Multi-parameter horizontal axis wind turbine three-dimensional wake flow model based on minimization Weber function

Abstract

The invention relates to the technical field of wind power generation, in particular to a multi-parameter horizontal axis wind turbine three-dimensional wake flow model based on a minimization Weber function, different from widely adopted Gaussian distribution, the model considers the influence of wind shear and the mass loss caused by the wind shear, and the model is a three-dimensional wake flow model based on the minimization Weber function. By inputting information of incoming wind conditions and parameters of the wind turbine, the wake flow speed at any position of the downstream wind direction of the wind turbine can be quickly calculated, and the complexity of the model is reduced. According to the design, the wind turbine wake flow characteristics and flow field distribution can be accurately simulated, the accuracy of performance evaluation and optimization of a wind power generation system is improved, the model is verified through a wind tunnel experiment and published data, and the result shows that the horizontal plane of the hub height follows Weber distribution; the wake flow speed is in an asymmetric Weber shape in a wake flow area along the height of a hub, and it is proved that the model can accurately and rapidly calculate the wake flow speed of any given downstream spatial position, so that the energy utilization rate is improved, and the energy cost is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of wind power generation, in particular to a three-dimensional wake model of a multi-parameter horizontal axis wind turbine based on minimizing a Weibull function. Background Art

[0002] In the critical process of accelerating the transformation of the global energy structure to renewable energy, wind power generation has become one of the core pillars of the energy field with its significant advantages of sustainability and pollution-free. The precise grasp and in-depth analysis of the characteristics of wind turbine wakes are undoubtedly the key to unlocking the secrets of efficient operation and optimized layout of wind power generation systems, and play an irreplaceable and key role in promoting the vigorous development of the wind power industry and improving energy utilization efficiency.

[0003] The early Jensen wake model, as a foundational achievement in this field, made a preliminary exploration of the attenuation and expansion laws of the wake velocity with a simple and intuitive linear relationship, laying the foundation for subsequent research. However, its architecture is relatively simple and can only outline the macroscopic outline of the wake, but it is unable to cope with the complex and subtle changes in the microscopic structure of the wake and the deep coupling interaction mechanism between multiple physical factors. Key elements such as the fine structure of the airflow vortex in the wake, the random evolution characteristics of turbulence, and the microscopic fluctuation details of the velocity field and pressure field are all beyond its field of view, making it difficult to cope with complex working conditions.

[0004] The Gaussian distribution model has also been widely used in the field of wake velocity distribution characterization, and has shown certain descriptive capabilities in specific ideal scenarios. However, in actual wind farms, wakes are affected by factors such as topography and atmospheric environment, and exhibit significant asymmetric and irregular dynamic characteristics, which are difficult for the Gaussian model to accurately describe. Especially in wind farms with special terrain such as complex mountains and offshore areas, its prediction accuracy drops sharply, which is seriously deviated from the actual situation and cannot provide solid theoretical support for the precise layout and efficient operation of wind farms.

[0005] As technological exploration continues to deepen, the key influence of wind shear on the evolution of wakes has gradually surfaced. Wind shear causes deep distortion of the vertical distribution of wake velocity, breaking the ideal uniform flow assumption and forming a complex velocity gradient structure. In high mountain or coastal gradient wind field environments, wind shear and wakes are intertwined, causing strong turbulent mixing, irregular energy diffusion and wake trajectory deviation, which greatly weakens the power output stability of downstream wind turbines and increases the risk of structural fatigue damage, becoming one of the core bottlenecks restricting the improvement of wind power system reliability and economy. The early wake models ignored this key factor, which greatly reduced their prediction accuracy under complex wind field conditions and made it difficult to effectively guide engineering practice.

[0006] The law of conservation of mass, as a basic principle of the physical world, occupies a core position in the construction of wake models. In the whole process of wake development, the dynamic change of mass is closely related to the spatiotemporal evolution of the velocity field, the energy transfer and dissipation, and the evolution of the macroscopic morphology of the flow field, forming a complex causal network. However, in the process of architecture design and derivation, the early wake models failed to fully and deeply integrate the essence of the law of conservation of mass, causing the simulation results to deviate from the trajectory of the real physical process. The key tasks such as quantitative evaluation of key wake parameters and accurate prediction of wake propagation range and intensity are unsatisfactory, and cannot meet the stringent demands of modern wind farm refined design and intelligent operation and maintenance management for high-precision models.

