Wind power plant frequency modulation dynamic equivalent modeling method, device, equipment and medium

Abstract

The invention discloses a wind power plant frequency modulation dynamic equivalent modeling method, device and equipment and a medium, and belongs to the field of power system planning operation. The method comprises the steps that working parameters of all wind turbine generators in the frequency modulation process are obtained and serve as training data for generating a Koopman operator; according to the training data, wind turbine generator dynamic characteristic identification based on a state space dimension raising mode is carried out, and a Koopman operator capable of reflecting a high-dimensional linear relation is obtained; based on the obtained Koopman operator, dividing the wind power plant into a plurality of machine groups by adopting a gap measurement method; and aggregating a plurality of units in the same unit group based on an invariant criterion of output characteristics of the units before and after equivalence. According to the method, the condition that the fans exit frequency modulation due to wind speed out-of-limit or other faults can be better identified, so that the grouping result is more accurate, the actual dynamic characteristics of the wind power plant can be more accurately reflected, the modeling and simulation process of the wind power plant can be simplified, each fan can participate in system frequency modulation more efficiently, and the system efficiency is improved. And the operation stability of the power system can be enhanced.

Description

Technical Field

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

[0002] With the development of economy and society, the global energy demand has shown an explosive growth trend, which inevitably accelerates the consumption of traditional fossil fuel resources such as oil and natural gas. At the same time, people are paying more and more attention to the environmental pollution caused by the use of traditional fossil energy, and are beginning to seek cleaner and more sustainable energy solutions.

[0003] Vigorously developing wind power can reduce carbon emissions to a certain extent and alleviate the energy crisis, but the large-scale access of wind power to the grid will cause a series of new problems. In traditional power grids, most generators are composed of hydropower units and thermal power units, which have a large moment of inertia. When the system frequency fluctuates, the kinetic energy contained in the rotor can spontaneously respond to the unbalanced power load, effectively reduce the frequency fluctuation, and have good stability. This feature makes the traditional synchronous machine show strong tolerance when facing voltage and frequency changes. In contrast, since new energy power generation equipment contains a large number of power electronic components, its rotor is decoupled from the system frequency, and the output power depends on the corresponding control strategy. It has poor anti-interference ability, which is not conducive to the stability of the system. Therefore, as the proportion of new energy power generation increases, the inertia of the system will decrease, posing a threat to frequency stability.

[0004] At present, wind turbines participate in system frequency regulation mainly by adding additional power control to active power control. However, due to the presence of a large number of power electronic components in wind turbines, their frequency regulation characteristics are significantly different from those of traditional synchronous machines, which complicates the dynamic mechanism of power system frequency and makes it difficult to simply analyze its dynamic characteristics. When studying the frequency regulation problem of wind farms, the detailed model has the problems of large order and high computational complexity. In order to improve the operational stability of the power system under high wind power ratio, it is necessary to establish a dynamic equivalent modeling method for wind farm frequency regulation that takes into account the dynamic operating conditions of wind farms, and provide relevant departments with certain engineering application references. Summary of the invention

[0005] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the object of the present 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 by the present invention is:

[0007] A wind farm frequency regulation dynamic equivalent modeling method comprises the following steps:

[0008] Obtaining the operating parameters of each wind turbine during the frequency modulation process as training data for generating the Koopman operator;

[0009] According to the training data, the dynamic characteristics of the wind turbine are identified based on the state space dimension increase method to obtain the Koopman operator that can reflect the high-dimensional linear relationship;

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

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

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

[0013] Furthermore, the input wind speed of the downstream wind turbine is obtained by:

[0014] The Jessen model is introduced to take into account the wind speed of the downstream wind turbine with the wake effect. The headwind speed v of the downstream wind turbine is k It is expressed as:

[0015]

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

[0017]

[0018] Where R is the radius of the fan blade, C T is the thrust coefficient.

