Leader broadband oscillation order reduction method suitable for network tracking / constructing type hybrid wind power plant

Abstract

The invention discloses a dominant broadband oscillation order reduction method suitable for a network tracking / constructing type hybrid wind power plant. The method comprises the following steps: firstly, establishing a full-order small-signal model of the hybrid wind power plant, and identifying a dominant broadband oscillation mode in combination with an energy contribution degree and a controllable observability criterion; secondly, state variable division and order reduction modeling are carried out based on the singular perturbation principle, and the calculation complexity is reduced while the dominant modal precision is kept; and finally, model simplification and dynamic characteristic consistency are realized through module interface matching and stability verification. According to the method, the reduced-order model of the hybrid wind power plant can be quickly obtained under the condition that main dynamic characteristics are not influenced, and reliable technical support is provided for broadband oscillation analysis and control optimization of a power system.

Description

Technical Field

[0001] This invention relates to the field of new energy grid connection control and power system stability analysis technology, and in particular to a method for reducing the order of the dominant broadband oscillation applicable to hybrid wind farms with integrated / structured grids. Background Technology

[0002] With the continuous growth of installed capacity of new energy sources, the penetration rate of wind farms in the power system is constantly increasing. Grid-Forming (GFM) and Grid-Following (GFL) converters are gradually forming a hybrid grid-connected structure, with fundamental differences in control strategies, power regulation, and voltage support methods. Grid-Following converters rely on grid voltage for phase-locked control to achieve power following output; while grid-forming converters achieve independent voltage support and frequency regulation through virtual synchronization control. When the two types of converters operate collaboratively in the same grid, the electrical and control links within the system are coupled, generating complex dynamic characteristics across frequency bands. Especially under weak grid conditions, the interaction between voltage loops, current loops, and power control loops can easily induce broadband oscillations, thus affecting the dynamic stability of the power system.

[0003] Currently, research on the dynamic characteristics of wind farms mostly employs full-order small-signal modeling methods, which analyze the frequency domain response of the system by establishing high-dimensional state equations that include electrical, control, and mechanical components. While this approach can comprehensively describe the dynamic behavior of the system, the sheer number of state variables and the high matrix dimension result in significant computational complexity, making it difficult to meet the needs of real-time engineering analysis and dynamic simulation. To address this, some studies have attempted to reduce the model order using eigenvalue truncation or energy mode reduction methods. However, these methods often ignore the differences between grid-type and follow-grid-type control structures, making it difficult for the reduced-order model to maintain the accuracy of the dominant oscillation modes. Furthermore, traditional order reduction methods lack stability feedback mechanisms. When key fast dynamic variables are ignored during simplification, numerical problems such as matrix singularities and eigenvalue drift can easily arise, leading to a decrease in the computability and accuracy of the reduced-order model. In addition, existing methods are still imperfect in terms of multi-timescale partitioning and module interface matching, failing to accurately reflect the dynamic interaction characteristics of power, voltage, and frequency in hybrid wind farms.

[0004] In summary, the process of broadband oscillation modeling and stability analysis for hybrid wind farms with and without grid connection still faces challenges such as excessively high model dimensionality, difficulty in extracting dominant oscillation characteristics, and insufficient stability of the reduced-order system. Particularly within the broadband oscillation range, due to the ineffective separation of dynamics at different time scales, existing reduced-order models struggle to maintain the accuracy of the dominant modes while simultaneously ensuring computational efficiency and numerical stability. Therefore, there is an urgent need for a hybrid wind farm reduced-order modeling method that can balance dominant broadband oscillation characteristics with modeling efficiency, enabling reasonable reduction of dynamic characteristics across multiple time scales and accurate preservation of key oscillation modes. Summary of the Invention

[0005] To address the problems of existing technologies, embodiments of the present invention provide a method for reducing the order of the dominant broadband oscillation applicable to hybrid wind farms with / within a grid. The technical solution is as follows:

[0006] On the one hand, a method for reducing the order of the dominant broadband oscillation applicable to hybrid wind farms with / with grids is provided, including the following steps:

[0007] (1) Establish a full-order small-signal model of a hybrid wind farm that includes grid-connected wind farms and grid-connected wind farms. The model is based on the wind farm output power, grid bus voltage, frequency and phase angle signals to construct an input-output mapping relationship and form a system state equation that reflects the power-voltage coupling characteristics and dynamic interaction of the wind farm.

[0008] (2) Perform modal analysis on the full-order small-signal model, calculate the eigenvalues ​​and eigenvectors of the system, and identify the dominant broadband oscillation mode based on the oscillation frequency, damping ratio and energy distribution characteristics;

[0009] (3) Based on the results of the dominant mode analysis, state variables that have significant response to the frequency band of the mode are selected and divided into a set of slow state variables and a set of fast state variables based on energy contribution, controllability, and observability.

[0010] (4) Based on the partitioning results, a reduced-order model of singular perturbation is established. While maintaining the dominant oscillation mode and damping characteristics of the system, fast dynamic components are ignored and the equivalent state equations between slow dynamic variables are reconstructed to form a reduced-order small-signal model.

[0011] (5) Modular interface matching is performed on the reduced-order model. The power output terminal of the grid-connected wind farm module is coupled with the grid bus voltage node, the current control terminal of the grid-connected wind farm module is associated with the reactive power support interface, and a bidirectional dynamic feedback relationship between modules is established based on the bus voltage, frequency and reactive power signal to form a hybrid wind farm reduced-order system with a unified input and output channel.

