Multi-objective optimization method for wind farm layout and yaw control based on nested collaborative optimization architecture

Abstract

The application provides a wind farm layout and yaw control multi-objective optimization method based on a nested collaborative optimization architecture. A three-layer nested collaborative optimization architecture is established. The outer layer iteratively searches for a wind turbine position vector through a multi-objective optimization module to obtain a Pareto optimal solution set between annual power generation and land use efficiency. The middle layer annual power generation evaluation module quantitatively evaluates the power generation potential of each candidate wind turbine layout scheme generated in the iteration process. The inner layer yaw optimization module is called to obtain the optimal output power of each candidate wind turbine layout scheme under different wind conditions. The optimal output powers are weighted and summarized according to their occurrence probabilities, and the corresponding collaborative design annual power generation is output to feedback to the outer layer multi-objective optimization module. The yaw control optimization result is directly embedded in the wind farm layout design scheme, realizing the collaborative optimization of the wind turbine spatial layout and the yaw control strategy, which is very beneficial to improve the power generation efficiency of the wind farm in the region with limited land resources.

Description

Technical Field

[0001] This invention relates to multi-objective collaborative design, and in particular to a multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture, belonging to the field of wind power generation technology. Background Technology

[0002] In optimizing wind farm layouts, the core objective is often maximizing annual power generation, while other influencing factors are often given limited consideration. For example: 1) Ignoring the constraints of limited land resources leads to low energy output per unit area when land utilization is too low, exacerbating the problem of land scarcity; 2) Inadequate wake control strategies, such as... Figure 1 As shown, most wind turbine clusters adopt traditional control strategies, which only aim to maximize the power generation of individual wind turbines. This reduces the overall power generation efficiency of the wind farm and seriously affects the economic viability of the entire wind farm.

[0003] In recent years, yaw-based wake steering has been proven to effectively reduce wake interference between wind turbines, improving power generation performance and providing a new dimension of regulation for optimizing spatial layout. However, most existing studies treat layout design and operation control separately, and have not fully explored the potential of their synergistic optimization in improving land use efficiency. Especially in areas with limited land resources, balancing energy output and land use has become a key technical challenge for achieving sustainable wind power development.

[0004] Therefore, this paper proposes a multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture, in order to increase the annual power generation of wind farms and reduce the footprint of wind turbines, thereby achieving system-level optimization of power generation performance and land use efficiency. Summary of the Invention

[0005] The purpose of this invention is to solve the above problems and provide a multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture.

[0006] The technical solution of this invention is: a multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture. This method is executed based on a multi-level computational framework. It constructs a three-level nested collaborative optimization architecture, using wind turbine spatial layout variables and wind turbine yaw control variables as design variables. This architecture includes an outer multi-objective optimization module (set from the outside in and with bidirectional information interaction), a middle-level annual power generation assessment module, and an inner yaw optimization module. The outer multi-objective optimization module uses a multi-objective optimization algorithm to iteratively search the wind turbine position vector to obtain the Pareto criterion between annual power generation and land use efficiency. The optimal solution set, in which each candidate wind turbine layout scheme generated during the iterative search process is sent to the intermediate layer annual power generation assessment module; the intermediate layer annual power generation assessment module connects the outer layer multi-objective optimization module and the inner layer yaw optimization module, and obtains the optimal output power of each candidate wind turbine layout scheme under different wind conditions by calling the inner layer yaw optimization module, and statistically summarizes each optimal output power according to the preset wind resource statistical distribution, thereby evaluating the collaborative design annual power generation, and feeding the collaborative design annual power generation back to the outer layer multi-objective optimization module to continue to guide the subsequent multi-objective optimization iteration process.