[0007] Practices in multiple fields such as industrial manufacturing and meteorological forecasting fully demonstrate the unique advantages of the Weibull function in dealing with complex random phenomena and accurately characterizing failure and reliability characteristics. With its flexible parameter adjustment mechanism, it can accurately capture the differences in the microscopic distribution of random variables and keenly capture the risk characteristics of the tail of the probability distribution, injecting new vitality into the innovation and optimization of the wind turbine wake model. Although there have been occasional explorations in previous studies, its huge potential in the construction of wake models has not been deeply explored, and a general wake model system with wide adaptability and ultra-high precision has not yet been built. In particular, there are shortcomings in the system's integration of the complex dynamic effects of wind shear and the deep physical constraints of mass conservation. It is difficult to fully and high-fidelity simulate the panoramic view of the coupled evolution of multiple physical quantities of the wake under complex working conditions, and it is unable to support the refined management needs of wind farms from planning and layout, operation and control to equipment maintenance throughout the entire life cycle, which seriously hinders the wind power industry's development process towards intelligence and efficiency. In this context, the development of innovative wake models is imminent and has become the core mission of breaking through the bottleneck of industry development and promoting the iterative upgrading of wind power generation technology. In view of this, we propose a three-dimensional wake model for horizontal axis wind turbines with multiple parameters based on minimizing the Weibull function. Summary of the invention

[0008] The object of the present invention is to provide a three-dimensional wake model of a horizontal axis wind turbine with multiple parameters based on minimizing the Weibull function, so as to solve the problems raised in the above-mentioned background technology.

[0009] In order to solve the above technical problems, the purpose of the present invention is to provide a multi-parameter three-dimensional wake model of a horizontal axis wind turbine based on minimizing the Weibull function. The model is derived and calculated based on the Jensen wake model, combined with the Weibull function and taking into account the wind shear effect and the law of conservation of mass. The specific derivation and calculation process of the model includes the following steps:

[0010] S1. First, a three-dimensional rectangular coordinate system is established with the center of the wind turbine hub as the coordinate origin, the wake flow direction is the x-axis, the wake horizontal direction is the y-axis, and the wake vertical direction is the z-axis;

[0011] S2. Combining the Jensen wake model with the Weber function, a two-dimensional Weber wake model under uniform incoming flow conditions in the horizontal plane is derived, and then it is corrected by wind shear and the law of conservation of mass to obtain a two-dimensional Weber wake model in the vertical plane;

[0012] S3. The vertical plane and horizontal plane wake models are combined to obtain a three-dimensional Weber wake model.

[0013] As a further improvement of the present technical solution, in step S1, when establishing a three-dimensional rectangular coordinate system, the coordinate system is established with the origin strictly positioned at the center of the wind turbine hub to ensure that the x, y, and z axes of the wake are perpendicular to each other.

[0014] As a further improvement of the present technical solution, step S2 specifically includes the following process:

[0015] S2.1. Based on the characteristics of the probability density function of the Weibull distribution, the normalization function of the Weibull distribution is adjusted to be minimized;

[0016] S2.2, use the Jensen model to accurately display the linear relationship between the velocity distribution in the wake region and the downstream position x;

[0017] S2.3, derive the two-dimensional full wake model of the xz plane in the wake region under uniform incoming flow conditions;

[0018] S2.4, introduce wind shear to correct the vertical distribution of wake velocity;

[0019] S2.5. The same specification mass conservation law is used to further correct the vertical distribution of wake velocity.

[0020] As a further improvement of the present technical solution, in step S2.1, the Weibull distribution is often used as a tool to deal with failure or reliability measurement. The goal is usually to build a failure analysis model. The Weibull distribution is mostly used in industrial manufacturing, weather forecasting, extreme value theory and other fields. It is often used for failure or reliability measurement in multiple fields. Applying the Weibull function to the wake model can make the wake prediction more accurate. It is known that the probability density function of the Weibull distribution is:

[0021]

[0022] Among them, f(x,λ,k) is the probability density of Weibull distribution, x is a random variable, k is a shape parameter, λ is a scaling factor, and e is the base of the natural logarithm; when λ=1, it is called the minimized Weibull distribution; since when x<0, f(x,λ,k)=0, which is meaningless, the normalized function image of the minimized Weibull distribution is adjusted, considering the shape parameter k as a variable, so that:

[0023]

[0024] Where f is the Weibull function.

[0025] As a further improvement of the technical solution, in step S2.2, the Jensen model provides a wind speed attenuation equation for the turbine wake, assuming that the axisymmetric expansion downstream of the wake is described by a constant wake attenuation constant; the Jensen model shows that the velocity distribution in the wake region is linearly related to the downstream position x; when the downstream position of x is given, the wake velocity distribution at the position x is uniform, which can be expressed as:

[0026]

[0027] In the formula, u w is the wind speed of the turbine wake, u h ub is the wind speed at the hub center, i.e., the incoming wind speed; k1 is the Jensen wake expansion coefficient, which is k1=0.075 in onshore wind farms and is used to accurately quantify the radial expansion rate of the wake; r0 is the initial wake radius, which is used to strictly define the initial spatial scope of the wake; a is the axial induction factor, which is used to deeply reflect the axial effect of the wind rotor on the airflow; D is the diameter of the wind turbine, which directly determines the scale effect of the wind rotor; C T It is the thrust coefficient, which is closely related to the wind rotor force and power output characteristics.

