A wind farm frequency modulation dynamic equivalence modeling method, device, equipment and medium

Abstract

The application discloses a wind farm frequency modulation dynamic equivalent modeling method, device, equipment and medium, and belongs to the field of power system planning and operation. The method comprises the following steps: obtaining the working parameters of each wind turbine in the frequency modulation process as the training data for generating a Koopman operator; performing wind turbine dynamic characteristic identification based on a state space dimension increasing mode according to the training data to obtain a Koopman operator capable of reflecting high-dimensional linear relationships; dividing the wind farm into multiple groups by using a gap measure method based on the obtained Koopman operator; and performing the aggregation of multiple wind turbines in the same group based on the equivalent pre-and-post wind turbine output characteristic invariable criterion. The application can better identify the situation that the wind turbine exits the frequency modulation due to wind speed overrun or other faults, and therefore the grouping result is more accurate and can more accurately reflect the actual dynamic characteristics of the wind farm, which is helpful to simplify the wind farm modeling and simulation process, make the wind turbines more efficiently participate in the system frequency modulation, and enhance the stability of power system operation.

Description

Technical Field

[0001] This invention relates to the field of power system planning and operation, and in particular to a method, apparatus, equipment and medium for dynamic equivalent modeling of wind farm frequency regulation. Background Technology

[0002] With economic and social development, global energy demand has experienced explosive growth, inevitably accelerating the consumption of traditional fossil fuels such as oil and natural gas. At the same time, people are increasingly concerned about the environmental pollution caused by the use of traditional fossil fuels and are beginning to seek cleaner and more sustainable energy solutions.

[0003] Developing wind power can reduce carbon emissions to some extent and alleviate the energy crisis, but large-scale grid connection of wind power will trigger a series of new problems. In traditional power grids, generator units are mostly composed of hydropower and thermal power units, which contain large rotational inertia. When the system frequency fluctuates, the kinetic energy contained in the rotor can spontaneously respond to unbalanced power loads, effectively mitigating frequency fluctuations and exhibiting good stability. This characteristic makes traditional synchronous machines exhibit strong tolerance to voltage and frequency changes. In contrast, new energy power generation equipment contains a large number of power electronic components, and its rotor is decoupled from the system frequency. Its output power depends on the corresponding control strategy, resulting in poor disturbance rejection capability and hindering system stability. Therefore, as the proportion of new energy power generation increases, the system inertia will decrease, threatening frequency stability.

[0004] Currently, wind turbines participate in system frequency regulation mainly by adding additional power control to active power control. However, due to the large number of power electronic components in wind turbines, their frequency regulation characteristics differ significantly from those of traditional synchronous machines. This complicates the dynamic mechanism of power system frequency, making it difficult to analyze their dynamic characteristics simply. Detailed models used in studying wind farm frequency regulation suffer from high order and computational complexity. To improve the operational stability of power systems with high wind power ratios, it is necessary to establish a dynamic equivalent modeling method for wind farm frequency regulation that considers the dynamic operating conditions of wind farms, providing relevant departments with engineering application references. Summary of the Invention

[0005] In order to at least partially solve one of the technical problems existing in the prior art, the purpose of this invention is to provide a method, device, equipment and medium for dynamic equivalent modeling of wind farm frequency regulation based on Koopman theory.

[0006] The first technical solution adopted in this invention is:

[0007] A method for dynamic equivalent modeling of frequency regulation in wind farms includes the following steps:

[0008] The operating parameters of each wind turbine during the frequency regulation process are obtained and used as training data to generate the Koopman operator.

[0009] Based on the training data, the dynamic characteristics of wind turbines are identified using a state space dimensionality upgrade approach, and a Koopman operator that can reflect high-dimensional linear relationships is obtained.

[0010] Based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using the gap measure method;

[0011] Aggregation of multiple units in the same group is carried out based on the criterion that the output characteristics of the units before and after the equivalence remain unchanged.

[0012] Furthermore, the operating parameters include input wind speed, active power reference value, rotational speed, rotor current, and generator transient electromotive force; wherein, the input wind speed includes the input wind speed of the upstream wind turbine and the input wind speed of the downstream wind turbine.

[0013] Furthermore, the input wind speed of the downstream wind turbine is obtained in the following way:

[0014] Introducing the Jessen model to account for the wake effect of the downstream wind turbine wind speed, the oncoming wind speed v of the downstream wind turbine. k Represented as:

[0015]

[0016] In the formula, G k Let d be the set of upstream wind turbines i that have a wake effect on downstream wind turbine k, v0 be the uniform input wind speed of the upstream wind turbines, and d be the set of upstream wind turbines i that have a wake effect on downstream wind turbine k. i,k σ represents the distance between upstream wind turbine i and downstream wind turbine k in the same wind speed direction; i (d i,k (v0) is the wind speed attenuation coefficient, which is defined as:

[0017]

[0018] In the formula, R is the radius of the wind turbine blade, and C T This is the thrust coefficient.

[0019] Furthermore, taking the center of the downstream wind turbine k as the origin, the opposite direction of the unified input wind speed as the positive x-axis, and arbitrarily choosing the perpendicular line to one side of the x-axis as the positive y-axis, a rectangular coordinate system is established. The coordinates (x, y) of wind turbine i, which has a wake effect, are then defined for wind turbine k. i ,y i The set consisting of ) is shown below:

[0020] S k ={(x i,y i )|x i =d i,k ,c(d i,k )-r(d i,k )≤y i ≤c(d i,k )+r(d i,k ),i∈G k}

[0021] In the formula, S k For G k The set of coordinates of the upstream wind turbines in the middle, c(d i,k ) represents wind turbine i in x i =0, the ordinate of the wake center point, r(d i,k ) represents wind turbine i in x i The radius of the wake effect at point 0; (x i ,y i () represents the coordinates of the upstream wind turbine.