[0007] Furthermore, in the aforementioned multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture: the inner-layer yaw optimization module, given the candidate wind turbine layout and its wind conditions, uses a yaw optimization algorithm to solve for the optimal yaw angle of each wind turbine, and returns the optimal power of the wind farm to the middle-layer annual power generation assessment module; the yaw optimization algorithm is any optimization algorithm used to solve single-objective optimization problems, and its function is to optimize the yaw angle of each wind turbine under specific wind conditions to maximize the output power of the wind farm. Preferably, a generalized sequence refinement method is used, which aims to maximize the output power of the wind farm and solves for the optimal yaw angle of each wind turbine and the optimal power of the wind farm under the corresponding wind conditions.

[0008] Specifically, the power output of the wind farm is evaluated using a power evaluation model or calculation method that characterizes the wake evolution and wind turbine interaction effect under yaw operation conditions. The power evaluation model includes, but is not limited to, analytical wake models, potential flow theory-based models, dynamic wake models, and data-driven surrogate models.

[0009] Preferably, the power assessment model adopts an analytical wake model, wherein the analytical wake model adopts the Gauss-Curl Hybrid (GCH) wake model; the GCH wake model, based on the classic Gaussian wake model, introduces lateral and vertical velocity components induced by yaw to describe the influence of wake deflection, fluid entrainment effect and secondary yaw effect on the downstream wind turbine inflow conditions; and the wind turbine aerodynamic forces are calculated through a pre-constructed aerodynamic performance lookup table.

[0010] Furthermore, in the aforementioned multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture: the land use efficiency is characterized by capacity density or equivalent land area, where capacity density is the ratio of the total installed capacity of wind turbines to the equivalent land area of ​​the wind farm; and the equivalent land area is the area of ​​the smallest convex polygon that encloses all wind turbine locations.

[0011] Furthermore, in the aforementioned multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture: the multi-objective optimization algorithm can be any algorithm used to solve multi-objective optimization problems, including but not limited to multi-objective gradient algorithms, multi-objective heuristic optimization algorithms, multi-objective ε-constraint methods, multi-objective weighted sum methods, and surrogate model-assisted multi-objective optimization.

[0012] Preferably, the multi-objective optimization algorithm employs the non-dominated sorting genetic algorithm NSGA-II or an improved form thereof.

[0013] Furthermore, in the aforementioned multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture: the collaboratively designed annual power generation is evaluated based on discretized representative wind conditions. The annual power generation is obtained by weighted summation of the steady-state total output power under each representative wind condition and its probability of occurrence. The calculation model is as follows:

[0014]

[0015] in, This indicates the number of representative wind conditions (or wind condition sub-boxes) used for annual power generation assessment; Indicates the total number of hours within the evaluation period; Indicates the first The annual probability or frequency weight of each wind condition, satisfying... ; Indicates the wind farm in the 1st The total output power corresponding to the optimal yaw angle under each wind condition.

[0016] Compared with existing technologies, the technical solution of this invention provides a repeatable and scalable optimization decision-making method for the planning and design of high-density and high-efficiency wind farm projects. This method directly embeds the yaw control optimization results into the wind farm layout design scheme, achieving synergistic optimization of wind turbine spatial layout and yaw control strategy. This establishes an effective trade-off between energy output and land use efficiency. Compared to the traditional wind farm layout design scheme with a fixed yaw angle of 0°, the synergistic design strategy proposed in this invention can significantly improve the land use efficiency of wind farms without reducing annual power generation, effectively reducing the land requirement per kilowatt-hour, thus providing strong technical support for the intensive layout and large-scale development of wind farms. Attached Figure Description

[0017] Figure 1 This is a schematic diagram illustrating the working principle of the traditional wind farm layout design method (tra-AEP).

[0018] Figure 2 This is a schematic diagram illustrating the operational principle of the Co-AEP (Co-Wind Farm Layout Design) method of the present invention.

[0019] Figure 3 This is a schematic diagram of the initial wind farm layout using a regular array format, as per the present invention.

[0020] Figure 4 This is a schematic diagram of wind resource conditions using a discretized wind direction-wind speed joint distribution form, as presented in this invention.

[0021] Figure 5 A schematic diagram comparing the annual power generation-capacity density Pareto front of wind farms under the traditional wind farm layout design method (tra-AEP) and the collaborative wind farm layout design method (co-AEP) in this case.