[0019] Furthermore, a rectangular coordinate system is established by taking the center of the downstream wind turbine group k as the origin of the coordinates, taking the opposite direction of the uniform input wind speed direction as the positive direction of the x-axis, and taking any vertical line on one side of the x-axis as the positive direction of the y-axis. The coordinates (x i ,y i ) is as follows:

[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 G k The coordinate set of the upstream wind turbine in, c(d i,k ) is the wind turbine i at x i = 0, the vertical coordinate of the wake center point, r(d i,k ) is the wind turbine i at x i = 0 wake effect radius; (x i ,y i ) are the coordinates of the upstream wind turbine;

[0022] When the wind direction changes, the effect of the wake will also change. Assuming that the wind direction changes from 0° to θ, the center line is also deflected by θ. At this time, the radius of the wake effect becomes:

[0023] r(θ)=r(0).cos(θ)

[0024] Therefore, it is necessary to calibrate the coordinates in the wind farm. Assuming that when the wind direction is 0°, the coordinates of the wind turbine are (x(0), y(0)). When the wind direction changes, the coordinates of the corresponding wind turbine become:

[0025]

[0026] Finally, combined with the geographical location of the downstream wind turbines, the input wind speed of the downstream wind turbines is calculated.

[0027] Furthermore, the dynamic characteristics of the wind turbine generator set are identified based on the state space dimension-raising method according to the training data to obtain the Koopman operator that can reflect the high-dimensional linear relationship, including:

[0028] The nonlinear dynamic model of the doubly-fed asynchronous wind turbine is established, and the expression is:

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

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

[0031] The speed ω r , rotor current I rd and the transient potential E of the generator as state variables, and the input wind speed and active power reference value P 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 is the speed at time k, I rd,k is the rotor current at time k, E d,k is the direct axis transient potential of the kth generator, E q,k is the quadrature axis transient potential of the kth generator; P ref,k , v w,k are the active power reference value and input wind speed at time k respectively;

[0035] The observation function ψ is introduced to represent the wind turbine state variable from the state space To the observation space A mapping relationship between , and the Koopman operator is obtained The effects are 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] According to the above formula, the optimization problem is obtained, which is expressed as follows:

[0039]

[0040] Wherein, matrices A and B are linear invariant matrices;

[0041] The Koopman operator is approximated by obtaining the matrix [A, B] by extending the 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 increased dimension; It is the estimated value of the state variable of the original system at the next moment. Matrices A, B and C are all linear constant matrices.

[0046] Furthermore, the value of the linear constant matrix C is solved by the least squares method:

[0047]

[0048] Using a data-driven approach to solve the matrix [A, B], the following input and output data sets were 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 of X, Y, and U, substitute them into the following formula to solve the matrix values ​​of 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 the norm of the matrix, and its analytical solution is:

[0054]

[0055] In the formula, Represents the pseudoinverse of a matrix.

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

[0057] The gap measure is used to calculate the gap measure value between each wind turbine: In Hilbert space, assuming that the graph of the linear operator Z is G(Z), then 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 as follows:

[0058]

[0059] In the formula, δ(Z1, Z2) represents the gap measure value, N and M are the coprime factors of the system, that is, Z = MN -1 and N*N+M*M=I, * is the conjugate operator, H ∞ is the set of all rational transfer functions, Q is an arbitrary Hilbert matrix;

[0060] The two wind turbines with gap measurement values ​​less than a preset value are classified into the same wind turbine group, thus completing the grouping of the wind farm.

[0061] Furthermore, the aggregation of multiple units in the same group based on the criterion of unchanged output characteristics of the units before and after equivalence includes:

[0062] After the wind turbines in the field are grouped, each group of wind turbines is equivalent to one unit in principle, with the output characteristics of the units before and after the equivalent remain unchanged. The establishment of the clustered wind turbine unit equivalent model includes the following three steps:

[0063] Establish an equivalent fan model;

[0064] Establish an equivalent generator model;

[0065] Establish an equivalent collector circuit model.