[0012] (6) Perform stability verification on the reduced-order system. When the singularity or numerical instability of the fast dynamic subsystem matrix is ​​detected, some variables are re-partitioned and the reduced-order model is reconstructed based on the sensitivity analysis results of the state variables to ensure the numerical stability and computability of the system under multi-timescale modeling.

[0013] (7) Perform order reduction operation on the grid-connected wind farm module and the grid-connected wind farm module respectively. The grid-connected module retains the main variables that reflect the dynamic characteristics of DC bus voltage, rotor angle and active power, while the grid-connected module retains the key control variables that characterize voltage synchronization, reactive power support and frequency regulation characteristics, so as to obtain a reduced-order model that can accurately characterize the broadband oscillation behavior dominated by the hybrid wind farm.

[0014] Furthermore, the full-order small-signal model established in step (1) includes three parts: a grid-connected wind farm subsystem, a grid-connected wind farm subsystem, and a common bus coupling system. Each part achieves input-output interaction through voltage, current, and frequency signals. The common bus coupling system is used to uniformly describe the dynamic power transfer relationship between the two types of wind farms and the power grid.

[0015] Furthermore, the process of identifying the dominant mode in step (2) includes:

[0016] The system matrix is ​​subjected to generalized eigenvalue decomposition. The energy participation index is calculated based on the oscillation frequency and damping ratio of each mode, and the dominant oscillation frequency band is determined based on the energy concentration. When the energy participation exceeds a preset threshold, the mode is determined to be the dominant broadband oscillation mode.

[0017] Furthermore, in step (3), when filtering state variables, the energy contribution of each state variable in the dominant mode frequency band and its projection contribution in the system input and output response are calculated. When the energy contribution of a variable is higher than a preset threshold and the projection contribution ratio reaches a set value, the variable is included in the slow state variable set for retention, so as to improve the ability of the reduced-order model to maintain the dominant broadband oscillation characteristics of the system.

[0018] Furthermore, the singular perturbation-form reduced-order small-signal model established in step (4) includes the following process:

[0019] (1) Based on the result of variable partitioning, the system state equation is split into a slow dynamic subsystem and a fast dynamic subsystem;

[0020] (2) In the multi-timescale modeling framework, high-frequency dynamic components in fast dynamic subsystems are ignored;

[0021] (3) Reconstruct the equivalent state equation based on the coupling relationship between slow dynamic variables to form a reduced-order intermediate model;

[0022] (4) Maintain the dominant mode and damping characteristics of the system to obtain the final reduced-order model that reflects the dominant oscillation behavior of the hybrid wind farm.

[0023] Furthermore, the module interface matching in step (5) includes:

[0024] (1) Dynamically couple the power output terminal of the grid-connected wind farm module to the AC bus voltage node;

[0025] (2) Connect the current control terminal of the grid-type wind farm module to the reactive power support interface of the power grid;

[0026] (3) Introduce virtual impedance control signals into the grid-type module to achieve coordination between voltage regulation and power angle synchronous control;

[0027] (4) Establish a two-way feedback relationship between bus voltage, reactive power, frequency and phase angle signals, so as to realize the module assembly of energy transfer and control quantity interaction consistency.

[0028] Furthermore, in step (6), when verifying the stability of the reduced-order system, the numerical stability is determined by detecting the real part of the eigenvalues ​​of the fast dynamic subsystem matrix and the condition number criterion. When it is determined that the system has singular or unstable characteristics, the high-sensitivity variables are reclassified into the slow state variable set based on the state variable sensitivity analysis results, and the reduced-order model is reconstructed to ensure system stability and simulation accuracy.

[0029] Furthermore, when performing modular order reduction operations in step (7), the grid-connected module uses DC side voltage, mechanical speed and power output as the main state variables, while the grid-connected module uses matching control signal, reactive power support coefficient and frequency adjustment as key variables. A reduced-order hybrid wind farm model is formed through a unified bus coupling interface, thereby maintaining the coordination and consistency between power dynamics and voltage support response.

[0030] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements all the steps of the dominant broadband oscillation order reduction method applicable to grid-type hybrid wind farms.

[0031] On the other hand, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, it implements all the steps of the dominant broadband oscillation order reduction method applicable to grid-connected hybrid wind farms.

[0032] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows:

[0033] This invention provides a method for reducing the dominant broadband oscillation mode applicable to hybrid wind farms with and without grids. By establishing a full-order small-signal model that includes both grid-connected and grid-connected wind farms, and combining the energy contribution and controllability / observability criteria, the dominant broadband oscillation mode is identified, thereby achieving accurate division of dynamics across multiple time scales.

[0034] This invention employs singular perturbation modeling and variable selection mechanisms to significantly reduce the system model order and improve modeling efficiency and numerical stability while maintaining the dominant oscillation mode and damping characteristics. Simultaneously, a modular interface matching strategy ensures the consistency of bidirectional coupling between power, voltage, and frequency signals, improving the dynamic coordination performance between network-type and follow-network-type modules.

[0035] The method of this invention achieves high-precision order reduction while preserving the key dynamic characteristics of the system. It can effectively improve simulation speed and computational stability without sacrificing the accuracy of the dominant mode, and provide reliable model support for broadband oscillation analysis and control strategy optimization of hybrid wind farms. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart illustrating a method for reducing the order of the dominant broadband oscillation applicable to a hybrid wind farm with a grid structure, according to Embodiment 1 of the present invention.