[0022] When the wind direction changes, the effect of the wake also changes. Assuming the wind direction changes from 0° to θ, and the centerline also deflects by θ, the radius of the wake effect becomes:

[0023] r(θ) = r(0)cos(θ)

[0024] Therefore, the coordinates within the wind farm need to be corrected. Assuming the wind direction is 0°, the coordinates of the wind turbine are (x(0), y(0)). When the wind direction changes, the corresponding coordinates of the wind turbine become:

[0025]

[0026] Finally, taking into account the geographical location of the downstream wind turbines, the input wind speed of the downstream wind turbines was calculated.

[0027] Furthermore, the step of identifying the dynamic characteristics of wind turbines based on the state space dimensionality increase method using training data to obtain a Koopman operator that reflects high-dimensional linear relationships includes:

[0028] A nonlinear dynamic model of a doubly-fed asynchronous wind turbine is established, expressed as follows:

[0029] X r,k+1 =f(X) r,k ,u k )

[0030] In the formula, u k X is the control input at time k. r,k Let be the state variable of the wind turbine r at time k, and f be the mapping of nonlinear dynamics;

[0031] Rotation speed ω r Rotor current I rd Using the generator transient electromotive force E as a state variable, the input wind speed and active power reference value P are used. ref As a control variable, the expression is:

[0032] X k =[ω r,k I rd,k E d,k E q,k ]

[0033]

[0034] In the formula, ω r,k Let I be the rotational speed at time k. rd,k Let E be the rotor current at time k. d,k Let E be the direct-axis transient electromotive force of the k-th generator. q,k P is the quadrature-axis transient electromotive force of the k-th generator; ref,k v w,k These are the reference value of active power and the input wind speed at time k, respectively;

[0035] Introducing the observation function ψ, which represents the state variables of the wind turbine from the state space. To the observation space A mapping relationship is used to obtain the Koopman operator. Its function is represented as follows:

[0036]

[0037] In the formula, x(k) is the state variable of the unit at time k, and u(k) is the control input at time k;

[0038] Based on the above formula, the optimization problem is obtained as follows:

[0039]

[0040] In the formula, matrices A and B are linear invariant matrices;

[0041] The Koopman operator is approximated by obtaining a matrix [A,B] using the extended dynamic mode decomposition algorithm. Therefore, the high-dimensional linear model based on the Koopman operator is expressed as:

[0042] z(k+1)=Az(k)+Bu(k)

[0043]

[0044] z(k)=[ψ1(x(k)),ψ2(x(k)),...,ψ N (x(k))] T .

[0045] In the formula, z(k) is the state variable in the high-dimensional space, and N is the dimension of the higher-dimensional space; These are estimates of the original system state variables at the next time step, and matrices A, B, and C are all linear time-invariant matrices.

[0046] Furthermore, the value of the linear time-invariant matrix C is solved using the least squares method:

[0047]

[0048] Using a data-driven approach to solve for matrix [A,B], the following input-output dataset was collected from the controlled nonlinear system x(k+1)=f(x(k),u(k)):

[0049] X=[x(1),x(2)...,x(P)]; Y=[x(2),x(3),...x(P+1)]; U=[u(1),u(2)...,u(P)]

[0050] After obtaining the data for X, Y, and U, substitute them into the following formula to solve for the values ​​of matrices A, B, and C:

[0051] min A,B ||Y lift -AX lift -BU|| F

[0052] min C ||X-CX lift || F

[0053] In the formula, X lift =[ψ(x(1)),...ψ(x(P))], Y lift =[ψ(x(2)),...ψ(x(P+1))], where F represents finding the norm of the matrix, and its analytical solution is:

[0054]

[0055] In the formula, This represents the pseudo-inverse of a matrix.

[0056] Furthermore, based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using a gap metric method, including:

[0057] The gap measure is used to calculate the gap measure value between each wind turbine: In Hilbert space, assuming the graph of the linear operator Z is G(Z), the gap measure of two closed operators G(Z1) and G(Z2) is expressed as the distance between them, and the gap measure between the two transformed DFIG linear dynamic models is expressed in the following form:

[0058]

[0059] In the formula, δ(Z1,Z2) represents the gap measure value, and N and M are the coprime factors of the system, i.e., satisfying Z=MN. -1 And N*N+M*M=I, * is the conjugate operator, H ∞ Let Q be the set of all rational transfer functions, and let Q be any Hilbert matrix.

[0060] Two wind turbines with a gap measurement value less than the preset value are grouped into the same wind turbine group, thus completing the grouping of the wind farm.

[0061] Furthermore, the aggregation of multiple units within the same generating group based on the criterion of unchanged output characteristics before and after equivalent operation includes:

[0062] After grouping the wind turbines in the field, each group of turbines is equivalent to a single unit, adhering to the principle of maintaining the output characteristics of the equivalent units before and after. The establishment of the clustered wind turbine equivalent model includes the following three steps:

[0063] Establish an equivalent wind turbine model;

[0064] Establish an equivalent generator model;

[0065] Establish an equivalent collector circuit model.