[0066] The second technical solution adopted by the present invention is:

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

[0068] A data acquisition module is used to obtain the working parameters of each wind turbine in the frequency modulation process as training data for generating the Koopman operator;

[0069] The operator calculation module is used to identify the dynamic characteristics of the wind turbine based on the state space dimension increase 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 the wind farm into multiple clusters based on the obtained Koopman operator and the gap measurement 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 by the present invention is:

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

[0074] The fourth technical solution adopted by the present invention is:

[0075] A computer-readable storage medium stores 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 implement a wind farm frequency regulation dynamic equivalent modeling method as described above.

[0076] The fifth technical solution adopted by the present invention is:

[0077] A computer program product or a 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 the processor executes the computer instructions, so that the computer device executes the above method.

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

[0079] (1) Based on the Koopman theory, the present invention performs grouping through dynamic data in the frequency modulation process, and can identify wind turbines that are faulty or have exceeded the speed limit from the changes in the state quantity, and classify them into the same group. Compared with the traditional algorithm, it can handle the situation in which some wind turbines exit the frequency modulation due to environmental changes or faults of the unit itself in actual operation. Therefore, the grouping result is more accurate and can more accurately reflect the actual dynamic characteristics of the wind farm.

[0080] (2) Aiming at the problem of wind farm frequency regulation under dynamic operation conditions of wind farms, the present invention proposes a wind farm frequency regulation dynamic equivalent modeling method 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments of the present invention or the drawings of related technical solutions in the prior art are introduced below. It should be understood that the drawings introduced below are only for the convenience of clearly describing 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 work.

[0082] Figure 1 It is a flow chart of steps of a method for dynamic equivalent modeling of wind farm frequency regulation based on Koopman theory in an embodiment of the present invention;

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

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

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

[0086] Figure 5 Schematic diagram of the working principle of Koopman theory in an embodiment of the present invention;

[0087] Figure 6 is a diagram of the clearance measurement values ​​between wind turbines in a wind farm in the example part of the embodiment of the present invention;

[0088] Figure 7 is a comparison diagram of frequency response curves of some systems in the example of the present invention;

[0089] Figure 8 is a comparison diagram of active output response curves of some examples in the embodiment of the present invention;

[0090] Fig. 9 1 is a rotation speed comparison diagram of the fan 23 and the fan 24 during the frequency modulation process in the example part of the embodiment of the present invention. DETAILED DESCRIPTION

[0091] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limitations of the present invention. For the step numbers in the following embodiments, they are only provided for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0092] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., and orientations or positional relationships indicated are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0093] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0094] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0095] Example 1

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

[0097] S1. Obtaining the working parameters of each wind turbine set (referred to as wind turbine or set) during the frequency modulation process as training data for generating a Koopman operator.

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

[0099] S11, the Jessen model is introduced to take into account the downstream wind speed of the wind turbine with the wake effect, such as Figure 2 The model is constructed as follows:

[0100] First, there are many wind turbines in the wind farm, and the downstream units are affected by multiple upstream wind turbines. Therefore, the headwind speed v of the downstream wind turbine k is k It can be expressed as:

[0101]

[0102] In the formula, G k is the set of upstream wind turbines i that have wake effects on downstream wind turbine k, d i,kis the distance from the upstream wind turbine i to the downstream wind turbine k in the direction of uniform wind speed, σ i (d i,k ,v0) is the attenuation coefficient of wind speed, and v0 is the uniform input wind speed of the upstream wind turbine.

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

[0104]

[0105] Where R is the radius of the fan blade, C T is the thrust coefficient.