[0038] Figure 2 This is a schematic diagram of the hybrid wind farm structure of Embodiment 1 of the present invention;

[0039] Figure 3 This is a schematic diagram of the participation factor of the dominant mode in the network type according to Embodiment 1 of the present invention;

[0040] Figure 4 This is a schematic diagram of the network-type dominant mode participation factor in Embodiment 1 of the present invention;

[0041] Figure 5 This is a schematic diagram of the interface relationship of the grid-connected system of the hybrid wind farm in Embodiment 1 of the present invention;

[0042] Figure 6 The reactive power Q at the outlet of the grid-type wind turbine in Embodiment 1 of the present invention is... g2 A schematic diagram comparing transient response curves;

[0043] Figure 7The outlet d-axis voltage u of the grid-type wind turbine in Embodiment 1 of the present invention g2d A schematic diagram comparing transient response curves;

[0044] Figure 8 The outlet q-axis voltage u of the grid-type wind turbine in Embodiment 1 of the present invention g2q A schematic diagram comparing transient response curves;

[0045] Figure 9 The grid-connected DC capacitor voltage u in Embodiment 1 of the present invention DC1 A schematic diagram comparing transient response curves;

[0046] Figure 10 This is a schematic diagram of a hybrid wind farm-dominated broadband oscillation order reduction system according to Embodiment 2 of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0048] Example 1

[0049] This embodiment provides a method for reducing the order of the dominant broadband oscillation applicable to hybrid wind farms with and without grids. See [link to relevant documentation]. Figure 1 This includes the following steps:

[0050] Step (1) Establish a full-order small-signal model of a hybrid wind farm that includes grid-connected wind farms and grid-connected wind farms. The model is based on the wind farm output power, grid bus voltage, frequency and phase angle signals to construct an input-output mapping relationship and form a system state equation that reflects the power-voltage coupling characteristics and dynamic interaction of the wind farm.

[0051] Specifically, the full-order small-signal model established in step (1) includes three parts: a grid-connected wind farm subsystem, a grid-connected wind farm subsystem, and a common bus coupling system. Each part achieves input-output interaction through voltage, current, and frequency signals. The common bus coupling system is used to uniformly describe the dynamic power transfer relationship between the two types of wind farms and the power grid.

[0052] Step (2) Perform modal analysis on the full-order small-signal model, calculate the eigenvalues ​​and eigenvectors of the system, and identify the dominant broadband oscillation mode based on the oscillation frequency, damping ratio and energy distribution characteristics;

[0053] Specifically, the process of identifying the dominant mode in step (2) includes:

[0054] The system matrix is ​​subjected to generalized eigenvalue decomposition. The energy participation index is calculated based on the oscillation frequency and damping ratio of each mode, and the dominant oscillation frequency band is determined based on the energy concentration. When the energy participation exceeds a preset threshold, the mode is determined to be the dominant broadband oscillation mode.

[0055] Step (3) Based on the dominant mode analysis results, select state variables that have significant response to the frequency band of the mode, and divide them into a slow state variable set and a fast state variable set based on energy contribution, controllability, and observability.

[0056] Specifically, in step (3), when filtering state variables, the energy contribution of each state variable in the dominant mode frequency band and its projection contribution in the system input and output response are calculated. When the energy contribution of a variable is higher than a preset threshold and the projection contribution ratio reaches a set value, the variable is included in the slow state variable set for retention, so as to improve the ability of the reduced-order model to maintain the dominant broadband oscillation characteristics of the system.

[0057] Step (4) Based on the partitioning results, establish a reduced-order model of singular perturbation form. While maintaining the dominant oscillation mode and damping characteristics of the system, ignore the fast dynamic components and reconstruct the equivalent state equations between the slow dynamic variables to form a reduced-order small-signal model.

[0058] Specifically, the singular perturbation-form reduced-order small-signal model established in step (4) includes the following process:

[0059] (1) Based on the result of variable partitioning, the system state equation is split into a slow dynamic subsystem and a fast dynamic subsystem;

[0060] (2) In the multi-timescale modeling framework, high-frequency dynamic components in fast dynamic subsystems are ignored;

[0061] (3) Reconstruct the equivalent state equation based on the coupling relationship between slow dynamic variables to form a reduced-order intermediate model;

[0062] (4) Maintain the dominant mode and damping characteristics of the system to obtain the final reduced-order model that reflects the dominant oscillation behavior of the hybrid wind farm.

[0063] Step (5) Modular interface matching is performed on the reduced-order model. The power output terminal of the grid-connected wind farm module is coupled with the grid bus voltage node, the current control terminal of the grid-connected wind farm module is associated with the reactive power support interface, and a bidirectional dynamic feedback relationship between modules is established based on the bus voltage, frequency and reactive power signal to form a hybrid wind farm reduced-order system with a unified input and output channel.

[0064] Specifically, the module interface matching in step (5) includes:

[0065] (1) Dynamically couple the power output terminal of the grid-connected wind farm module to the AC bus voltage node;

[0066] (2) Connect the current control terminal of the grid-type wind farm module to the reactive power support interface of the power grid;

[0067] (3) Introduce virtual impedance control signals into the grid-type module to achieve coordination between voltage regulation and power angle synchronous control;

[0068] (4) Establish a two-way feedback relationship between bus voltage, reactive power, frequency and phase angle signals, so as to realize the module assembly of energy transfer and control quantity interaction consistency.

