A broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of direct-drive wind turbine systems based on mode-damped energy functions.

Abstract

This invention discloses a broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of a direct-drive wind turbine system based on a mode-damped energy function. The method includes: constructing a mode-damped energy function for the direct-drive wind turbine system; analyzing the small-disturbance stability energy of the system based on the mode-damped energy function; validating the direct-drive wind turbine system based on the analysis results to obtain an evaluation model; and evaluating the direct-drive wind turbine system to be evaluated based on the evaluation model to obtain the evaluation results. This invention avoids complex modeling while simultaneously quantifying the mode-damped energy to determine the changes in the overall system damping level caused by each grid-connected unit and the impact of grid connection of the direct-drive wind turbine on oscillations.

Description

Technical Field

[0001] This invention belongs to the field of small-disturbance stability technology of direct-drive wind turbine grid connection to power system, and particularly relates to a broadband oscillation evaluation method for small-disturbance stability and sensitivity indicators of direct-drive wind turbine system based on mode damping energy function. Background Technology

[0002] Given the increasing prevalence of wind power grid connection in new power systems, the system's inertia level is continuously decreasing. Furthermore, the volatility and randomness of wind power further complicate the analysis of low-frequency oscillations in these systems, posing new challenges to the safe and stable operation of new power systems. Current research largely focuses on the impact of direct-drive wind turbines on low-frequency oscillations from single perspectives such as turbine parameters, converter control strategies, or overall system impedance models, lacking comprehensive modeling of direct-drive wind turbines or the entire system. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a broadband oscillation evaluation method for direct-drive wind turbine systems based on mode-damped energy functions, including small-disturbance stability and sensitivity indices. This method avoids complex modeling while quantifying the changes in the overall system damping level caused by each grid-connected unit and the impact of grid connection of direct-drive wind turbines on oscillations. Furthermore, by constructing small-disturbance stability evaluation and sensitivity indices for direct-drive wind turbine systems based on mode-damped energy, a reasonable small-disturbance stability control strategy for grid-connected direct-drive wind turbines is provided.

[0004] To achieve the above objectives, this invention provides a broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of a direct-drive wind turbine system based on a mode-damped energy function, comprising:

[0005] Construct the mode damping energy function of the system including the direct-drive wind turbine;

[0006] The small-disturbance stable energy of the system containing a direct-drive fan is analyzed based on the mode damping energy function.

[0007] The direct-drive fan system was validated based on the analysis results, and an evaluation model was obtained.

[0008] The evaluation model is used to evaluate the direct-drive fan system to be evaluated, and the evaluation results are obtained.

[0009] Optionally, a new energy power system model considering the damping coefficient needs to be constructed before constructing the damping energy function of the system mode including direct-drive wind turbines.

[0010] Optionally, constructing a new energy power system model that considers the damping coefficient includes:

[0011]

[0012] Among them, U d U q The voltages I along the d-axis and q-axis are respectively. d I q The voltages along the d-axis and q-axis are respectively, X d X d ' represents the synchronous reactance and transient reactance along the d-axis, respectively, and X represents the d-axis reactance. q E is the synchronous reactance of the q-axis. f E is the stator electromagnetic electromotive force. q E q ' represents the no-load electromotive force and transient electromotive force along the q-axis, respectively, and T represents the q-axis. d0 ' is the d-axis transient time constant, M is the inertial time constant, and P is the d-axis transient time constant. m P e ω and ω0 represent the mechanical power and electromagnetic power of the generator, respectively, D is the winding damping coefficient, δ is the generator power angle, and ω and ω0 are the generator rotor angular velocity and the initial value of the generator rotor angular velocity, respectively.

[0013] Optionally, constructing the mode damping energy function for a direct-drive wind turbine system includes:

[0014] Construct the state line equations for a system with a direct-drive fan under small disturbances;

[0015] Solve the linear equations of the state;

[0016] The voltage angle increment at the node is obtained based on the solution of the state linear equation; the number of position and small disturbance characteristic roots among all state variables is obtained based on the voltage angle increment, and the mode damping energy function of the system containing the direct-drive wind turbine is constructed.