[0022] Figure 6 This diagram illustrates the relationship between annual power generation and equivalent land area of ​​a wind farm under the traditional wind farm layout design method (tra-AEP) and the collaborative wind farm layout design method (co-AEP) in this case, as well as the land-saving ratio analysis. Detailed Implementation

[0023] The following is in conjunction with the appendix Figures 2-6 The technical solution of the present invention will be described in detail with specific embodiments to make it easier to understand and master. It should be noted that this invention is applicable to wind farms with varying numbers of turbines, different spatial boundary conditions, multiple layout constraints, and various types of wind turbine units, and has broad applicability and scalability. The accompanying drawings show only some feasible embodiments and do not constitute a limitation on the scope of application and protection of this invention. For those skilled in the art, based on an understanding of the technical solution of this invention, other forms of wind farm layout schemes can be designed according to actual application scenarios without creative effort, and equivalent technical effects can be achieved.

[0024] First, a typical example is selected for numerical verification, such as... Figure 3 As shown, the example uses a regular array of initial wind farm layouts, with all turbine coordinates located within a square area for subsequent layout optimization and comparative analysis. The total number of turbines is N=9, and the boundary size of each turbine is L=18D, where D is the turbine diameter. Figure 4As shown, wind resource conditions are represented by a discretized wind direction-speed joint distribution. Each wind direction sector corresponds to the frequency of occurrence and representative wind speed of different wind conditions, which are used to construct a statistical evaluation model for annual power generation (AEP). This wind resource distribution serves as a unified input condition for multi-objective optimization and annual power generation calculation, ensuring a fair comparison of different design schemes in the following examples and comparative examples under the same wind condition assumptions.

[0025] Example

[0026] Step 1: The outer multi-objective optimization module uses NSGA-II to iteratively search for wind farm layout schemes. NSGA-II maintains the non-dominated nature of the solution while preserving the diversity of the solution set distribution in the objective space through non-dominated sorting and crowding distance mechanisms, thus effectively characterizing the trade-offs between multiple objectives. In this embodiment, the individual encoding of NSGA-II is a continuous real-number vector, used to represent the planar coordinates of each wind turbine. For a layout containing N wind turbines, the dimension of the individual vector is 2N, where the first N variables correspond to the x-coordinates of each wind turbine, and the last N variables correspond to the y-coordinates of each wind turbine. NSGA-II uses simulated binary crossover (SBX) and polynomial mutation (PM) to generate offspring individuals, where the crossover probability can be set to 0.95, the mutation probability can be set to 0.05, the SBX distribution index can be set to 15, and the PM distribution index can be set to 20. The maximum number of iterations is used as the termination criterion, preferably set to 500, that is, NSGA-II stops after running for 500 generations. Each candidate wind turbine layout generated during the iterative search process must meet engineering feasibility constraints, preferably including: 1) minimum turbine spacing constraint, i.e., the distance between any two wind turbines is not less than a given threshold, which is 2D in this embodiment, where D is the turbine diameter; 2) boundary constraint, i.e., the wind turbine coordinates should be located inside the given site boundary. Candidate layouts that violate the constraints can be handled by discarding, repairing, or using a penalty function. The outer multi-objective optimization module sends the candidate layout schemes generated during the iteration process to the middle-layer annual power generation assessment module to obtain their annual power generation evaluation value, and performs non-dominated ranking and congestion distance calculation in conjunction with land use efficiency indicators; when the termination criterion is met, the Pareto optimal solution set and its corresponding objective function value are output.

