Improved singular perturbation reduced order method for subsynchronous oscillation analysis of direct-drive wind farms

Abstract

The application discloses an improved singular perturbation reduced-order method suitable for sub-synchronous oscillation (SSO) analysis of a direct-drive wind farm (DDWF). Firstly, the dominant role of each oscillation mode of the DDWF system in system dynamic characteristics is quantified based on a dominant degree analysis principle. Secondly, according to the size of the dominant degree of each oscillation mode, a reserved mode set of the DDWF system including the dominant oscillation mode and the SSO mode of the DDWF system is established under the framework of a reserved mode set determination principle. Thirdly, on the basis of the factor analysis result of all the reserved modes, state variables having a relatively strong correlation with the reserved modes are screened out as slow dynamic variables, and multi-time scale division of the DDWF system is completed. Finally, on the basis of the multi-time scale division of the DDWF, a singular perturbation reduced-order system of the DDWF is finally established based on a singular perturbation principle. The improved singular perturbation reduced-order method can reduce the order of the DDWF system to the maximum extent, improve simulation efficiency, fully retain dynamic characteristics and SSO characteristics of the full-order system of the DDWF, and provide strong support for SSO problem analysis of large-scale DDWF incorporated into a weak power grid system.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and more specifically to an improved method for reducing the order of singular perturbations in direct-drive wind farms (DDWF) suitable for subsynchronous oscillation (SSO) analysis. Background Technology

[0002] The large-scale integration of wind power into the power system may induce subsynchronous oscillations (SSO). In recent years, several SSO incidents caused by wind farm grid connection have occurred both domestically and internationally. Therefore, it is necessary to study the SSO problem of direct-drive wind farms (DDWFs) integrated into weak power grid systems.

[0003] Currently, the main research methods for subsynchronous switching (SSO) in direct-drive wind farms are impedance analysis and eigenvalue analysis. Eigenvalue analysis can not only characterize the degree of subsynchronous interaction between different devices but also obtain all the characteristic information of the system, hence its widespread application. However, in actual power system operation, multiple direct-drive wind farms (DDWFs) are often connected to a weak power grid through the same connection point. In this case, while eigenvalue analysis based on the full-order system model can accurately describe the system's dynamic characteristics, it increases the difficulty of numerical calculations, consumes a large amount of computational resources, and may even cause the "curse of dimensionality." Therefore, it is necessary to study corresponding DDWF order reduction methods to adapt to SSO analysis of DDWFs connected to weak power grid systems.

[0004] Because the mechanical and power electronic equipment contained in a DDWF (Doubly-Funded Wind Farm) have different response speeds, DDWFs exhibit transient processes at multiple time scales, classifying them as multi-time-scale systems. To balance computational efficiency and accuracy, the order of a full-order DDWF system can be reduced by ignoring small-time-scale imbalance states. Singular perturbation theory, as an order reduction method based on multi-time-scale characteristics, is widely used in various power systems such as doubly-fed wind farms and microgrids. However, existing singular perturbation order reduction methods and existing improved DDWF singular perturbation order reduction methods aim to ensure the consistency of the static and dynamic characteristics of the system before and after order reduction. They focus on the multi-time-scale partitioning process of the system and achieve the elimination of specific system states by calculating the magnitude of the singular perturbation parameters corresponding to each state variable. Since the order reduction process does not consider the preservation of the system's SSO (Self-Solution) mode, it is unclear whether the DDWF reduced-order system established using existing singular perturbation order reduction methods can retain the SSO characteristics of the full-order system. Therefore, the DDWF reduced-order system obtained using existing singular perturbation order reduction methods cannot be applied to the SSO analysis of DDWF systems connected to weak power grids.

[0005] To reproduce the dynamic characteristics of the full-order system while ensuring that the DDWF-reduced system exhibits consistent SSO characteristics with the full-order system, the dominant oscillation mode should be identified before singular perturbation reduction. Then, the set of modes to be retained in the DDWF-reduced system, including the SSO mode and the dominant oscillation mode, should be determined. In classical control theory, the dominant oscillation mode is usually identified manually based on the distribution of eigenvalues ​​in the s-plane. The effectiveness of this method depends heavily on the researcher's experience and the distribution characteristics of the eigenvalues; therefore, the dominant oscillation mode determination results obtained by this method are highly random. Thus, it is necessary to study an objective and effective method for determining the dominant oscillation mode.