[0017] Optionally, the analysis of the small-disturbance stable energy of the system containing the direct-drive wind turbine based on the mode-damped energy function includes:

[0018] Construct a small-disturbance stability evaluation index for a direct-drive wind system based on the mode-damped energy function;

[0019] Construct a grid connection sensitivity index for direct-drive wind turbines based on the damping energy of oscillation key link modes;

[0020] The small-disturbance stable energy of the system containing the direct-drive fan is analyzed based on the evaluation index and the sensitivity index.

[0021] Optionally, small-disturbance stability evaluation indices for direct-drive wind systems based on mode-damped energy functions include:

[0022]

[0023] Where, λ KGDESSSIFor small-disturbance stability evaluation indicators of direct-drive wind systems, n is the number of key participating units in the oscillation, and V DiMAX1 V DiMAX2 These are the first and second peaks of the damping energy in mode i of the key unit, respectively.

[0024] Optionally, the grid connection sensitivity index of direct-drive wind turbines based on the damping energy of oscillation key link modes includes:

[0025]

[0026] Where, λ DMDESI V is the grid connection sensitivity index for direct-drive wind turbines. bk V ak denoted as mode damping energy of the k-th oscillation key participating unit before and after intervention, respectively; n is the number of oscillation key participating units; and ΔPG is the change in the output active power of the direct-drive wind turbine.

[0027] Technical effects of this invention: This invention discloses a broadband oscillation evaluation method for direct-drive wind turbine systems based on mode-damped energy functions, including small-disturbance stability and sensitivity indices. Based on the energy method of transient problems and combined with small-disturbance stability analysis theory, it establishes the relationship between energy and the state variables of each generator unit, constructing a mode-damped energy function for the direct-drive wind turbine system. This avoids complex modeling while quantifying the changes in the overall system damping level and the impact of grid connection of direct-drive wind turbines on oscillations through mode-damped energy theory. Furthermore, through the constructed small-disturbance stability evaluation and sensitivity indices for direct-drive wind turbine systems based on mode-damped energy, a reasonable small-disturbance stability control strategy for grid-connected direct-drive wind turbines is provided. The reliability of the proposed method is confirmed through damping verification. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0029] Figure 1 This is a wiring diagram of the 9-node system of Embodiment 3 of the present invention;

[0030] Figure 2 This is a schematic diagram of the mode damping energy distribution under mode 1 of the present invention;

[0031] Figure 3 This is a schematic diagram of the mode damping energy distribution in mode 2 of the present invention;

[0032] Figure 4 This is a schematic diagram of the damping energy distribution in an embodiment of the present invention;

[0033] Figure 5 This is a schematic diagram of the damping energy amplitude of the key unit mode after the output of DDSG1 is increased according to an embodiment of the present invention;

[0034] Figure 6 This is a schematic diagram of the system mode damping energy distribution under the dominant oscillation mode in an embodiment of the present invention;

[0035] Figure 7 This is a schematic diagram of the change in damping energy in DDSG2 mode before and after the increase in output in an embodiment of the present invention. (a) shows the change in damping energy of Ddsg1, (b) shows the change in damping energy of Ddsg2, (c) shows the change in damping energy of Ddsg3, and (d) shows the change in damping energy of Ddsg7.

[0036] Figure 8 This is a flowchart illustrating the broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of a direct-drive wind turbine system based on the mode damping energy function, according to an embodiment of the present invention. Detailed Implementation

[0037] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0038] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0039] like Figure 8 As shown, this embodiment provides a broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of a direct-drive wind turbine system based on mode-damped energy functions, including:

[0040] Construct the mode damping energy function of the system including the direct-drive wind turbine;

[0041] Analysis of the small-disturbance stability energy of a system containing a direct-drive fan based on the mode-damped energy function;

[0042] The direct-drive fan system was validated based on the analysis results, and an evaluation model was obtained.

[0043] The evaluation model is used to evaluate the direct-drive fan system to be evaluated, and the evaluation results are obtained.