[0028] As a further improvement of the technical solution, in step S2.3, the specific process of deriving the two-dimensional full wake model of the wake region xz plane under uniform incoming flow conditions includes:

[0029] Ignoring the influence of wind shear, it is assumed that the wind speed in the vertical direction is equal to the wind speed in the center of the hub; it can be assumed that the wake velocity expression on the xz plane in the wake area is:

[0030]

[0031] Among them, u 0(x,z) is the wake velocity on the xz plane in the wake region, B and A are unknown variables and must be determined under uniform inflow conditions; , is a dimensionless quantity in the vertical direction, and it is assumed that the wake radius in the vertical direction is expressed as:

[0032] r z =k z x+r0 (5)

[0033] Among them, r z is the vertical wake radius, k z It represents the expansion coefficient of the wake in the vertical direction, and adopts the expression of anisotropic wake expansion coefficient, namely:

[0034]

[0035] Among them, I0 represents the incoming flow intensity, which is used to accurately characterize the dynamic changes of the incoming flow intensity;

[0036] When the wake radius extends to the boundary, the wake velocity is equal to the incoming flow velocity; at this time:

[0037]

[0038] Assuming k is a variable in the interval, in the Weibull function, when the dimensionless number in the horizontal direction is 1.2, the probability that a point falls on the Weibull function f is 99.9%; therefore , can be ignored, so B=1;

[0039] Assume that the mass flux of the Weber model is equal to the mass flux of the Jensen model, that is:

[0040]

[0041] Based on the critical condition of the wake radius boundary (the wake velocity jumps to the incoming flow velocity at the moment of touching the boundary) and the mass flux equation (dynamic balance of mass flux of Weber model and Jensen model), we get the following through rigorous mathematical derivation and numerical solution:

[0042]

[0043] Therefore, the two-dimensional wake model in the xz plane is obtained as follows:

[0044]

[0045] Among them, u 0(x,z) is the wake velocity of the two-dimensional wake model.

[0046] As a further improvement of the present technical solution, in step S2.4, the center of the wind turbine hub is taken as the coordinate origin, and the absolute height above the ground is represented as z. Since the wake velocity is an asymmetric Weber shape along the hub height in the wake area, the vertical distribution of the wake velocity is corrected by considering the wind shear. When deriving the model, the physical essence of the asymmetric Weber distribution of the wake velocity in the vertical direction is deeply understood, and the wind shear model is used to simulate the wind speed characteristics of the upstream of the wind turbine:

[0047]

[0048] Among them, u (z) is the wind speed upstream of the wind turbine, i.e., wind shear; α is the wind shear index, which is determined by the local topography and atmospheric environment of the wind farm; z h ub is the hub height; taking uniform inflow as the inflow condition, the difference between the wind shear and the wind speed at the hub center is:

[0049] Δu=u (z) -u h ub (12)

[0050] Among them, Δu is the difference between wind shear and the wind speed at the center of the hub.

[0051] As a further improvement of the present technical solution, in step S2.5, considering the wind shear inflow, the existence of Δu leads to an additional mass loss Δm, the mass difference Δm and the vertical profile corrected wake velocity u (x,z) They are shown as follows:

[0052]

[0053] in, dz represents the vertical profile corrected wake velocity u (x,z) The mass flux of

[0054] The change of mass loss along the height direction will make the velocity in the wake area present an asymmetric distribution. Considering the conservation of mass, the modified derivation is carried out, and the temporal and spatial changes of mass flux and the dynamic correlation of velocity distribution are deeply integrated. The simultaneous equations (12)-(14) are obtained:

[0055]

[0056] Among them, u (x,z) The wake velocity of the two-dimensional wake model considering wind shear; based on this, it is assumed that the three-dimensional velocity distribution in the wake area is:

[0057]

[0058] In the formula, u (x,y,z) is the three-dimensional velocity in the wake region;

[0059] Where C is the quantity to be determined; the derivation of mass conservation is for the xz plane, so when y = 0, u (x,0,z) =u (x,z) , then according to equation (15)-(16) we can solve C:

[0060]

[0061] Among them, C is the key parameter to be obtained.

