Grey-box heterogeneous doubly-fed wind farm low frequency oscillation suppression method based on virtual damping modulation

Abstract

The application discloses a kind of grey-box isomeric doubly-fed wind farm low-frequency oscillation suppression method based on virtual damping modulation, comprising: 1 grey-box isomeric doubly-fed wind farm is divided into white box and black box unit, and the state space model of all white box units of traditional doubly-fed induction generator, virtual synchronous machine control and installation additional damping controller is established;2 improve subspace identification method to obtain black box unit model;3. white box and black box model are coupled by feedback interconnection, and the overall state space model of wind farm is constructed;4 determine target low-frequency oscillation mode based on coefficient matrix;5 real-time extraction and target mode strong correlation common bus power signal, combined with adaptive time-varying gain generates virtual synchronous machine damping coefficient adjustment amount;6 according to complex mode controllability factor and unit distribution coefficient, allocate the virtual damping modulation instruction of each white box unit.The application realizes the identification and suppression of grey-box isomeric doubly-fed wind farm low-frequency oscillation, and improves the ability of wind farm damping low-frequency oscillation.

Description

Technical Field

[0001] This invention belongs to the field of stability analysis and control technology of new energy wind farms, specifically involving a method for suppressing low-frequency oscillations in gray box heterogeneous doubly fed wind farms based on virtual damping modulation. Background Technology

[0002] In wind farms, with the continuous integration of wind turbines equipped with virtual synchronous machine (VSG) technology, low-frequency oscillations within these wind farms are becoming increasingly prominent, posing a significant challenge to the safe and stable operation of the power grid. Actual doubly-fed induction generator (DFIG) wind farms are often heterogeneous systems, simultaneously containing traditional DFIG units employing control strategies such as VSG, additional damping controllers (SDC), or no such control strategies. Some units have well-defined models (considered white boxes), while detailed mechanistic models for others (especially third-party or older units) are difficult to obtain (considered black boxes), forming gray-box systems. Accurate, unified models cannot be established for stability analysis in such gray-box systems.

[0003] In this scenario, existing low-frequency oscillation analysis and suppression methods face fundamental challenges: traditional control methods based on accurate global models (such as LQR) fail due to incomplete models; fully data-driven methods rely on massive amounts of data and have poor physical interpretability; and methods based on mode separation struggle to reliably construct the core modal observability vector within a black-box model. Therefore, a low-frequency oscillation suppression method for gray-box heterogeneous doubly-fed wind farms based on virtual damping modulation is needed to achieve low-frequency oscillation suppression even with incomplete model information. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the above-mentioned technologies and propose a low-frequency oscillation suppression method for gray-box heterogeneous doubly-fed wind farms based on virtual damping modulation. The aim is to obtain the overall state-space equation of the wind farm by accurately modeling the white-box units and identifying the black-box units in the heterogeneous doubly-fed wind farm, thereby identifying the most dangerous low-frequency oscillation modes of the wind farm, and rationally allocating virtual damping modulation commands to specific white-box units through an adaptive control method. This can effectively suppress the target low-frequency oscillation modes and improve the operational stability of the gray-box heterogeneous doubly-fed wind farm.

[0005] The present invention adopts the following technical solution to solve the technical problem: The present invention provides a method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation, characterized by the following steps: Step S1: Divide all the doubly fed induction generators (DFIGs) in the gray box heterogeneous doubly fed wind farm into white box units with known detailed structural parameters and black box units with unknown detailed structural parameters. Then, divide each white box unit into traditional white box DFIG units, white box DFIG units controlled by virtual synchronous machines (VSGs), and white box DFIG units with additional damping controllers (SDCs). The state-space equations for each white-box unit were established using mechanistic modeling methods and then linearized to obtain... Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed in Taiwan; Step S2: Construct containing Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of the overall white-box DFIG unit with SDC installed in Taiwan; Step S3: The input and output vectors of the linearized continuous-time state-space model of the overall white-box unit are used as the output and input vectors of the state-space model of the black-box unit, respectively. In the subspace identification method, a block recursive least squares method with regularization and forgetting weight is introduced to determine the coefficient matrix of the state-space model of the black-box unit. Based on the singular value relative energy ratio criterion and the complexity penalty coefficient, the optimal order of the state-space model of the black-box unit is determined, thereby obtaining the discrete-time state-space model of the black-box unit corresponding to the coefficient matrix under the optimal order. Step S4: After performing a continuous transformation on the discrete-time state-space model of the black box unit, a continuous-time state-space model of the black box unit is obtained. The continuous-time state-space model of the black box unit is then coupled with the linearized continuous-time state-space model of the overall white box unit through a feedback interconnection structure, thereby obtaining the overall state-space model of the gray box heterogeneous doubly fed wind farm. Step S5: Calculate the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. Eigenvalue analysis was performed, and the low-frequency oscillation mode with the minimum damping was selected as the target low-frequency oscillation mode to be suppressed. And obtain the corresponding oscillation frequency. ; Step S6: Convert the real-time acquired common bus power deviation signal vector The input is fed into an adaptive bandpass filter based on a second-order generalized integral to obtain a signal component strongly correlated with the target's low-frequency oscillation mode. This generates a mode for suppressing the target low-frequency oscillations. and its corresponding oscillation frequency Damping coefficient adjustment of the virtual synchronizer ; Step S7: Adjustment of damping coefficient based on virtual synchronizer and target low-frequency oscillation mode The corresponding right eigenvector Determine the first Complex mode controllability factor of the target low-frequency oscillation mode of a VSG-controlled white-box DFIG unit With unit allocation coefficient Thus, the first Virtual damping modulation commands for VSG-controlled white-box DFIG units Furthermore, based on the virtual damping modulation command set Coordinate multiple units to suppress low-frequency oscillations of the target.