[0044] Furthermore, constructing a new energy power system model that considers the damping coefficient includes:

[0045] Construct a single-machine infinite bus system. The generator is modeled as a third-order generator with damping considered. The excitation system is a static excitation system with constant mechanical power. Distributed capacitance and losses in the lines are neglected. The reactance is denoted by X. The voltage of the single-machine infinite bus system is... Where U is a constant, the unit value mathematical model of the generator dq coordinate is shown in equation (1) below:

[0046]

[0047] In equation (1), U d U q These refer to the voltages along the d-axis and q-axis, respectively. d I q These refer to the voltages along the d-axis and q-axis, respectively. d X d ' refers to the synchronous reactance and transient reactance of the d-axis, respectively, and X... q The synchronous reactance of the q-axis, E f This refers to the stator electromagnetic electromotive force, E q E q ' refers to the no-load electromotive force and transient electromotive force along the q-axis, respectively, and T d0 ' refers to the d-axis transient time constant, M refers to the inertial time constant, and P... m P e These refer to the mechanical power and electromagnetic power of the generator, respectively. D refers to the winding damping coefficient, δ refers to the generator power angle, and ω and ω0 refer to the generator rotor angular velocity and its initial value, respectively.

[0048] Linearizing equation (1) yields equation (2):

[0049]

[0050] In equation (2), ΔP e and ΔE q It is algebraic quantity:

[0051]

[0052] When a single-machine infinite bus system is in steady-state operation and Δω approaches 0, then ΔP e ≈ΔT e ;

[0053] Single-machine infinite bus system (excluding virtual excitation system adjustment ΔE) f In steady-state conditions (ω0=1) and when Δω is very small, ΔP e ≈ΔT e Written as:

[0054]

[0055] When only the damped component of the mode energy is considered, the damped component in the generator output power increment is as shown in equation (5):

[0056] ΔP de =T e Δω=D e Δω 2 ω0(5),

[0057] Furthermore, the construction of the mode damping energy function for a direct-drive wind turbine system includes:

[0058] Under small disturbances, the system containing the direct-drive fan can be represented by a linear state equation, as shown in equation (6) below:

[0059]

[0060] In equation (6), ΔX = [Δx G Δx Ddsg ] T This refers to an n-dimensional state variable; Δx G =[Δδ i ,Δω i ,Δe iq ] T This refers to the state variables of a synchronous generator; Δx Ddsg =[Δv ωi ,Δω i ,,Δθ i ,Δi qsi ,Δi qci ] T This refers to the state variable of the wind turbine; ΔU N =[Δu1,Δθ1,Δu2,Δθ2,…,Δu i ,Δθ i ] T , where Δu n ,Δθ n These refer to the increment of node voltage magnitude and the increment of angle, respectively. A, B, C, and D refer to the coefficient matrix.

[0061] The general form of the solution to the state equation is:

[0062]

[0063] In equation (7) ψ j φ j This refers to the left and right eigenvectors; λ j (j=1,...,n) refers to the eigenvalues; x0 refers to the initial value of the state variable, and the specific matrix form is shown in equation (8):

[0064]

[0065] The voltage angle increment at node i is shown in equation (9) below:

[0066]

[0067] In equation (9), p refers to the position of the state variable among all state variables, and q refers to the number of small disturbance eigenvalues. The mode damping energy function is constructed as shown in equation (10) below:

[0068]

[0069] The expression for the damping-related quantity of the generator output power increment in the system is shown in equation (11) below:

[0070] ΔP de =T e Δω=D e Δω 2 ω0 (11),

[0071] The voltage angle increment at node i is shown in equation (12) below:

[0072]

[0073] In the formula: F = -D -1 C;

[0074] The active power increment and voltage angle increment at the generator outlet are simplified, where A1-A n This refers to the power increment coefficient, B1-B n This refers to the voltage angle increment coefficient, and the final simplified result is expressed as follows (13):

[0075]

[0076] Therefore, the mode damping energy expression of the generator at this time can be represented by the following equation (14):

[0077]

[0078] In this case, the mode damping energy of the system consists of two parts: autocorrelation mode and cross-correlation mode.

[0079]

[0080] The current priority is to accurately identify the dominant oscillation mode before conducting further analysis. Therefore, the cross-correlation mode is ignored. At this time, the mode damping energy expression of the system is as follows (16):

[0081]

[0082] Furthermore, the analysis of the small-disturbance stable energy of the system containing the direct-drive wind turbine based on the mode-damped energy function includes:

[0083] Construct a small-disturbance stability evaluation index for a direct-drive wind system based on the mode-damped energy function;

[0084] Construct a grid connection sensitivity index for direct-drive wind turbines based on the damping energy of oscillation key link modes;

[0085] The small-disturbance stable energy of the system containing the direct-drive fan is analyzed based on the evaluation index and the sensitivity index.