[0106] Secondly, the center of the downstream wind turbine k is taken as the origin of the coordinates, the opposite direction of the uniform input wind speed direction is taken as the positive direction of the x-axis, and the vertical line on one side of the x-axis is taken as the positive direction of the y-axis to establish a rectangular coordinate system. The coordinates (x i ,y i ) is as follows:

[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 G k The coordinate set of the upstream wind turbine in, c(d i,k ) is the wind turbine i at x i = 0, the vertical coordinate of the wake action center point, (x i ,y i ) is the coordinate of the upstream wind turbine, r(d i,k ) is the wind turbine i at x i = 0, the wake effect radius is defined as:

[0109]

[0110] Finally, when the wind direction changes, the effect of the wake will also change, such as Figure 3Assume that under the original uniform wind speed, the wake effect radius of the upstream wind turbine k on the downstream wind turbine i is r(0). When the wind direction deflects counterclockwise by θ, the center line also deflects counterclockwise by θ relative to the original. At this time, the wake effect radius of the upstream wind turbine k on the downstream wind turbine i becomes:

[0111] r(θ)=r(0).cos(θ)

[0112] Therefore, it is necessary to calibrate the coordinates in the wind farm. Assuming that the coordinates of the wind turbine are (x0, y0) under the original wind direction of uniform wind speed, when the wind direction changes, the corresponding wind turbine coordinates become:

[0113]

[0114] Based on the above wake effect model 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 in the frequency modulation process ref , speed ω r , rotor current I rd As well as the transient potential E of the generator, these data and 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 is established using Matlab / Simulink. The system includes two synchronous machines and a wind farm. Figure 4 As shown. There are 24 units in the wind farm with a rated capacity of 2MW; each wind turbine is boosted by a 0.69 / 35kV machine-end transformer, and then collected at the export bus through the collector line, and then the transformer transmits the electric energy to the large power grid; the minimum speed limit for the unit to participate in frequency regulation is 0.7pu, that is, when the rotor speed is lower than this value, the frequency regulation will be exited; the simulation step is set to 0.001s, and the simulation time is 50s. In order to better illustrate the technical solution and its effects of the present invention, this embodiment demonstrates the feasibility of this method through simulation, as shown below:

[0117] Initial wind speed 13m / s, wind direction θ=π / 6, disturbance: when running to 1s, the system load suddenly increases by 50MW, and the wind farm participates in the system frequency regulation. According to the geographical location of each wind turbine and considering the influence of the wake effect, its input wind speed can be calculated. In addition, the key operating parameters of the wind turbine, including the initial input wind speed, rotor speed, droop control coefficient and virtual inertia coefficient of each wind turbine, are summarized in Table 1.

[0118] Table 1 Parameters of each fan

[0119] Fan Wind speed m / s 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. According to the training data, the dynamic characteristics of the wind turbine are identified based on the state space dimensionality increase method to obtain the Koopman operator that can reflect the high-dimensional linear relationship.

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

[0122] S21. The Koopman operator is introduced to identify the dynamic characteristics of the wind turbine. A nonlinear dynamic model of a doubly fed asynchronous wind turbine (DFIG) is established, which can be expressed as:

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

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

[0125] S22, select the detailed model and the speed ω r Among them, the speed and the d-axis component of the rotor side current I rd , transient potential E are coupled. Therefore, the above variables are used as state variables. At the same time, the active power reference value P ref It has a strong correlation with the electromagnetic torque, and the wind speed v w Determines the mechanical torque of the unit. The imbalance between electromagnetic torque and mechanical torque will cause the speed to change. ref and v w As a control variable. It can be expressed as:

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

[0127]

[0128] Among them, the subscript k represents the kth moment, I rd is the d-axis component of the rotor side current; E is the transient potential of the generator; P ref,k , v w,k are the active power reference value and input wind speed at time k respectively.

[0129] S23. In order to transform the nonlinear dynamic model of DFIG into a linear model, the observation function ψ(x) is introduced. The effect of the Koopman operator can be further obtained as follows:

[0130] ψ(x)=[ψ1(x),ψ2(x),…,ψ N (x)] T

[0131] Where N is the system dimension in the observation space.

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

[0133]

[0134] In the formula, It is a nonlinear dimensionality-raising function. In this embodiment, Hermite polynomials are used to construct an orthogonal observation space basis.