[0006] The low-frequency oscillation suppression method for gray-box heterogeneous doubly-fed wind farms based on virtual damping modulation described in this invention is also characterized in that step S2 includes: Step S2-1: Let The linearized continuous-time state-space model of a traditional white-box DFIG unit includes: State variables of traditional white-box DFIG units , Input vector of traditional white-box DFIG unit , Output vector of traditional white box DFIG unit Where T represents the transpose operation, For the first conventional white-box DFIG unit, For the first State variables of a traditional white-box DFIG unit; make A linearized continuous-time state-space model of a VSG-controlled white-box DFIG unit includes: State variables of a VSG-controlled white-box DFIG unit , Input vector of a VSG-controlled white-box DFIG unit , Output vector of VSG-controlled white-box DFIG unit ;in, For the first VSG-controlled white-box DFIG unit, the state variables are... For the first State variables of a VSG-controlled white-box DFIG unit; make A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed in Taiwan, including: State variables of white-box DFIG units with SDC installed , Input vector of white-box DFIG unit with SDC installed , Output vector of white-box DFIG unit with SDC installed ; For the first white-box DFIG unit equipped with SDC, the state variables are... For the first State variables of a white-box DFIG unit with SDC installed; Step S2-2: Use equation (1) to establish a linearized continuous-time state-space model of all white-box units in the gray-box heterogeneous doubly-fed wind farm: (1) In equation (1), ∆ represents linearization; d represents differentiation; Indicates time; Let represent the white box state coefficient matrix, and , diag represents a diagonal matrix, express State coefficient matrix of traditional white-box DFIG units, express State coefficient matrix of a VSG-controlled white-box DFIG unit. express State coefficient matrix of a white-box DFIG unit with SDC installed in Taiwan; Represents the white-box input coefficient matrix; This represents the white-box output coefficient matrix; This represents the white box feedforward matrix.

[0007] Furthermore, step S3 is performed as follows: Step S3-1: Define the state-space model of the black-box unit of the gray-box heterogeneous doubly-fed wind farm using equation (2). Input vector at time step and Output vector at time step : (2) In equation (2), The total number of moments; Step S3-2: Construct the input vector using equation (3) Hankel tensor and output vector Hankel tensor : (3) In equation (3), Indicates the historical offset as Historical data volume is The past input tensor, and ; Indicates the future offset as The future data volume is The future input tensor, and ; Indicates the historical offset as Historical data volume is The past output tensor, and ; Indicates the future offset as The future data volume is The future output tensor, and ; Step S3-3: Based on the subspace orthogonal projection theory, construct the extended state-space model of the black-box unit without state variables using equation (4): (4) In equation (4), express The Middle Arriving Future output blocks composed of row tensors; For the parameter matrix of the generalized observability-controllability tensor product; Indicates the amount of historical data. The augmented historical information matrix express Center front Historical output blocks composed of row tensors express Center front Historical input blocks composed of row tensors; and These represent the future data volume as follows: The Toeplitz convolution parameter matrix of the lower triangular block for the future deterministic input and the future random innovation; express The Middle Arriving Future input blocks composed of row tensors; Indicates the future data volume as The future information matrix; Step S3-4: Define the first using equation (5) Row recursive regression matrix : (5) In equation (5), express The first line to the second line Line-future input block; express The first line to the second line Future Information Matrix; Step S3-5: Minimize equation (6) to obtain the first... The row estimation parameter matrix includes: The Middle Generalized observability-controllability tensor product estimation parameter matrix , The Middle Toeplitz convolution estimation parameter matrix for lower triangular blocks of future deterministic input and The Middle The parameter matrix of the lower triangular block Toeplitz convolution for row-future stochastic innovations : (6) In equation (6), For the first Line objective function; For the first Forgetting factor in the next iteration For the first Forgetting factor in the next iteration; For the first The next iteration The Middle Linear future output block; For the first In the nth iteration Row recursive regression matrix; The regularization coefficient is used. It is a norm; This represents the total number of iterations. This represents the summation operation; Step S3-6: Use equation (7) to obtain the first... Future Information Estimation Matrix : (7) In equation (7), for The Middle Linear future output block; Step S3-7: Vectorize all row estimation parameter matrices using equation (8) and project them onto the structured feature space: (8) In equation (8), vec represents vectorization operation; Represents the parameter matrix for estimating the generalized observability-controllability tensor product of all rows; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future deterministic inputs; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future random information; Represents the projection matrix; yes The corresponding structured feature space, yes The corresponding structured feature space; yes The corresponding structured feature space, and , For the state-space model of the black box unit in Input vector at time 1 The impulse response sequence; Step S3-8: Construction Hankel tensor and to After performing singular value decomposition, the left singular matrix is ​​obtained. Right singular matrix and diagonal matrix ,in, For the first One singular value; The number of singular values; Step S3-9: Based on the singular value relative energy ratio criterion, establish equation (9) to determine the optimal range of the order of the state-space model of the black box unit. ,in, Indicates the lowest order. Indicates the highest order: (9) In equation (9), An index indicating the candidate order; Represents positive integers; The preset energy accumulation threshold is defined by min, which indicates that the minimum value is taken during the calculation. Step S3-10: Use equation (10) to obtain the coefficient matrix of the discrete-time state-space model of the black-box unit of the gray-box heterogeneous doubly-fed wind farm, including: black-box state coefficient matrix. Black box input coefficient matrix Black box output coefficient matrix Black box feedforward matrix : (10) In equation (10), This represents the conjugate transpose operation; express Column 1 to Column 2 Left-side singular matrix; express The first line to the second line Row, Column 1 to Column 2 Left-side singular matrix; express Column 1 to Column 2 Right-side singular matrices; Indicates order, and ; Step S3-11: Establish equation (11) to determine the optimal order of the state-space model of the black box unit. : (11) In equation (11), For order The objective function is as follows; For order The first corresponding state-space model of the black box unit Predict output at any given time; argmin is the complexity penalty coefficient; argmin represents the factor that makes argmin the complexity penalty coefficient. The input variable value when the minimum value is obtained; Step S3-12: Based on the optimal order The coefficient matrix of the state-space model of the black box unit is obtained, thus yielding the discrete-time state-space model of the black box unit.