[0066] The second technical solution adopted in this invention is:

[0067] A wind farm frequency regulation dynamic equivalent modeling device includes:

[0068] The data acquisition module is used to acquire the operating parameters of each wind turbine during the frequency regulation process, which are used as training data to generate the Koopman operator.

[0069] The operator calculation module is used to identify the dynamic characteristics of wind turbines based on the state space dimensionality upgrade method according to the training data, and obtain the Koopman operator that can reflect the high-dimensional linear relationship.

[0070] The wind farm clustering module is used to divide a wind farm into multiple clusters based on the obtained Koopman operator and using the gap measure method.

[0071] The equivalent modeling module is used to aggregate multiple units in the same group based on the criterion that the output characteristics of the units before and after equivalence remain unchanged.

[0072] The third technical solution adopted in this invention is:

[0073] An electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement a wind farm frequency regulation dynamic equivalent modeling method as described above.

[0074] The fourth technical solution adopted in this invention is:

[0075] A computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement a wind farm frequency regulation dynamic equivalent modeling method as described above.

[0076] The fifth technical solution adopted in this invention is:

[0077] A computer program product or computer program includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions to cause the computer device to perform the method described above.

[0078] Compared with the prior art, the present invention has the following advantages and effects:

[0079] (1) Based on Koopman theory, this invention uses dynamic data during frequency regulation to group wind turbines, identifying those that have malfunctioned or exceeded their speed limits from changes in state variables, and grouping them into the same cluster. Compared with traditional algorithms, this invention can handle situations where some wind turbines may exit frequency regulation due to environmental changes or turbine malfunctions during actual operation. Therefore, the clustering results are more accurate and can more accurately reflect the actual dynamic characteristics of the wind farm.

[0080] (2) This invention addresses the problem of wind farm frequency regulation under dynamic operating conditions. It proposes a dynamic equivalent modeling method for wind farm frequency regulation based on Koopman theory. This method helps to simplify the wind farm modeling and simulation process, enables each wind turbine to participate in system frequency regulation more efficiently, helps to enhance the stability of power system operation, and provides relevant departments with certain engineering application references. Attached Figure Description

[0081] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0082] Figure 1 This is a flowchart illustrating the steps of a dynamic equivalent modeling method for wind farm frequency regulation based on Koopman theory in an embodiment of the present invention.

[0083] Figure 2 This is a diagram of the wake effect model in an embodiment of the present invention;

[0084] Figure 3 This is a model diagram of the downward wake effect in the wind direction according to an embodiment of the present invention;

[0085] Figure 4 This is a diagram of a three-machine, nine-node system including a wind farm in an embodiment of the present invention;

[0086] Figure 5 This is a schematic diagram illustrating the working principle of the Koopman theory in an embodiment of the present invention;

[0087] Figure 6 This is a diagram showing the gap measurement values ​​between wind turbines in a wind farm within the example section of this invention.

[0088] Figure 7 This is a comparison chart of the system frequency response curves in the example section of this invention;

[0089] Figure 8 This is a comparison chart of the active power output response curves in the calculation examples of this invention.

[0090] Figure 9 This is a comparison diagram of the rotational speeds of fan 23 and fan 24 during frequency adjustment in a calculation example of this invention. Detailed Implementation

[0091] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0092] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0093] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0094] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0095] Example 1

[0096] like Figure 1 As shown, this embodiment provides a dynamic equivalent modeling method for wind farm frequency regulation based on Koopman theory. This method helps simplify the wind farm modeling and simulation process, enabling each wind turbine to participate more efficiently in system frequency regulation and enhancing the stability of power system operation. The method specifically includes the following steps:

[0097] S1. Obtain the operating parameters of each wind turbine (hereinafter referred to as wind turbine or unit) during the frequency regulation process, and use them as training data to generate the Koopman operator.

[0098] As an optional implementation, step S1 specifically includes the following steps:

[0099] S11. Introducing the Jessen model to account for the downstream wind turbine speed due to wake effects, such as... Figure 2 As shown. The model is constructed as follows:

[0100] First, there are numerous wind turbines within the wind farm, and downstream units are affected by multiple upstream turbines. Therefore, the oncoming wind speed v of the downstream turbine k is... k It can be represented as:

[0101]

[0102] In the formula, G k Let d be the set of upstream wind turbines i that have a wake effect on downstream wind turbine k. i,kLet σ be the distance between upstream wind turbine i and downstream wind turbine k in the same wind speed direction. i (d i,k (v0) is the wind speed attenuation coefficient, where v0 is the uniform input wind speed of the upstream wind turbine.

[0103] The wind speed attenuation coefficient is defined as:

[0104]

[0105] In the formula, R is the radius of the wind turbine blade, and C T This is the thrust coefficient.

[0106] Secondly, taking the center of downstream wind turbine k as the origin, the opposite direction of the uniform input wind speed as the positive x-axis, and arbitrarily choosing the perpendicular line to one side of the x-axis as the positive y-axis, a rectangular coordinate system is established. This system defines the coordinates (x, y) of wind turbine i, which has a wake effect, relative to wind turbine k. i ,y i The set consisting of ) is shown below:

[0107] S k ={(x i y i )|x i =d i，k ,c(d i，k )-r(d i，k )≤y i ≤c(d i，k )+r(d i，k ), i∈G k}

[0108] In the formula, S k For G k The set of coordinates of the upstream wind turbines in the middle, c(d i,k ) represents wind turbine i in x i =0, the ordinate of the wake center point, (x i ,y i Let r(d) be the coordinates of the upstream wind turbine. i,k ) represents wind turbine i in x i The radius of the wake effect at point 0 is defined as:

[0109]

[0110] Finally, when the wind direction changes, the effect of the wake will also change, such as... Figure 3As shown. Assuming the wind direction is initially uniform, the radius of the wake effect of the upstream fan k on the downstream fan i is r(0). When the wind direction deflects counterclockwise by θ, the centerline also deflects counterclockwise by θ relative to its original position. The radius of the wake effect of the upstream fan k on the downstream fan i then becomes:

[0111] r(θ) = r(0)cos(θ)

[0112] Therefore, the coordinates within the wind farm need to be corrected. Assuming the wind turbine's coordinates were (x0, y0) under a uniform wind speed and direction, the corresponding turbine coordinates become:

[0113]

[0114] Based on the wake effect model described above and the geographical location of each wind turbine, its input wind speed can be calculated.