[0062] As a further improvement of the technical solution, in step S3, the multi-parameter horizontal axis wind turbine three-dimensional wake model that minimizes the Weibull function is:

[0063]

[0064] In the formula, u (x,y,z)is the final three-dimensional velocity in the wake region.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] 1. In the multi-parameter horizontal axis wind turbine three-dimensional wake model based on minimizing the Weibull function, the model constructs a three-dimensional rectangular coordinate system with the center of the wind turbine hub as the coordinate origin. On the basis of the Jensen wake model, the Weibull function is integrated, and the wind shear effect and the law of conservation of mass are comprehensively considered and derived. The construction process of the model is: first set according to the above coordinate system, then derive the two-dimensional Weber wake model under the condition of uniform incoming flow in the horizontal plane, and obtain the two-dimensional model in the vertical plane after wind shear and mass conservation law correction. Finally, the three-dimensional Weber wake model of the vertical and horizontal wake models is integrated to accurately simulate the wind turbine wake characteristics and flow field distribution, and improve the accuracy of wind power generation system performance evaluation and optimization;

[0067] 2. In the multi-parameter horizontal axis wind turbine three-dimensional wake model based on minimizing the Weibull function, in terms of accuracy improvement, the relative error of horizontal section verification is mostly within 7%, and the vertical section is mostly within 5%, accurately presenting the wake velocity distribution. The horizontal and vertical distribution characteristics at the hub height are in line with reality, such as the horizontal Weber distribution without top hat distribution and the vertical asymmetric Weber shape, providing a reliable basis for wind turbine layout and performance evaluation;

[0068] 3. In the multi-parameter horizontal axis wind turbine three-dimensional wake model based on minimizing the Weibull function, in terms of computational efficiency, the wind shear and mass conservation are integrated to optimize the computational process, reduce the dimensionality of complex physical processes, reduce computing resources and time consumption, improve the timeliness of simulation prediction, help engineers quickly evaluate solutions, and accelerate the optimization and iteration of wind farm design;

[0069] 4. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function has strong adaptability. It takes into account wind shear and mass loss, and flexibly adjusts parameters to adapt to multi-terrain and climate wind fields, such as mountainous and offshore wind fields, to ensure stable and accurate simulation and prediction, and provide key support for the planning and operation of wind farms in different environments, thereby comprehensively improving the comprehensive benefits of wind energy development and utilization and industrial competitiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is an exemplary basis function comparison diagram in the present invention;

[0071] Figure 2 Schematic diagram of velocity difference of an exemplary three-dimensional wake model in the present invention;

[0072] Figure 3 A line graph comparing the prediction accuracy of the horizontal direction of the exemplary three-dimensional wake model of the present invention;

[0073] Figure 4 It is a line graph comparing the prediction accuracy of the vertical direction of the exemplary three-dimensional wake model in the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] Example 1

[0076] like Figure 1-Figure 2 As shown, this embodiment provides a multi-parameter three-dimensional wake model of a horizontal axis wind turbine based on minimizing the Weibull function. The model is derived and calculated based on the Jensen wake model, combined with the Weibull function, and taking into account the wind shear effect and the law of conservation of mass. The specific derivation and calculation process of the model includes the following steps:

[0077] S1. First, a three-dimensional rectangular coordinate system is established with the center of the wind turbine hub as the coordinate origin, the wake flow direction is the x-axis, the wake horizontal direction is the y-axis, and the wake vertical direction is the z-axis;

[0078] In this step, when establishing a three-dimensional rectangular coordinate system, the coordinate system is established with the origin strictly located at the center of the wind turbine hub to ensure that the x, y, and z axes of the wake are perpendicular to each other. This architecture strictly ensures that the movement of the wake in all directions and the change in its characteristics are accurately described, providing an indispensable basic framework for the subsequent model derivation and accurate quantitative analysis of the multi-dimensional evolution of the wake under complex working conditions, and strongly supporting the high-fidelity simulation and refined analysis of the wind farm environment by the wake model, playing a key supporting role in the overall performance optimization process of the wind power generation system.

[0079] S2. Combining the Jensen wake model with the Weber function, a two-dimensional Weber wake model under uniform incoming flow conditions in the horizontal plane is derived, and then the two-dimensional Weber wake model in the vertical plane is obtained by correcting it through wind shear and the law of conservation of mass. The specific process includes the following:

[0080] S2.1. Based on the characteristics of the probability density function of the Weibull distribution, the normalized function of the minimized Weibull distribution is adjusted in a targeted manner. In view of the limitations of the application scenarios of the conventional Weibull distribution, the function is adjusted to adapt to the requirements of the wake model construction, laying a solid foundation for accurately describing the wake velocity distribution law and expanding the depth and breadth of the application of the Weibull function in the wake research field.