[0027] Step 2: The intermediate-layer annual power generation assessment module iterates through all representative wind conditions for the given candidate wind turbine layout scheme, and calls the inner-layer yaw optimization module for each wind condition to obtain the optimal output power of the wind farm under that wind condition. Subsequently, the intermediate-layer annual power generation assessment module weights and sums the optimal output power under each representative wind condition according to its corresponding occurrence probability, thereby obtaining the collaborative design annual power generation corresponding to the candidate wind turbine layout scheme. This annual power generation evaluation value is fed back to the outer-layer multi-objective optimization module for subsequent non-dominated ranking and congestion distance calculation. In this embodiment, the statistical distribution of wind resources is represented by discretized representative wind conditions, including wind direction, wind speed, and turbulence intensity, and each representative wind condition is assigned a corresponding annual occurrence probability. The collaborative design annual power generation is jointly determined by the wind turbine spatial layout variables and the yaw control strategy, and is used to characterize the annual expected energy output of the wind farm under a given statistical distribution of wind resources. In this embodiment, the collaborative design annual power generation is calculated using a discrete wind condition probability weighting method, and its mathematical expression is as follows:

[0028]

[0029] Where: N B N represents the number of representative wind conditions (or wind condition sub-units) used for annual power generation assessment; h This represents the total number of hours within the evaluation period, preferably 8760. This represents the annual probability or frequency weight of the b-th wind condition, satisfying... ; This represents the total output power corresponding to the optimal yaw angle of the wind farm under the b-th wind condition.

[0030] The process of calling the inner-layer yaw optimization module involves the inner layer using the Generalized Serial-Refine (GSR) method to solve for the optimal yaw angle of each wind turbine in the wind farm, given the current candidate turbine layout and representative wind conditions. The optimal power of the wind farm under the corresponding wind conditions is then output to the intermediate-layer module. The GSR method ensures reproducibility while obtaining high-quality solutions at a low computational cost, making it particularly suitable for inner-layer yaw optimization scenarios with repeated calls under multiple wind conditions. Specifically, given the turbine layout and wind conditions (wind direction, wind speed, and turbulence intensity), the incoming wind direction is used as the positive X-axis for coordinate transformation of all turbines. The turbines are sorted according to their coordinate values, and the GSR optimization is performed on each turbine sequentially from smallest to largest. For each turbine, the optimal yaw angle is searched within the candidate yaw angle set of the current round, and the candidate yaw angle range for the next round is updated accordingly. During this process, the candidate range is adaptively narrowed through multiple iterations to obtain the optimal yaw angle value. In calculating the output power of a wind farm, this embodiment employs a Gauss-Curl Hybrid (GCH) wake model that incorporates a secondary flow around the turbine. Based on the classic Gaussian wake model, the GCH wake model introduces lateral and vertical velocity components induced by yaw, used to describe the influence of wake deflection, fluid entrainment, and secondary yaw effect on the downstream turbine's inflow conditions under yaw operating conditions, thereby characterizing the wake evolution process under yaw conditions.

[0031] Comparative Example

[0032] Step 1: The NSGA-II algorithm is used to perform a multi-objective optimization search for wind farm layout schemes. NSGA-II uses the wind turbine plane coordinates as design variables, generates offspring through simulated binary crossover and polynomial mutation, and uses the maximum number of iterations as the termination criterion, preferably set to 500. During the iteration process, candidate layout schemes that do not meet the minimum turbine spacing constraints and site boundary constraints are eliminated or modified. Once the termination criterion is met, a Pareto optimal solution set satisfying the constraints is obtained. The objective functions of the multi-objective optimization include the traditional design annual power generation and land use efficiency. The traditional design annual power generation is calculated without considering yaw control; that is, during the multi-objective optimization process, the yaw angle of all wind turbines is fixed at zero.

[0033] Step 2: In the above multi-objective optimization process, the traditional design annual power generation is calculated based on a preset statistical distribution of wind resources. Under the condition that the yaw angle of all wind turbines is fixed at zero, the steady-state total output power of the wind farm under various representative wind conditions is calculated, and the traditional design annual power generation is calculated using a discrete wind condition probability weighting method. Its mathematical expression is shown below.

[0034]

[0035] Where: N B N represents the number of representative wind conditions (or wind condition sub-units) used for annual power generation assessment; h This represents the total number of hours within the evaluation period, preferably 8760. Indicates the first The annual probability or frequency weight of each wind condition, satisfying... ; Indicates the wind farm in the 1st Total output power corresponding to a yaw angle of 0 under all wind conditions.