[0115] S12. Obtain the active power reference value P of each wind turbine during frequency regulation. ref Rotational speed ω r Rotor current I rd The transient electromotive force E of the generator, along with the calculated wind speed of the wind turbine, are used as training data for generating the Koopman operator.

[0116] In this embodiment, a three-machine, nine-node wind power grid-connected simulation model was established using Matlab / Simulink. The system includes two synchronous machines and one wind farm, such as... Figure 4 As shown in the figure. The wind farm has 24 turbines with a rated capacity of 2MW. Each turbine is stepped up by a 0.69 / 35kV terminal transformer, and the power is collected at the outlet bus via collector lines, then transmitted to the main power grid by another transformer. The minimum speed limit for turbines to participate in frequency regulation is 0.7pu; that is, the turbine will exit frequency regulation when the rotor speed is below this value. The simulation step size is set to 0.001s, and the simulation duration is 50s. To better illustrate the technical solution and effects of this invention, this embodiment demonstrates the feasibility of the method through simulation, as shown below:

[0117] The initial wind speed was 13 m / s, and the wind direction was θ = π / 6. The disturbance was a sudden increase in system load of 50 MW within 1 second of operation, coinciding with the wind farm's participation in system frequency regulation. Based on the geographical location of each wind turbine and considering the wake effect, its input wind speed can be calculated. Furthermore, key operating parameters of the wind turbines, including the initial input wind speed, rotor speed, droop control coefficient, and virtual inertia coefficient for each turbine, are summarized in Table 1.

[0118] Table 1 Parameters of each fan

[0119] Fan Wind speed m / s Rotational speed / pu <![CDATA[Drooping coefficient / K p > <![CDATA[Inertia coefficient / K d > 1 13 0.829 2.3 1 2 11.84 0.755 2.1 0.7 3 11.51 0.734 2 0.9 4 11.34 0.723 1.9 1.2 5 10.57 0.674 1.8 0.7 6 9.95 0.635 1.8 0.6 7 13 0.829 2.2 0.8 8 12.10 0.772 2.1 1.1 9 11.36 0.725 2 0.7 10 11.05 0.705 1.9 0.4 11 10.70 0.682 1.7 0.6 12 10.50 0.669 1.8 0.8 13 13 0.829 2.3 0.8 14 11.83 0.755 2.1 0.9 15 11.98 0.764 2.1 0.7 16 11.04 0.704 2 0.5 17 11.19 0.714 1.8 0.9 18 10.92 0.697 1.7 0.8 19 13 0.829 2.2 0.6 20 12.38 0.790 2 0.8 21 12.31 0.785 2.1 0.8 22 11.87 0.757 1.9 1 23 12.35 0.788 1.7 0.9 24 11.92 0.760 1.6 0.8

[0120] S2. Based on the training data, identify the dynamic characteristics of wind turbines using a state-space dimensionality-upgrading method to obtain the Koopman operator that can reflect high-dimensional linear relationships.

[0121] As an optional implementation, step S2 specifically includes the following steps:

[0122] S21. Introduce the Koopman operator to identify the dynamic characteristics of the wind turbine. Establish a nonlinear dynamic model of the doubly fed induction generator (DFIG), which can be expressed as:

[0123] X r,k+1 =f(X) r,k ,u k )

[0124] Among them, u k X is the control input at time k. r,k Let be the state variable of unit r at time k, and f be the mapping of the nonlinear dynamics of the system.

[0125] S22. Select the rotational speed ω from the detailed model. r Related state variables. Among them, the rotational speed and the d-axis component of the rotor-side current I. rd The transient potential E and the above variables are coupled. Therefore, these variables are treated as state variables. Meanwhile, the active power reference value P... ref It has a strong correlation with electromagnetic torque, while wind speed v w The imbalance between the electromagnetic torque and the mechanical torque determines the unit's mechanical torque, and this imbalance will cause a change in speed. Therefore, P... ref and v w As a control variable, it can be represented as:

[0126] X k =[ω r,k I rd,k E d,k E q,k ]

[0127]

[0128] Where the subscript k represents time k, I rd P is the d-axis component of the rotor-side current; E is the generator transient electromotive force; ref,k v w,k These represent the reference value of active power and the input wind speed at time k, respectively.

[0129] S23. To transform the nonlinear dynamic model of DFIG into a linear model, an observation function ψ(x) is introduced. The Koopman operator's action is further shown below:

[0130] ψ(x)=[ψ1(x),ψ2(x),…,ψ N (x)] T

[0131] In the formula, N is the system dimension in the observation space.

[0132] Therefore, ψ(X) can be... r,k ,u k ) is defined as an augmented observation variable with a certain structure:

[0133]

[0134] In the formula, As a nonlinear increasing-dimensional function, this embodiment uses Hermite polynomials to construct an orthogonal observation space basis.