[0006] Based on the above research, this invention proposes an improved singular perturbation order reduction method for direct-drive wind farms suitable for subsynchronous oscillation analysis. First, by calculating the dominance of each oscillation mode in the DDWF system, the dominant role of each oscillation mode on the system's dynamic characteristics is quantified. Second, based on the magnitude of the dominance of each oscillation mode, and with the principle of minimizing the DDWF system order, a set of retained modes for the DDWF order reduction system is established, including the dominant oscillation mode and the SSO mode. Third, based on the factor analysis results of all retained modes, state variables with strong correlation to the retained modes are selected as slow dynamic variables, completing the multi-timescale partitioning of the DDWF system. Finally, based on the multi-timescale partitioning of the DDWF, and based on the singular perturbation principle, a DDWF singular perturbation order reduction system is finally established. This improved DDWF singular perturbation order reduction method, based on the principle that the dynamic characteristics and SSO characteristics of the DDWF system remain unchanged before and after order reduction, provides a detailed DDWF system singular perturbation order reduction process. This method can significantly reduce the order of DDWF systems, while the reduced-order DDWF system can fully reproduce the dynamic characteristics and SSO characteristics of the full-order DDWF system, thus possessing certain economic and practical value. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to propose an improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis.

[0008] The technical solution adopted in this invention is as follows.

[0009] An improved method for order reduction of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis, is proposed. First, based on the principle of dominance analysis, the dominant role of each oscillation mode in the dynamic characteristics of the DDWF system is quantified. Second, according to the magnitude of the dominance of each oscillation mode, and with the principle of minimizing the order of the DDWF system, a set of retained modes for the DDWF order reduction system is established, including the dominant oscillation mode and the SSO mode. Third, based on the factor analysis results of all retained modes, state variables with strong correlation to the retained modes are selected as slow dynamic variables, completing the multi-timescale partitioning of the DDWF system. Finally, based on the multi-timescale partitioning of the DDWF and the principle of singular perturbation, the DDWF singular perturbation order reduction system is finally established.

[0010] As a preferred technical solution of the present invention, the solution includes the following steps:

[0011] S1: Establish a full-order small-signal model of the DDWF system and obtain the eigenvalues ​​corresponding to all oscillation modes of the system.

[0012] S2: Based on the principle of dominance analysis, calculate the dominance of each oscillation mode in the DDWF system.

[0013] Based on the principle of dominance analysis, the dominance of each oscillation mode of the DDWF system is calculated, and the degree of dominance of each oscillation mode of the DDWF system on the dynamic characteristics of the system is quantified.

[0014] S3: Establish the set of retained modes for the DDWF system and complete the multi-timescale partitioning of the DDWF system.

[0015] Based on the dominance of each oscillation mode in the DDWF system, and within the framework of the principles for determining the retained mode set of the DDWF system, a retained mode set including the dominant oscillation mode and the SSO mode is established. Participation factor analysis is performed on all retained modes to screen out state variables with strong correlations to each retained mode as slow dynamic variables, thus completing the multi-timescale partitioning of the DDWF system.

[0016] S4: Based on singular perturbation theory, establish a DDWF singular perturbation order reduction system.

[0017] Step S2, based on the principle of dominance analysis, calculates the dominance of each oscillation mode in the DDWF system. The specific strategy is as follows:

[0018] S21: Construct a specific DDWF system output matrix

[0019] Based on actual research needs, a specific DDWF system output matrix is ​​constructed to characterize the dynamic characteristics of the DDWF system.

[0020] S22: Calculate the dominance of each oscillation mode in the DDWF system

[0021] Based on the output matrix of a specific system, and using the principle of dominance analysis, the dominance of each oscillation mode in the DDWF system is calculated to quantify the degree of dominance of each oscillation mode on the dynamic characteristics of the system. The calculation method for the dominance of each oscillation mode in the DDWF system is shown in equations (1)-(5).

[0022] Λ=V -1 AV = diag(λ1...λ k ...λ n (1)

[0023]

[0024] In the formula, A is the DDWF system state matrix; B is the DDWF system input matrix; and C is the DDWF system output matrix.

[0025] V is the characteristic matrix of matrix A; λ1...λ k ...λ n These are the characteristic values ​​of the DDWF system.

[0026] DDWF system oscillation mode λ i The dominance of the system output matrix is ​​shown in equation (4).

[0027]

[0028] In the formula, D ij-h The calculation method is shown in equation (5).