[0086] Furthermore, the small-disturbance stability evaluation index for direct-drive wind systems based on mode-damped energy functions includes:

[0087] To quantify the stability of small disturbances from an energy perspective, this invention maps the degree of small disturbances in the system to the stability of the damping energy of the key generator units involved in the oscillation. By analyzing the damping energy consumed by each generator under different oscillation modes, amplitude, and frequency, the stability of different oscillation components under the corresponding oscillation modes is quantified. This allows for the detection of the dominant oscillation mode of the system and the distribution of its mode damping energy. Furthermore, the damping energy of the generator unit with the highest energy distribution level—the key generator unit mode—is identified. This leads to a quantitative analysis of the system's small disturbance stability, and a key generator unit mode damping energy stability index λ is proposed. KGDESSSI (Key Generatordampling energy small signal stabilityindex), which is shown in equation (17) below:

[0088]

[0089] Where, λ KGDESSSI For small-disturbance stability evaluation indicators of direct-drive wind systems, n is the number of key participating units in the oscillation, and V DiMAX1 V DiMAX2 These are the first and second peaks of the damping energy in mode i of the key unit, respectively. The value of this index is proportional to the attenuation of the mode damping energy at this time. That is, the smaller the index value, the worse the stability of the system under small disturbances, and vice versa.

[0090] Furthermore, the grid connection sensitivity index for direct-drive wind turbines based on the damping energy of oscillation key link modes includes:

[0091] Existing research shows that in grid-connected power systems with direct-drive wind turbines, the amplitude and decay rate of the damping energy of the key participating unit mode can reflect the degree of influence of the output change of a direct-drive wind turbine at a specific location on the oscillation. To intuitively demonstrate the impact of direct-drive wind turbines at different locations on the small-disturbance stability of the grid-connected system, this invention proposes a sensitivity index λ for the damping energy of the direct-drive wind turbine mode. DMDESI (Direct drive synchronousgeneratorMode Dampling Energy SensitivityIndex):

[0092]

[0093] Where, λ DMDESI V is the grid connection sensitivity index for direct-drive wind turbines. bk V ak denoted as mode damping energy of the k-th key oscillation unit before and after intervention, n is the number of key oscillation units, and ΔPG is the change in the active power output of the direct-drive wind turbine. This index can be used to quantitatively analyze the influence of direct-drive wind turbines at different locations on oscillation. In addition, the optimal grid connection location of the direct-drive wind turbine can be determined based on the sensitivity index, which can ensure the installed capacity of the direct-drive wind turbine and maximize the stability of the system under small disturbances.

[0094] A specific application example of this invention is as follows:

[0095] (1) 3-machine 9-node system

[0096] The study scenario considers a 3-unit, 9-node system with direct-drive wind turbines integrated, and nodes 4, 7, and 9 are considered as candidate nodes for grid connection of the direct-drive wind turbines. Each node is connected to a 20MW direct-drive wind turbine unit, with a maximum capacity of 50MW. This study aims to explore how to utilize λ... KGDESSSI and λ DMDESI Determine the impact of increased output from each direct-drive fan unit on system stability and sensitivity. The system wiring diagram is as follows: Figure 1 As shown,

[0097] First, regarding Figure 2 , Figure 3 The mode damping energy distribution under the two oscillation modes is shown. Mode 2 is taken as the dominant oscillation mode, and the mode damping energy distribution of each unit under this mode is as follows: Figure 4 As shown, the key units participating in the oscillation at this time are identified as: Synchronous Generator No. 3, Wind Turbine No. 2, and Wind Turbine No. 3. The output of direct-drive wind turbines No. 4, 7, and 9 is increased respectively. At this time, the wind power penetration rate in the system increases. The change in mode damping energy of the key units caused by the increase in the output of the direct-drive wind turbines under the dominant oscillation mode is calculated as follows: Figure 5As shown.