[0135] S24. The Koopman operator theory is introduced. By upgrading the state variables to a high-dimensional space, the Koopman operator is used to perform a global linear description of the nonlinear dynamic model of DFIG. Its working principle is as follows: Figure 5 As shown. The Koopman operator is the linear evolution operator after the original state variables are mapped to the high-dimensional space, and its function is expressed as follows:

[0136]

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

[0138] S25. Extended Dynamic Mode Decomposition (EDMD) is introduced to perform finite-dimensional approximation of the Koopman operator. The extended modal decomposition method essentially approximates the infinite-dimensional matrix K by calculating the finite-dimensional matrix K. Operator, thereby converting the infinite-dimensional linear system into a finite-dimensional linear system for solution analysis. Therefore, solving the finite-dimensional approximate matrix K based on the extended modal decomposition method can be converted into an optimization problem, which is described as:

[0139]

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

[0141] Assume that n and m are the dimensions of the state variables and control inputs in the system, respectively. Since there is no need to predict the input of future control, the last m components in the above formula can be omitted. At the same time, the first n rows of the matrix K can be decomposed into the matrix A n×n and matrix B n×m The form of (in the following formula, represented by matrix A and matrix B), that is, K n×(n+m) =[A n×n , B n×m ], then the optimization problem can be further expressed as:

[0142]

[0143] Wherein, matrices A and B are linear invariant matrices.

[0144] Through the Koopman operator theory and EDMD data-driven approximation method, the 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] Among them, z(k) is the state variable in the high-dimensional space; It is the estimated value of the state variable of the original system at the next moment. Matrices A, B and C are all linear constant matrices. Among them, the value of matrix C can be solved by the least squares method:

[0149]

[0150] After obtaining the A, B, and C matrices, the nonlinear dynamic system can be transformed into a high-dimensional linear model. The original state variable x(k) is upgraded to a high-dimensional space by the observation function and then evolved through the A and B matrices. The C matrix can then map it back to the original state space to obtain the predicted value of the state variable x(k+1) at the next moment.

[0151] S26. Use a data-driven approach to solve the matrix K. First, according to the Koopman theory, the linear dynamic model obtained by DFIG transformation can be expressed as:

[0152]

[0153] Among them, the matrix is the finite-dimensional approximation of the infinite-dimensional Koopman operator. Then the following input and output data sets were 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 of X, Y, and U, substitute them into the following formula to solve the matrix values ​​of 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 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 groups using the gap measurement method.

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

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

[0163] In Hilbert space, assuming that the graph of a linear operator Z is G(Z), then the gap between 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; is the gap measure between linear operator graphs; Π G(Z) is the projection of any vector in the Hilbert space onto the graph G(Z). To simplify the calculation, coprime decomposition is used here to calculate the difference between the two systems. The expression is as follows:

[0167]

[0168] Among them, N T ,M T ∈H ∞ And meet and H ∞ is the set of all rational transfer functions, * is the conjugate operator, and I is the unit value. From this we can get:

[0169]

[0170] Where Q is an arbitrary Hilbert matrix.

[0171] Therefore, the gap measure between the two transformed DFIG linear dynamic kinetic models can be expressed as follows:

[0172]

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

[0174] S32, classify the gap measurement values ​​less than the preset value into one category, and complete the grouping of the wind farm. When the gap measurement value is small, it means that the dynamic characteristics of the two wind turbines are relatively close, and they can be classified into the same wind turbine group. On the contrary, it means that the dynamic difference between the two wind turbines is large, and they need to be classified 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 color in the figure indicates that the gap measurement value between the two wind turbines is small, which means that the dynamic behaviors of the two wind turbines are similar during the frequency modulation process and they can be classified as the same wind turbine group. The lighter color indicates that the gap measurement value between the two wind turbines is large, which means that the dynamic behaviors of the two wind turbines are very different and need to be classified as different wind turbine groups. The gap measurement values ​​are divided by spectral clustering to complete the dynamic clustering of the wind farm.