[0069] Step (6) performs stability verification on the reduced-order system. When the fast dynamic subsystem matrix is ​​found to have singularity or numerical instability, some variables are re-partitioned and the reduced-order model is reconstructed based on the sensitivity analysis results of the state variables to ensure the numerical stability and computability of the system under multi-timescale modeling.

[0070] Furthermore, in step (6), when verifying the stability of the reduced-order system, the numerical stability is determined by detecting the real part of the eigenvalues ​​of the fast dynamic subsystem matrix and the condition number criterion. When it is determined that the system has singular or unstable characteristics, the high-sensitivity variables are reclassified into the slow state variable set based on the state variable sensitivity analysis results, and the reduced-order model is reconstructed to ensure system stability and simulation accuracy.

[0071] Step (7) performs order reduction operations on the grid-connected wind farm module and the grid-connected wind farm module respectively. The grid-connected module retains the main variables that reflect the dynamic characteristics of DC bus voltage, rotor angle and active power, while the grid-connected module retains the key control variables that characterize voltage synchronization, reactive power support and frequency regulation characteristics, so as to obtain a reduced-order model that can accurately characterize the broadband oscillation behavior dominated by the hybrid wind farm.

[0072] Furthermore, when performing modular order reduction operations in step (7), the grid-connected module uses DC side voltage, mechanical speed and power output as the main state variables, while the grid-connected module uses matching control signal, reactive power support coefficient and frequency adjustment as key variables. A reduced-order hybrid wind farm model is formed through a unified bus coupling interface, thereby maintaining the coordination and consistency between power dynamics and voltage support response.

[0073] To facilitate a fuller understanding of the present invention by those skilled in the art, the following description, in conjunction with the technical process, further illustrates this embodiment. It should be noted that the sequence of steps, parameter settings, and mathematical derivations described in the embodiments aim to elucidate the working principle and preferred implementation path of the hybrid wind farm-dominated broadband oscillation order reduction method proposed in this invention. Under different grid strength, generator capacity, line impedance, and control strategy configurations, the relevant modeling methods, parameter values, and simulation scenarios can be adjusted or equivalently replaced according to actual needs without affecting the basic concept, core features, and expected technical effects of this method.

[0074] In this embodiment, the complete technical solution provided by the present invention is as follows. This solution comprehensively considers the differences in control characteristics between grid-connected and grid-connected wind farms. Through steps such as full-order small-signal modeling, dominant mode identification, state variable screening, singular perturbation order reduction, and module interface matching, it achieves the preservation and efficient modeling of the dominant broadband oscillation characteristics of hybrid wind farms. The specific process includes a system modeling stage, a dominant mode analysis stage, a state variable partitioning stage, a reduced-order model establishment stage, and a model stability verification stage. Data association and model coupling are achieved between each stage through input / output signals and dynamic feedback, thus constituting a complete reduced-order modeling process.

[0075] The complete technical solution of this invention includes the following steps:

[0076] Step 1: Establish a full-order small-signal model of the grid-connected / grid-connected hybrid wind farm system, divide it into modules, and solve the oscillation modes of the full-order small-signal model for different modules.

[0077] like Figure 2 The hybrid wind farm grid-connected system is divided into three modules: grid-connected wind farm, grid-connected wind farm, and AC grid. Eigenvalue analysis is performed on the full-order systems of the established grid-connected wind farm and grid-connected wind farm to obtain their oscillation modes.

[0078] Step 2: Quantify the degree of dominance of each oscillation mode on the dynamic characteristics of the system through dominance analysis.

[0079] The oscillation modes of the system are decoupled by similarity matrix transformation. The eigenvector matrix V of the system is obtained by eigenvalue decomposition. Using the similarity transformation shown in equation (1), the state matrix A of the system is transformed into a diagonal matrix Λ, thereby making the oscillation modes of the system independent.

[0080] Λ=V -1 AV (1)

[0081] After similarity matrix transformation, the state-space model of the system is represented as:

[0082]

[0083] In the formula, ΔX n×1 =V n×n Δz n×1 .

[0084] Dominance can simultaneously reflect the degree of influence of system eigenvalues ​​on the dynamic characteristics of the system and the dynamic characteristics of each output variable. This is achieved by calculating the transformed input matrix V. -1 Using B and the output matrix CV, the dominance of each mode is evaluated. The sub-dominance formula is expressed as:

[0085]

[0086] In the formula, i = 1 to n, j = 1 to q, h = 1 to p; b Λih c Λji V -1 Elements in the B and CV matrices; λ i This is a system characteristic value. D i-jh That is to say, in b Λih c Λji Under the action, λ i For ΔY j The dominant role of λ. i λ can be calculated by summing the subdominant degrees of all output variables ΔY. i Dominance of ΔY.

[0087]

[0088] The dominance of each oscillation mode in the full-order system of grid-connected and grid-connected wind farms was calculated separately. To preserve the broadband oscillation characteristics of the system as much as possible, the top three modes that have the greatest influence on the dynamic characteristics of the system were defined as the dominant oscillation modes.

[0089] Step 3: Combining the contribution of the dominant oscillation mode participation factor with the weight of the Hankel singular value, divide the fast and slow state variables and construct a reduced-order small-signal model with different module singular perturbation forms.

