Optimal configuration method of damping controller for wind power grid-connected system with similar oscillation modes under parameter perturbation

Abstract

The present invention discloses an optimal configuration method of a damping controller for a wind power grid-connected system with similar oscillation modes under parameter perturbation, including: 1. establishing a linearized state space model of the wind power grid-connected system and performing order reduction simplification; 2. obtaining the participation factor sensitivity of each wind turbine to the similar oscillation mode; 3. obtaining the optimal configuration position of the damping controller in the wind power grid-connected system. The present invention can establish a reduced-order linearized state space model suitable for analyzing similar oscillation modes of wind power grid-connected systems, and analyze the participation factor sensitivity of similar oscillation modes, thereby providing a theoretical basis for the optimal configuration of damping controllers for similar oscillation modes.

Description

Technical Field

[0001] The present invention belongs to the field of power system stability analysis and control, and in particular relates to an optimal configuration method of a damping controller of a wind power grid-connected system with a similar oscillation mode under parameter perturbation. Background Art

[0002] With the introduction of new power systems in my country, the penetration rate of wind power in my country's power grid has increased year by year. However, there are oscillation problems in wind power grid connection, such as the subsynchronous oscillation of the grid-connected system of Hami direct-drive wind farm in Xinjiang, the subsynchronous oscillation of the grid-connected system of Guyuan doubly-fed wind farm in Hebei, the subsynchronous oscillation of the wind power-flexible direct current project in Nanhui, Shanghai and Nan'ao, Guangdong, and the medium-frequency oscillation of the European Borwin1 wind power-flexible direct current system. The oscillation of actual projects can easily cause wind turbine shutdown, equipment damage, and even lead to chain failures such as torsional vibration cutting of thermal power units. Therefore, designing a damping controller for the oscillation of wind power grid-connected systems is of great significance for the safe and stable operation of power systems.

[0003] At present, the design of oscillation damping controller for wind power grid-connected system mainly targets single oscillation mode and specific operating conditions, without considering the existence of multiple oscillation modes and parameter perturbation. The designed damping controller is generally fixedly configured on the wind turbine with the largest participation factor. However, there may be multiple similar oscillation modes in the actual wind power grid-connected system, and the participation factors of these similar oscillation modes are extremely sensitive to parameter changes, resulting in the initial installation of the damping controller after parameter perturbation. The position is not optimal, so the traditional damping controller configuration method lacks accuracy and applicability when used to suppress the oscillation of wind power grid-connected system. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a method for optimal configuration of damping controllers for similar oscillation modes of wind power grid-connected systems under parameter perturbations, so as to determine the optimal configuration position of damping controllers for similar oscillation modes under parameter perturbations, thereby achieving the optimal suppression effect of similar oscillation modes of wind power grid-connected systems under different operating conditions.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The present invention discloses an optimal configuration method for a damping controller of a wind power grid-connected system with similar oscillation modes under parameter perturbation. The wind power grid-connected system comprises: n wind turbines and an AC power grid, and any wind turbine is numbered as i, i=1, ..., n. The optimal configuration method for the damping controller is performed according to the following steps:

[0007] Step S1: Establish a linearized state space model of the wind power grid-connected system and perform order reduction simplification;

[0008] Step S1.1: Obtain the linearized state space model of the wind power grid-connected system:

[0009] Step S1.1.1: In the dq rotating coordinate system, use formula (1) to obtain the state space model of the i-th wind turbine group:

[0010]

[0011] In formula (1), d represents the differential, t represents the time, and x wi is the state variable of the i-th wind turbine, A wi is the state matrix of the i-th wind turbine, B wi is the input matrix of the i-th wind turbine, u wi is the input variable of the i-th wind turbine, C i represents the voltage interface coefficient between the i-th wind turbine and the AC grid, u d 、u q are the d-axis and q-axis voltages at the common connection point, respectively;

[0012] Step S1.1.2: In the dq rotating coordinate system, use formula (2) to obtain the state space model of the AC power grid:

[0013]

[0014] In formula (2), x g is the state variable of the AC power grid, A g is the state matrix of the AC power grid, B g is the input matrix of the AC power grid, u g is the input variable of the AC power grid, D i represents the current interface coefficient between the i-th wind turbine and the AC grid, i di 、i qi are the d-axis and q-axis currents on the collector circuit of the i-th wind turbine respectively;

[0015] Step S1.1.3: Obtain the initial operating point p of the i-th wind turbine through power flow calculation i and the initial operating point q of the AC grid;

[0016] Use formula (3) to establish the initial operating point p i The linearized state space model of the i-th wind turbine under operating conditions;

[0017]

[0018] In formula (3), Δx wi Represents x wi The increment, Δu d Indicates u d The increment, Δuq Indicates u q The increment of

[0019] The linearized state space model of the AC power grid under the operating condition of the initial operating point q is established using equation (4);

[0020]

[0021] In formula (4), Δx g Represents x g The increment, Δi di Indicates i di The increment, Δi qi Indicates i qi The increment of

[0022] Step S1.1.4: Use equation (5) to construct a linearized state space model of the grid-connected system of n wind turbines:

[0023]

[0024] In formula (5), E vi Represents C i The expanded matrix of F ti Indicates D i The expanded matrix of Indicates v ×(t v -2)-dimensional zero matrix, Indicates t v ×(s v -2)-dimensional zero matrix, t v is the dimension of the state matrix of a single wind turbine, s v is the dimension of the AC power grid;

[0025] Step S1.2: Reduced-order simplification of the linearized state-space model:

[0026] Step S1.2.1: Use the eigenvalue method to calculate the eigenvalues ​​λ1,λ2,…,λ of the state matrix in equation (5) tn+s , and select j similar oscillation modes λ from them h1 ,λ h2 ,…,λ hj ; Among them, λ tn+s represents the tn+sth eigenvalue of the state matrix, tn+s is the order of the state matrix of n wind turbines connected to the AC grid, λ hj represents the jth similar oscillation mode;

[0027] Step S1.2.2: Based on the participation factor analysis, the participation factors of j similar oscillation modes are obtained, thereby determining the dominant state variables f of j similar oscillation modes. d ={f dk |k=1,2,…,j}, and define the remaining non-dominant state variables as f r ;f dk represents the kth dominant state variable;

[0028] The linearized state space model before order reduction is established using equation (6):

[0029]

[0030] In formula (6), Δf d represents the dominant state variable f d The increment, Δf r represents the remaining non-dominant state variables f r The increment, A 11 Denotes Δf d The derivative of Δf d The coefficient relationship between 12 Denotes Δf d The derivative of Δf r The coefficient relationship between 21 Denotes Δf r The derivative of Δf d The coefficient relationship between 22 Denotes Δf r The derivative of Δf r The coefficient relationship between

[0031] Step S1.2.3 Let dΔf r / dt=0; and use equation (7) to obtain the reduced-order linearized state space model:

[0032]

[0033] In formula (7), A 22 The inverse matrix, A d is the state matrix of the reduced linearized state space model;

[0034] Step S2: Obtaining the participation factor sensitivity of each wind turbine to a similar oscillation mode;

[0035] Step S2.1: Get A d The eigenvalues ​​of l |l=1,2,…,m}, and the corresponding left eigenphasors U1,U2,…,U m and right characteristic phasors V1, V2, ..., V m; where m is A d The order of l Indicates A d The lth eigenvalue of m represents the mth left eigenvector, V m represents the mth right eigenvector;

[0036] Step S2.1.1: Solve equation (8) and obtain the state matrix A d The characteristic values ​​of:

[0037] |λ l E d -A d |=0 (8) In formula (8), E d is the state matrix A d Identity matrix of the same order;

[0038] Step S2.1.2: Use equation (9) to solve the lth eigenvalue λ l The corresponding left eigenvector U l and the right eigenvector V l :