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

[0177] After the wind turbines in the field are grouped, each group of wind turbines is equivalent to one unit in principle, with the output characteristics of the units before and after the equivalent remain unchanged. The clustered wind turbine equivalent model 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 fan model.

[0180] Assume that there are k wind turbines in the same wind turbine group and the equivalent wind speed v eq and equivalent speed ω eq Respectively expressed as:

[0181]

[0182] In the formula, v i is the effective input wind speed of the wind turbines in the group taking into account the wake effect, ω i is the 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 They are the equivalent generator rated capacity, active power stator impedance and stator resistance of the clustered wind turbine group.

[0186] S43. Establish an equivalent current collection circuit model.

[0187] The equivalent collector line model is generally divided into two types: overhead line and cable. For radial collector lines and trunk collector lines, the equivalent impedance can be expressed as:

[0188]

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

[0190] The traditional method clusters by the initial state before frequency modulation, while the Koopman theory clusters by similarity through the frequency modulation dynamic process. First, the dynamic frequency modulation curve of each unit is obtained through detailed model simulation, and then the Koopman operator that can characterize the dynamic characteristics of the frequency modulation of each wind turbine is obtained through the dimensionality increase transformation of the state space. Finally, the wind farm is clustered by calculating the gap measurement value between different units. The comparison of the clustering results of the two methods in the example is shown in Table 2:

[0191] Table 2 Comparison of fan grouping results

[0192] Traditional methods Koopman Algorithm Cluster 1 1,7,13,19 1,7,13,19 Cluster 2 2,3,8,14,15,20,21,22 2,3,8,14,20 Cluster 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] As can be seen from Table 2, the clustering results of wind farms under the traditional method are slightly different from those based on the Koopman algorithm. This is because the traditional method uses static data before frequency modulation as the basis for clustering, while the Koopman algorithm uses the similarity of dynamic behavior during the frequency modulation process as the basis for clustering. Based on the clustering results, the wind farm was equivalently modeled. Next, in order to verify the advantages of the wind farm frequency modulation dynamic equivalent modeling method based on Koopman operator theory, it 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 of the two methods in the example, the total output curve of the wind farm, and the speed comparison diagram of wind turbine 23 and wind turbine 24 during the frequency modulation process are shown in the figure below. Figure 7 , Figure 8 and Fig. 9 shown.

[0194] from Figure 7 and Figure 8 It can be seen from the figure that when the wind speed changes, the clustering effect of the traditional clustering method is not as good as that of the Koopman method. This is because some units have exceeded the speed limit and exited the frequency regulation due to their own frequency regulation capabilities and external environment, and the traditional clustering method is difficult to reflect complex and changing situations. For example, units 23 and 24 are classified into one category in the traditional algorithm because of their similar initial states, but in actual operation, Fig. 9 As shown in the figure, the speed of unit 23 exceeded the limit and exited the frequency modulation at about 5s, while the speed of unit 24 exceeded the limit and exited the frequency modulation at about 18s. Therefore, their dynamic characteristics are quite different, and the equivalent effect of grouping them together is poor. The equivalent method based on Koopman theory can identify the operating status of the unit from the dynamic curve of the unit, and the grouping effect is better.

[0195] Table 3 Comparison of average errors of dynamic response of equivalent units

[0196]

[0197] From the comparison of the average error of the dynamic response of equivalent units in Table 3, it can be seen that the equivalent model based on Koopman theory has a better equivalent effect than the traditional model. This is because the traditional equivalent general method generally clusters the initial state of the wind turbines in the wind farm, but in actual operation, due to environmental changes or unit failures, some wind turbines will exit the frequency modulation, and the traditional algorithm cannot identify this type of information. Therefore, the output characteristics of the traditional method are quite different from the detailed model. Based on the Koopman theory, the dynamic data in the frequency modulation process is clustered, and the wind turbines due to failure or speed limit exceeding can be identified from the changes in the state quantity, and they are classified into the same group, and the clustering result is more accurate. Therefore, the dynamic equivalent modeling of wind farm frequency modulation based on Koopman theory can more accurately reflect 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] A data acquisition module is used to obtain the working parameters of each wind turbine in the frequency modulation process as training data for generating the Koopman operator;

