subsynchronous frequency threshold value; finally, the extracted subsynchronous components are input into a transient energy flow model, and positioning and identification of the subsynchronous oscillation source are completed according to a positioning criterion. The application can realize joint decomposition of a multi-channel oscillation signal, has small interference from parameter setting, and can greatly improve the positioning precision of a power grid subsynchronous oscillation source.

Description

Technical Field

[0001] This invention belongs to the field of power system subsynchronous oscillation monitoring and tracing technology, and in particular relates to a method for locating the subsynchronous oscillation source of a wind farm based on multivariate complex modulation model decomposition. Background Technology

[0002] With the increasing penetration of renewable energy in the power system, a large number of power electronic devices have been widely connected and integrated into the power grid. These devices exhibit multi-timescale characteristics, and their complex interaction with the power grid exacerbates the subsynchronous oscillation problem. Recent oscillation incidents show that these oscillations have exhibited a wide-area propagation characteristic, spreading from local areas to the global scale. This undoubtedly poses a significant challenge to the source analysis of incidents and the effective suppression of oscillations. Therefore, timely and accurate location of the subsynchronous oscillation source in the power system can provide an important basis for the scientific formulation of suppression strategies and is of paramount importance for ensuring the safe and stable operation of the power system. Common decomposition methods used for subsynchronous oscillation source location include Empirical Mode Decomposition (EMD) and Multivariate Variational Mode Decomposition (MVMD). EMD can effectively decompose subsynchronous signals, but it is a single-channel decomposition method and does not consider the correlation between different channels, leading to unstable extraction of subsynchronous oscillation components. MVMD can achieve multi-channel decomposition of subsynchronous signals, but it has high requirements for parameter settings; unreasonable parameter settings can lead to inaccurate decomposition results. The Multivariate Complex Modulation Model Decomposition (MCMMD) method is an adaptive decomposition method for multi-channel signals, but its application in the localization of subsynchronous oscillation sources in power systems has not yet been reported.

[0003] Therefore, there is an urgent need for a new technical solution to address this problem. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition, which solves the problems of traditional subsynchronous oscillation source location, such as the inability to decompose multi-channel signals; and the fact that existing multivariate variational mode decomposition methods are greatly affected by parameter settings, which can easily lead to inaccurate decomposition results.

[0005] The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition includes the following steps, which are performed sequentially: Step S1: Measure and obtain the instantaneous values ​​of three-phase voltage and three-phase current at each node and line based on the synchronous phasor measurement device (PMU). Step S2: Convert the instantaneous values ​​of three-phase voltage and three-phase current from... abc Coordinate system transformation xy Using a coordinate system, the instantaneous values ​​of voltage and current are obtained. x shaft and y Axis component signal; Step S3: Construct a multivariate measurement matrix using the signal after coordinate system transformation, and perform signal decomposition based on the MCMMD algorithm using the multivariate complex modulation model decomposition, including: The signals of each channel of the multivariate measurement matrix are converted into analytical signal form respectively; Set the initialization parameters of the analytic signal and calculate the distribution of the analytic signal in the fractional domain. Iterate through different orders to find the one that makes The optimal order with the most concentrated energy And the frequency point with the highest amplitude at that order. The initial filter center frequency is calculated. ; The auxiliary parameters of multiple channels are iteratively updated using the alternating direction multiplier method. Based on the demodulated signal obtained by iterative updating of auxiliary parameters, the frequency increment is calculated and low-pass filtering is performed to iteratively update the frequency function of each channel; Calculate the multi-channel joint factor; Perform joint updates of multi-channel parameters; Perform convergence determination and output the results; Step S4: Perform a fast Fourier transform on the output to obtain the subsynchronous mode components; Step S5: Substitute the subsynchronous mode components into the transient energy flow model to calculate the transient energy flow, and determine whether it is a non-subsynchronous oscillation source based on the trend of the transient energy flow over time.

[0006] The instantaneous values ​​of the three-phase voltage and three-phase current are determined by abc Coordinate system transformation xy The expression for the coordinate system is: ; In the formula: and For nodes The instantaneous voltage at the corresponding location x shaft and y Axial components; and branch road instantaneous current x shaft and y Axial components; , and For nodes The instantaneous voltage at the corresponding location abc Quantity; , and branch road instantaneous current abc Quantity; This is the coordinate transformation matrix. ; In the formula: This is the synchronization angular frequency; The initial phase angle; Sampling time; At the same time, the transformation of the coordinate system will cause a transformation of the frequency: ; In the formula: for xy Frequency in a coordinate system; The base frequency is 50Hz; for abc Frequency in a coordinate system.