[0039]

[0040] In formula (9), V l T Indicates V l The transpose of

[0041] Step S2.2: Based on the dominant state variable f d Analyze the participation factors of similar oscillation modes and obtain the dominant state variable f d The sensitivity of the participation factor to similar oscillation modes, and obtain the sensitivity of the participation factor of each wind turbine to similar oscillation modes:

[0042] Step S2.2.1: Calculate the kth dominant state variable f dk Participation factor P of the lth similar oscillation mode kl =U kl V kl , where U kl is the right eigenvector U l The kth item, V kl is the left eigenvector V l The kth item of ;

[0043] Step S2.2.2: Use equation (10) to calculate the kth dominant state variable f as the parameter a changes. dk Participation factor sensitivity to the lth similar oscillation mode

[0044]

[0045] In formula (10), a(0) is the initial parameter of parameter a, Δa is the increment of parameter a; P kl (a) represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a; P kl (a) Partial derivative of a at a(0); P kl [a(0)+Δa] represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a(0)+Δa, P kl [a(0)] represents the participation factor of the kth dominant state variable in the lth similar oscillation mode at a(0); represents the limit when Δa approaches 0;

[0046] Step S2.2.3: When the i-th wind turbine contains y i The dominant state variables participate in similar oscillation modes, and the state variables are from z i to z i +y i When the parameter a changes, the participation factor sensitivity of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (11):

[0047]

[0048] In formula (11), P sl (a) is the participation factor of the sth dominant state variable in the lth adjacent oscillation mode at parameter a, P sl (a) The partial derivative of a at a(0), for of and; Indicates that at a(0)+Δa the zth i The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) the zth i The participation factor of the dominant state variable in the lth similar oscillation mode; Indicates that at a(0)+Δa the zth i +1 dominant state variable participates in the participation factor of the lth adjacent oscillation mode, Indicates that at a(0) the zth i +1 dominant state variable participation factor in the lth similar oscillation mode; Indicates that at a(0)+Δa the zth i +yi The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) the zth i +y i The participation factor of the dominant state variable in the lth similar oscillation mode;

[0049] Step S3: obtaining the optimal configuration position of the damping controller in the wind power grid-connected system;

[0050] Step S3.1: Obtain the participation factor of each wind turbine in the similar oscillation mode after parameter perturbation:

[0051] Step S3.1.1: Calculate the change in the participation factor of the ith wind turbine in the lth similar oscillation mode when the parameter perturbation is a0 using equation (12):

[0052]

[0053] In formula (12), P i|l is the participation factor of the ith wind turbine in the lth similar oscillation mode, P is the case when the parameter perturbation is a0 i|j The amount of change;

[0054] Step S3.1.2: Let the participation factor of the i-th wind turbine in the l-th similar oscillation mode under the initial operating condition be P i|l,0 , then when the parameter perturbation is a0, the participation factor of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (13):

[0055]

[0056] Step S3.2: Calculate the participation factors of each wind turbine for all similar oscillation modes after parameter perturbation and sort them; and obtain the optimal configuration position of the damping controller of the similar oscillation mode after parameter perturbation:

[0057] Step S3.2.1: Repeat the calculation of formula (13) when i = 1, 2, ..., n; l = 1, 2, ..., m, so as to obtain the participation factor of each wind turbine for all similar oscillation modes when the parameter perturbation is a0:

[0058]

[0059] In formula (14), It represents the sum of the participation factors of the first wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the second wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the nth wind turbine in all similar oscillation modes after the parameter perturbation when the parameter perturbation is a0;

[0060] Step S3.2.2: Sum the participation factors of each wind turbine for all similar oscillation modes and After descending sorting, according to the number e of damping controllers to be installed, the first e participation factors after descending sorting and the corresponding wind turbines are selected as the optimal configuration positions of the e damping controllers.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. Based on the idea of ​​ignoring the dynamic characteristics of non-dominant state variables, the present invention proposes a reduced-order linearized state space model for analyzing similar oscillation modes of wind power grid-connected systems, thereby effectively reducing the order of the theoretical analysis model and improving the calculation efficiency;