[0029]

[0030] Step S3 establishes the set of modes to be preserved in the DDWF reduced-order system and completes the multi-timescale partitioning of the DDWF system. The specific strategy is as follows:

[0031] S31: Based on the magnitude of the dominance of each oscillation mode of the DDWF system calculated in step S2, and within the framework of the principle for determining the reserved mode set of A1-A4, establish a reserved mode set of the DDWF system, including the dominant oscillation mode and the SSO mode of the DDWF system.

[0032] A1: The reserved mode set must include the dominant oscillation mode of the DDWF system and all SSO modes.

[0033] A2: After partitioning the fast and slow variables of the DDWF system according to the retention mode, in the singular perturbation form corresponding to the DDWF system, matrix A 22 It must be non-singular.

[0034] A3: Practice shows that assigning the dq components of the same variable to variable sets at different time scales may worsen the dynamic characteristics of the reduced-order system. Therefore, in the fast and slow variable partitioning results of the DDWF system, the dq components of the same variable should be in the same variable set at the same time scale, that is, they should be in either the fast variable set or the slow variable set simultaneously.

[0035] A4: Based on the above principles, the order of the DDWF reduced-order system should be minimized.

[0036] S32: Perform participation factor analysis on each retention mode in the DDWF system retention mode set;

[0037] S33: Define the state variables with a participation factor greater than 0.1 in any retained mode as slow dynamic variables, and the remaining state variables as fast dynamic variables, thereby completing the fast and slow variable division of the DDWF system.

[0038] Step S4, based on singular perturbation theory, establishes a DDWF singular perturbation order reduction system. The specific strategy is as follows:

[0039] Based on the DDWF multi-timescale partitioning results in step S3, a DDWF singular perturbation model is established according to equation (6).

[0040]

[0041] In the formula, Δx I For the slow dynamic variable set of the DDWF system; Δx II ε is the set of fast dynamic variables of the DDWF system; ε is the set of singular perturbation parameters of the DDWF system.

[0042] Let ε = 0, the DDWF full-order system degenerates into the form shown in equation (7), that is, the DDWF singular perturbation reduced-order system is established.

[0043]

[0044] The beneficial effects of this invention are as follows: First, by calculating the dominance of each oscillation mode in the DDWF system, the degree of dominance of each oscillation mode on the dynamic characteristics of the system is effectively quantified. Then, the dominant oscillation mode is identified based on the magnitude of its dominance, effectively avoiding the order reduction error that may result from manually identifying the dominant oscillation mode based on the location of eigenvalues. Finally, based on the principle of minimizing the order of the DDWF reduced system, the dominant oscillation mode and the SSO mode of the DDWF system are determined to form the retained mode set of the DDWF reduced system. Multi-timescale partitioning of the DDWF system is completed based on participation factor analysis, thereby establishing the DDWF singular perturbation reduced system. This method not only ensures that the DDWF reduced system accurately reproduces the dynamic characteristics of the full-order DDWF system, but also effectively preserves the SSO mode of the full-order DDWF system. Simulation analysis results before and after singular perturbation order reduction of the DDWF system verify the effectiveness and accuracy of the method of this invention.

[0045] Therefore, the advantages of this invention can be summarized as follows: First, by calculating the dominance of each oscillation mode in the DDWF system and then identifying the dominant oscillation mode, the potential errors in existing methods of manually identifying the dominant oscillation mode can be effectively avoided. Second, by establishing a set of retained modes for the DDWF system, including the dominant oscillation mode and the SSO mode, based on the principle of minimizing the order of the reduced-order DDWF system, the simulation scale of the DDWF system can be effectively reduced. Finally, the improved DDWF singular perturbation order reduction method described in this invention, by reproducing the retained modes of the reduced-order DDWF system, ensures that the reduced-order DDWF system has consistent SSO characteristics with the full-order system while simultaneously reproducing the dynamic characteristics of the DDWF system, filling the gap in previous singular perturbation order reduction studies that could not preserve SSO characteristics. The improved DDWF singular perturbation order reduction method described in this invention significantly improves simulation efficiency while ensuring the effectiveness of the reduced-order DDWF system, providing strong support for the SSO problem analysis of large-scale DDWF integration into weak power grid systems. Attached Figure Description

[0046] Figure 1 The flowchart of an improved singular perturbation reduction method for direct-drive wind farms, applicable to subsynchronous oscillation analysis, is provided by this invention.

[0047] Figure 2 The present invention provides an improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis, with a multi-timescale partitioning flowchart.