[0090] (1) First, participation factor analysis was performed on the dominant oscillation modes of different modules. Based on the participation degree, the speed of state variable partitioning in the system was determined, and the results are as follows: Figure 3 , Figure 4 As shown.

[0091] Based on the above participation data, the strongly correlated variable Δx T1 , Δi xg1 , Δi x1 , Δu DC1 , Δi qs Δx a1 Δx b1The variables are divided into slow-state variables to preserve the broadband oscillation characteristics of grid-connected wind farm systems; the strongly correlated variable Δu is also classified as a slow-state variable. DC2 Δx T2 Δx T5 Δx4, Δx p Δx T3 Δx T4 Δx5 and Δx6 are classified as slow state variables to preserve the broadband oscillation characteristics of matched control grid-type wind farm systems.

[0092] (2) The dynamic characteristics of the system are determined by the degree of influence of the state variables on the input and output. This correlation can be characterized by the Gram matrix. The controllability and observability of the Gram matrix are shown in Equation (5), and the Hankel singular values ​​are shown in Equation (6).

[0093]

[0094] In the formula, λ i () indicates the i-th eigenvalue obtained from the matrix within the parentheses.

[0095] Hankel singular values ​​do not directly correspond to the original state variables. Through equilibrium realization, the system coordinates can be transformed to a set of orthogonal state directions that balance controllability and observability, thus establishing a one-to-one correspondence between Hankel singular values ​​and state variables. The process is as follows:

[0096] Perform eigenvalue decomposition on matrices P and Q. This decomposes them into a pair of orthogonal matrices and a diagonal matrix:

[0097]

[0098] In the formula, U c U0 and U0 are the characteristic matrices of P and Q, respectively; S c S0 is a diagonal matrix, and its diagonal elements are the eigenvalues ​​of P and Q, respectively.

[0099] The product moment H is constructed based on the eigenma and the diagonal matrix, which is then used for further singular value decomposition.

[0100]

[0101] The product moment H is decomposed into singular values, which decomposes H into three matrices.

[0102]

[0103] In the formula, U H V H Σ is an orthogonal matrix, and Σ is a diagonal matrix.

[0104] Thus, the formula for the balance transformation matrix T is shown in equation (10).

[0105]

[0106] The state variables of the original system are transformed into a new set of state variables through the equilibrium transformation matrix T, so that the system satisfies the equilibrium condition in this new coordinate system: that is, the controllability and observability matrices are diagonalized. Therefore, the transformation between the equilibrium state variables and the original system state variables can be realized through equation (11), thereby realizing a one-to-one correspondence between Hankel singular values ​​and state variables.

[0107]

[0108] To further standardize Hankel singular values, they are normalized.

[0109]

[0110] To preserve the main dynamic behavior of the system, this paper adopts a two-stage retention criterion: first, the main state directions that enable the system's input-output response energy to reach 95% are retained through Hankel singular value screening; then, the projection contribution of the original state variables in these main directions is statistically analyzed, and the original variables whose cumulative contribution reaches 90% are further retained.

[0111] Based on the above principles, Hankel singular value solving was performed on both grid-connected direct-drive wind farms and grid-connected direct-drive wind farms. The results show that the first five state variables contribute a cumulative 90% to the slow state variables in the grid-connected wind farm. Therefore, Δx is added to the slow state variables. T3 and Δx T5 In grid-type wind farms, the first seven state variables contribute a cumulative 90% to the total. Therefore, Δi should be added to the slow state variables. xg2 , Δi yg2 Δx T6 and Δi qs .

[0112] (3) Based on the multi-timescale characteristics of the system, the system parameters are divided into fast state variables and slow state variables, forming a singular perturbation form as shown in equation (13), and the dynamic process of the fast state variables is ignored in order to achieve system order reduction.

[0113]

[0114] In the formula, n1 is the slow state variable number, n2 is the fast state variable number, and ε is the neglect factor.

[0115] When ε = 0, the reduced-order intermediate equation shown in equation (14) can be obtained. At this time, the dynamic characteristics of the fast state variables are ignored, while the steady-state characteristics of the system are preserved. Substituting equation (14) into equation (13) yields the reduced-order small-signal model shown in equation (15).

[0116]

[0117] In the formula, A T B T C T D T These are the low-order state matrix, low-order input matrix, low-order output matrix, and low-order direct connection matrix, respectively, and their specific expressions are shown in Equation (16).

[0118]

[0119] From equation (16), it can be seen that the requirement for reducing the order of the system using the singular perturbation method is A. n2×n2 The key to non-singularity lies in the reasonable division of fast and slow state variables. A properly divided reduced-order system can retain the dominant broadband oscillation modes of the full-order system while also reflecting its dynamic characteristics. Therefore, A... n2×n2 Singularity analysis, if A n2×n2 If A is a singular matrix, then further analysis of A is needed. n2×n2 The sparsity of A is determined by identifying the state variables that result in high sparsity under steady-state conditions. These variables are then reclassified as slow state variables, making A... n2×n2 Non-singular; if A n2×n2 If it is a non-singular matrix, then a reduced-order small-signal model as shown in equation (15) can be established to realize the reduction of the system order.