[0063] 2. The present invention calculates the sensitivity of the participation factor of each wind turbine to the similar oscillation mode under parameter perturbation, thereby pre-judging which parameter changes are likely to cause the dominant wind turbine of the similar oscillation mode to change, and determines the sensitive parameters that have a greater impact on the performance of the damping controller, which is conducive to the reasonable adjustment of the actual system parameters;

[0064] 3. The present invention obtains the participation factor of each wind turbine set to the similar oscillation mode after parameter perturbation based on the participation factor sensitivity of each wind turbine set to the similar oscillation mode under parameter perturbation, thereby determining the optimal configuration position of the damping controller of the similar oscillation mode after parameter perturbation, thereby improving the robustness of the damping controller design. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a structural diagram of the wind power grid-connected system of the present invention;

[0066] Figure 2 is a flow chart of the present invention;

[0067] Figure 3 It is a simplified flowchart of the present invention. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0069] In this embodiment, Figure 1 As shown, the wind power grid-connected system includes: n wind turbines and an AC power grid, and any wind turbine is numbered as i, i=1,…,n;

[0070] like Figure 2 As shown in the figure, the optimal configuration method of the damping controller of a wind power grid-connected system with a similar oscillation mode under parameter perturbation is carried out in the following steps:

[0071] Step S1: Establish a linearized state space model of the wind power grid-connected system and perform order reduction simplification;

[0072] Step S1.1: Obtain the linearized state space model of the wind power grid-connected system:

[0073] Step S1.1.1: In the dq rotating coordinate system, use formula (1) to obtain the state space model of the i-th wind turbine group:

[0074]

[0075] In formula (1), d represents the differential, t represents the time, and x wi is the state variable of the i-th wind turbine, A wi is the state matrix of the i-th wind turbine, B wi is the input matrix of the i-th wind turbine, u wi is the input variable of the i-th wind turbine, C i represents the voltage interface coefficient between the i-th wind turbine and the AC grid, u d 、u q are the d-axis and q-axis voltages at the common connection point, respectively;

[0076] Step S1.1.2: In the dq rotating coordinate system, use formula (2) to obtain the state space model of the AC power grid:

[0077]

[0078] In formula (2), x g is the state variable of the AC power grid, A g is the state matrix of the AC power grid, B g is the input matrix of the AC power grid, u g is the input variable of the AC power grid, D i represents the current interface coefficient between the i-th wind turbine and the AC grid, i di 、i qi are the d-axis and q-axis currents on the collector circuit of the i-th wind turbine respectively;

[0079] Step S1.1.3: Obtain the initial operating point p of the i-th wind turbine through power flow calculation i and the initial operating point q of the AC grid;

[0080] Use formula (3) to establish the initial operating point p i The linearized state space model of the i-th wind turbine under operating conditions;

[0081]

[0082] In formula (3), Δx wi Represents x wi The increment, Δu d Indicates u d The increment, Δu q Indicates u q The increment of

[0083] The linearized state space model of the AC power grid under the operating condition of the initial operating point q is established using equation (4);

[0084]

[0085] In formula (4), Δx g Represents x g The increment, Δi di Indicates i di The increment, Δi qi Indicates i qi The increment of

[0086] Step S1.1.4: Use equation (5) to construct a linearized state space model of the grid-connected system of n wind turbines:

[0087]

[0088] In formula (5), E vi Represents C i The expanded matrix of F ti Indicates D i The expanded matrix of Indicates v ×(t v -2)-dimensional zero matrix, Indicates t v ×(s v -2)-dimensional zero matrix, t v is the dimension of the state matrix of a single wind turbine, s v is the dimension of the AC power grid;

[0089] Step S1.2: Reduced-order simplification of the linearized state-space model:

[0090] Step S1.2.1: The reduced order simplified flow chart of the present invention is as follows Figure 3 As shown; the eigenvalue method is used to calculate the eigenvalues ​​λ1,λ2,…,λ of the state matrix in formula (5) tn+s , and select the j similar oscillation modes λ h1,λ h2 ,…,λ hj ; The j similar oscillation modes may include similar low-frequency oscillation modes, medium-frequency oscillation modes or high-frequency oscillation modes; where λ tn+s represents the tn+sth eigenvalue of the state matrix, tn+s is the order of the state matrix of n wind turbines connected to the AC grid, λ hj represents the jth of j similar oscillation modes;

[0091] Step S1.2.2: Based on the participation factor analysis, the participation factors of j similar oscillation modes are obtained, thereby determining the dominant state variables f of j similar oscillation modes. d ={f dk |k=1,2,…,j}, and define the remaining non-dominant state variables as f r ;f dk represents the kth dominant state variable; the dominant state variable of j similar oscillation modes refers to the state variable that participates in j similar oscillation modes to a greater extent; the non-dominant state variable of j similar oscillation modes refers to the state variable that participates in j similar oscillation modes to a lesser extent;

[0092] The linearized state space model before order reduction is established using equation (6):

[0093]

[0094] In formula (6), Δf d represents the dominant state variable f d The increment, Δf r represents the remaining non-dominant state variables f r The increment, A 11 Denotes Δf d The derivative of Δf d The coefficient relationship between 12 Denotes Δf d The derivative of Δf r The coefficient relationship between 21 Denotes Δf r The derivative of Δf d The coefficient relationship between 22 Denotes Δf r The derivative of Δf r The coefficient relationship between

[0095] Step S1.2.3 Let dΔf r / dt=0, that is, ignoring the non-dominant state variable f r The dynamic characteristics of ; and use formula (7) to obtain the reduced-order linearized state space model:

[0096]

[0097] In formula (7), A 22 The inverse matrix, A d is the state matrix of the linearized state space model after order reduction; after order reduction, the order of the linearized state space model is reduced from d+r to d; d is the dominant state variable f d The dimension of r is the non-dominant state variable f r The dimension of

[0098] Step S2: Obtaining the participation factor sensitivity of each wind turbine to a similar oscillation mode;

[0099] Step S2.1: Get A d The eigenvalues ​​of l |l=1,2,…,m}, and the corresponding left eigenphasors U1,U2,…,U m and right characteristic phasors V1, V2, ..., V m ; where m is A d The order of l Indicates A d The lth eigenvalue of m represents the mth left eigenvector, V m represents the mth right eigenvector;

[0100] Step S2.1.1: Solve equation (8) and obtain the state matrix A d The characteristic values ​​of:

[0101] |λ l E d -A d |=0 (8) In formula (8), E d is the state matrix A d Identity matrix of the same order;

[0102] Step S2.1.2: Use equation (9) to solve the lth eigenvalue λ l The corresponding left eigenvector U l and the right eigenvector V l :

[0103]

[0104] In formula (9), V l T Indicates V l The transpose of

[0105] Step S2.2: Based on the dominant state variable f d Analyze the participation factors of similar oscillation modes and obtain the dominant state variable fd The sensitivity of the participation factor to similar oscillation modes, and obtain the sensitivity of the participation factor of each wind turbine to similar oscillation modes:

[0106] Step S2.2.1: Calculate the kth dominant state variable f dk Participation factor P of the lth similar oscillation mode kl =U kl V kl , where U kl is the right eigenvector U l The kth item, V kl is the left eigenvector V l The kth item of ;

[0107] Step S2.2.2: Use equation (10) to calculate the kth dominant state variable f as the parameter a changes. dk Participation factor sensitivity to the lth similar oscillation mode

[0108]