[0135] S24. Introducing the Koopman operator theory, by raising the dimensionality of the state variables to a higher-dimensional space, and then using the Koopman operator to perform a global linear description of the nonlinear dynamic model of DFIG, the working principle is as follows: Figure 5 As shown. The Koopman operator is a linear evolution operator that maps the original state variables to a higher-dimensional space. Its function is as follows:

[0136]

[0137] in, Here, ψ is the Koopman operator, and ψ is the observation function, which represents the state variables of the wind turbine from the state space. To the observation space A mapping relationship, This is a compound operation.

[0138] S25. The Extended Dynamic Mode Decomposition (EDMD) method is introduced to approximate the Koopman operator in finite dimensions. Essentially, EDMD approximates an infinite-dimensional Koopman operator by calculating a finite-dimensional matrix K. The operator transforms the infinite-dimensional linear system into a finite-dimensional linear system for solution and analysis. Therefore, solving for the finite-dimensional approximate matrix K based on the extended mode decomposition method can be transformed into an optimization problem, described as follows:

[0139]

[0140] In the formula, P is the number of measurements, and N is the system dimension in the observation space.

[0141] Assuming n and m are the dimensions of the state variables and control inputs in the system, respectively, since predicting future control inputs is not required, the last m components in the above equation can be omitted. Simultaneously, the first n rows of matrix K can be decomposed into matrix A. n×n Sum matrix B n×m The form (represented by matrices A and B in the following formula), i.e., K n×(n+m) =[A n×n B n×m The optimization problem can then be further expressed as:

[0142]

[0143] In the formula, matrices A and B are linear invariant matrices.

[0144] By using Koopman operator theory and the EDMD data-driven approximation method, a matrix [A,B] can be obtained to approximate the Koopman operator. Therefore, the high-dimensional linear model based on the Koopman operator can be expressed as:

[0145] z(k+1)=Az(k)+Bu(k)

[0146]

[0147] z(k)=[ψ1(x(k)),ψ2(x(k)),...,ψ N (x(k))] T .

[0148] Where z(k) is the state variable in the high-dimensional space; These are estimates of the state variables of the original system at the next time step. Matrices A, B, and C are all linear time-invariant matrices. The value of matrix C can be obtained using the least squares method.

[0149]

[0150] After obtaining matrices A, B, and C, the nonlinear dynamic system can be transformed into a high-dimensional linear model. Specifically, the original state variable x(k) evolves through matrices A and B after being elevated to a higher-dimensional space by the observation function. Then, matrix C maps it back to the original state space, yielding the predicted value of the state variable x(k+1) for the next time step.

[0151] S26. Solve for matrix K using a data-driven approach. First, according to Koopman's theory, the linear dynamic model obtained from the DFIG transformation can be expressed as:

[0152]

[0153] Among them, matrix This is a finite-dimensional approximation of the infinite-dimensional Koopman operator. Then, the following input-output dataset was collected from the controlled nonlinear system x(k+1)=f(x(k),u(k)):

[0154] X=[x(1),x(2)...,x(P)]; Y=[x(2),x(3),...x(P+1)]; U=[u(1),u(2)...,u(P)]

[0155] After obtaining the data for X, Y, and U, substitute them into the following formula to solve for the values ​​of matrices A, B, and C:

[0156] min A,B ||Y lift -AX lift -BU|| F

[0157] min C ||X-CX lift || F

[0158] In the formula, X lift =[ψ(x(1)),...ψ(x(P))], Y lift =[ψ(x(2)),...ψ(x(P+1))], where F represents finding the norm of the matrix, and its analytical solution is:

[0159]

[0160] S3. Based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using the gap measure method.

[0161] In some embodiments, step S3 includes the following steps:

[0162] S31. Calculate the gap measurement value between each fan using the gap measurement method.

[0163] In Hilbert space, assuming the graph of the linear operator Z is G(Z), then the gapness of two closed operators G(Z1) and G(Z2) can be expressed as the distance between them:

[0164] δ(Z1,Z2)=δ(G(Z1),G(Z2))=

[0165]

[0166] In the formula, δ(·) represents the gap measurement value; Π is the gap measure between linear operator graphs; G(Z) Let G(Z) be the projection of any vector in Hilbert space onto the graph G(Z). To simplify the calculation, coprime decomposition is used to calculate the difference between the two systems, as shown in the following expression:

[0167]

[0168] Where, N T M T ∈H ∞ And satisfy and H ∞ Let be the set of all rational transfer functions, * be the conjugate operator, and I be the unit quantity. Therefore, we can obtain:

[0169]

[0170] In the formula, Q is an arbitrary Hilbert matrix.

[0171] Therefore, the gap measure between the two transformed DFIG linear dynamic models can be expressed in the following form:

[0172]

[0173] In the formula, δ(Z1,Z2) represents the gap measure value, and N and M are the coprime factors of the system, i.e., satisfying Z=MN. -1 And N*N+M*M=I, * is the conjugate operator, H ∞ Let Q be the set of all rational transfer functions, and let Q be any Hilbert matrix.

[0174] S32. Group wind farms with gap measurement values ​​less than the preset value into one category, thus completing the grouping of wind farms. When the gap measurement value is small, it indicates that the dynamic characteristics of the two wind turbines are relatively similar, and they can be grouped into the same wind turbine group. Conversely, it indicates that the dynamic differences between the two wind turbines are large, and they need to be grouped into different wind turbine groups.