[0008] Furthermore, step S4 is performed as follows: Step S4-1: Use the inverse discretization method based on the zero-order hold assumption to... , , , State coefficient matrix converted to a continuous-time state-space model of a black-box unit Input coefficient matrix Output coefficient matrix Feedforward matrix ; Step S4-2: Using equation (12), obtain the linearized continuous-time state-space model of the overall white-box unit and the continuous-time state-space model of the black-box unit in the gray-box heterogeneous wind farm: (12) In equation (12), Represents the state variables of the entire white box unit; Represents the state variables of the black-box unit; , These represent the input and output vectors of the black-box unit, respectively. Step S4-3: Establish the overall state-space model of the gray box heterogeneous doubly-fed wind farm using equation (13): (13) In equation (13), Let represent the state variables of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and , Let represent the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and we have: (14) In equation (14), Represents the identity matrix.

[0009] Furthermore, in step S6, the damping coefficient adjustment amount of the virtual synchronizer is established using equation (15). : (15) In equation (15), Let be the time-varying gain matrix, and we have: (16) In equation (16), For learning rate; is the forgetting factor of the time-varying gain matrix.

[0010] Furthermore, in step S7, equation (17) is used to... Assigned as the first Virtual damping modulation commands for VSG-controlled white-box DFIG units , used to determine the first The adjustment amount of the virtual damping coefficient of the VSG in the VSG-controlled white box DFIG unit; (17) In equation (17), Indicates the first Adjustment margin coefficient of VSG-controlled white-box DFIG unit; Indicates the first The real unit vector of the white-box DFIG unit controlled by VSG, where Re represents the operation of taking the real part of the complex number; Indicates the first A VSG-controlled white-box DFIG unit detects the target's low-frequency oscillation mode. The complex modal controllability factor is given by: (18) In equation (18), For the first Related to the virtual damping coefficient in a VSG-controlled white-box DFIG unit The structure selection matrix composed of state components. for dimensionality; Indicates the first The phase reference vector of the VSG-controlled white-box DFIG unit, and ; The phase value is a complex number. It is the imaginary unit.

[0011] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program that supports the processor in executing the low-frequency oscillation suppression method for gray box heterogeneous doubly fed wind farms, and the processor is configured to execute the program stored in the memory.

[0012] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, performs the steps of the method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly fed wind farm.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention addresses the modeling problem of heterogeneous doubly-fed induction generator (DFIG) wind farms with partially white-box and partially black-box configurations. It employs a hybrid modeling strategy combining white-box mechanism modeling with improved subspace identification in the black-box configuration. Using measurable input and output data, the coefficient matrix of the overall state-space model of the gray-box heterogeneous DFIG wind farm is established. Furthermore, the most dangerous low-frequency oscillation mode to be suppressed was identified, laying the analytical foundation for oscillation suppression control.

[0014] 2. This invention addresses the challenge of applying traditional control methods relying on precise modal state observation to gray-box heterogeneous doubly-fed wind farms. Therefore, a frequency-locked-virtual damping modulation control method is designed. This method extracts the oscillation component strongly correlated with the target low-frequency oscillation from the wide-area measured common bus power signal using an adaptive bandpass filter, and generates the virtual synchronous machine damping coefficient adjustment online using an adaptive law aimed at minimizing oscillation energy. This design avoids the unknown state variables within the black-box unit, relying solely on the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. The provided modal information enables direct feedback control.

[0015] 3. This invention introduces a coordination strategy based on complex mode controllability factors and unit allocation coefficients in the virtual damping modulation command allocation stage. This is achieved by analyzing the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. By analyzing the right eigenvector and relevant state variables of the white-box units, the controllability and optimal control phase of each VSG-controlled white-box DFIG unit for the target oscillation mode were determined, and commands were allocated accordingly. This method achieves multi-unit coordinated damping optimization, effectively suppressing wind farm oscillations while ensuring the rationality of control actions for each unit. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of a gray-box heterogeneous doubly-fed wind farm structure. Figure 3a This is a traditional DFIG structure diagram; Figure 3b This is a diagram showing the interconnections between the various parts in a traditional DFIG state-space model. Figure 4 VSG control structure diagram; Figure 5 This is the SDC control structure diagram; Figure 6 This is a schematic diagram of the recursive least squares method. Figure 7 This is a model diagram of a gray-box heterogeneous doubly fed wind farm closed-loop system. Detailed Implementation

[0017] In this embodiment, a low-frequency oscillation suppression method for gray-box heterogeneous doubly-fed wind farms based on virtual damping modulation is proposed. This method combines white-box mechanism modeling with black-box spatial identification to construct the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. This involves identifying dangerous oscillation frequencies. Furthermore, a frequency-locked, virtual damped modulation control method is designed: this method does not rely on observation of the internal state of the black box, but instead extracts the target frequency oscillation component from the common bus power signal through an adaptive bandpass filter, and generates a virtual synchronous machine damping coefficient adjustment using an adaptive law aimed at minimizing oscillation energy. Based on... The obtained complex mode controllability factor is used to rationally allocate virtual damping modulation commands to the VSG-controlled white-box DFIG unit, effectively suppressing the target low-frequency oscillation mode of the gray-box heterogeneous doubly-fed wind farm. Specifically, such as Figure 1 As shown, the method includes the following steps: Step S1: Divide all the doubly-fed induction generators (DFIGs) in the gray-box heterogeneous doubly-fed wind farm into white-box units with known detailed structural parameters and black-box units with unknown detailed structural parameters. See the schematic diagram of the gray-box heterogeneous doubly-fed wind farm structure. Figure 2 Each white-box unit is further divided into a traditional white-box DFIG unit, a white-box DFIG unit controlled by a virtual synchronous machine (VSG), and a white-box DFIG unit equipped with an additional damping controller (SDC). The state-space equations for each white-box unit were established using mechanistic modeling methods and then linearized to obtain... Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed.