[0109] In formula (10), a(0) is the initial parameter of parameter a, Δa is the increment of parameter a; P kl (a) represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a; P kl (a) Partial derivative of a at a(0); P kl [a(0)+Δa] represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a(0)+Δa, P kl [a(0)] represents the participation factor of the kth dominant state variable in the lth similar oscillation mode at a(0); represents the limit when Δa approaches 0; according to formula (10), it can be pre-determined which parameter changes the participation factors of similar oscillation modes are more sensitive to, thus providing a reference for parameter adjustment of the actual system;

[0110] Step S2.2.3: When the i-th wind turbine contains y i The dominant state variables participate in similar oscillation modes, and the state variables are from z i to z i +y i When the parameter a changes, the participation factor sensitivity of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (11):

[0111]

[0112] In formula (11), Psl (a) is the participation factor of the sth dominant state variable in the lth adjacent oscillation mode at parameter a, P sl (a) The partial derivative of a at a(0), for of and; Indicates that at a(0)+Δa the zth i The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) the zth i The participation factor of the dominant state variable in the lth similar oscillation mode; Indicates that at a(0)+Δa the zth i +1 dominant state variable participates in the participation factor of the lth adjacent oscillation mode, Indicates that at a(0) the zth i +1 dominant state variable participation factor in the lth similar oscillation mode; Indicates that at a(0)+Δa the zth i +y i The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) the zth i +y i The participation factor of the dominant state variable in the lth similar oscillation mode;

[0113] Step S3: obtaining the optimal configuration position of the damping controller in the wind power grid-connected system;

[0114] Step S3.1: Obtain the participation factor of each wind turbine in the similar oscillation mode after parameter perturbation:

[0115] Step S3.1.1: Calculate the change in the participation factor of the ith wind turbine in the lth similar oscillation mode when the parameter perturbation is a0 using equation (12):

[0116]

[0117] In formula (12), P i|l is the participation factor of the ith wind turbine in the lth similar oscillation mode, P is the case when the parameter perturbation is a0 i|j The amount of change;

[0118] Step S3.1.2: Let the participation factor of the i-th wind turbine in the l-th similar oscillation mode under the initial operating condition be P i|l,0, then when the parameter perturbation is a0, the participation factor of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (13):

[0119]

[0120] Step S3.2: Calculate the participation factors of each wind turbine for all similar oscillation modes after parameter perturbation and sort them; and obtain the optimal configuration position of the damping controller of the similar oscillation mode after parameter perturbation:

[0121] Step S3.2.1: Repeat the calculation of formula (13) when i = 1, 2, ..., n; l = 1, 2, ..., m, so as to obtain the participation factor of each wind turbine for all similar oscillation modes when the parameter perturbation is a0:

[0122]

[0123] In formula (14), It represents the sum of the participation factors of the first wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the second wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the nth wind turbine in all similar oscillation modes after the parameter perturbation when the parameter perturbation is a0;

[0124] Step S3.2.2: The participation factors and shown in formula (14) reflect the degree of participation of wind turbines in similar oscillation modes, which determines the optimal installation position of the damping controller of similar oscillation modes (the damping controller of similar oscillation modes is generally configured on wind turbines with larger participation factors and). Therefore, the participation factors and of each wind turbine for all similar oscillation modes are set to After descending sorting, according to the number e of damping controllers to be installed, the first e participation factors after descending sorting and the corresponding wind turbines are selected as the optimal configuration positions of the e damping controllers.