[0007] The multivariate measurement matrix is ​​as follows: ; In the formula: The total number of sampling points corresponds to the number of sampling times in the multivariate measurement matrix. Therefore, Also represents the first Each sampling time; For the first Current at each sampling time x Axial components; For the first Current at each sampling time y Axial components; For the first Voltage at each sampling time x Axial components; For the first Voltage at each sampling time y Axial components.

[0008] The conversion of each channel signal of the multivariate measurement matrix into analytic signals is achieved through Hilbert transform, which converts the signals into complex analytic signals. The expression for this transformation is as follows: ; In the formula: For Hilbert transform; , and These are the instantaneous amplitude, frequency function, and initial phase, respectively. For demodulated signals; It is a modulated signal; For instantaneous frequency estimation; It is a time-domain signal.

[0009] The initialization parameters include the initial values ​​of the Lagrange multipliers. Initial value of leakage factor Smoothing factor Convergence threshold ; The distribution of the signal in the fractional-order domain Represented as: ; In the formula: The rotation angle; For kernel functions; For instantaneous frequency index; The initial filter center frequency The calculation formula is: .

[0010] The auxiliary parameters include the demodulated signal, the demodulated signal, the estimated signal, the leakage factor, and the Lagrange multipliers. The iterative update of the auxiliary parameters is performed using the alternating direction multiplier method, specifically: ; ; ; ; In the formula: This represents the number of iterations. For the first Channel 1 The modulation signal of the next iteration; , The total number of channels; For the first The instantaneous frequency estimate after the next iteration; For the first Channel 1 The demodulated signal of the next iteration; For the first The original oscillation signal of the channel; For the first Channel 1 The estimated signal for the next iteration; It is the conjugate transpose; For the first Channel 1 The leakage factor of the next iteration; For the first Channel 1 Lagrange multipliers in the next iteration; It is a second-order differential operator. ; The frequency function Iterative updates are represented as: ; In the formula: It is a smoothing factor; Unit operator; For the first Channel 1 Frequency increment of the next iteration ; In the formula: It is the imaginary part; It is the real part.

[0011] The formula for the multi-channel joint factor is: ; In the formula: For the first The multichannel joint factor of a channel represents the proportion of the energy of that channel to the total energy. For the first Channel 1 The instantaneous energy of the next iteration signal is given by the formula: ; The multi-channel parameter joint update involves weighted fusion of the parameters from each channel to obtain the global common parameters for the next iteration, namely: ; In the formula: It is a multi-channel joint factor; for The instantaneous frequency matrix of each channel; for The leakage factor sequence of each channel; for A sequence of Lagrange multipliers for each channel; ; The convergence determination formula is as follows: ; In the formula: The predefined convergence threshold; If the convergence criterion is not met, then let Repeat the iterative update of auxiliary parameters until the convergence condition is met; if the convergence condition is met, output the result. The final decomposition result of each channel .

[0012] The subsynchronous mode components are selected through a set frequency threshold range and represented by a subsynchronous mode matrix: ; In the formula: , These are obtained after being filtered by frequency threshold. x The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point , These are obtained after being filtered by frequency threshold. y The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point This represents the total number of sampling points.

[0013] The formula for the transient energy flow model is: ; In the formula, For the first L Transient energy at each sampling point ; The criteria for identifying a subsynchronous oscillation source are as follows: If the value shows an upward trend over time, it indicates a continuous injection of energy into the power grid, and the sampling point is determined to be a subsynchronous oscillation source; otherwise, If the value decreases over time, it indicates that the energy is continuously absorbed, and the sampling point is determined to be a non-subsynchronous oscillation source.