[0048] Figure 3 The diagram shows a computational example of a DDWF connected to a weak AC power grid, used to verify the effectiveness of the improved DDWF singular perturbation order reduction method described in this invention.

[0049] Figure 4For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... sref When the DC capacitor voltage U jumps from 50.27 rad / s to 60.27 rad / s, the DC capacitor voltage U of the full-order and reduced-order DDWF systems are... dc and the dq-axis component of the machine-side current i ds i qs Comparison chart of dynamic response characteristics.

[0050] Figure 5 For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... sref When the speed increases from 50.27 rad / s to 60.27 rad / s, the rotor rotational angular velocity ω and the phase-locked loop output phase angle θ of the full-order and reduced-order DDWF systems are... PLL and the d-axis component of the grid-connected current i dg Comparison chart of dynamic response characteristics.

[0051] Figure 6 For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... sref Comparison of the dynamic response characteristics of the grid-connected active power P of the full-order DDWF system and the reduced-order system when the power increases by a step from 50.27 rad / s to 60.27 rad / s. Detailed Implementation

[0052] This invention provides an improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis. To make the objectives, technical solutions, and effects of this invention clearer, the specific implementation schemes of this invention are described in detail below with reference to the accompanying drawings and examples. The specific examples described in this invention are only for explaining the invention and are not intended to limit the invention.

[0053] 1. Detailed Description of the Invention

[0054] Figure 1 A flowchart illustrating an improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis, is provided by this invention. (Refer to...) Figure 1 The present invention describes an improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis, comprising:

[0055] S1: Establish a full-order small-signal model of the DDWF system and find the eigenvalues ​​corresponding to all oscillation modes of the system;

[0056] S2: Based on the principle of dominance analysis, calculate the dominance of each oscillation mode in the DDWF system;

[0057] S3: Establish the set of modes to be preserved in the DDWF reduced-order system and complete the multi-timescale partitioning of the DDWF system;

[0058] S4: Based on singular perturbation theory, establish the DDWF singular perturbation order reduction system.

[0059] Furthermore, the following specific steps are included:

[0060] S1: Establish a full-order small-signal model of the DDWF system and obtain the eigenvalues ​​corresponding to all oscillation modes of the system.

[0061] S2: Based on the principle of dominance analysis, calculate the dominance of each oscillation mode in the DDWF system.

[0062] Based on the principle of dominance analysis, the dominance of each oscillation mode in the DDWF system is calculated, and the degree of dominance of each oscillation mode in the dynamic characteristics of the DDWF system is quantified.

[0063] S21: Construct a specific DDWF system output matrix according to actual research needs to characterize the dynamic characteristics of the DDWF system;

[0064] S22: Based on the output matrix of a specific system, the dominance of each oscillation mode of the DDWF system is calculated according to the principle of dominance analysis, so as to quantify the degree of dominance of each oscillation mode on the dynamic characteristics of the system.

[0065] Based on the output matrix of a specific system, and using the principle of dominance analysis, the dominance of each oscillation mode in the DDWF system is calculated to quantify the degree of dominance of each oscillation mode on the dynamic characteristics of the system. The calculation method for the dominance of each oscillation mode in the DDWF system is shown in equations (8)-(12).

[0066] A = V -1 AV = diag(λ1...λ k ...λ n (8)

[0067]

[0068] In the formula, A is the DDWF system state matrix; B is the DDWF system input matrix; and C is the DDWF system output matrix.

[0069] V is the characteristic matrix of matrix A; λ1...λ k ...λ n These are the characteristic values ​​of the DDWF system.

[0070] DDWF system oscillation mode λ i The dominance of the system output matrix is ​​shown in equation (11).

[0071]

[0072] In the formula, D ij-h The calculation method is shown in equation (12).

[0073]

[0074] S3: Establish the set of retained modes for the DDWF system and complete the multi-timescale partitioning of the DDWF system.

[0075] Reference Figure 2 Based on the dominance of each oscillation mode in the DDWF system, and within the framework of the principles for determining the retained mode set of the DDWF system, a retained mode set including the dominant oscillation mode and the SSO mode is established. Participation factor analysis is performed on all retained modes to select state variables with strong correlation to each retained mode as slow dynamic variables, thus completing the multi-timescale partitioning of the DDWF system.

[0076] S31: Based on the magnitude of the dominance of each oscillation mode of the DDWF system calculated in step S2, and within the framework of the Al-A4 reserved mode set determination principle, establish a DDWF system reserved mode set including the dominant oscillation mode and the SSO mode of the DDWF system.