Claims

1. An optimal configuration method for a damping controller of a wind power grid-connected system with similar oscillation modes under parameter perturbation, the wind power grid-connected system comprising: n wind turbines and an AC power grid, and any wind turbine is numbered as i, i=1,…,n; characterized in that the optimal configuration method of the damping controller is performed according to the following steps: Step S1: Establish a linearized state space model of the wind power grid-connected system and perform order reduction simplification; Step S1.1: Obtain the linearized state space model of the wind power grid-connected system: Step S1.1.1: In the dq rotating coordinate system, use formula (1) to obtain the state space model of the i-th wind turbine group: (1) In formula (1), d represents the differential, t represents the time, and x wi is the state variable of the i-th wind turbine, A wi is the state matrix of the i-th wind turbine, B wi is the input matrix of the i-th wind turbine, u wi is the input variable of the i-th wind turbine, C i represents the voltage interface coefficient between the ith wind turbine and the AC grid, u d 、u q are the d-axis and q-axis voltages at the common connection point, respectively; Step S1.1.2: In the dq rotating coordinate system, use formula (2) to obtain the state space model of the AC power grid: (2) In formula (2), x g is the state variable of the AC power grid, A g is the state matrix of the AC power grid, B g is the input matrix of the AC power grid, u g is the input variable of the AC power grid, D i represents the current interface coefficient between the i-th wind turbine and the AC grid, i di 、i qi are the d-axis and q-axis currents on the collector circuit of the i-th wind turbine respectively; Step S1.1.3: Obtain the initial operating point p of the i-th wind turbine through power flow calculation i and the initial operating point q of the AC grid; Use formula (3) to establish the initial operating point p i The linearized state space model of the i-th wind turbine under operating conditions; (3) In formula (3), Represents x wi The increment of Indicates u d The increment of Indicates u q The increment of The linearized state space model of the AC power grid under the operating condition of the initial operating point q is established using equation (4); (4) In formula (4), Represents x g The increment of Indicates i di The increment of Indicates i qi The increment of Step S1.1.4: Use equation (5) to construct a linearized state space model of the grid-connected system of n wind turbines: (5) In formula (5), E vi Represents C i The expansion matrix of E vi =[C i ]; F ti Indicates D i The expansion matrix of F ti =[ D i ]; Indicates v ×(t v -2)-dimensional zero matrix, Indicates t v ×(s v -2)-dimensional zero matrix, t v is the dimension of the state matrix of a single wind turbine, s v is the dimension of the AC power grid; Step S1.2: Reduced-order simplification of the linearized state-space model: Step S1.2.1: Use the eigenvalue method to calculate the eigenvalues ​​λ1,λ2,…,λ of the state matrix in equation (5) tn+s , and select j similar oscillation modes λ from them h1 ,λ h2 ,…,λ hj ; Among them, λ tn+s represents the tn+sth eigenvalue of the state matrix, tn+s is the order of the state matrix of n wind turbines connected to the AC grid, λ hj represents the jth similar oscillation mode; Step S1.2.2: Based on the participation factor analysis, the participation factors of j similar oscillation modes are obtained, thereby determining the dominant state variables f of j similar oscillation modes. d ={f dk | k=1,2,…,j}, and define the remaining non-dominant state variables as f r ;f dk represents the kth dominant state variable; The linearized state space model before order reduction is established using equation (6): (6) In formula (6), Δf d represents the dominant state variable f d The increment, Δf r represents the remaining non-dominant state variables f r The increment, A 11 Denotes Δf d The derivative of Δf d The coefficient relationship between 12 Denotes Δf d The derivative of Δf r The coefficient relationship between 21 Denotes Δf r The derivative of Δf d The coefficient relationship between 22 Denotes Δf r The derivative of Δf r The coefficient relationship between Step S1.2.3 Let dΔf r / dt=0; and use equation (7) to obtain the reduced-order linearized state space model: (7) In formula (7), A-1 22 is A 22 The inverse matrix, A d is the state matrix of the reduced linearized state space model; Step S2: Obtaining the participation factor sensitivity of each wind turbine to a similar oscillation mode; Step S2.1: Get A d The eigenvalues ​​of l | l=1,2,…,m}, and the corresponding left eigenphasors U1,U2,…, U m and right characteristic phasors V1, V2, ..., V m ; where m is A d The order of l Indicates A d The lth eigenvalue of m represents the mth left eigenvector, V m represents the mth right eigenvector; Step S2.1.1: Solve equation (8) and obtain