[0120] The selected grid-connected direct-drive wind farm example in this invention, after initially dividing the fast and slow state variables, A n2×n2 Since it is a singular matrix, the singular perturbation form cannot be directly applied for order reduction; slow state variables need to be added. According to A... n2× The sparsity of n2 allows for the addition of slow state variables Δx5, Δω, Δx2, Δx4, and Δx3. Similarly, in the grid-type direct-drive wind farm example selected in this invention, after initially dividing the fast and slow state variables, A... n2×n2 It is also a singular matrix, and its order cannot be directly reduced using the singular perturbation form; slow state variables need to be added. According to A... n2×n2 Given the sparsity, we supplement Δx2, Δx3, Δω, Δx7, and Δx8 as slow state variables.

[0121] Thus, the division of fast and slow state variables is complete. The slow variable set of the grid-connected direct-drive wind farm contains a total of 14 state variables. Therefore, the order of the grid-connected direct-drive wind farm reduced system is 14. The division results are shown in equations (17) and (18).

[0122]

[0123] The slow variable set of a grid-type direct-drive wind farm contains 18 state variables, therefore the order of the reduced-order system of the grid-type direct-drive wind farm is 18. The partitioning results are shown in equations (19) and (20).

[0124]

[0125] Step 4: Connect each module based on the electrical connection relationship of the system to obtain a complete grid-connected / grid-connected hybrid wind farm grid-connected system reduced-order model.

[0126] After obtaining the reduced-order models of the grid-connected and grid-connected direct-drive wind farm modules respectively, according to Figure 5 The electrical connections between the modules within the system are shown, and the input and output ports of each state-space model submodule are connected to obtain the reduced-order small-signal model of the grid-connected / grid-connected hybrid wind farm system. At this point, the reduced-order small-signal model of the grid-connected / grid-connected hybrid wind farm is complete, and the 52nd-order full-order small-signal model is reduced to a 36th-order reduced-order small-signal model.

[0127] Application Examples

[0128] The accuracy of the reduced-order small-signal model was verified by comparing and analyzing the transient responses of the full-order and reduced-order systems of a grid-connected / gathered hybrid wind farm. The total simulation time was set to 8 seconds, and the reactive power command value Q of the gathered-grid GSC controller was set at 3 seconds. gref2 It jumps from 0 to 0.1 Mvar. Figures 6-9 The reactive power Q at the outlet of the grid-type wind turbine was compared between the full-order system and the reduced-order system. g2 ;Outlet d-axis voltage u of grid-type fan g2d ; Outlet q-axis voltage u of grid-type fan g2q ; and the voltage u of the grid-type DC capacitor DC1 The transient response curve.

[0129] Depend on Figures 6-9 It can be seen that the transient response changes of each variable in the reduced-order system of the grid-connected hybrid wind farm are in good agreement with those of the full-order system, and the steady-state values ​​of the reduced-order system before and after the step change are consistent with the steady-state values ​​of the corresponding variables in the full-order system.

[0130] The results of comparing the retention modes of the downgraded system in the grid-connected / grid-connected hybrid wind farm are shown in Table 1.

[0131] Table 1 Comparison of Retention Modes for Downgraded Systems in Hybrid Grid-connected / Grid-connected Wind Farms

[0132]

[0133] As shown in Table 1, the downgraded system of the integrated / grid-connected wind farm retains 10 oscillation modes, and the retained modes are basically consistent with the full-order system, with an average error of only 1.08%. Therefore, the obtained downgraded system of the integrated / grid-connected wind farm can well reflect the broadband oscillation characteristics of the full-order system.

[0134] In summary, the established reduced-order system of the hybrid wind farm can well reflect the transient response characteristics and preserved mode eigenvalues ​​of the full-order system, thus verifying the accuracy of the established reduced-order small-signal model.

[0135] Example 2

[0136] To further illustrate the technical solution of the present invention, a system embodiment for implementing the method for reducing the dominant broadband oscillation of a hybrid wind farm is given below. This system is applicable to the identification of dominant modes, order reduction modeling, and stability analysis of grid-connected and grid-connected hybrid wind farms, and can achieve fully automated processing in engineering operation and simulation calculations.

[0137] like Figure 10 As shown, the system provided in this embodiment includes: a modeling module, a modality recognition module, a variable filtering module, a reduced-order modeling module, an interface matching module, a stability verification module, and a control execution module.

[0138] Each module transmits information through a data bus and signal interaction unit, forming a reduction-order analysis system centered on multi-timescale modeling. Specifically, the model modeling module constructs a full-order small-signal model of the hybrid wind farm; the modal identification module extracts the dominant broadband oscillation modes of the system; the variable selection module divides state variables based on energy contribution and controllability / observability criteria; the reduction-order modeling module generates a low-order small-signal model based on singular perturbation theory; the interface matching module coordinates the interaction of power, voltage, and frequency signals between grid-connected and grid-following wind farms; the stability verification module verifies the numerical stability and modal consistency of the reduced-order system; and the control execution module handles model operation and result output, as detailed below:

[0139] 1. Model building module

[0140] This module is used to read the wind farm topology and control parameters, establish a full-order small-signal model including grid-connected and grid-connected units, grid lines and bus nodes, and generate state-space equations.

[0141] 2. Modality recognition module

[0142] By performing eigenvalue decomposition and energy mode analysis on the system matrix, the dominant broadband oscillation frequency band is identified, and the corresponding modal eigenvalues ​​and damping information are transmitted to the variable selection module.

[0143] 3. Variable Filtering Module

[0144] Based on the energy contribution and variable projection contribution results, a set of key slow dynamic variables is selected, and high-frequency dynamic variables are identified as fast variables to provide input for order reduction modeling.

