A method for dividing a fleet based on a wind farm wake model

Abstract

The application discloses a kind of based on wind field wake model cluster division method.It includes the following steps: improving PARK wake model, join the influence of yaw angle to wake;Utilize the wake information between wind turbine, construct wind field wake weight undirected graph;Spectral clustering algorithm is fused with wake model, based on graph theory and optimization theory, wind field wake weight undirected graph is divided into independent subgraph, realize reasonable cluster division.Based on the improved wind field wake model, more accurate wake information is obtained, and the theoretical basis of spectral clustering is also used, which can not only minimize the ignored wind field wake effect, but also ensure the balance of the number of wind turbines between different wind field subsets as much as possible.The more reasonable cluster division strategy of the application is conducive to improving the efficiency of parallel optimization of wind farm power generation.

Description

TECHNICAL FIELD

[0001] The application belongs to the application of graph theory and machine learning in the field of energy, and particularly relates to a cluster division method based on a wind farm wake model. BACKGROUND

[0002] Energy problems have become the primary problem to be solved in the world today, so countries and organizations are actively committed to exploring new alternative energy technologies to promote economic transformation in the energy field. In this regard, renewable energy is attracting much attention because of its renewable and pollution-free characteristics, and it has great potential and advantages. In China, the wind power industry, as an important part of the renewable energy industry, is rapidly developing. However, to achieve efficient wind power generation, higher requirements are placed on technological innovation.

[0003] The wake effect in a wind farm refers to the process in which wind flows through a wind turbine, the wind speed behind the rotor decreases, and the power generation of downstream wind turbines decreases. To reduce the wake effect and improve overall power generation, field-level optimization control has received widespread attention. Cluster division in advance is a key step to improve the efficiency of parallel optimization of wind farms.

[0004] Currently, there are few methods for wind farm cluster division, and most of them are manually divided. Manual division can only be applied to wind farms with neat layouts, and the accuracy of cluster division can only be guaranteed at a specific wind direction. Since the wind conditions are usually complex, manual division cannot guarantee stable parallel optimization under any wind conditions. Some methods establish a wake weight directed graph based on a wake model, and then use the idea of deep tree search to divide the cluster. The main problem of this method is that the number of cluster divisions is determined by the number of the first row of wind turbines, and cannot be adjusted. Too few cluster divisions will result in too low parallel optimization efficiency, and too many cluster divisions will result in too much ignored wake and too large final error of the optimization result. In addition, this type of method may not be the optimal division result from the perspective of the entire wind farm. SUMMARY

[0005] To make up for the shortcomings of the prior art, the application provides a cluster division method based on a wind farm wake model, which can reasonably divide the cluster for a specific wind farm under different wind directions and ensure the balance of the number of wind turbines in the subset while ignoring as few wake effects as possible. This method is based on a multivariate coupled wake model, establishes a wind farm wake weight undirected graph, then uses a spectral clustering algorithm to divide the graph, and realizes wind farm cluster division, providing a reference for subsequent wind farm parallel optimization control. The technical scheme of the application is as follows:

[0006] A cluster division method based on a wind farm wake model, the method comprising the following steps:

[0007] Step 1, constructing a multivariate coupled wake model;

[0008] Step 2, based on the wake model information, the wind farm wake weight undirected graph is established;

[0009] Step 3, the wind farm wake weight undirected graph is preprocessed, and the isolated points are removed, and all isolated points are saved as independent machine groups;

[0010] Step 4, the wind farm wake weight undirected graph is cut based on the spectral clustering method;

[0011] Step 5, the independent machine groups of isolated points are merged, the index mode is used to save the division results, different wind directions are replaced, steps 2-5 are repeated, and the running results under all wind directions are saved.

[0012] Further, the wake model in step 1 is an improved model based on the PARK model, which can realize joint control of the shaft factor and the yaw angle of all wind turbines, and the optimization control objective function of the wake model is as follows:

[0013]

[0014] s.t.α i，min ≤α i ≤α i , max,

[0015] o i，min ≤o i ≤o i，max ,

[0016] (i = 1...n).

[0017] Wherein, P represents the total wind farm power generation, ρ represents the air density, A represents the windward surface of the wind turbine, C p represents the power generation coefficient, u i represents the wind speed in front of the wind turbine i, U ∞ . represents the environmental wind speed, θ W represents the environmental wind direction, α i and o i respectively represent the control variables of the wind turbine i, the shaft factor and the yaw angle.