[0014] Through the above design scheme, the present invention can bring the following beneficial effects: This invention proposes a multivariate complex modulation model decomposition (MCMMD) method combined with transient energy flow (TEF) to locate subsynchronous oscillation sources. First, the instantaneous values ​​of three-phase voltage and three-phase current obtained from PMU measurements at nodes and lines are transformed into coordinates... abc coordinate system transformation xy Coordinate system, compared to direct coordinates abcTraditional methods for analyzing three-phase raw signals can significantly reduce the amplitude flooding effect of power frequency components on weak subsynchronous oscillation modes, reducing errors caused by fundamental interference at the source. Next, a multivariate measurement matrix is ​​constructed for MCMMD decomposition. MCMMD is used to adaptively decouple multi-channel coupled oscillation signals, effectively improving mode aliasing and endpoint effects. Further, FFT spectrum analysis is performed on each mode after MCMMD decomposition, and subsynchronous mode components are screened using subsynchronous frequency thresholds. Fast Fourier Transform spectrum analysis is then performed on each independent mode output by MCMMD decomposition, and power frequency and supersynchronous irrelevant components are eliminated using preset subsynchronous frequency interval thresholds, accurately screening effective subsynchronous oscillation modes. Finally, the extracted subsynchronous mode components are substituted into a transient energy flow model, and the subsynchronous oscillation source is located using oscillation source localization criteria. This invention can decompose multi-channel signals, is less affected by parameter settings, and has high accuracy in locating subsynchronous oscillation sources. Attached Figure Description

[0015] Figure 1 This is a flowchart of the wind farm subsynchronous oscillation source localization method based on multivariate complex modulation model decomposition according to the present invention; Figure 2 This is a diagram of an equivalent improved four-machine eleven-node test system in an embodiment of the present invention; Figure 3 This is a waveform diagram of the A-phase current of the wind field when subsynchronous oscillation is excited and 40dB noise is added in an embodiment of the present invention; Figure 4 This is the FFT spectrum of the wind field A-phase current in an embodiment of the present invention when subsynchronous oscillation is excited and 40dB noise is added; Figure 5 The wind field subsynchronous mode component decomposition waveform and corresponding spectrum diagram are shown in the embodiment of the present invention with an additional 40dB noise in the multivariate complex modulation model decomposition method. Figure 6 This is a diagram showing the transient energy flow results when 40dB of noise is added in an embodiment of the present invention. Figure 7 This is a diagram showing the transient energy flow results when 15dB of noise is added in an embodiment of the present invention. Detailed Implementation

[0016] A method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition, such as Figure 1 As shown, the steps include the following steps, and the following steps are performed in sequence: Step S1: Measure and obtain the instantaneous values ​​of the three-phase voltage and three-phase current of the nodes and lines based on the synchronous phasor measurement unit (PMU).

[0017] Step S2: Convert the instantaneous values ​​of three-phase voltage and three-phase current from... abc Coordinate system transformation xy Coordinate system.

[0018] Based on the instantaneous values ​​of voltage and current obtained in step S1, a coordinate system transformation is performed, i.e., equation (1): (1); In the formula: and For nodes The instantaneous voltage at the corresponding location x shaft and y Axial components; and branch road instantaneous current x shaft and y Axial components; , and For nodes The instantaneous voltage at the corresponding location abc Quantity; , and branch road instantaneous current abc Quantity; The coordinate transformation matrix is ​​given by equation (2): (2); In the formula: This is the synchronization angular frequency; This is the initial phase angle.

[0019] It is worth noting that the transformation of the coordinate system will cause a transformation of the frequency, i.e., equation (3): (3); In the formula: for xy Frequency in a coordinate system; The base frequency is 50Hz; for abc Frequency in a coordinate system.

[0020] Step S3: Signal decomposition based on the Multivariate Complex Modulation Model Decomposition (MCMMD) algorithm.

[0021] Step S3-1: Obtain the multivariate measurement matrix Based on the signals processed in steps S1 and S2, a multivariate measurement matrix is ​​constructed, i.e., equation (4): (4); In the formula: The total number of sampling points corresponds to the number of sampling times in the multivariate measurement matrix. Therefore, Also represents the first Each sampling time; For the first Current at each sampling time x Axial components; For the first Current at each sampling time y Axial components; For the first Voltage at each sampling time x Axial components; For the first Voltage at each sampling time y Axial components.

[0022] Step S3-2: Convert the multivariate measurement matrix into the form of an analytical signal. The multivariate measurement matrix established based on step S3-1 X Perform a Hilbert transform on each channel signal to convert it into a complex analytic signal, i.e., equation (5): (5); In the formula: For Hilbert transform; , and These are the instantaneous amplitude, frequency function, and initial phase, respectively. For demodulated signals; It is a modulated signal; For instantaneous frequency estimation; It is a time-domain signal.