[0081] In this step, Weibull distribution is often used as a tool to deal with failure or reliability measurement. The goal is usually to build a failure analysis model. Weibull distribution is often used in industrial manufacturing, weather forecasting, extreme value theory and other fields. It is often used for failure or reliability measurement in multiple fields. Applying the Weibull function to the wake model can make the wake prediction more accurate. The probability density function of the known Weibull distribution is:

[0082]

[0083] Among them, f(x,λ,k) is the probability density of Weibull distribution, x is a random variable, k is a shape parameter, λ is a scaling factor, and e is the base of the natural logarithm; when λ=1, it is called the minimized Weibull distribution; since when x<0, f(x,λ,k)=0, which is meaningless, the normalized function image of the minimized Weibull distribution is adjusted, considering the shape parameter k as a variable, so that:

[0084]

[0085] Among them, f is the Weber function, which effectively expands the function's ability to describe the complex characteristics of the wake and injects core power into the precise construction of the wake model;

[0086] Among them, the graphics before and after adjustment and Gaussian contrast are Figure 1 As shown, in the figure, k=3 is taken as an example.

[0087] S2.2. Use the Jensen model to accurately display the linear relationship between the velocity distribution in the wake area and the downstream position x. This model assumes that the axisymmetric expansion of the wake downstream is controlled by a constant wake attenuation constant. Based on this characteristic, it provides the core theoretical support for determining the wake velocity at different downstream positions and is the key basis for quantifying the wake velocity distribution.

[0088] In this step, the Jensen model provides a wind speed decay equation for the turbine wake, assuming that the axisymmetric expansion of the wake downstream is described by a constant wake decay constant; the Jensen model shows that the velocity distribution in the wake region is linearly related to the downstream position x; when the downstream position of x is given, the wake velocity distribution at position x is uniform, which can be expressed as:

[0089]

[0090] In the formula, u w is the wind speed of the turbine wake, u h ubis the wind speed at the hub center, i.e., the incoming wind speed; k1 is the Jensen wake expansion coefficient, which is k1=0.075 in onshore wind farms and is used to accurately quantify the radial expansion rate of the wake; r0 is the initial wake radius, which is used to strictly define the initial spatial scope of the wake; a is the axial induction factor, which is used to deeply reflect the axial effect of the wind rotor on the airflow; D is the diameter of the wind turbine, which directly determines the scale effect of the wind rotor; C T is the thrust coefficient, which is closely related to the rotor force and power output characteristics. This equation, with its concise and sophisticated mathematical form, strictly defines the linear variation law of the wake area velocity with the downstream position x, builds a core pillar for the precise structure of the velocity field of the two-dimensional wake model, plays a mainstay role in the quantitative analysis of the velocity distribution of the wake model, and provides key theoretical guidance for the accurate prediction of the spatiotemporal evolution of the wake velocity.

[0091] S2.3. Derive the two-dimensional full wake model of the xz plane in the wake region under uniform incoming flow conditions; in the process, it is reasonably assumed that the wind speed in the vertical direction is equal to the wind speed at the center of the hub, and key variables and parameters are introduced. After rigorous mathematical derivation and boundary condition limitation (such as the speed change when the wake radius extends to the boundary), a complete model expression is constructed to accurately describe the spatial distribution of the wake velocity;

[0092] In this step, the specific process of deriving the two-dimensional full wake model of the xz plane in the wake region under uniform incoming flow conditions includes:

[0093] Ignoring the influence of wind shear, it is assumed that the wind speed in the vertical direction is equal to the wind speed in the center of the hub; it can be assumed that the wake velocity expression on the xz plane in the wake area is:

[0094]

[0095] Among them, u 0(x,z) is the wake velocity on the xz plane in the wake region, B and A are unknown variables and must be determined under uniform inflow conditions; , is a dimensionless quantity in the vertical direction, and it is assumed that the wake radius in the vertical direction is expressed as:

[0096] r z =k z x+r0 (5)

[0097] Among them, r z is the vertical wake radius, k z It represents the expansion coefficient of the wake in the vertical direction. In this scheme, the anisotropic wake expansion coefficient expression is preferably used, that is:

[0098]

[0099] Among them, I0 represents the incoming flow intensity, which is used to accurately characterize the dynamic changes of the incoming flow intensity;

[0100] When the wake radius extends to the boundary, the wake velocity is equal to the incoming flow velocity; at this time:

[0101]

[0102] After a large amount of data testing, it is found that the value of k is always between 2.7 and 3.3. For the sake of rigor, it is still assumed that k is a variable within the interval. In the Weber function, when the dimensionless number in the horizontal direction is 1.2, the probability that a point falls on the Weber function f is 99.9%; therefore , can be ignored, so B=1;

[0103] Assume that the mass flux of the Weber model is equal to the mass flux of the Jensen model, that is:

[0104]

[0105] Based on the critical condition of the wake radius boundary (the wake velocity jumps to the incoming flow velocity at the moment of touching the boundary) and the mass flux equation (dynamic balance of mass flux of Weber model and Jensen model), we get the following through rigorous mathematical derivation and numerical solution:

[0106]

[0107] Therefore, the two-dimensional wake model in the xz plane is obtained as follows:

[0108]

[0109] Among them, u 0(x,z) is the wake velocity of the two-dimensional wake model; Equation (10) builds a stable two-dimensional core framework for the three-dimensional wake model, comprehensively describes the complex situation of the wake plane velocity distribution with fine parameters and accurate formulas, deeply explores the microscopic evolution mechanism of the velocity field in the wake plane, and lays a solid foundation for the multi-dimensional expansion of the wake model.

[0110] S2.4. Introduce wind shear to correct the vertical distribution of wake velocity. Since the wake velocity is asymmetric Weber-shaped in the vertical direction, the wind shear model is used to simulate the wind speed characteristics of the upstream wind, accurately quantify the impact of wind shear, ensure that the vertical distribution of the wake velocity fits the actual working conditions, and improve the adaptability of the model to complex wind field environments.

[0111] In this step, the center of the wind turbine hub is taken as the coordinate origin, and the absolute height above the ground is represented as z. Since the wake velocity is an asymmetric Weber shape along the hub height in the wake area, the vertical distribution of the wake velocity is corrected by considering wind shear. When deriving the model, the physical nature of the asymmetric Weber distribution of the wake velocity in the vertical direction is deeply understood, and the wind shear model is used to simulate the wind speed characteristics upstream of the wind turbine:

[0112]

[0113] Among them, u (z) is the wind speed upstream of the wind turbine, i.e., wind shear; α is the wind shear index, which is determined by the local topography and atmospheric environment of the wind farm; z h ub is the hub height; taking uniform inflow as the inflow condition, the difference between the wind shear and the wind speed at the hub center is:

[0114] Δu=u (z) -u h ub 12

[0115] Among them, Δu is the difference between wind shear and the wind speed at the center of the hub. This is used as the key correction parameter to deeply optimize the vertical distribution pattern of the wake velocity, so that the model can seamlessly integrate the key influencing factors of wind shear, greatly improve the accuracy of describing the vertical heterogeneity of the wake velocity in the actual wind field, and strongly enhance the model's ability to adapt to the dynamic changes of the vertical diversity of complex wind field environments, ensuring that the wake model is accurately close to the vertical wind speed evolution trajectory of the actual wind field.

[0116] S2.5. The vertical distribution of wake velocity is further modified by the same specification mass conservation law; the additional mass loss caused by wind shear and the change of vertical profile velocity are fully considered, and the series of equations are rigorously derived to make the wake velocity model accurate and reliable under the mass conservation criterion, thereby enhancing the physical significance and practical value of the model;

[0117] In this step, the presence of wind shear inflow leads to an additional mass loss Δm, mass difference Δm and vertical profile corrected wake velocity u. (x,z) They are shown as follows:

[0118]

[0119] in, dz represents the vertical profile corrected wake velocity u (x,z) The mass flux of

[0120] The change of mass loss along the height direction will make the velocity in the wake region present an asymmetric distribution, such as Figure 2 As shown in the figure, the wake velocity change extending from top to bottom toward the negative direction of the x-axis is the change in the wake velocity considering the wind shear effect; the mass conservation is considered for correction and derivation, and the temporal and spatial changes of mass flux and the dynamic correlation of velocity distribution are deeply integrated; the simultaneous equations (12)-(14) are obtained:

[0121]

[0122] Among them, u (x,z) The wake velocity of the two-dimensional wake model considering wind shear; based on this, it is assumed that the three-dimensional velocity distribution in the wake area is:

[0123]

[0124] In the formula, u (x,y,z) is the three-dimensional velocity in the wake region;

[0125] Where C is the quantity to be determined; the derivation of mass conservation is for the xz plane, so when y = 0, u (x,0,z) =u (x,z) , then according to equation (15)-(16) we can solve C:

[0126]

[0127] Among them, C is the key parameter to be obtained; through deep constraints and optimization corrections of strict mass conservation laws, it is ensured that the wake model strictly follows the conservation principles of physical essence in all aspects, deeply improves the accuracy of detailed description of complex dynamic changes of wake mass-velocity interaction, and strongly enhances the model's ability to reveal the deep mechanism of coupling of multiple physical quantities in the wake, laying a solid physical foundation for the wake model to simulate complex wind field wakes with high fidelity.