[0077] A1: The reserved mode set must include the dominant oscillation mode of the DDWF system and all SSO modes.

[0078] A2: After partitioning the fast and slow variables of the DDWF system according to the retention mode, in the singular perturbation form corresponding to the DDWF system, matrix A 22 It must be non-singular.

[0079] A3: Practice shows that assigning the dq components of the same variable to variable sets at different time scales may worsen the dynamic characteristics of the reduced-order system. Therefore, in the fast and slow variable partitioning results of the DDWF system, the dq components of the same variable should be in the same variable set at the same time scale, that is, they should be in either the fast variable set or the slow variable set simultaneously.

[0080] A4: Based on the above principles, the order of the DDWF reduced-order system should be minimized.

[0081] S32: Perform participation factor analysis on each retention mode in the set of retention modes of the DDWF reduced-order system;

[0082] S33: Define the state variables with a participation factor greater than 0.1 in any retained mode as slow dynamic variables, and the remaining state variables as fast dynamic variables, thereby completing the fast and slow variable division of the DDWF system.

[0083] S4: Based on singular perturbation theory, establish a DDWF singular perturbation order reduction system.

[0084] Based on the DDWF multi-timescale partitioning results in step S3, a DDWF singular perturbation model is established according to equation (13).

[0085]

[0086] In the formula, Δx I For the slow dynamic variable set of the DDWF system; Δx II ε is the set of fast dynamic variables of the DDWF system; ε is the set of singular perturbation parameters of the DDWF system.

[0087] Let ε = 0, the DDWF full-order system degenerates into the form shown in equation (14), that is, the DDWF singular perturbation reduced-order system is established.

[0088]

[0089] 2. Verification of the technical feasibility of this invention

[0090] Engineering simulation example system model such as Figure 3 As shown, the simulation results are as follows: Figure 4 , Figure 5 , Figure 6 As shown, the effectiveness of the present invention is verified.

[0091] Figure 4 For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... sref When the DC capacitor voltage U jumps from 50.27 rad / s to 60.27 rad / s, the DC capacitor voltage U of the full-order and reduced-order DDWF systems are... dc and the dq-axis component of the machine-side current i ds i qs Comparison chart of dynamic response characteristics. Figure 5 For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... sref When the speed increases from 50.27 rad / s to 60.27 rad / s, the rotor rotational angular velocity ω and the phase-locked loop output phase angle θ of the full-order and reduced-order DDWF systems are... PLL and the d-axis component of the grid-connected current i dg Comparison chart of dynamic response characteristics. Figure 6 For the example of DDWF being connected to a weak AC power grid system, before and after applying the order reduction method described in this invention, when the reference value of the wind turbine's rotational angular velocity ω... srefComparison of the dynamic response characteristics of the grid-connected active power P of the full-order DDWF system and the reduced-order system when the power increases by a step from 50.27 rad / s to 60.27 rad / s.

[0092] Depend on Figure 4 , Figure 5 , Figure 6 As can be seen, in the example DDWF connected to a weak AC power grid system, the improved DDWF singular perturbation order reduction method described in this invention is used to reduce the order of the full-order DDWF system. Before and after the order reduction, the dynamic response characteristics of the reduced-order DDWF system and the full-order DDWF system are basically the same, that is, the reduced-order DDWF system can retain the dynamic characteristics of the full-order DDWF system in detail.

[0093] Table 1 shows a comparison of the SSO modes of the full-order DDWF system before and after order reduction when the improved DDWF singular perturbation order reduction method described in this invention is used to reduce the order of the full-order DDWF system after it is connected to a weak AC power grid system. As shown in Table 1, both the full-order DDWF system and the reduced-order DDWF system have three identical SSO modes, meaning the reduced-order DDWF system can retain all the SSO modes of the full-order system in detail.

[0094] Table 1

[0095]

[0096] The simulation results above demonstrate that when the DDWF reduced-order system established using the improved DDWF singular perturbation reduction method described in this invention is used instead of the full-order system for subsynchronous oscillation analysis of a DDWF integrated into a weak AC power grid, the DDWF reduced-order system can exhibit dynamic characteristics and SSO characteristics consistent with the full-order system. The simulation results verify the effectiveness and feasibility of the improved DDWF singular perturbation reduction method described in this invention.