[0145] 4. Order Reduction Modeling Module

[0146] The singular perturbation decomposition method is used to divide the state equation into time scales and reduce variables, while preserving the dominant oscillation mode and damping characteristics, thus generating a reduced-order small-signal model.

[0147] 5. Interface Matching Module

[0148] It is used to realize signal interaction between network-type and follow-network-type modules, unify the power output terminal, voltage node and frequency support interface to the common bus coupling unit, and establish the dynamic coupling relationship between the electrical and control layers through virtual impedance signals.

[0149] 6. Stability Verification Module

[0150] By analyzing the changes in the real part of the eigenvalues ​​of the reduced-order system matrix and the condition number index, we can detect whether there are numerical singularities or instabilities in the reduced-order model. If an anomaly is detected, we can feed back to the variable filtering module to reclassify the state variables.

[0151] 7. Control Execution Module

[0152] This module includes a graphical modeling interface and a simulation execution engine, which are used to automate the order reduction process on the computer and output analysis results including modal frequencies, damping ratios, system sensitivity, and model consistency.

[0153] During system operation, the modules collaborate via a data exchange bus. The full-order small-signal model generated by the model modeling module serves as the system input. The modal recognition module extracts features from it and transmits the recognition results to the variable filtering module. After classifying the state variables, the variable filtering module reduces the model based on the classification results. The generated reduced-order model is assembled by the interface matching module to form a complete hybrid wind farm reduced-order system. Subsequently, the stability verification module tests the system matrix characteristics to ensure stable and reliable results. Finally, the control execution module outputs the reduced-order model and simulation analysis report, realizing a closed-loop process from modeling to analysis.

[0154] Through the modular design described above, the system provided in this embodiment achieves fully automated and visualized operation of the broadband oscillation order reduction process in hybrid wind farms, featuring clear structure, independent modules, and efficient data interaction. This system can be widely applied to dynamic stability analysis, parameter optimization, and control strategy verification of new energy power systems, providing unified technical support for the joint modeling and engineering evaluation of grid-connected and grid-linked wind farms.

[0155] In another embodiment of the present invention, a computer-readable storage medium is provided having a computer program stored thereon.

[0156] When the program is executed by the processor, it is used to implement all the steps of the dominant broadband oscillation order reduction method applicable to the grid-type hybrid wind farm described in Embodiment 1 above.

[0157] This computer program can be deployed on servers, simulation analysis terminals, or local computer environments. By calling the instruction logic of modules such as system modeling, modal recognition, variable filtering, singular perturbation reduction, and interface matching, it can achieve fully automated operation from data input to reduced model output.

[0158] The storage medium can be a read-only memory (ROM), random access memory (RAM), disk storage, optical disk storage, flash memory, solid-state drive, memory card, or other electronic media capable of storing program code.

[0159] By storing executable instructions in the medium, the entire process of full-order modeling, dominant mode identification, variable partitioning, reduced-order model generation, and stability verification of a hybrid wind farm can be realized on a computer.

[0160] This enables the programmatic implementation and generalized deployment of the dominant broadband oscillation order reduction modeling method proposed in this invention.

[0161] In another embodiment of the present invention, an electronic device is provided for performing the hybrid wind farm-dominated broadband oscillation order reduction method described in Embodiment 1 above.

[0162] The electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor.

[0163] When the processor executes the computer program, it sequentially completes steps such as system modeling, dominant mode identification, variable screening, order reduction modeling, interface matching, and stability verification, thereby outputting the order reduction small-signal model of the hybrid wind farm and related analysis results.

[0164] The electronic device may be a computer server, a simulation analysis workstation, an industrial control unit, a cloud computing node, or an embedded computing module.

[0165] During operation, the memory is used to store data and program instructions, the processor is responsible for performing logical operations and task scheduling, and data communication is achieved through the bus and input / output interface.

[0166] When this electronic device is deployed in a power grid simulation platform or a new energy monitoring system, it can realize real-time calculation, data update and result visualization of hybrid wind farm reduced-order modeling, providing computational support for oscillation analysis and control optimization of new energy power systems.

[0167] In summary, the dominant broadband oscillation reduction method proposed in this invention, applicable to hybrid wind farms with grid connection and grid-connected turbines, focuses on the dynamic coupling relationship between grid-connected converters and grid-connected turbines in hybrid wind farms. By constructing a unified small-signal model, identifying the dominant oscillation mode, and performing variable selection and singular perturbation reduction modeling, it achieves accurate simplification of the system model while preserving the dominant dynamic characteristics. The system embodiment of this invention further modularizes the above method, realizing integrated processing of data input, modeling calculation, interface matching, and stability verification. This method and system can be widely applied to broadband oscillation analysis, stability assessment, and control strategy optimization in new energy power systems, featuring clear model structure, high computational efficiency, and strong interpretability of results.