[0098] from Figure 5 It can be observed that in a 3-machine 9-node system, after the output of the direct-drive wind turbines at each node increases, the damping energy of each key unit mode changes, but this does not change the oscillation key unit of the system and the dominant oscillation mode of the system.

[0099] To verify the above viewpoint, the mode damping energy small disturbance stability index of each key unit was calculated, and the λ of the dominant oscillation mode after the direct-drive wind turbine output increased can be obtained. KGDESSSI As shown in Table 1, observe the changes in the damping energy of the key unit mode before and after the increase in the wind turbine output at each node, and conduct an in-depth analysis of the influence law of the oscillation of a certain direct-drive wind turbine.

[0100] Table 1

[0101]

[0102] Table 2 shows the changes in mode damping energy amplitude and sensitivity index before and after the increase in output of direct-drive fans 1, 2 and 3. By calculating the changes in mode damping energy amplitude and sensitivity index, it can be seen that the sensitivity of direct-drive fan 2 at node 4 is the smallest and its influence on oscillation is the weakest, while the sensitivity of direct-drive fan 3 at node 9 is the largest and its influence on oscillation is the strongest.

[0103] Table 2

[0104]

[0105] In addition, by combining the analysis of small disturbance stability assessment indicators, it can be seen that the connection of direct-drive wind turbines at nodes 7 and 9 can enhance system stability. The enhancement of node 9 is better than that of node 7. The connection of direct-drive wind turbine No. 2 at node 4 will worsen the system stability, but the impact is not significant. Therefore, it can be concluded that the grid connection order of the three direct-drive wind turbines should be node 9, node 7 and node 4.

[0106] The changes in damping ratio before and after increasing the output of the direct-drive fans at different locations were then verified, as shown in Table 3. Table 3 shows that the system damping ratio continuously changes as the output of the direct-drive fans at different locations increases. The damping ratio of direct-drive fan No. 2 decreases after the output increases, while the impact of direct-drive fan No. 3 on the system damping ratio is the most significant after the output increases, showing the best improvement effect and the most effective absorption of oscillation. This is basically consistent with the conclusions obtained from the proposed method, proving the feasibility of the proposed method.

[0107] Table 3

[0108]

[0109] (2) New England 10-machine 39-node system

[0110] To further verify the universality and objectivity of the proposed method, a 10-unit, 39-node system was selected, and the combined operation of multiple direct-drive fans was used as the operating condition.

[0111] First, direct-drive fans were connected to nodes 7, 20, 22, 23, 25, 29, and 31 respectively. The output of the direct-drive fans at different locations was increased by the same amplitude. The mode damping energy changes of each unit are as follows. Figure 6 As shown, the key oscillation components are direct-drive fans 1, 2, 3, and 7. Figure 7 This is a schematic diagram illustrating the change in damping energy in DDSG2 mode before and after the increase in output according to an embodiment of the present invention. Figure 7 (a) shows the change in damping energy of Ddsg1. Figure 7 (b) shows the change in damping energy of Ddsg2. Figure 7 (c) shows the change in damping energy of Ddsg3. Figure 7 (d) represents the change in damping energy of Ddsg7.

[0112] Increase the output of the direct-drive wind turbines at each grid connection node and calculate the key unit small-disturbance stability index λ at this time. KGDESSSI The results are shown in Table 4. In the 10-unit, 39-node system, as the output of the direct-drive fans at each node increases, the critical units of the system remain unchanged. Table 5 shows the magnitude of the damping energy change and sensitivity indicators of the critical unit mode when increasing the output of the direct-drive fans at different nodes. ΔV kb This refers to the change in damping energy of the key unit mode after the output of the same direct-drive fan is increased by the same amount. The impact of the increase in the output of the direct-drive fan at different nodes on the oscillation is also different, and the degree of change in damping energy of the key unit mode of the system is also different.

[0113] By analyzing λ in Tables 4 and 5 KGDESSSI , λ DMDESI Analysis of the two indicators reveals that increasing the output of direct-drive fans 1, 2, 3, 5, and 6 worsened system stability, with fans 1 and 2 experiencing a greater impact, while fans 3, 5, and 6 were less affected. However, adding fans 4 and 7 increased the system's small-disturbance stability index, with fan 7 showing a higher sensitivity index and a more significant impact on system oscillations. Clearly, this enhanced the system's small-disturbance stability. Therefore, assuming the maximum installed capacity at each connection point remains unchanged, the grid connection sequence for each direct-drive fan is 7-4-6-3-5-2-1.