[0018] Further, the step 1 specifically includes:

[0019] The existing PARK model is analyzed, the influence of the yaw angle is added, a multi-variable coupled wake model based on the PARK model is established, and the PARK model only represents the relationship between the downstream wind speed and the shaft factor:

[0020] u(d, r, a j ) = (1 - d)u(d, r, a j )U ∞ ,

[0021]

[0022] where δu represents the wake decay coefficient, α j represents the shaft factor of the wind turbine j, U ∞ is the ambient wind speed; d and r represent the position behind the wind turbine, refer to Figure 3 . R j represents the windward radius of the wind turbine.

[0023] The wake model adds the influence of yaw angle on the wake trajectory to the PARK model:

[0024]

[0025] r ij represents the wake offset, where respectively represent the wake offset caused by the position, rotating blades and yaw angle. θ ij represents the angle determined by the i, j positions, θ W represents the ambient wind direction. Further, the wake superposition area can be calculated, when the wind turbine i is affected by more than one upstream wind turbine, the wake decay factor is represented as follows:

[0026]

[0027] where γ is the influence of yaw angle on the wake decay coefficient, κ is the wake expansion coefficient, represents all upstream wind turbines that affect the wind turbine i, where α j , o j respectively represent the shaft factor and yaw angle of the upstream wind turbine, represents the wake superposition area, A i represents the windward area of the downstream wind turbine;

[0028] Further, the power generation of each wind turbine in the wind farm affected by the wake effect can be calculated, and optimization control is performed based on the target.

[0029] Further, the weight of each edge of the wind farm wake weight undirected graph in step 2 represents the strength of the wake effect, and is defined as follows:

[0030]

[0031] Further, the step 4 specifically includes:

[0032] Use i∈A to represent {i | v i ∈A), V={v1,..., v n} represents the set of all wind turbines, a wind turbine set and the wake effect between its complement is represented as follows:

[0033]

[0034] vol(A): = ∑ i∈A d i Used to represent the size of subset A, assuming a partition of k subsets, with non-empty subsets A1, ..., A2. k satisfy and A1∪...∪A k =V, in order to separate weakly correlated wind turbines as much as possible and ensure that the size of the subsets is as balanced as possible, an objective function Ncut is proposed, and the optimal value of Ncut is solved to achieve graph cutting:

[0035]

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] This invention, based on an improved wind farm wake model, obtains more accurate wake information. Furthermore, by utilizing the theoretical foundation of spectral clustering, it not only minimizes the neglected wind farm wake effect but also strives to ensure a balanced number of wind turbines across different wind farm subsets. The more rational turbine cluster partitioning strategy employed in this invention is beneficial for improving the power generation efficiency of wind farms optimized in parallel. Attached Figure Description

[0038] Figure 1 This is a flowchart of the cluster partitioning method of the present invention;

[0039] Figure 2 This is a block diagram of a multivariable wake model;

[0040] Figure 3 This is a schematic diagram of the PARK model;

[0041] Figure 4 This is a schematic diagram of the wake superposition area;

[0042] Figure 5 This is a schematic diagram illustrating the effect of yaw angle on the wake trajectory;

[0043] Figure 6 Figure a is a schematic diagram of an undirected graph of wake weights based on wind field wakes, where Figure a is a schematic diagram of wind field wakes and Figure b is an undirected graph of wake weights.

[0044] Figure 7 This is a diagram showing the results of classifying aircraft groups under different wind directions. Detailed Implementation

[0045] The application will be further described below in conjunction with the accompanying drawings and specific embodiments. The following examples are only used to more clearly illustrate the technical solutions of the application, and cannot be used to limit the protection scope of the application.

[0046] The application provides a cluster division method based on a wind field wake model. A wind field with 81 wind turbines is regularly distributed. The flow chart of the method is shown in Figure 1 The specific implementation of the method includes the following steps:

[0047] Step 1: improving the PARK model to construct a multi-variable coupled wake model.

[0048] Specifically, in step 1, a multi-variable coupled wind field wake model is established. The wind field wake model is shown in Figure 2 The wind field wake model is obtained by inputting the wind field layout and the output results of the controller, and based on wake expansion calculation and wake trajectory calculation, the wake superposition area is obtained, and then the power generation of each wind turbine under the consideration of the wake can be calculated through the wake attenuation model, and the whole field power generation is calculated.