[0018] Step S1-1: Constructing a traditional white-box DFIG unit includes a wind turbine, drive shaft system, induction generator, DC capacitor, transformer, pitch angle control, rotor-side converter RSC, and grid-side converter GSC, with the following structure: Figure 3a As shown, the interconnections of the various parts are as follows: Figure 3b As shown, the state-space equations for each conventional white-box DFIG unit are thus established: (1) In equation (1), ∆ represents linearization; d represents differentiation; t Indicates time; This represents the stator d-axis voltage of each conventional white-box DFIG generator unit; This represents the stator q-axis voltage of each conventional white-box DFIG generator unit; This represents the d-axis current output by each traditional white-box DFIG unit; This represents the output q-axis current of each traditional white-box DFIG generator unit; the state variables of each traditional white-box DFIG generator unit. T represents the transpose operation. For wind turbine rotation speed, The rotor speed, For the twist angle, The pitch angle is the propeller angle. , These represent the d-axis and q-axis currents of the DFIG stator, respectively. , These represent the d-axis and q-axis currents of the DFIG rotor, respectively. This indicates the DC capacitor voltage of the DFIG unit. , , , , , , , , There are 9 intermediate state variables; , , , These are the state coefficient matrix, input coefficient matrix, output coefficient matrix, and feedforward matrix for the state space equations of each traditional white-box DFIG unit.

[0019] Step S1-2: The direct power control strategy of the rotor-side converter RSC in the traditional DFIG unit is transformed into a virtual synchronous control strategy that simulates the electromechanical transient characteristics of a synchronous generator. This changes the control structure of the rotor-side converter RSC in the traditional DFIG unit, resulting in a VSG-controlled DFIG unit. The VSG control structure diagram is shown below. Figure 4 And establish the state-space equations for each VSG-controlled DFIG unit: (2) In equation (2), This represents the stator d-axis voltage of each VSG-controlled white-box DFIG unit; This represents the stator q-axis voltage of each VSG-controlled white-box DFIG unit; This indicates the d-axis current output by each VSG-controlled white-box DFIG unit; This indicates the output q-axis current of each VSG-controlled white-box DFIG unit; For each VSG-controlled white-box DFIG unit, the state variables are... Let dq be the transformation angle of VSG in the RSC coordinate system. VSG speed, , , , , There are 5 intermediate state variables; , , , These are the state coefficient matrix, input coefficient matrix, output coefficient matrix, and feedforward matrix of the state space equations for each VSG-controlled white-box DFIG unit.

[0020] Step S1-3: Add an additional damping control signal channel to the control loop of the rotor-side converter RSC in a conventional DFIG unit to change the control structure of the rotor-side converter RSC in the conventional DFIG unit, thereby obtaining a DFIG unit with SDC installed. See the SDC control structure diagram. Figure 5 And establish the state-space equations for the DFIG units with SDC installed: (3) In equation (3), This represents the stator d-axis voltage of each white-box DFIG unit equipped with SDC; This represents the stator q-axis voltage of each white-box DFIG unit equipped with SDC; This indicates the output d-axis current of each white-box DFIG unit equipped with SDC; This represents the output q-axis current of each white-box DFIG unit equipped with an SDC; the state variables of each white-box DFIG unit equipped with an SDC. , , , There are 3 intermediate state variables; , , , For each white-box DFIG unit equipped with SDC, the state matrix, input matrix, output matrix, and feedforward matrix are respectively the state-space equations.

[0021] Step S2: Construct containing Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of the overall white-box DFIG unit with SDC installed in Taiwan; Step S2-1: Let The linearized continuous-time state-space model of a traditional white-box DFIG unit includes: State variables of traditional white-box DFIG units , Input vector of traditional white-box DFIG unit , Output vector of traditional white box DFIG unit Where T represents the transpose operation, For the first conventional white-box DFIG unit, For the first State variables of a traditional white-box DFIG unit.

[0022] make A linearized continuous-time state-space model of a VSG-controlled white-box DFIG unit includes: State variables of a VSG-controlled white-box DFIG unit , Input vector of a VSG-controlled white-box DFIG unit , Output vector of VSG-controlled white-box DFIG unit ;in, For the first VSG-controlled white-box DFIG unit, the state variables are... For the first The state variables of a white-box DFIG unit controlled by a VSG.

[0023] make A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed in Taiwan, including: State variables of white-box DFIG units with SDC installed , Input vector of white-box DFIG unit with SDC installed , Output vector of white-box DFIG unit with SDC installed ; For the first white-box DFIG unit equipped with SDC, the state variables are... For the first State variables of a white-box DFIG unit with SDC installed.

[0024] Step S2-2: Use equation (4) to establish a linearized continuous-time state-space model of all white-box units in the gray-box heterogeneous doubly-fed wind farm: (4) In equation (4), Let represent the white box state coefficient matrix, and , diag represents a diagonal matrix, express State coefficient matrix of traditional white-box DFIG units, express State coefficient matrix of a VSG-controlled white-box DFIG unit. express State coefficient matrix of a white-box DFIG unit with SDC installed in Taiwan; Represents the white-box input coefficient matrix; This represents the white-box output coefficient matrix; This represents the white box feedforward matrix.

[0025] Step S3: The input and output vectors of the linearized continuous-time state-space model of the overall white-box unit are used as the output and input vectors of the state-space model of the black-box unit, respectively. In the subspace identification method, a block recursive least squares method with regularization and forgetting weighting is introduced to determine the coefficient matrix of the state-space model of the black-box unit. Based on the singular value relative energy ratio criterion and the complexity penalty coefficient, the optimal order of the state-space model of the black-box unit is determined, thereby obtaining the discrete-time state-space model of the black-box unit corresponding to the coefficient matrix under the optimal order.

[0026] Step S3-1: Define the state-space model of the black-box unit in the gray-box heterogeneous doubly-fed wind farm using equation (5). Input vector at time step and Output vector at time step They are respectively: (5) In equation (5), This represents the total number of moments.