[0168] It should be understood that the embodiments of the present invention are only used to illustrate the principles and features of the present invention, and are not intended to limit the scope of protection of the present invention. For those skilled in the art, any adjustments, improvements, or equivalent substitutions to the structural form, algorithm parameters, and signal flow of each module without departing from the principles of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for dominant wide frequency oscillation damping order reduction suitable for hub / grid type hybrid wind farms, characterized in that, The method comprises the following steps: (1) establishing a full-order small-signal model of a hybrid wind farm comprising a grid-following wind farm and a grid-forming wind farm, the model being based on wind farm output power, grid bus voltage, frequency and phase angle signals to build input-output mapping relationships and form system state equations reflecting wind farm power-voltage coupling characteristics and dynamic interactions; (2) performing modal analysis on the full-order small-signal model to calculate eigenvalues and eigenvectors of the system, and identifying a dominant wide-frequency oscillation mode according to oscillation frequency, damping ratio and energy distribution characteristics; (3) based on the analysis results of the dominant mode, selecting state variables that have a significant response in the frequency band of the mode, and dividing the state variables into a slow state variable set and a fast state variable set according to energy contribution and controllability and observability; (4) according to the division results, establishing a singular perturbation form of a reduced-order model, ignoring fast dynamic components and reconstructing equivalent state equations among slow dynamic variables while keeping the dominant oscillation mode and damping characteristics of the system, to form a reduced-order small-signal model; (5) performing modular interface matching on the reduced-order model, coupling the power output end of the grid-following wind farm module with the grid bus voltage node, associating the current control end of the grid-forming wind farm module with the reactive power support interface, and establishing a two-way dynamic feedback relationship between modules according to bus voltage, frequency and reactive power signals to form a hybrid wind farm reduced-order system with unified input-output channels; (6) performing stability checking on the reduced-order system, and when singularity or numerical instability is detected in the fast dynamic subsystem matrix, re-dividing and reconstructing the reduced-order model according to state variable sensitivity analysis results to ensure numerical stability and calculability of the system under multi-time scale modeling; (7) performing reduced-order operation on the grid-following wind farm module and the grid-forming wind farm module respectively, wherein the grid-following module retains main variables reflecting direct current bus voltage, rotor angle and active power dynamic characteristics, and the grid-forming module retains key control variables representing voltage synchronization, reactive power support and frequency regulation characteristics, to obtain a reduced-order model with lower order and capable of accurately representing dominant wide-frequency oscillation behavior of the hybrid wind farm.

2. The method of claim 1, wherein, The full-order small-signal model established in step (1) comprises a grid-following wind farm subsystem, a grid-forming wind farm subsystem and a common bus coupling system, each part realizing input-output interaction through voltage, current and frequency signals, wherein the common bus coupling system is used to uniformly describe dynamic power transfer relationships between the two types of wind farms and the grid.

3. The method of claim 1, wherein, The process of identifying the dominant mode in step (2) comprises: performing generalized eigenvalue decomposition on the system matrix, calculating an energy participation index according to the oscillation frequency and damping ratio of each mode, and determining the dominant oscillation frequency band according to the energy concentration degree; when the energy participation index exceeds a preset threshold, the mode is determined as a dominant wide-frequency oscillation mode.

4. The method of claim 1, wherein, In the step (3), when screening the state variables, the energy contribution degree of each state variable in the dominant mode frequency band and the projection contribution in the system input and output response are calculated. When the energy contribution degree of a variable is higher than a preset threshold and the projection contribution ratio reaches a set value, the variable is included in the slow state variable set for retention, so as to improve the retention ability of the reduced order model to the dominant wide frequency oscillation characteristics of the system.

5. The method of claim 1, wherein, The singular perturbation form reduced order small signal model established in the step (4) includes the following processes: (1) According to the variable division result, the system state equation is divided into a slow dynamic subsystem and a fast dynamic subsystem; (2) In the multi-time scale modeling framework, the high frequency dynamic components in the fast dynamic subsystem are ignored; (3) The equivalent state equation is reconstructed according to the coupling relationship between the slow dynamic variables to form a reduced order intermediate model; (4) The dominant mode and damping characteristics of the system are maintained to obtain the final reduced order model reflecting the dominant oscillation behavior of the hybrid wind farm.

6. The method of claim 1, wherein, The module interface matching in the step (5) includes: (1) The power output end of the grid-connected wind farm module is dynamically coupled with the AC bus voltage node; (2) The current control end of the grid-constructing wind farm module is associated with the grid reactive power support interface; (3) A virtual impedance control signal is introduced in the grid-constructing module to realize the coordination of voltage regulation and power angle synchronous control; (4) The bidirectional feedback relationship of bus voltage, reactive power, frequency and phase angle signals is established to realize the consistency of energy transmission and control quantity interaction in module assembly.

7. The method of claim 1, wherein, When checking the stability of the reduced order system in the step (6), the numerical stability of the fast dynamic subsystem matrix is judged by detecting the real part of the eigenvalue and the condition number criterion. When it is determined that the system has singular or unstable characteristics, the high sensitivity variable is re-divided into the slow state variable set according to the state variable sensitivity analysis result, and the reduced order model is re-constructed to ensure the stability and simulation accuracy of the system.

8. The method of claim 1, wherein, When the modular reduced order operation is performed in the step (7), the grid-connected module takes the DC side voltage, mechanical speed and power output as the main state variables, the grid-constructing module takes the matching control signal, reactive power support coefficient and frequency regulation as the key variables, and the reduced order hybrid wind farm model is formed through the unified bus coupling interface, so as to keep the coordination of power dynamic and voltage support response.

9. A computer readable storage medium having stored thereon a computer program for implementing all the steps of the dominant wide frequency oscillation reduction method for the grid-connected / grid-constructing hybrid wind farm according to any one of claims 1 to 8 when the program is executed by a processor.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that, The processor executes the computer program to implement all the steps of the dominant wide frequency oscillation reduction method for the grid-connected / grid-constructing hybrid wind farm according to any one of claims 1 to 8.

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