[0201] The operator calculation module is used to identify the dynamic characteristics of the wind turbine based on the state space dimension increase 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 the wind farm into multiple clusters based on the obtained Koopman operator and the gap measurement 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 the device is a wind farm frequency regulation dynamic equivalent modeling device of an embodiment of the present invention, and the principle of solving the problem by the device is similar to that of the method, the implementation of the device can refer to the implementation process of the above method embodiment, and the repeated parts will not be repeated.

[0205] Example 3

[0206] An embodiment of the present invention further provides an electronic device, the electronic device comprising a processor and a memory, the memory storing 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 being loaded and executed by the processor to implement the following Figure 1 A dynamic equivalent modeling method for wind farm frequency regulation is shown.

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

[0208] The processor may include one or more processing cores. The processor uses various interfaces and lines to connect the various parts of the entire server, and executes various functions of the server and processes data by running or executing instructions, programs, code sets or instruction sets stored in the memory, and calling data stored in the memory. Optionally, the processor can be implemented in at least one hardware form of digital signal processing (DSP), field programmable gate array (FPGA), and programmable logic array (PLA). The processor can integrate one or a combination of a central processing unit (CPU) and a modem. Among them, the CPU mainly processes the operating system and application programs; the modem is used to process wireless communications. It can be understood that the above-mentioned modem may not be integrated into the processor, but implemented separately through a chip.

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

[0210] Example 4

[0211] The embodiment of the present invention further provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, the at least one program, the code set or instruction set is loaded and executed by a processor to implement the following Figure 1 A dynamic equivalent modeling method for wind farm frequency regulation is shown.

[0212] Those skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable rewritable read-only memory (EEPROM), a compact disc (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

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

[0214] Example 5

[0215] In some possible implementations, various aspects of the method of the embodiment of the present invention may also be implemented in the form of a program product, which includes a program code. When the program product is run on a computer device, the program code is used to enable the computer device to execute the steps of a method for dynamic equivalent modeling of wind farm frequency regulation according to various exemplary embodiments of the present application described above in this specification. Among them, the executable computer program code or "code" for executing each embodiment may be written in a high-level programming language 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 the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0217] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0218] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A wind farm frequency modulation dynamic equivalent modeling method, characterized in that: The following steps are involved: Obtaining the operating parameters of each wind turbine during the frequency modulation process as training data for generating the Koopman operator; According to the training data, the dynamic characteristics of the wind turbine are identified based on the state space dimension increase method to obtain the Koopman operator that can reflect the high-dimensional linear relationship; Based on the obtained Koopman operator, the wind farm is divided into multiple groups using the gap measurement method; Aggregation of multiple units in the same group is performed based on the criterion that the output characteristics of the units before and after equivalence remain unchanged.

2. A wind farm frequency modulation dynamic equivalent modeling method according to claim 1, characterized in that: The working parameters include input wind speed, active power reference value, rotation speed, rotor current and generator transient potential; wherein the input wind speed includes the input wind speed of the upstream wind turbine group and the input wind speed of the downstream wind turbine group.

3. A wind farm frequency modulation dynamic equivalent modeling method according to claim 2, characterized in that: The input wind speed of the downstream wind turbine is obtained by: The Jessen model is introduced to take into account the wind speed of the downstream wind turbine with the wake effect. The headwind speed v of the downstream wind turbine is k It is expressed as: In the formula, G k is the set of upstream wind turbines i that have wake effect on downstream wind turbine k, v0 is the uniform input wind speed of the upstream wind turbines, d i,k is the distance from wind turbine i to wind turbine k; σ i (d i,k ,v0) is the attenuation coefficient of wind speed, which is defined as: Where R is the radius of the fan blade, C T is the thrust coefficient.