[0023] Step S3-3: Initialize parameters The initialization parameters used to reconstruct the time-domain signal include the initial values ​​of the Lagrange multipliers. λ 0, initial value of leakage factor v 0, smoothing factor μ Convergence threshold ε The distribution of the signal in the fractional domain is calculated using the fractional Fourier transform, i.e., equation (6): (6); In the formula: The rotation angle; For kernel functions; This is the instantaneous frequency index.

[0024] After calculating the signal distribution in the fractional-order domain using equation (6), it is necessary to iterate through different orders to find the distribution that makes the signal distribution in the fractional-order domain more efficient. The optimal order with the most concentrated energy And the frequency point with the highest amplitude at that order. .

[0025] From the found and Calculate the initial filter center frequency That is, equation (7): (7);

[0026] Step S3-4: Iterative update of auxiliary parameters Based on the initialization parameters obtained in step S3-3, the demodulated modulation signal, demodulated signal, estimated signal, leakage factor, and Lagrange multipliers are iteratively updated for multiple channels using the alternating direction multiplier method, i.e., equations (8) to (12): (8); (9); (10); (11); (12); In the formula: This represents the number of iterations. For the first Channel 1 The modulation signal of the next iteration; , The total number of channels; For the first The instantaneous frequency estimate after the next iteration; For the first Channel 1 The demodulated signal of the next iteration; For the first The original oscillation signal of the channel; For the first Channel 1 The estimated signal for the next iteration; It is the conjugate transpose; For the first Channel 1 The leakage factor of the next iteration; For the first Channel 1 Lagrange multipliers in the next iteration; It is a second-order differential operator. (13); Step S3-5: Frequency function iterative update Based on the demodulated signal obtained from the update iteration in steps S3-4, the frequency increment is calculated and low-pass filtered to update the frequency function of each channel, i.e., equations (14) and (15): (14); (15); In the formula: For the first Channel 1 Frequency increment of the next iteration; It is a smoothing factor; Unit operator.

[0027] Step S3-6: Calculate the multi-channel joint factor Based on the single-channel parameters updated in steps S3-4 and S3-5, the instantaneous energy ratio of each channel signal is calculated, i.e., the multi-channel joint factor, as shown in equation (16): (16); In the formula: For the first The multichannel joint factor of a channel represents the proportion of the energy of that channel to the total energy. For the first Channel 1 The instantaneous energy of the next iteration signal, i.e., equation (17): (17); Step S3-7: Joint update of multi-channel parameters The parameters of each channel are weighted and fused to obtain the global common parameters for the next iteration, i.e., equation (18): (18); In the formula: It is a multi-channel joint factor; for The instantaneous frequency matrix of each channel; for The leakage factor sequence of each channel; for A sequence of Lagrange multipliers for each channel; i.e., equation (19): (19); Step S3-8: Convergence Determination and Result Output This invention determines whether the iteration converges using a convergence criterion, namely equation (20): (20); In the formula: For a predefined convergence threshold, in this invention The value is 1×10 -6 .

[0028] If equation (20) is not satisfied, then let Return to steps S3-S4 and continue iterating; if satisfied, output. The final decomposition result of each channel .

[0029] Step S4: Fast Fourier Transform Perform a Fast Fourier Transform on all the single-mode signals obtained in step 3 to obtain the frequency of each mode. The mode of the subsynchronous frequency range is selected according to equation (21).

[0030] (twenty one); If equation (21) is satisfied, then the mode is determined to be a subsynchronous mode, and the subsynchronous mode matrix is ​​equation (22): (twenty two); In the formula: , These are obtained after being filtered by frequency threshold. x The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point , These are obtained after being filtered by frequency threshold. y The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point This represents the total number of sampling points.

[0031] Step S5: Calculate transient energy flow Substituting the subsynchronous mode component obtained in step S4 into the transient energy flow model, i.e., equation (23): (twenty three); In the formula, For the first L Transient energy at each sampling point ; The criteria for identifying a subsynchronous oscillation source are as follows: If the value shows an upward trend over time, it indicates a continuous injection of energy into the power grid, and the sampling point is determined to be a subsynchronous oscillation source; otherwise, If the value decreases over time, it indicates that the energy is continuously absorbed, and the sampling point is determined to be a non-subsynchronous oscillation source.

[0032] Example: This invention employs, as follows Figure 2The equivalent improved four-machine eleven-node test system shown is an example to verify the effectiveness and feasibility of the method proposed in this invention. The equivalent improved four-machine eleven-node test system adds a doubly fed wind farm and introduces one node to the traditional four-machine eleven-node test system. It consists of 12 nodes (as shown in 1-12) including doubly fed wind farm DFIGs (Doubly Fed Induction Generators), synchronous motors (G1-G4), transformers, and transmission lines.