[0128] S3, combining the vertical plane and horizontal plane wake models to obtain a three-dimensional Weber wake model;

[0129] Specifically, in this step, the multi-parameter horizontal axis wind turbine three-dimensional wake model that minimizes the Weibull function is:

[0130]

[0131] In the formula, u (x,y,z) is the final three-dimensional velocity in the wake area; this expression comprehensively integrates the dynamic influence of wind shear, the intrinsic constraints of mass conservation and the microscopic characteristics of the Weber function, and uses rigorous mathematical logic and fine parameter configuration to comprehensively and accurately characterize the complex spatiotemporal evolution of the three-dimensional velocity distribution in the wake area, providing a solid and reliable theoretical model support for core application scenarios such as multi-condition simulation of wind turbine wakes, optimization decision-making of wind farm layout, and accurate prediction of power generation efficiency. It deeply drives the development of wind power technology towards intelligent and precise high-level development, significantly improves the comprehensive benefits of wind energy resource development and utilization and the core competitiveness of the industry, and reshapes the new technical landscape for performance evaluation and optimization of wind power systems.

[0132] Verification Example

[0133] A series of wind tunnel tests were conducted by the Garrad Hassan Group at the Engineering Laboratory (MEL) in Marchwood using a 1 / 160 scale simulated wind turbine in an atmospheric boundary layer wind tunnel. The artificial surface roughness of the wind tunnel was set to uniform to simulate uniform flat terrain, and the roughness length was set to 0.075m. The full-scale wind turbine rotor diameter is 43.2m and the hub height is 50m. Horizontal measurements were used to verify the wake model.

[0134] At the hub height, the inflow velocity u0 = 5.3 m / s, TSR = 2.9, and the thrust coefficient C T =0.62 to verify the effectiveness of the horizontal plane. By comparing with the measured points, it can be seen that the Weber model can well predict the horizontal wake loss, and the accuracy can be well adjusted by adjusting different k values, such as Figure 3 shown.

[0135] The vertical validation set uses the UP-2 wind speed u measured by the WP350 lidar in May 2019. h ub =9.2m / s, thrust coefficient C T =0.72, the average incoming flow intensity within 10 minutes is I0=0.11, and the fitted wind shear index is α=0.14.

[0136] like Figure 4 As shown in the figure, the experimental results show that the model has better accuracy in the vertical direction. Although the wake model obviously underestimates the wake velocity in the lower wake region when x=8D, this may be due to the complex ground environment in the actual wind field, which may have steep slopes or vegetation, increasing the complexity of the wake turbulence changes in the lower wake region, resulting in poor prediction accuracy of the wake model here. The overall observation verifies the accuracy and practicality of the proposed wake model in the vertical direction.

[0137] Those skilled in the art will appreciate that the process of implementing all or part of the steps of the above embodiments may be completed by hardware, or may be completed by instructing related hardware through a program.

[0138] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A three-dimensional wake model of a multi-parameter horizontal axis wind turbine based on minimizing the Weibull function, characterized in that: The model is derived and calculated based on the Jensen wake model, combined with the Weber function and taking into account the wind shear effect and the law of conservation of mass. The specific derivation and calculation process of the model includes the following steps: S1. First, a three-dimensional rectangular coordinate system is established with the center of the wind turbine hub as the coordinate origin, the wake flow direction is the x-axis, the wake horizontal direction is the y-axis, and the wake vertical direction is the z-axis; S2. Combining the Jensen wake model with the Weber function, a two-dimensional Weber wake model under uniform incoming flow conditions in the horizontal plane is derived, and then it is corrected by wind shear and the law of conservation of mass to obtain a two-dimensional Weber wake model in the vertical plane; S3. The vertical plane and horizontal plane wake models are combined to obtain a three-dimensional Weber wake model.

2. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 1, characterized in that: In step S1, when establishing a three-dimensional rectangular coordinate system, the coordinate system is established by strictly positioning the origin at the center of the wind turbine hub to ensure that the x, y, and z axes of the wake are perpendicular to each other.

3. The multi-parameter horizontal axis wind turbine three-dimensional wake model based on minimizing the Weibull function according to claim 1, characterized in that: The step S2 specifically includes the following process: S2.

1. Based on the characteristics of the probability density function of the Weibull distribution, the normalization function of the Weibull distribution is adjusted to be minimized; S2.2, use the Jensen model to accurately display the linear relationship between the velocity distribution in the wake region and the downstream position x; S2.3, derive the two-dimensional full wake model of the xz plane in the wake region under uniform incoming flow conditions; S2.4, introduce wind shear to correct the vertical distribution of wake velocity; S2.