[0027] Step S3-2: Construct the input vector using equation (6) Hankel tensor and output vector Hankel tensor : (6) In equation (6), Indicates the historical offset as Historical data volume is The past input tensor, and ; Indicates the future offset as The future data volume is The future input tensor, and ; Indicates the historical offset as Historical data volume is The past output tensor, and ; Indicates the future offset as The future data volume is The future output tensor, and .

[0028] Step S3-3: Based on the basic state-space equations, the extended state-space model can be obtained. Based on the subspace orthogonal projection theory, the extended state-space model expression without state variables can then be constructed.

[0029] Step S3-3-1: Based on the basic state-space equations, the extended state-space model is obtained as follows: (7) In equation (7), express Center front Historical output blocks composed of row tensors; express Center front Historical input blocks composed of row tensors; express The Middle Arriving Future input blocks composed of row tensors; express The Middle Arriving Future output blocks composed of row tensors; and These represent the historical state matrix and the future state matrix, respectively. and These represent the past data volume as follows: The parameters of the Toeplitz convolution matrix of the lower triangular block with past deterministic input and random innovation; and These represent the future data volume as follows: The Toeplitz convolution parameter matrix of the lower triangular block for the future deterministic input and the future random innovation; Indicates the future data volume as The future information matrix; This indicates the amount of past data. Past information matrix; and It is an inverse generalized controllable matrix; and These represent the extended future and past observability matrices, respectively. This represents the relationship matrix.

[0030] Step S3-3-2: Because equation (7) contains elements that cannot be directly measured It needs to be expressed using equation (8).

[0031] (8) In equation (8), -1 represents the inverse operation.

[0032] Step S3-3-3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] Substituting expression (8) into equation (7) and simplifying, we get... The expression (9): (9) In equation (9), Represents the state transition matrix; Represents the input transformation matrix; Indicates the output transformation matrix; This represents an augmented historical information matrix; Represents the transformation matrix; due to the stability of the Kalman filter, when When large enough, Substituting this into equation (7), we can construct an extended state-space model of the black-box unit without state variables using equation (10): (10) In equation (10), Indicates the amount of historical data. An augmented historical information matrix; The parameter matrix is ​​the tensor product matrix of the generalized observability-controllability.

[0033] Step S3-4: Adopt a block-based recursive orthogonalization strategy, and use equation (11) to define the first... Row recursive regression matrix : (11) In equation (11), express The first line to the second line Line-future input block; express The first line to the second line Future Information Matrix.

[0034] Step S3-5: Establish the recursive least squares formula (12) with regularization and forgetting weighting, and solve for the minimization of formula (12). The principle diagram of the recursive least squares method can be found in [the diagram]. Figure 6 , obtained the The row estimation parameter matrix includes: The Middle Generalized observability-controllability tensor product estimation parameter matrix , The Middle Toeplitz convolution estimation parameter matrix for lower triangular blocks of future deterministic input and The Middle The parameter matrix of the lower triangular block Toeplitz convolution for row-future stochastic innovations : (12) In equation (12), For the first Line objective function; For the first Forgetting factor in the next iteration For the first Forgetting factor in the next iteration; For the first The next iteration The Middle Linear future output block; For the first In the nth iteration Row recursive regression matrix; The regularization coefficient is used. It is a norm; This represents the total number of iterations. This indicates a summation operation.

[0035] Step S3-5-1: Minimize equation (12), and then use equation (13) to obtain the recursive least squares identification formula with regularization and forgetting weighting for a fixed row: (13) In equation (13), and They represent the first Second and third Estimating the parameter matrix of the generalized observability-controllability tensor product under the next iteration; and They represent the first Second and third The parameter matrix for estimating the lower triangular block Toeplitz convolution of the future deterministic input in the next iteration; and They represent the first Second and third The parameter matrix for estimating the Toeplitz convolution of the lower triangular block of the future random innovation under the next iteration; and They represent the first Second and third Gain matrix under the next iteration; Indicates the first Future output block in the next iteration; and They represent the first Second and third The covariance matrix under the next iteration.

[0036] Step S3-6: Use equation (14) to obtain the first... Future Information Estimation Matrix : (14) In equation (14), for The Middle Line up to the future output block.

[0037] Step S3-7: Vectorize all row estimation parameter matrices using equation (15) and project them onto the structured feature space: (15) In equation (15), vec represents vectorization operation; Represents the parameter matrix for estimating the generalized observability-controllability tensor product of all rows; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future deterministic inputs; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future random information; Represents the projection matrix; yes The corresponding structured feature space, yes The corresponding structured feature space; yes The corresponding structured feature space, and , For the state-space model of the black box unit in Input vector at time 1 The impulse response sequence.

[0038] Step S3-8-1: Construction Hankel tensor : (16) Step S3-8-2: Use equation (17) to... After performing singular value decomposition, the left singular matrix is ​​obtained. Right singular matrix and diagonal matrix ,in, For the first One singular value; The number of singular values; (17) Step S3-9: Based on the singular value relative energy ratio criterion, establish equation (18) to determine the optimal range of the order of the state-space model of the black box unit. , Indicates the lowest order. Indicates the highest order: (18) In equation (18), An index indicating the candidate order; Represents positive integers; A preset energy accumulation threshold (typically 0.95–0.99) is used to select different thresholds to obtain... min indicates the minimum value operation.

[0039] Step S3-10: Use equation (19) to obtain the coefficient matrix of the discrete-time state-space model of the black-box unit of the gray-box heterogeneous doubly-fed wind farm, including: black-box state coefficient matrix. Black box input coefficient matrix Black box output coefficient matrix Black box feedforward matrix : (19) In equation (19), This represents the conjugate transpose operation; express Column 1 to Column 2 Left-side singular matrix; express The first line to the second line Row, Column 1 to Column 2 Left-side singular matrix; express Column 1 to Column 2 Right-side singular matrices; Indicates order, and .

[0040] Step S3-11: Establish equation (20) to determine the optimal order of the state-space model of the black box unit. n * This achieves a balance between model accuracy and complexity. (20) In equation (20), For order The objective function is as follows; For order The first corresponding state-space model of the black box unit Predict output at any given time; argmin is the complexity penalty coefficient; argmin represents the factor that makes argmin the complexity penalty coefficient. The input variable value when the minimum value is obtained.