[0175] Specifically, the clearance measurement values ​​between the fans in the example are as follows: Figure 6 As shown in the figure, the darker areas represent smaller gap metric values ​​between two wind turbines, indicating strong similarity in their dynamic behavior during frequency regulation, suggesting they can be grouped into the same wind turbine group. The lighter areas represent larger gap metric values, indicating significant differences in their dynamic behavior, requiring them to be grouped into different wind turbine groups. Spectral clustering is used to classify the gap metric values, thus completing the dynamic grouping of the wind farm.

[0176] S4. Aggregate multiple units in the same group based on the criterion that the output characteristics of the equivalent units remain unchanged before and after.

[0177] After grouping the wind turbines within the site, each group of turbines is equivalent to a single turbine unit, adhering to the principle of maintaining unchanged output characteristics before and after equivalence. The equivalent model of clustered wind turbine units mainly includes: equivalent wind turbine model, equivalent generator model, and equivalent collector line model.

[0178] As an optional implementation, step S4 specifically includes the following steps:

[0179] S41. Establish an equivalent wind turbine model.

[0180] Assuming there are k turbines in the same wind turbine group, and the equivalent wind speed v eq and equivalent rotational speed ω eq They are represented as follows:

[0181]

[0182] In the formula, v i ω is the effective input wind speed for the group's wind turbines and wake effect. i The rotational speed of each fan in the group.

[0183] S42. Establish an equivalent generator model, the expression of which is:

[0184]

[0185] In the formula, S eq P eq X s_eq R s_eq These are the equivalent generator rated capacity, active power, stator impedance, and stator resistance of the clustered wind turbine group, respectively.

[0186] S43. Establish an equivalent collector circuit model.

[0187] Equivalent collector circuit models are generally divided into two types: overhead lines and cables. For radial collector circuits and trunk collector circuits, the equivalent impedance can be expressed as follows:

[0188]

[0189] In the formula, Z eq This is the equivalent impedance of the collector line.

[0190] Traditional methods group wind farms based on their initial states before frequency regulation, while Koopman-based methods perform similarity clustering based on the dynamic frequency regulation process. First, detailed model simulations are used to obtain the dynamic frequency regulation curves of each turbine. Then, a Koopman operator characterizing the dynamic frequency regulation characteristics of each turbine is obtained through an up-dimensional transformation of the state space. Finally, the wind farm is grouped by calculating the gap measure between different turbines. Table 2 shows a comparison of the grouping results of the two methods in the example.

[0191] Table 2 Comparison of Fan Grouping Results

[0192] Traditional methods Koopman algorithm Group 1 1,7,13,19 1,7,13,19 Group 2 2,3,8,14,15,20,21,22 2,3,8,14,20 Group 3 4,5,6,9,10,11,12,16,17,18 4,5,9,10,11,12,15,16,21,23 Cluster 4 23,24 6,17,18,22,24

[0193] Table 2 shows that the clustering results of the wind farm obtained by the traditional method differ slightly from those obtained by the Koopman algorithm. This is because the traditional method uses static data before frequency regulation as the clustering basis, while the Koopman algorithm uses the similarity of dynamic behavior during the frequency regulation process as the clustering basis. Based on the clustering results, equivalent modeling of the wind farm was performed. Next, to verify the advantages of the wind farm frequency regulation dynamic equivalent modeling method based on Koopman operator theory, this can be demonstrated by comparing the dynamic curves generated by the two different modeling methods with the dynamic curves of the detailed model. The system frequency response curves, total power output curves of the wind farm, and speed comparison diagrams of wind turbines 23 and 24 during the frequency regulation process are compared in the example. Figure 7 , Figure 8 and Figure 9 As shown.

[0194] from Figure 7 and Figure 8 As can be seen, when wind speed changes, the traditional clustering method's grouping and equivalence effect is not as good as the Koopman method. This is because some units, due to their own frequency regulation capabilities and external environmental influences, experience speed exceeding limits and thus exit frequency regulation. Traditional clustering methods cannot accurately reflect complex and changing situations. For example, units 23 and 24 are grouped together in the traditional algorithm because of their similar initial states, but in actual operation, such as... Figure 9 As shown, unit 23 experienced a speed limit violation and exited frequency regulation in about 5 seconds, while unit 24 experienced the same violation in about 18 seconds. Therefore, their dynamic characteristics differ significantly, resulting in poor equivalence when grouped together. The equivalence method based on Koopman theory, however, can identify the operating status of the units from their dynamic curves, achieving better grouping results.

[0195] Table 3 Comparison of Average Errors in Dynamic Response of Equivalent Units

[0196]

[0197] As can be seen from the comparison of the average error of the equivalent unit dynamic response in Table 3, the equivalent model based on Koopman theory performs better than the traditional model. This is because traditional equivalent methods generally cluster the wind turbines in the wind farm from their initial state. However, in actual operation, due to environmental changes or turbine malfunctions, some wind turbines may exit frequency regulation, and traditional algorithms cannot identify this information. Therefore, the output characteristics of traditional methods differ significantly from the detailed model. In contrast, Koopman theory-based clustering, which uses dynamic data during frequency regulation, can identify wind turbines that have malfunctioned or exceeded their speed limits from changes in state variables, and group them into the same cluster, resulting in more accurate clustering. Therefore, the dynamic equivalent modeling of wind farm frequency regulation based on Koopman theory more accurately reflects the actual dynamic characteristics of the wind farm.