[0036] The following is a comparative analysis of the embodiments and the comparative examples.

[0037] like Figure 5 As shown, the Pareto front comparison results of the embodiment (co-AEP design mode) and the comparative example (tra-AEP design mode) in the target space of "annual power generation - capacity density" are provided. In this example, the horizontal axis represents annual power generation (AEP), and the vertical axis represents capacity density (unit: MW / km²). The higher the capacity density, the higher the installed capacity that can be arranged within the same land area.

[0038] Depend on Figure 5 The following conclusions can be drawn: 1) Compared with the comparative example, the Pareto front corresponding to the embodiment shifts to the "upper right direction" as a whole, indicating that the embodiment achieves higher annual power generation at the same capacity density level, or that the embodiment has a higher capacity density at the same annual power generation level; 2) In areas with higher capacity density (i.e., more stringent land use constraints), the Pareto solution of the comparative example degenerates rapidly, while the embodiment can still maintain a higher annual power generation level, indicating that yaw control has a significant effect on mitigating wake loss under high-density layout conditions; 3) The local AEP interval in the figure has been magnified, and it can be clearly seen that within the same annual power generation interval, the capacity density corresponding to the embodiment is always higher than that of the comparative example, further verifying the superiority of the embodiment in the Pareto sense.

[0039] like Figure 6 As shown, a comparison is provided between the annual power generation and the equivalent land area of ​​the wind farm for the embodiment (co-AEP design mode) and the comparative example (tra-AEP design mode). The red curve represents the embodiment, while the blue curve represents the comparative example. The right vertical axis shows the land-saving ratio of the embodiment relative to the comparative example. .

[0040] Depend on Figure 6The following conclusions can be drawn: 1) For any given annual power generation level, the equivalent land area required by the embodiment is significantly smaller than that of the comparative embodiment. This result indicates that by embedding yaw control optimization in the layout optimization process, the embodiment can significantly reduce the land requirement of the wind farm without reducing power generation; 2) The land-saving ratio of the embodiment The variation with annual power generation shows a clear nonlinear trend, reaching a relatively high level in the medium-to-high power generation range, indicating that the embodiment has more outstanding land-saving potential in the "high-performance-high-density" operation range.

[0041] In summary, the multi-objective collaborative design method for wind farm layout and yaw control proposed in this case not only improves the power generation efficiency of wind farms, but also puts into practice the concept of "trading space for control" at the system level, realizing intensive land use and effectively saving land resources. In the scenario of high-density development of wind farms and intensive land use, the engineering application value of this collaborative design method is very significant.

[0042] In the technical solution of this invention, the key technology is to directly embed the yaw control optimization results into the multi-objective optimization process of the layout scheme. By unifying the wind turbine spatial layout and yaw control optimization into a multi-objective nested collaborative optimization architecture, the power generation performance of the wind farm is improved and the land use efficiency is increased, thereby achieving the dual goals of increasing annual power generation and reducing land area. Figure 4 and Figure 5 The key feature is that the optimization performance of the multi-objective collaborative design method for wind farm layout and yaw control in this case is superior to that of traditional wind farm layout design methods.

[0043] Thus, the technical solution of this invention can significantly reduce the equivalent land area of ​​wind farms without reducing annual power generation; moreover, the Pareto front obtained by it is superior to traditional wind farm layout design methods in terms of annual power generation-capacity density target space, providing a quantitative technical method and support for wind farm planning in areas with limited land resources.

[0044] As can be seen from the above description, compared with the prior art, the technical solution of this invention provides a repeatable and scalable optimization decision-making method for high-density and high-efficiency wind farm engineering applications. By directly embedding the yaw control optimization results into the wind farm layout design scheme, the annual power generation (AEP) and capacity density or equivalent land area (i.e., installed capacity per unit land area) of the wind farm are simultaneously optimized, achieving the best balance between energy output and land use efficiency. Compared with the traditional wind farm layout design method with a fixed yaw angle of 0°, the collaborative design strategy proposed in this invention can significantly improve land use efficiency and save more than 20% of land occupation while maintaining the same annual power generation conditions. In addition, the joint design annual power generation of this invention, as an evaluation index in multi-objective optimization, can directly participate in the performance evaluation and ranking of wind farm layout schemes, which helps to promote the efficient and sustainable development of wind power development and is applicable to wind farm planning and collaborative design in areas with limited land resources.