[0049] The PARK model describes the relationship between the shaft factor and the wake attenuation coefficient, and then calculates the downstream wind speed. The PARK model is shown in Figure 3 The relationship between the downstream wind speed and the wake attenuation factor is:

[0050] u(d, r, α j )=(1-δu(d, r, α j ))U ∞ ,

[0051] Where δu represents the wake attenuation coefficient, α j represents the shaft factor of the wind turbine j, and U ∞ is the environmental wind speed. The wake attenuation factor is represented as follows:

[0052]

[0053] Where d and r represent the position behind the wind turbine, which can be known from Figure 3 R j represents the windward surface radius of the wind turbine.

[0054] The wake attenuation factor of the downstream wind turbine is also related to the wake superposition area and the yaw angle of the upstream wind turbine, as shown in Figure 4 When a wind turbine is affected by more than one upstream wind turbine, it is represented as follows:

[0055]

[0056] represents all upstream wind turbines affecting wind turbine i, where αj , o j denote the shaft factor and yaw angle of the upstream wind turbine, respectively, denote the wake superposition area, A i denote the windward area of the downstream wind turbine. From Figure 5 it can be seen that the yaw angle has three parts of influence on the wake trajectory of the wind turbine: caused by the relative position of the wind turbines, caused by the wind turbine due to the interaction between the vertically varying wind speed profile and the rotating blades, caused by the yaw angle. The overall trajectory offset of the wind turbine wake is represented as follows:

[0057]

[0058] r ij denote the wake offset, where denote the wake offset caused by the position, rotating blades and yaw angle, respectively. θ ij denote the angle determined by the i, j positions, θ W denote the ambient wind direction.

[0059] The wake superposition area can be calculated through the overall trajectory offset of the wake, and then the wind speed captured by the downstream wind turbine can be obtained, and finally the power generation of each wind turbine and the entire wind farm can be calculated:

[0060]

[0061]

[0062] where P denotes the total wind farm power generation, p denotes the air density, A denotes the windward area of the wind turbine, C p denotes the power generation coefficient, u i denotes the wind speed in front of the wind turbine i, U ∞ denotes the ambient wind speed, θ W denotes the ambient wind direction, a i and o i denote the control variable shaft induction factor and yaw angle of the wind turbine i, respectively.

[0063] Step 2, based on the wake information, a wind farm wake weight undirected graph is established.

[0064] Specifically, in step 2, based on the wake information, a wind farm wake weight undirected graph is established, as shown in Figure 6 . Each wind turbine is regarded as a point, and the purpose is to divide the wind turbines into different subsets, and the wake effect of the wind turbines in the subset is obvious, and the wake effect between the subsets can be ignored. An undirected graph G=(V, E) is used to represent the wake, V={v1,..., v n ) represents the set of all wind turbines. E represents the edge set, and the edges between all points have a weight w greater than or equal to 0ij , means as follows:

[0065]

[0066] A wind farm with 81 wind turbines was used for testing, with a lateral distance of 400m and a longitudinal distance of 560m between the turbines. The parameter settings in the wake model are shown in Table 1.

[0067]

[0068]

[0069] Step 3: Preprocess the undirected graph of wind field wake weights, remove isolated points, and save all isolated points as independent clusters.

[0070] Specifically, in step 3, outliers are removed, all outliers are saved as independent clusters, and the rows and columns containing the outliers are deleted from the undirected graph of wind field wake weights. The preprocessed undirected graph is used as input to the spectral clustering algorithm, and no singular values ​​will appear in the matrix calculation.

[0071] Step 4: Define the clustering objective function based on spectral clustering and cut the graph.

[0072] Specifically, in step 4, spectral clustering is performed. The degree matrix D is a diagonal matrix, with the degree values ​​of the diagonal elements being d. i Vertex v i The degree is defined as follows:

[0073]

[0074] Suppose there is a set of wind turbines Let A denote its complement, and let i∈A denote {i|v}. i The tail effect between a subset and its complement is expressed as:

[0075]

[0076] vol(A): = ∑ i∈A d i This is used to represent the size of subset A. Assume we divide the dataset into k subsets, with non-empty subsets A1, ..., A2. k satisfy and A1∪...∪A k =V. To separate weakly correlated wind turbines as much as possible and ensure that the size of the subsets is as balanced as possible, an objective function Ncut is proposed:

[0077]

[0078]

[0079] Definition of indicator vector h j = (h 1，j ,..., h n，j )':

[0080]

[0081] The matrix H is then set to contain k indicator vectors as columns. The key tool for spectral clustering is the Laplacian matrix, which without normalization is:

[0082] L = D - W

[0083] With normalization, the Laplacian matrix is:

[0084] L sym : = D -1 / 2 LD -1 / 2 = I - D -1 / 2 WD -1 / 2

[0085] Relaxing the discrete condition and introducing T = D 1 / 2 H, we obtain the goal of spectral clustering:

[0086]

[0087] This is done by solving a standard trace minimization problem for T, which contains the top k eigenvectors of the normalized graph Laplacian L sym as columns. By solving this problem, the spectral clustering algorithm outputs the cluster indices of the wind turbines, with wind turbines having the same index belonging to the same cluster.