[0033] The parameters of each doubly fed wind turbine in the doubly fed wind farm are shown in Table 1.

[0034]

[0035] In this invention, the proportional gain of the rotor-side converter of the doubly fed wind turbine in the doubly fed wind farm is 0.1 at the beginning. The proportional gain increases from 0.1 to 0.2 at 2 seconds, which excites subsynchronous oscillation. Figure 3 To improve the equivalent four-machine eleven-node test system when subsynchronous oscillation occurs and 40dB noise is added, the A-phase current waveform of the wind field is analyzed by FFT spectrum analysis, taking the A-phase current of 4 to 7 seconds as an example. Figure 4 To improve the equivalent four-machine eleven-node test system, the FFT spectrum of the wind farm A-phase current in the wind farm between 4 and 7 seconds was obtained when subsynchronous oscillation occurred and 40dB noise was added. By observing the spectrum, it can be determined that a subsynchronous oscillation with a frequency of 33Hz occurred in the system. Figure 5 To apply the MCMMD method to decompose the coordinate-transformed signal into subsynchronous mode components and FFT spectra of the wind farm when subsynchronous oscillations occur and 40dB of noise is added, the following steps are performed: Figure 5 It can be seen that the MCMMD method extracts a frequency of 17Hz (50Hz-33Hz) in x shaft and y The current and voltage of the shaft are subsynchronous oscillation components, and as can be seen from the corresponding FFT spectrum, the spectrum has only one peak. Figure 6 To obtain the results by substituting the subsynchronous mode components obtained from the decomposition with an added 40dB noise into the transient energy flow model, from... Figure 6 The data shows that the wind energy is continuously rising, indicating that the wind is continuously injecting energy into the system, which is identified as an oscillation source, consistent with the simulation settings. Figure 7 The transient energy flow results obtained by applying the MCMMD decomposition method combined with the transient energy flow model when an additional 15dB noise is added are derived from... Figure 7 It can be seen that the transient energy flow of the wind field is continuously upward, which is an oscillation source, consistent with the simulation settings. This verifies the effectiveness and noise resistance of the method proposed in this invention for locating subsynchronous oscillation sources.

[0036] Contents not described in detail herein are existing technologies known to those skilled in the art. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some technical features without departing from the spirit and scope of the invention to adapt to specific circumstances. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition, characterized in that: Includes the following steps, And the following steps are performed in sequence. Step S1: Measure and obtain the instantaneous values ​​of three-phase voltage and three-phase current at each node and line based on the synchronous phasor measurement device (PMU). Step S2: Convert the instantaneous values ​​of three-phase voltage and three-phase current from... abc Coordinate system transformation xy Using a coordinate system, the instantaneous values ​​of voltage and current are obtained. x shaft and y Axis component signal; Step S3: Construct a multivariate measurement matrix using the signal after coordinate system transformation, and perform signal decomposition based on the MCMMD algorithm using the multivariate complex modulation model decomposition, including: The signals of each channel of the multivariate measurement matrix are converted into analytical signal form respectively; Set the initialization parameters of the analytic signal and calculate the distribution of the analytic signal in the fractional domain. Iterate through different orders to find the one that makes The optimal order with the most concentrated energy And the frequency point with the highest amplitude at that order. The initial filter center frequency is calculated. ; The auxiliary parameters of multiple channels are iteratively updated using the alternating direction multiplier method. Based on the demodulated signal obtained by iterative updating of auxiliary parameters, the frequency increment is calculated and low-pass filtering is performed to iteratively update the frequency function of each channel; Calculate the multi-channel joint factor; Perform joint updates of multi-channel parameters; Perform convergence determination and output the results; Step S4: Perform a fast Fourier transform on the output to obtain the subsynchronous mode components; Step S5: Substitute the subsynchronous mode components into the transient energy flow model to calculate the transient energy flow, and determine whether it is a non-subsynchronous oscillation source based on the trend of the transient energy flow over time.

2. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 1, characterized in that: The instantaneous values ​​of the three-phase voltage and three-phase current are determined by abc Coordinate system transformation xy The expression for the coordinate system is: ； In the formula: and For nodes The instantaneous voltage at the corresponding location x shaft and y Axial components; and branch road instantaneous current x shaft and y Axial components; , and For nodes The instantaneous voltage at the corresponding location abc Quantity; , and branch road instantaneous current abc Quantity; This is the coordinate transformation matrix. ； In the formula: This is the synchronization angular frequency; The initial phase angle; Sampling time; At the same time, the transformation of the coordinate system will cause a transformation of the frequency: ； In the formula: for xy Frequency in a coordinate system; The base frequency is 50Hz; for abc Frequency in a coordinate system.

3. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 1, characterized in that: The multivariate measurement matrix is ​​as follows: ； In the formula: The total number of sampling points corresponds to the number of sampling times in the multivariate measurement matrix. Therefore, Also represents the first Each sampling time; For the first Current at each sampling time x Axial components; For the first Current at each sampling time y Axial components; For the first Voltage at each sampling time x Axial components; For the first Voltage at each sampling time y Axial components.

4. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 3, characterized in that: The conversion of each channel signal of the multivariate measurement matrix into analytic signals is achieved through Hilbert transform, which converts the signals into complex analytic signals. The expression for this transformation is as follows: ； In the formula: For Hilbert transform; , and These are the instantaneous amplitude, frequency function, and initial phase, respectively. For demodulated signals; It is a modulated signal; For instantaneous frequency estimation; It is a time-domain signal.

5. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 4, characterized in that: The initialization parameters include the initial values ​​of the Lagrange multipliers. Initial value of leakage factor Smoothing factor Convergence threshold ; The distribution of the signal in the fractional-order domain Represented as: ； In the formula: The rotation angle; For kernel functions; For instantaneous frequency index; The initial filter center frequency The calculation formula is: 。 6. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 1, characterized in that: The auxiliary parameters include the demodulated signal, the demodulated signal, the estimated signal, the leakage factor, and the Lagrange multipliers. The iterative update of the auxiliary parameters is performed using the alternating direction multiplier method, specifically: ； ； ； ； In the formula: This represents the number of iterations. For the first Channel 1 The modulation signal of the next iteration; , The total number of channels; For the first The instantaneous frequency estimate after the next iteration; For the first Channel 1 The demodulated signal of the next iteration; For the first The original oscillation signal of the channel; For the first Channel 1 The estimated signal for the next iteration; It is the conjugate transpose; For the first Channel 1 The leakage factor of the next iteration; For the first Channel 1 Lagrange multipliers in the next iteration; It is a second-order differential operator. ； The frequency function Iterative updates are represented as: ； In the formula: It is a smoothing factor; Unit operator; For the first Channel 1 Frequency increment of the next iteration ； In the formula: It is the imaginary part; It is the real part.

7. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 6, characterized in that: The formula for the multi-channel joint factor is: ； In the formula: For the first The multichannel joint factor of a channel represents the proportion of the energy of that channel to the total energy. For the first Channel 1 The instantaneous energy of the next iteration signal is given by the formula: ； The multi-channel parameter joint update involves weighted fusion of the parameters from each channel to obtain the global common parameters for the next iteration, namely: ； In the formula: It is a multi-channel joint factor; for The instantaneous frequency matrix of each channel; for The leakage factor sequence of each channel; for A sequence of Lagrange multipliers for each channel; ； The convergence determination formula is as follows: ； In the formula: The predefined convergence threshold; If the convergence criterion is not met, then let Repeat the iterative update of auxiliary parameters until the convergence condition is met; if the convergence condition is met, output the result. The final decomposition result of each channel .

8. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 1, characterized in that: The subsynchronous mode components are selected through a set frequency threshold range and represented by a subsynchronous mode matrix: ； In the formula: , These are obtained after being filtered by frequency threshold. x The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point , These are obtained after being filtered by frequency threshold. y The current and voltage of the shaft in the first... Subsynchronous oscillation components at each sampling point This represents the total number of sampling points.

9. The method for locating subsynchronous oscillation sources in wind farms based on multivariate complex modulation model decomposition according to claim 8, characterized in that: The formula for the transient energy flow model is: ； In the formula, For the first L Transient energy at each sampling point ; The criteria for identifying a subsynchronous oscillation source are as follows: If the value shows an upward trend over time, it indicates a continuous injection of energy into the power grid, and the sampling point is determined to be a subsynchronous oscillation source; otherwise, If the value decreases over time, it indicates that the energy is continuously absorbed, and the sampling point is determined to be a non-subsynchronous oscillation source.

Images