[0041] Step S3-12: Based on the optimal order The coefficient matrix of the state-space model of the black box unit is obtained, thus yielding the discrete-time state-space model of the black box unit.

[0042] Step S4: After performing a continuous transformation on the discrete-time state-space model of the black box unit, a continuous-time state-space model of the black box unit is obtained. The continuous-time state-space model of the black box unit is then coupled with the linearized continuous-time state-space model of the overall white box unit through a feedback interconnection structure, thereby obtaining the overall state-space model of the gray box heterogeneous doubly fed wind farm. Step S4-1: Use the inverse discretization method based on the zero-order hold assumption to... , , , State coefficient matrix converted to a continuous-time state-space model of a black-box unit Input coefficient matrix Output coefficient matrix Feedforward matrix .

[0043] Step S4-1-1: Coefficient matrix of the discrete-time state-space model of the black-box unit , , , Coefficient matrix of continuous-time state-space model of black box unit , , , The following mathematical relationship exists between them: (twenty one) In equation (21), The sampling period.

[0044] Step S4-1-2: Obtain the coefficient matrix of the continuous-time state-space model of the black-box unit in the heterogeneous doubly-fed wind farm according to equation (21). , , , Expression (22): (twenty two) Step S4-2: Using equation (23), obtain the linearized continuous-time state-space model of the overall white-box unit and the continuous-time state-space model of the black-box unit in the gray-box heterogeneous wind farm: (twenty three) In equation (23), Represents the state variables of the entire white box unit; Represents the state variables of the black-box unit; , These represent the input and output vectors of the black box unit, respectively.

[0045] Step S4-3: Based on the fact that the white-box and black-box units in a heterogeneous doubly-fed wind farm can form a feedback interconnection closed-loop system, the overall state-space model of the gray-box heterogeneous doubly-fed wind farm is established using equation (24). The closed-loop system model of the gray-box heterogeneous doubly-fed wind farm is shown in [reference needed]. Figure 7 : (twenty four) In equation (24), Let represent the state variables of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and , Let represent the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and we have: (25) In equation (25), M Represents the identity matrix.

[0046] Step S5: Calculate the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. Eigenvalue analysis was performed, and the low-frequency oscillation mode with the minimum damping was selected as the target low-frequency oscillation mode to be suppressed. And obtain the corresponding oscillation frequency. ; Step S5-1: Based on the coefficient matrix Determine the characteristic equation (26): (26) In equation (26), the first eigenvalues , Indicates the first A damping, Indicates the first One oscillation angular frequency, Indicates the first One right eigenvector, It is the imaginary unit.

[0047] Step S5-2: According to equation (27), we obtain The corresponding number oscillation frequency : (27) Step S5-3: Select the low-frequency oscillation mode of the gray box heterogeneous doubly fed wind farm according to equation (28), and take the mode with the smallest damping as the target low-frequency oscillation mode to be suppressed. and its corresponding oscillation frequency : (28) Step S6: Convert the real-time acquired common bus power deviation signal vector The input is fed into an adaptive bandpass filter based on a second-order generalized integral to obtain a signal component strongly correlated with the target's low-frequency oscillation mode. This generates a mode for suppressing the target's low-frequency oscillations. and its corresponding oscillation frequency The damping coefficient adjustment of the virtual synchronizer VSG .

[0048] Step S6-1: Establish an adaptive bandpass filter based on the second-order generalized integral using equation (29). Select the active and reactive signal deviation components of the common bus. The target frequency oscillation component is obtained by passing through this filter. .

[0049] (29) In equation (29), The damping coefficient; Indicates the target's low-frequency oscillation angular frequency; This represents a complex variable.

[0050] Step S6-2: Use equation (30) to establish the damping coefficient adjustment of the virtual synchronizer used to suppress the low-frequency oscillation of the target. : (30) In equation (30), The gain matrix is ​​time-varying, and the model is adjusted online following an adaptive law of oscillatory energy gradient descent: (31) In equation (31), For learning rate; is the forgetting factor of the time-varying gain matrix.

[0051] Step S6-3: The stability of the adaptive law online adjustment model (31) can be analyzed by constructing a Lyapunov function of the following form: (32) In equation (32), the gain matrix , It is the ideal gain matrix; This represents the trace operation; it can be proven that under equation (31), Thus ensuring asymptotic convergence and Bounded.

[0052] Step S7: Adjustment of damping coefficient based on virtual synchronizer and target low-frequency oscillation mode The corresponding right eigenvector Determine the first Complex mode controllability factor of the target low-frequency oscillation mode of a VSG-controlled white-box DFIG unit With unit allocation coefficient Thus, the first Virtual damping modulation commands for VSG-controlled white-box DFIG units Furthermore, based on the virtual damping modulation command set Coordinate multiple units to suppress low-frequency oscillations of the target.

[0053] Step S7-1: Use equation (33) to... Assigned as the first Virtual damping modulation commands for VSG-controlled white-box DFIG units , used to determine the first The adjustment of the virtual damping coefficient of the VSG in the VSG-controlled white-box DFIG unit ensures the coordination of multi-unit control and improves the overall efficiency of low-frequency oscillation suppression. (33) In equation (33), Indicates the first Adjustment margin coefficient of VSG-controlled white-box DFIG unit; Indicates the first Real unit vector of a VSG-controlled white-box DFIG unit ( ), representing active and reactive power control weights; Re represents the operation of taking the real part of a complex number; Indicates the first A VSG-controlled white-box DFIG unit detects the target's low-frequency oscillation mode. The complex modal controllability factor is given by: (34) In equation (34), For the first Related to the virtual damping coefficient in a VSG-controlled white-box DFIG unit The structure selection matrix composed of state components. for dimensionality; Indicates the first The phase reference vector of the VSG-controlled white-box DFIG unit, and ; The phase value is a complex number. It is the imaginary unit.