4. A wind farm frequency modulation dynamic equivalent modeling method according to claim 1, characterized in that: The method of identifying the dynamic characteristics of the wind turbine generator system based on the state space dimension-upgrading method according to the training data to obtain the Koopman operator that can reflect the high-dimensional linear relationship includes: The nonlinear dynamic model of the doubly-fed asynchronous wind turbine is established, and the expression is: X r,k+1 =f(X r,k ,u k ) In the formula, u k is the control input at time k, X r,k is the state variable of wind turbine r at time k, and f is the mapping of nonlinear dynamics; The speed ω r , rotor current I rd and the transient potential E of the generator as state variables, and the input wind speed and active power reference value P 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 is the speed at time k, I rd,k is the rotor current at time k, E d,k is the direct axis transient potential of the kth generator, E q,k is the quadrature axis transient potential of the kth generator; P ref,k , v w,k are the active power reference value and input wind speed at time k respectively; Define ψ(x) as a function with the wind turbine observable as variable, and get the Koopman operator The effects are 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; According to the above formula, the optimization problem is obtained, which is expressed as follows: Wherein, matrices A and B are linear invariant matrices; The Koopman operator is approximated by extending the dynamic mode decomposition algorithm to obtain the matrix [A, B] 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 increased dimension; It is the estimated value of the state variable of the original system at the next moment, and the matrix C is a linear constant matrix.

5. A wind farm frequency modulation dynamic equivalent modeling method according to claim 4, characterized in that: The value of the linear constant matrix C is solved by the least squares method: Using a data-driven approach to solve the matrix [A, B], the following input and output data sets were 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 of X, Y, and U, substitute them into the following formula to solve the matrix values ​​of A, B, and C: doesn't A,B ||Y lift -SURE lift -BU|| F min C ||X-CX lift || F Where, X lift =[ψ(x(1)),...ψ(x(P))],Y lift =[ψ(x(2)),...ψ(x(P+1))], where F represents the norm of the matrix, and its analytical solution is: In the formula, Represents the pseudoinverse of a matrix.

6. A wind farm frequency modulation dynamic equivalent modeling method according to claim 1, characterized in that: The wind farm is divided into multiple groups by using a gap measurement method based on the obtained Koopman operator, including: The gap measure is used to calculate the gap measure value between each wind turbine: In Hilbert space, assuming that the graph of the linear operator Z is G(Z), then 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 as follows: In the formula, δ(Z1, Z2) represents the gap measure value, N and M are the coprime factors of the system, that is, Z = MN -1 and N * N+M * M=I, * is the conjugate operator, H ∞ is the set of all rational transfer functions, Q is an arbitrary Hilbert matrix; The two wind turbines with gap measurement values ​​less than a preset value are classified into the same wind turbine group, thus completing the grouping of the wind farm.

7. A wind farm frequency modulation dynamic equivalent modeling method according to claim 1, characterized in that: The aggregation of multiple units in the same group based on the criterion of unchanged output characteristics of the units before and after equivalence includes: After the wind turbines in the field are grouped, each group of wind turbines is equivalent to one unit in principle, with the output characteristics of the units before and after the equivalent remain unchanged. The establishment of the clustered wind turbine unit equivalent model includes the following three steps: Establish an equivalent fan model; Establish an equivalent generator model; Establish an equivalent collector circuit model.

8. A wind farm frequency modulation dynamic equivalent modeling device, characterized in that: include: A data acquisition module is used to obtain the working parameters of each wind turbine in the frequency modulation process as training data for generating the Koopman operator; The operator calculation module is used to identify the dynamic characteristics of the wind turbine based on the state space dimension increase 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 the wind farm into multiple clusters based on the obtained Koopman operator and the gap measurement 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.

9. 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 described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The storage medium 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 according to any one of claims 1 to 7.

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