[0198] Example 2

[0199] This embodiment provides a wind farm frequency regulation dynamic equivalent modeling device, including:

[0200] The data acquisition module is used to acquire the operating parameters of each wind turbine during the frequency regulation process, which are used as training data to generate the Koopman operator.

[0201] The operator calculation module is used to identify the dynamic characteristics of wind turbines based on the state space dimensionality upgrade method according to the training data, and obtain the Koopman operator that can reflect the high-dimensional linear relationship.

[0202] The wind farm clustering module is used to divide a wind farm into multiple clusters based on the obtained Koopman operator and using the gap measure method.

[0203] The equivalent modeling module is used to aggregate multiple units in the same group based on the criterion that the output characteristics of the units before and after equivalence remain unchanged.

[0204] Since this device is a wind farm frequency regulation dynamic equivalent modeling device according to an embodiment of the present invention, and the principle of the device in solving the problem is similar to that of the method, the implementation of this device can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0205] Example 3

[0206] This invention also provides an electronic device, which includes a processor and a memory. The memory stores at least one instruction, at least one program, a code set, or an instruction set. The at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to achieve the following: Figure 1 This paper presents a dynamic equivalent modeling method for frequency regulation in wind farms.

[0207] It is understood that the memory may include random access memory (RAM) or read-only memory. Optionally, the memory may include non-transitory computer-readable storage medium. The memory can be used to store instructions, programs, code, code sets, or instruction sets. The memory may include a stored program area and a stored data area, wherein the stored program area may store instructions for implementing an operating system, instructions for at least one function, instructions for implementing the various method embodiments described above, etc.; the stored data area may store data created according to the use of the server, etc.

[0208] A processor may include one or more processing cores. The processor connects to various parts of the server via various interfaces and lines, executing instructions, programs, code sets, or instruction sets stored in memory, and accessing data stored in memory to perform various server functions and process data. Optionally, the processor may be implemented using at least one of the following hardware forms: Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), and Programmable Logic Array (PLA). The processor may integrate one or more of the following: Central Processing Unit (CPU) and Modem. The CPU primarily handles the operating system and applications; the modem handles wireless communication. It is understood that the modem may also be implemented as a separate chip without being integrated into the processor.

[0209] Since this electronic device is the electronic device corresponding to the wind farm frequency regulation dynamic equivalent modeling method in the embodiment of the present invention, and the principle of solving the problem by this electronic device is similar to that of the method, the implementation of this electronic device can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0210] Example 4

[0211] This invention also provides a computer-readable storage medium storing at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to achieve the following: Figure 1 This paper presents a dynamic equivalent modeling method for frequency regulation in wind farms.

[0212] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, including read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-Erasable Programmable Read-Only Memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0213] Since the storage medium is the storage medium corresponding to the wind farm frequency regulation dynamic equivalent modeling method of the present invention, and the principle of the storage medium in solving the problem is similar to that of the method, the implementation of the storage medium can refer to the implementation process of the above method embodiment, and the repeated parts will not be described again.

[0214] Example 5

[0215] In some possible implementations, various aspects of the methods of the embodiments of the present invention can also be implemented as a program product comprising program code that, when run on a computer device, causes the computer device to perform the steps of a wind farm frequency regulation dynamic equivalent modeling method according to various exemplary embodiments of the present application described above. The executable computer program code or "code" for performing the various embodiments can be written in high-level programming languages ​​such as C, C++, C#, Smalltalk, Java, JavaScript, Visual Basic, Structured Query Language (e.g., Transact-SQL), Perl, or in various other programming languages.

[0216] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0217] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0218] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for dynamic equivalent modeling of frequency regulation in wind farms, characterized in that, Includes the following steps: The operating parameters of each wind turbine during the frequency regulation process are obtained and used as training data to generate the Koopman operator. Based on the training data, the dynamic characteristics of wind turbines are identified using a state space dimensionality upgrade approach, and a Koopman operator that can reflect high-dimensional linear relationships is obtained. Based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using the gap measure method; Aggregation of multiple units in the same group is carried out based on the criterion that the output characteristics of the units before and after the equivalence remain unchanged; Based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using the gap metric method, including: The gap measure is used to calculate the gap measure value between each wind turbine: In Hilbert space, assuming the graph of the linear operator Z is G(Z), the gap measure of two closed operators G(Z1) and G(Z2) is expressed as the distance between them, and the gap measure between the two transformed DFIG linear dynamic models is expressed in the following form: In the formula, δ(Z1,Z2) represents the gap measure value, and N and M are the coprime factors of the system, i.e., satisfying Z=MN. -1 and N * N+M * M = I, * is the conjugate operator, H ∞ Let Q be the set of all rational transfer functions, and let Q be any Hilbert matrix. Two wind turbines with a gap measurement value less than the preset value are grouped into the same wind turbine group, thus completing the grouping of the wind farm.

2. The wind farm frequency regulation dynamic equivalent modeling method according to claim 1, characterized in that, The operating parameters include input wind speed, active power reference value, rotational speed, rotor current, and generator transient electromotive force; wherein, the input wind speed includes the input wind speed of the upstream wind turbine and the input wind speed of the downstream wind turbine.

3. The wind farm frequency regulation dynamic equivalent modeling method according to claim 2, characterized in that, The input wind speed of the downstream wind turbine is obtained in the following way: Introducing the Jessen model to account for the wake effect of the downstream wind turbine wind speed, the oncoming wind speed v of the downstream wind turbine. k Represented as: In the formula, G k Let d be the set of upstream wind turbines i that have a wake effect on downstream wind turbine k, v0 be the uniform input wind speed of the upstream wind turbines, and d be the set of upstream wind turbines i that have a wake effect on downstream wind turbine k. i,k σ is the distance from wind turbine i to wind turbine k; i (d i,k (v0) is the wind speed attenuation coefficient, which is defined as: In the formula, R is the radius of the wind turbine blade, and C T This is the thrust coefficient.