[0054] Step S7-2: The physical essence of is to reflect the first The controllability and optimal control phase of the target oscillation mode by a VSG-controlled white-box DFIG unit. This factor is derived by extracting the target low-frequency oscillation mode. The corresponding right eigenvector The state components that are strongly correlated with the unit's damping coefficient are aligned to the reference direction. Thus, while preserving relative phase information, for The VSG-controlled white-box DFIG unit rationally allocates virtual damping modulation commands to improve the coordinated suppression effect. In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0055] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation, characterized in that, Includes the following steps: Step S1: Divide all the doubly fed induction generators (DFIGs) in the gray box heterogeneous doubly fed wind farm into white box units with known detailed structural parameters and black box units with unknown detailed structural parameters. Then, divide each white box unit into traditional white box DFIG units, white box DFIG units controlled by virtual synchronous machines (VSGs), and white box DFIG units with additional damping controllers (SDCs). The state-space equations for each white-box unit were established using mechanistic modeling methods and then linearized to obtain... Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed in Taiwan; Step S2: Construct containing Taiwan's traditional white box DFIG unit, VSG-controlled white-box DFIG unit A linearized continuous-time state-space model of the overall white-box DFIG unit with SDC installed in Taiwan; Step S3: The input and output vectors of the linearized continuous-time state-space model of the overall white-box unit are used as the output and input vectors of the state-space model of the black-box unit, respectively. In the subspace identification method, a block recursive least squares method with regularization and forgetting weight is introduced to determine the coefficient matrix of the state-space model of the black-box unit. Based on the singular value relative energy ratio criterion and the complexity penalty coefficient, the optimal order of the state-space model of the black-box unit is determined, thereby obtaining the discrete-time state-space model of the black-box unit corresponding to the coefficient matrix under the optimal order. Step S4: After performing a continuous transformation on the discrete-time state-space model of the black box unit, a continuous-time state-space model of the black box unit is obtained. The continuous-time state-space model of the black box unit is then coupled with the linearized continuous-time state-space model of the overall white box unit through a feedback interconnection structure, thereby obtaining the overall state-space model of the gray box heterogeneous doubly fed wind farm. Step S5: Calculate the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm. Eigenvalue analysis was performed, and the low-frequency oscillation mode with the minimum damping was selected as the target low-frequency oscillation mode to be suppressed. And obtain the corresponding oscillation frequency. ; Step S6: Convert the real-time acquired common bus power deviation signal vector The signal component, strongly correlated with the target's low-frequency oscillation mode, is obtained by inputting it to an adaptive bandpass filter based on a second-order generalized integral. This generates a mode for suppressing the target low-frequency oscillations. and its corresponding oscillation frequency Damping coefficient adjustment of the virtual synchronizer ; Step S7: Adjustment of damping coefficient based on virtual synchronizer and target low-frequency oscillation mode The corresponding right eigenvector Determine the first Complex mode controllability factor of the target low-frequency oscillation mode of a VSG-controlled white-box DFIG unit With unit allocation coefficient Thus, the first Virtual damping modulation commands for VSG-controlled white-box DFIG units Furthermore, based on the virtual damping modulation command set Coordinate multiple units to suppress low-frequency oscillations of the target.

2. The method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation according to claim 1, characterized in that, Step S2 includes: Step S2-1: Let The linearized continuous-time state-space model of a traditional white-box DFIG unit includes: State variables of traditional white-box DFIG units , Input vector of traditional white-box DFIG unit , Output vector of traditional white box DFIG unit Where T represents the transpose operation, For the first conventional white-box DFIG unit, For the first State variables of a traditional white-box DFIG unit; make A linearized continuous-time state-space model of a VSG-controlled white-box DFIG unit includes: State variables of a VSG-controlled white-box DFIG unit , Input vector of a VSG-controlled white-box DFIG unit , Output vector of VSG-controlled white-box DFIG unit ;in, For the first VSG-controlled white-box DFIG unit, the state variables are... For the first State variables of a VSG-controlled white-box DFIG unit; make A linearized continuous-time state-space model of a white-box DFIG unit with SDC installed in Taiwan, including: State variables of white-box DFIG units with SDC installed , Input vector of white-box DFIG unit with SDC installed , Output vector of white-box DFIG unit with SDC installed ; For the first white-box DFIG unit equipped with SDC, the state variables are... For the first State variables of a white-box DFIG unit with SDC installed; Step S2-2: Use equation (1) to establish a linearized continuous-time state-space model of all white-box units in the gray-box heterogeneous doubly-fed wind farm: (1) In equation (1), ∆ represents linearization; d represents differentiation; Indicates time; Let represent the white box state coefficient matrix, and , diag represents a diagonal matrix, express State coefficient matrix of traditional white-box DFIG units, express State coefficient matrix of a VSG-controlled white-box DFIG unit. express State coefficient matrix of a white-box DFIG unit with SDC installed in Taiwan; Represents the white-box input coefficient matrix; This represents the white-box output coefficient matrix; This represents the white box feedforward matrix.