[0045] The technical solution, working process, and implementation effects of the present invention have been described in detail above. It should be noted that the described examples are only typical examples of the present invention. In addition, the present invention may have many other specific implementation methods. All technical solutions formed by equivalent substitution or equivalent transformation fall within the scope of protection claimed by the present invention.

Claims

1. A multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture, wherein the method is executed based on a multi-level computational framework, characterized in that: A three-tiered nested collaborative optimization architecture is constructed, using wind turbine spatial layout variables and wind turbine yaw control variables as design variables. This architecture includes an outer multi-objective optimization module, a middle-layer annual power generation assessment module, and an inner yaw optimization module, arranged from the outside in and interacting bidirectionally. The outer multi-objective optimization module uses a multi-objective optimization algorithm to iteratively search the wind turbine position vector to obtain the Pareto optimal solution set between annual power generation and land use efficiency. Each candidate wind turbine layout scheme generated during the iterative search process is sent to the middle-layer annual power generation assessment module. The middle-layer annual power generation assessment module connects the outer multi-objective optimization module and the inner yaw optimization module. By calling the inner yaw optimization module, it obtains the optimal output power of each candidate wind turbine layout scheme under different wind conditions. Based on a preset wind resource statistical distribution, it statistically summarizes each optimal output power to evaluate the collaboratively designed annual power generation. This collaboratively designed annual power generation is then fed back to the outer multi-objective optimization module to guide subsequent multi-objective optimization iterations.

2. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 1, characterized in that: Given the candidate wind turbine layout and wind conditions, the inner layer yaw optimization module uses a yaw optimization algorithm to solve for the optimal yaw angle of each wind turbine and returns the optimal power of the wind farm to the middle layer annual power generation assessment module.

3. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 2, characterized in that: The yaw optimization algorithm is any optimization algorithm used to solve a single-objective optimization problem. Its function is to optimize the yaw angle of each wind turbine under specific wind conditions in order to maximize the output power of the wind farm.

4. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 3, characterized in that: The yaw optimization algorithm employs a generalized sequence refinement method.

5. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 3, characterized in that: The power output of the wind farm is evaluated using a power evaluation model or calculation method that characterizes the wake evolution and wind turbine interaction effect under yaw operation conditions. The power evaluation model includes, but is not limited to, analytical wake models, potential flow theory-based models, dynamic wake models, and data-driven proxy models.

6. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 1, characterized in that: The land use efficiency is characterized by capacity density or equivalent land area. The capacity density is the ratio of the total installed capacity of wind turbines to the equivalent land area of ​​the wind farm. The equivalent land area is the area of ​​the smallest convex polygon that encloses all wind turbine locations.

7. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 1, characterized in that: The multi-objective optimization algorithm is any algorithm used to solve multi-objective optimization problems, including but not limited to multi-objective gradient algorithms, multi-objective heuristic optimization algorithms, multi-objective ε-constraint methods, multi-objective weighted sum methods, and surrogate model-assisted multi-objective optimization.

8. The multi-objective optimization method for wind farm layout and yaw control based on a nested collaborative optimization architecture as described in claim 1, characterized in that: The annual power generation of the collaborative design is evaluated based on discretized representative wind conditions. The annual power generation is obtained by weighted summation of the steady-state total output power and its occurrence probability under each representative wind condition. The calculation model is as follows: in, This indicates the number of representative wind conditions (or wind condition sub-boxes) used for annual power generation assessment; Indicates the total number of hours within the evaluation period; Indicates the first The annual probability or frequency weight of each wind condition, satisfying... ; Indicates the wind farm in the 1st The total output power corresponding to the optimal yaw angle under each wind condition.

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