[0088] Step 5, merge the isolated point cluster, save the division result in the form of index, and save the running result under all wind directions.

[0089] Specifically, in step 5, the isolated point subset saved in advance in step 3 is merged, and the complete cluster division result is output. Change different wind directions, repeat steps 2-5, and save the cluster division result under all wind directions to provide a lookup table result for subsequent parallel optimization.

[0090] Figure 7 The cluster division results under several special wind conditions are shown, and the same shape indicates that the wind turbines belong to the same cluster.

[0091] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for fleet division based on wind farm wake model, characterized in that, The method comprises the following steps: Step 1, constructing a multi-variable coupled wake model, specifically comprising: Analyzing the existing PARK model, adding the influence of the yaw angle, establishing a multi-variable coupled wake model based on the PARK model, and the PARK model only represents the relationship between the downstream wind speed and the shaft factor: u(d, r, a j ) = (1 - δu(d, r, a j )) U ∞ , wherein δu represents a wake decay coefficient, a j represents a shaft factor of the fan j, U ∞ is an ambient wind speed; d represents a lateral distance from the center of the impeller, r represents a longitudinal distance from the center of the impeller, R j represents a face radius of the fan; The wake model adds the influence of the yaw angle on the wake trajectory on the basis of the PARK model: r ij denotes wake deflection, where denotes wake deflection due to position, rotating blades and yaw angle, respectively, θ ij denotes the angle determined by i, j position, θ W denotes ambient wind direction; Further, the wake superposition area is calculated, when the fan i is affected by more than one upstream fan, the wake attenuation factor is represented as follows: where γ is the effect of yaw angle on the wake decay coefficient, k is the wake expansion coefficient, denotes all upstream wind turbines that influence wind turbine i, where α j denotes the upstream wind turbine's hub height, j denotes the upstream wind turbine's hub height, denotes the wake overlap area, A i denotes the downstream wind turbine's swept area; Further, the power generation of each fan in the wind farm under the influence of the wake effect is calculated, and optimization control is performed taking the power generation as the target; Step 2, based on the information of the wake model, a wind farm wake weight undirected graph is established, wherein the weight of each edge of the wind farm wake weight undirected graph represents the strength of the wake effect, and is defined as follows: Step 3, preprocessing the wind farm wake weight undirected graph, eliminating isolated points, and saving all isolated points as independent machine groups; Step 4, cutting the wind farm wake weight undirected graph based on the spectral clustering method, specifically comprising: Let i∈A denote {i | v i ∈A}, V = {v1,..., v n} denote all fan sets, a fan set and its complement wake effect between them is represented as follows: vol(A): =∑ i∈A d i vol(A) is used to represent the size of subset A, assuming that k subsets are divided, non-empty subsets A1,...,Ak k satisfy and A1∪...∪A k =V, in order to separate the weak relevance fan as much as possible, and to ensure that the size of the subset is as balanced as possible, a target function Ncut is proposed to solve the optimal value of Ncut to realize graph cutting: Step 5, merging the independent machine groups of isolated points, saving the division results in the form of index, replacing different wind directions, repeating steps 2-5, and saving the running results under all wind directions.

2. The method of claim 1, wherein, The wake model in the step 1 is an improved model based on the PARK model, realizing joint control of the shaft factor and the yaw angle of all fans, and the optimization control target function of the wake model is as follows: s.t. a i,min ≤ a i ≤ a i,max o i,min ≤o i ≤o i,max (i = 1...n) where P represents the total wind farm power generation, p represents the air density, A represents the wind fan windward surface, C p represents the power generation coefficient, u i represents the wind speed in front of the wind fan i, U ∞ represents the ambient wind speed, Q W represents the ambient wind direction, a i and o i respectively represent the control variable axis induction factor and yaw angle of the wind fan i.

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