4. The wind farm frequency regulation dynamic equivalent modeling method according to claim 1, characterized in that, The step of identifying the dynamic characteristics of wind turbines based on the training data using a state-space dimensionality-upgrading approach, and obtaining a Koopman operator that reflects high-dimensional linear relationships, includes: A nonlinear dynamic model of a doubly-fed asynchronous wind turbine is established, expressed as follows: X r,k+1 =f(X r,k ,u k ) In the formula, u k X is the control input at time k. r,k Let be the state variable of the wind turbine r at time k, and f be the mapping of nonlinear dynamics; Rotation speed ω r Rotor current I rd Using the generator transient electromotive force E as a state variable, the input wind speed and active power reference value P are used. ref As a control variable, the expression is: X k =[ω r,k THE rd,k AND d,k AND q,k ] In the formula, ω r,k Let I be the rotational speed at time k. rd,k Let E be the rotor current at time k. d,k Let E be the direct-axis transient electromotive force of the k-th generator. q,k P is the quadrature-axis transient electromotive force of the k-th generator; ref,k v w,k These are the reference value of active power and the input wind speed at time k, respectively; Define ψ(x) as a function of the observables of the wind turbine generator as variables, and obtain the Koopman operator. Its function is represented as follows: In the formula, x(k) is the state variable of the unit at time k, and u(k) is the control input at time k; Based on the above formula, the optimization problem is obtained as follows: In the formula, matrices A and B are linear invariant matrices; The Koopman operator is approximated by obtaining the matrix [A,B] using the extended dynamic mode decomposition algorithm. Therefore, the high-dimensional linear model based on the Koopman operator is expressed as: z(k+1)=Az(k)+Bu(k) z(k)=[ψ1(x(k)),ψ2(x(k)),...,ψ N (x(k))] T . In the formula, z(k) is the state variable in the high-dimensional space, and N is the dimension of the higher-dimensional space; It is an estimate of the state variables of the original system at the next time step, and matrix C is a linear time-invariant matrix.

5. The wind farm frequency regulation dynamic equivalent modeling method according to claim 4, characterized in that, The value of the linear time-invariant matrix C is obtained by the least squares method: Using a data-driven approach to solve for matrix [A,B], the following input-output dataset was collected from the controlled nonlinear system x(k+1)=f(x(k),u(k)): X=[x(1),x(2)...,x(P)]; Y=[x(2),x(3),...x(P+1)]; U=[u(1),u(2)...,u(P)] After obtaining the data for X, Y, and U, substitute them into the following formula to solve for the values ​​of matrices A, B, and C: doesn't A,B ||Y lift -SURE lift -BU|| F min C ||X-CX lift || F In the formula, X lift =[ψ(x(1)),...ψ(x(P))], Y lift =[ψ(x(2)),...ψ(x(P+1))], where F represents finding the norm of the matrix, and its analytical solution is: In the formula, This represents the pseudo-inverse of a matrix.

6. The wind farm frequency regulation dynamic equivalent modeling method according to claim 1, characterized in that, The aggregation of multiple units in the same unit group based on the criterion of unchanged output characteristics before and after equivalent operation includes: After grouping the wind turbines in the field, each group of turbines is equivalent to a single unit, adhering to the principle of maintaining the output characteristics of the equivalent units before and after. The establishment of the clustered wind turbine equivalent model includes the following three steps: Establish an equivalent wind turbine model; Establish an equivalent generator model; Establish an equivalent collector circuit model.

7. A wind farm frequency regulation dynamic equivalent modeling device, characterized in that, include: The data acquisition module is used to acquire the operating parameters of each wind turbine during the frequency regulation process, which are used as training data to generate the Koopman operator. The operator calculation module is used to identify the dynamic characteristics of wind turbines based on the state space dimensionality upgrade method according to the training data, and obtain the Koopman operator that can reflect the high-dimensional linear relationship. The wind farm clustering module is used to divide a wind farm into multiple clusters based on the obtained Koopman operator and using the gap measure method. The equivalent modeling module is used to aggregate multiple units in the same group based on the criterion that the output characteristics of the units before and after equivalence remain unchanged. Based on the obtained Koopman operator, the wind farm is divided into multiple turbine clusters using the gap metric method, including: The gap measure is used to calculate the gap measure value between each wind turbine: In Hilbert space, assuming the graph of the linear operator Z is G(Z), the gap measure of two closed operators G(Z1) and G(Z2) is expressed as the distance between them, and the gap measure between the two transformed DFIG linear dynamic models is expressed in the following form: In the formula, δ(Z1,Z2) represents the gap measure value, and N and M are the coprime factors of the system, i.e., satisfying Z=MN. -1 and N * N+M * M = I, * is the conjugate operator, H ∞ Let Q be the set of all rational transfer functions, and let Q be any Hilbert matrix. Two wind turbines with a gap measurement value less than the preset value are grouped into the same wind turbine group, thus completing the grouping of the wind farm.

8. An electronic device, characterized in that, The electronic device includes a processor and a memory, wherein the memory stores at least one instruction, at least one program, a code set, or an instruction set, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by a processor to implement the method as described in any one of claims 1 to 6.

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