[0097] In summary, the improved singular perturbation reduction method for direct-drive wind farms, applicable to subsynchronous oscillation analysis, described in this invention, can significantly reduce the simulation scale of DDWF systems integrated into weak AC grids while fully reproducing the dynamic characteristics and SSO characteristics of the full-order DDWF system. When determining the dominant oscillation modes of the DDWF system, based on the principle of dominance analysis, the degree of dominance of each oscillation mode on the system's dynamic characteristics is quantified, effectively avoiding the reduction error that may be caused by artificially identifying the dominant oscillation modes based on the position of eigenvalues ​​in the s-plane. Based on the principle of minimizing the order of the reduced DDWF system, a set of retained modes for the reduced DDWF system, including the dominant oscillation modes and SSO modes, is determined. Slow-dynamic variables of the DDWF system are identified through participation factor analysis of each retained mode, completing the multi-timescale partitioning of the DDWF system. Compared with existing singular perturbation order reduction methods, the improved DDWF singular perturbation order reduction method described in this invention can significantly reduce the scale of DDWF integration into weak AC power grid systems and improve simulation efficiency, while fully reproducing the dynamic characteristics and SSO characteristics of the full-order DDWF system.

[0098] Finally, it should be noted that the above examples of the present invention are merely illustrative and not intended to limit the implementation of the invention. Although the applicant has described the present invention in detail with reference to preferred embodiments, those skilled in the art can make other variations and modifications based on the above description. It is impossible to exhaustively list all possible implementations here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An improved method for reducing the order of singular perturbations in direct-drive wind farms, suitable for subsynchronous oscillation analysis, characterized in that, Includes the following steps: S1: Establish a full-order small-signal model of the DDWF system and find the eigenvalues ​​corresponding to all oscillation modes of the system; S2: Based on the principle of dominance analysis, calculate the dominance of each oscillation mode in the DDWF system; Based on the principle of dominance analysis, the dominance of each oscillation mode of the DDWF system is calculated, and the degree of dominance of each oscillation mode of the DDWF system on the dynamic characteristics of the system is quantified. S3: Establish the set of modes to be retained in the DDWF system and complete the multi-timescale partitioning of the DDWF system; Based on the dominance of each oscillation mode in the DDWF system, and within the framework of the principle for determining the set of retained modes in the DDWF system, a set of retained modes in the DDWF system, including the dominant oscillation mode and the SSO mode, is established. Participation factor analysis was performed on all retention modes to screen out state variables that are strongly correlated with each retention mode as slow dynamic variables, thus completing the multi-timescale partitioning of the DDWF system. S4: Based on singular perturbation theory, establish a DDWF singular perturbation reduced-order system; Step S3 establishes the DDWF system's retained mode set and completes the multi-timescale partitioning of the DDWF system. The specific strategy is as follows: S31: Based on the magnitude of the dominance of each oscillation mode of the DDWF system calculated in step S1, and under the framework of the principle for determining the reserved mode set of A1-A4, establish a reserved mode set of the DDWF system, including the dominant oscillation mode and the SSO mode of the DDWF system. A1: The reserved mode set must include the dominant oscillation mode and all SSO modes of the DDWF system; A2: After partitioning the fast and slow variables of the DDWF system according to the retention mode, in the singular perturbation form corresponding to the DDWF system, matrix A 22 Must be non-singular; A3: In the fast and slow variable partitioning results of the DDWF system, the dq components of the same variable should be in the same time scale variable set, that is, they should be in either the fast variable set or the slow variable set at the same time. A4: Based on the above principles, the order of the DDWF reduced-order system should be minimized; S32: Perform participation factor analysis on each retention mode in the DDWF system retention mode set; S33: Define the state variables with a participation factor greater than 0.1 in any retained mode as slow dynamic variables, and the remaining state variables as fast dynamic variables, thereby completing the fast and slow variable division of the DDWF system.

2. The improved method for reducing the order of singular perturbations in direct-drive wind farms, applicable to subsynchronous oscillation analysis, as described in claim 1, is characterized in that... Step S2, based on the principle of dominance analysis, calculates the dominance of each oscillation mode in the DDWF system. The specific strategy is as follows: S21: Construct a specific DDWF system output matrix; Based on actual research needs, a specific DDWF system output matrix is ​​constructed to characterize the dynamic characteristics of the DDWF system. S22: Calculate the dominance of each oscillation mode in the DDWF system; Based on the specific output matrix of the DDWF system, and using the principle of dominance analysis, the dominance of each oscillation mode of the DDWF system is calculated to quantify the degree of dominance of each oscillation mode on the dynamic characteristics of the system.

Images