[0114] Table 4

[0115]

[0116] Table 5

[0117]

[0118] To verify the reliability of the proposed strategy, the changes in system damping ratio were observed after increasing the output of direct-drive fans at different locations. The output of direct-drive fans 1-7 was increased, and the changes in system damping ratio under the dominant oscillation mode were also observed. It was found that the system damping ratio decreased after increasing the output of direct-drive fans 1, 2, 3, 5, and 6, indicating a deterioration in system stability. However, the system damping ratio increased after increasing the output of direct-drive fans 4 and 7, with fan 7 showing a larger change. Therefore, system stability improved, with fan 7 achieving optimal system stability after the output increase. Furthermore, the change in system damping ratio after increasing the output of fan 4 was smaller, indicating a smaller change in system stability. This is consistent with the conclusions of the proposed method, proving its feasibility.

[0119] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A broadband oscillation evaluation method for small-disturbance stability and sensitivity indices of a direct-drive wind turbine system based on mode-damped energy functions, characterized in that, include: Construct the mode damping energy function of the system including the direct-drive wind turbine; The small-disturbance stable energy of the system containing a direct-drive fan is analyzed based on the mode damping energy function. The direct-drive fan system was validated based on the analysis results, and an evaluation model was obtained. The evaluation model is used to evaluate the direct-drive fan system to be evaluated, and the evaluation results are obtained. Before constructing the damping energy function of a system including direct-drive wind turbines, it is necessary to construct a new energy power system model that considers the damping coefficient. Constructing a new energy power system model that considers the damping coefficient includes: Among them, U d U q The voltages I along the d-axis and q-axis are respectively. d I q The voltages along the d-axis and q-axis are respectively, X d X d ' represents the synchronous reactance and transient reactance along the d-axis, respectively, and X represents the d-axis reactance. q E is the synchronous reactance of the q-axis. f E is the stator electromagnetic electromotive force. q E q ' represents the no-load electromotive force and transient electromotive force along the q-axis, respectively, and T represents the q-axis. d0 ' is the d-axis transient time constant, M is the inertial time constant, and P is the d-axis transient time constant. m P e These represent the mechanical power and electromagnetic power of the generator, respectively; D is the winding damping coefficient; δ is the generator power angle; and ω and ω0 are the generator rotor angular velocity and the initial value of the generator rotor angular velocity, respectively. Constructing the mode damping energy function for a system including a direct-drive wind turbine includes: Construct the state linear equations of a system with a direct-drive fan under small disturbances; Solve the linear equations of the state; The voltage angle increment at the node is obtained based on the solution of the state linear equation; the number of position and small disturbance characteristic roots among all state variables is obtained based on the voltage angle increment, and the mode damping energy function of the system containing the direct-drive wind turbine is constructed. The analysis of the small-disturbance stable energy of a system containing a direct-drive wind turbine based on the aforementioned mode-damped energy function includes: Construct a small-disturbance stability evaluation index for a direct-drive wind system based on the mode-damped energy function; Construct a grid connection sensitivity index for direct-drive wind turbines based on the damping energy of oscillation key link modes; The small-disturbance stable energy of the system containing a direct-drive fan is analyzed based on the evaluation index and the sensitivity index. The small-disturbance stability evaluation index for direct-drive wind systems based on mode-damped energy functions includes: Where, λ KGDESSSI For small-disturbance stability evaluation indicators of direct-drive wind systems, n is the number of key participating units in the oscillation, and V DiMAX1 V DiMAX2 These are the first and second peaks of the damping energy in mode i of the key unit, respectively. The grid connection sensitivity index for direct-drive wind turbines based on the damping energy of oscillation key element modes includes: Where, λ DMDESI V is the grid connection sensitivity index for direct-drive wind turbines. bk V ak denoted as mode damping energy of the k-th oscillation key participating unit before and after intervention, respectively; n is the number of oscillation key participating units; and ΔPG is the change in the output active power of the direct-drive wind turbine.

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