the state matrix A d The characteristic values ​​of: (8) In formula (8), E d is the state matrix A d Identity matrix of the same order; Step S2.1.2: Use equation (9) to solve the lth eigenvalue λ l The corresponding left eigenvector U l and the right eigenvector V l : (9) In formula (9), express The transpose of Step S2.2: Based on the dominant state variable f d Analyze the participation factors of similar oscillation modes and obtain the dominant state variable f d The sensitivity of the participation factor to similar oscillation modes, and obtain the sensitivity of the participation factor of each wind turbine to similar oscillation modes: Step S2.2.1: Calculate the kth dominant state variable f dk Participation factor P of the lth similar oscillation mode kl =U kl V kl , where U kl is the right eigenvector U l The kth item, V kl is the left eigenvector V l The kth item of ; Step S2.2.2: Use equation (10) to calculate the kth dominant state variable f as the parameter a changes. dk Participation factor sensitivity to the lth similar oscillation mode : (10) In formula (10), a(0) is the initial parameter of parameter a, Δa is the increment of parameter a; P kl (a) represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a; P kl (a) Partial derivative of a at a(0); P kl [a(0)+Δa] represents the participation factor of the kth dominant state variable in the lth adjacent oscillation mode at a(0)+Δa, P kl [a(0)] represents the participation factor of the kth dominant state variable in the lth similar oscillation mode at a(0); represents the limit when Δa approaches 0; Step S2.2.3: When the i-th wind turbine contains y i The dominant state variables participate in similar oscillation modes, and the state variables are from z i to z i +y i When the parameter a changes, the participation factor sensitivity of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (11): : (11) In formula (11), P sl (a) is the participation factor of the sth dominant state variable in the lth adjacent oscillation mode at parameter a, P sl (a) The partial derivative of a at a(0), for , , , …, of and; Indicates that at a(0)+Δa The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) The participation factor of the dominant state variable in the lth similar oscillation mode; Indicates that at a(0)+Δa The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) The participation factor of the dominant state variable in the lth similar oscillation mode; Indicates that at a(0)+Δa The participation factor of the dominant state variable in the lth similar oscillation mode, Indicates that at a(0) The participation factor of the dominant state variable in the lth similar oscillation mode; Step S3: obtaining the optimal configuration position of the damping controller in the wind power grid-connected system; Step S3.1: Obtain the participation factor of each wind turbine in the similar oscillation mode after parameter perturbation: Step S3.1.1: Calculate the change in the participation factor of the ith wind turbine in the lth similar oscillation mode when the parameter perturbation is a0 using equation (12): : (12) In formula (12), P i|l is the participation factor of the ith wind turbine in the lth similar oscillation mode, P is the case when the parameter perturbation is a0 i|l The amount of change; Step S3.1.2: Let the participation factor of the i-th wind turbine in the l-th similar oscillation mode under the initial operating condition be P i|l,0 , then when the parameter perturbation is a0, the participation factor of the i-th wind turbine to the l-th similar oscillation mode is calculated using formula (13): : (13) Step S3.2: Calculate the participation factors of each wind turbine for all similar oscillation modes after parameter perturbation and sort them; and obtain the optimal configuration position of the damping controller of the similar oscillation mode after parameter perturbation: Step S3.2.1: Repeat the calculation of formula (13) when i=1,2,…,n; l=1,2,…,m, so as to obtain the participation factor of each wind turbine for all similar oscillation modes when the parameter perturbation is a0: (14) In formula (14), It represents the sum of the participation factors of the first wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the second wind turbine in all similar oscillation modes after parameter perturbation when the parameter perturbation is a0; It represents the sum of the participation factors of the nth wind turbine in all similar oscillation modes after the parameter perturbation when the parameter perturbation is a0; Step S3.2.2: Sum the participation factors of each wind turbine for all similar oscillation modes and After descending sorting, according to the number e of damping controllers to be installed, the first e participation factors after descending sorting and the corresponding wind turbines are selected as the optimal configuration positions of the e damping controllers.

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