5. The same specification mass conservation law is used to further correct the vertical distribution of wake velocity.

4. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 3, characterized in that: In step S2.1, the Weibull distribution is often used as a tool to deal with failure or reliability measurement. The goal is usually to build a failure analysis model. It is known that the probability density function of the Weibull distribution is: Among them, f(x,λ,k) is the probability density of Weibull distribution, x is a random variable, k is a shape parameter, λ is a scaling factor, and e is the base of the natural logarithm; when λ=1, it is called the minimized Weibull distribution; since when x<0, f(x,λ,k)=0, which is meaningless, the normalized function image of the minimized Weibull distribution is adjusted, considering the shape parameter k as a variable, so that: Where f is the Weibull function.

5. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 4, characterized in that: In step S2.2, the Jensen model provides a wind speed decay equation for the turbine wake, assuming that the axisymmetric expansion of the wake downstream is described by a constant wake decay constant; the Jensen model shows that the velocity distribution in the wake region is linearly related to the downstream position x; when the downstream position of x is given, the wake velocity distribution at the position x is uniform, which can be expressed as: In the formula, u w is the wind speed of the turbine wake, u hub is the wind speed at the hub center, i.e., the incoming wind speed; k1 is the Jensen wake expansion coefficient; r0 is the initial wake radius; a is the axial induction factor; D is the wind turbine diameter; C T is the thrust coefficient.

6. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 5, characterized in that: In step S2.3, the specific process of deriving the two-dimensional full wake model of the wake region xz plane under uniform incoming flow conditions includes: Ignoring the influence of wind shear, it is assumed that the wind speed in the vertical direction is equal to the wind speed in the center of the hub; it can be assumed that the wake velocity expression on the xz plane in the wake area is: Among them, u 0(x,z) is the wake velocity on the xz plane in the wake region, B and A are unknown variables and must be determined under uniform inflow conditions; is a dimensionless quantity in the vertical direction, and it is assumed that the wake radius in the vertical direction is expressed as: r z =k z x+r0 (5) Among them, r z is the vertical wake radius, k z It represents the expansion coefficient of the wake in the vertical direction, and adopts the expression of anisotropic wake expansion coefficient, namely: Among them, I0 represents the incoming flow intensity; When the wake radius extends to the boundary, the wake velocity is equal to the incoming flow velocity; at this time: Assuming k is a variable in the interval, in the Weibull function, when the dimensionless number in the horizontal direction is 1.2, the probability that a point falls on the Weibull function f is 99.9%; therefore can be ignored, thus obtaining B = 1; Assume that the mass flux of the Weber model is equal to the mass flux of the Jensen model, that is: Solving for this yields: Therefore, the two-dimensional wake model in the xz plane is obtained as follows: Among them, u 0(x,z) is the wake velocity of the two-dimensional wake model.

7. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 6, characterized in that: In step S2.4, the center of the wind turbine hub is taken as the coordinate origin, and the absolute height above the ground is represented as z. Since the wake velocity is an asymmetric Weber shape along the hub height in the wake region, the vertical distribution of the wake velocity is corrected by considering the wind shear; when deriving the model, the wind shear model is used to simulate the wind speed characteristics upstream of the wind turbine: Among them, u (z) is the wind speed upstream of the wind turbine, i.e., wind shear; α is the wind shear index, which is determined by the local topography and atmospheric environment of the wind farm; z hub is the hub height; taking uniform inflow as the inflow condition, the difference between the wind shear and the wind speed at the hub center is: Δu=u (z) -u hub (12) Among them, Δu is the difference between wind shear and the wind speed at the center of the hub.

8. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 7, characterized in that: In step S2.5, considering the wind shear inflow, the existence of Δu leads to an additional mass loss Δm, the mass difference Δm and the vertical profile corrected wake velocity u (x,z) They are shown as follows: in, represents the vertical profile corrected wake velocity u (x,z) The mass flux of The change of mass loss along the height direction will make the velocity in the wake area present an asymmetric distribution. Considering the conservation of mass, the modified derivation is carried out. The simultaneous equations (12)-(14) are obtained: Among them, u (x,z) The wake velocity of the two-dimensional wake model considering wind shear; based on this, it is assumed that the three-dimensional velocity distribution in the wake area is: In the formula, u (x,y,z) is the three-dimensional velocity in the wake region; Where C is the quantity to be determined; the derivation of mass conservation is for the xz plane, so when y = 0, u (x,0,z) =u (x,z) , then according to equation (15)-(16) we can solve C: Among them, C is the key parameter to be obtained.

9. The multi-parameter three-dimensional wake model of horizontal axis wind turbine based on minimizing the Weibull function according to claim 8, characterized in that: In step S3, the multi-parameter horizontal axis wind turbine three-dimensional wake model that minimizes the Weibull function is: In the formula, u (x,y,z) is the final three-dimensional velocity in the wake region.

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