3. The method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation according to claim 2, characterized in that, Step S3 is performed as follows: Step S3-1: Define the state-space model of the black-box unit of the gray-box heterogeneous doubly-fed wind farm using equation (2). Input vector at time step and Output vector at time step : (2) In equation (2), The total number of moments; Step S3-2: Construct the input vector using equation (3) Hankel tensor and output vector Hankel tensor : (3) In equation (3), Indicates the historical offset as Historical data volume is The past input tensor, and ; Indicates the future offset as The future data volume is The future input tensor, and ; Indicates the historical offset as Historical data volume is The past output tensor, and ; Indicates the future offset as The future data volume is The future output tensor, and ; Step S3-3: Based on the subspace orthogonal projection theory, construct the extended state-space model of the black-box unit without state variables using equation (4): (4) In equation (4), express The Middle Arriving Future output blocks composed of row tensors; For the parameter matrix of the generalized observability-controllability tensor product; The amount of historical data is The augmented historical information matrix express Center front Historical output blocks composed of row tensors express Center front Historical input blocks composed of row tensors; and These represent the future data volume as follows: The Toeplitz convolution parameter matrix of the lower triangular block for the future deterministic input and the future random innovation; express The Middle Arriving Future input blocks composed of row tensors; Indicates the future data volume as The future information matrix; Step S3-4: Define the first using equation (5) Row recursive regression matrix : (5) In equation (5), express The first line to the second line Line-future input block; express The first line to the second line Future Information Matrix; Step S3-5: Minimize equation (6) to obtain the first... The row estimation parameter matrix includes: The Middle Generalized observability-controllability tensor product estimation parameter matrix , The Middle Toeplitz convolution estimation parameter matrix for lower triangular blocks of future deterministic input and The Middle The parameter matrix of the lower triangular block Toeplitz convolution for row-future stochastic innovations : (6) In equation (6), For the first Line objective function; For the first Forgetting factor in the next iteration For the first Forgetting factor in the next iteration; For the first The next iteration The Middle Linear future output block; For the first In the nth iteration Row recursive regression matrix; The regularization coefficient is used. It is a norm; This represents the total number of iterations. This represents the summation operation; Step S3-6: Use equation (7) to obtain the first... Future Information Estimation Matrix : (7) In equation (7), for The Middle Linear future output block; Step S3-7: Vectorize all row estimation parameter matrices using equation (8) and project them onto the structured feature space: (8) In equation (8), vec represents vectorization operation; Represents the parameter matrix for estimating the generalized observability-controllability tensor product of all rows; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future deterministic inputs; This represents the lower triangular block Toeplitz convolution estimation parameter matrix for all rows of future random information; Represents the projection matrix; yes The corresponding structured feature space, yes The corresponding structured feature space; yes The corresponding structured feature space, and , For the state-space model of the black box unit in Input vector at time 1 The impulse response sequence; Step S3-8: Construction Hankel tensor and to After performing singular value decomposition, the left singular matrix is ​​obtained. Right singular matrix and diagonal matrix ,in, For the first One singular value; The number of singular values; Step S3-9: Based on the singular value relative energy ratio criterion, establish equation (9) to determine the optimal range of the order of the state-space model of the black box unit. ,in, Indicates the lowest order. Indicates the highest order: (9) In equation (9), Index indicating the candidate order; Represents positive integers; The preset energy accumulation threshold is defined by min, which indicates that the minimum value is taken during the calculation. Step S3-10: Use equation (10) to obtain the coefficient matrix of the discrete-time state-space model of the black-box unit of the gray-box heterogeneous doubly-fed wind farm, including: black-box state coefficient matrix. Black box input coefficient matrix Black box output coefficient matrix Black box feedforward matrix : (10) In equation (10), This represents the conjugate transpose operation; express Column 1 to Column 2 Left-side singular matrix; express The first line to the second line Row, Column 1 to Column 2 Left-side singular matrix; express Column 1 to Column 2 Right-side singular matrices; Indicates order, and ; Step S3-11: Establish equation (11) to determine the optimal order of the state-space model of the black box unit. : (11) In equation (11), For order The objective function is as follows; For order The first corresponding state-space model of the black box unit Predict output at any given time; argmin is the complexity penalty coefficient; argmin represents the factor that makes argmin the minimum time complexity penalty coefficient. The input variable value when the minimum value is obtained; Step S3-12: Based on the optimal order The coefficient matrix of the state-space model of the black box unit is obtained, thus yielding the discrete-time state-space model of the black box unit.

4. The method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation according to claim 3, characterized in that, Step S4 is performed as follows: Step S4-1: Use the inverse discretization method based on the zero-order hold assumption to... , , , State coefficient matrix converted to a continuous-time state-space model of a black-box unit Input coefficient matrix Output coefficient matrix Feedforward matrix ; Step S4-2: Using equation (12), obtain the linearized continuous-time state-space model of the overall white-box unit and the continuous-time state-space model of the black-box unit in the gray-box heterogeneous wind farm: (12) In equation (12), Represents the state variables of the entire white box unit; Represents the state variables of the black-box unit; , These represent the input and output vectors of the black-box unit, respectively. Step S4-3: Establish the overall state-space model of the gray box heterogeneous doubly-fed wind farm using equation (13): (13) In equation (13), Let represent the state variables of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and , Let represent the coefficient matrix of the overall state-space model of the gray-box heterogeneous doubly-fed wind farm, and we have: (14) In equation (14), Represents the identity matrix.

5. The method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation according to claim 4, characterized in that, In step S6, the damping coefficient adjustment amount of the virtual synchronizer is established using equation (15). : (15) In equation (15), Let be the time-varying gain matrix, and we have: (16) In equation (16), For learning rate; is the forgetting factor of the time-varying gain matrix.

6. The method for suppressing low-frequency oscillations in a gray-box heterogeneous doubly-fed wind farm based on virtual damping modulation according to claim 5, characterized in that, In step S7, formula (17) is used to... Assigned as the first Virtual damping modulation commands for VSG-controlled white-box DFIG units , used to determine the first The adjustment amount of the virtual damping coefficient of the VSG in the VSG-controlled white box DFIG unit; (17) In equation (17), Indicates the first Adjustment margin coefficient of VSG-controlled white-box DFIG unit; Indicates the first The real unit vector of the white-box DFIG unit controlled by VSG, where Re represents the operation of taking the real part of the complex number; Indicates the first A VSG-controlled white-box DFIG unit detects the target's low-frequency oscillation mode. The complex modal controllability factor is given by: (18) In equation (18), For the first Related to the virtual damping coefficient in a VSG-controlled white-box DFIG unit The structure selection matrix composed of state components. for dimensionality; Indicates the first The phase reference vector of the VSG-controlled white-box DFIG unit, and ; The phase value is a complex number. It is the imaginary unit.

7. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the low-frequency oscillation suppression method for gray box heterogeneous doubly fed wind farms according to any one of claims 1-6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the low-frequency oscillation suppression method for gray box heterogeneous doubly fed wind farms according to any one of claims 1-6.

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