Wind power plant whole-field global wake flow analysis method based on yaw control

Abstract

The invention relates to the technical field of wind turbine generator wake flow calculation, in particular to a wind power plant whole-field global wake flow analysis method based on yaw control, which comprises the following steps: acquiring wind turbine parameters in a wind power plant and terrain and inflow parameters of an operating environment; comprise the position of a wind turbine, the diameter of a wind wheel, the height of a hub, a yaw angle, a thrust coefficient, the inflow wind speed of flat terrains, the inflow wind speed of complex terrains and turbulence intensity; based on the theorem of momentum conservation and mass conservation, the wake flow transverse offset generated by yaw of the wind turbine is calculated; based on the inflow parameters and the wake flow transverse offset, the downstream wake flow width of the wind turbine is calculated, and the wake flow area range is determined; based on the theorem of conservation of mass and a partial cosine distribution function, calculating the initial velocity loss of the wake flow in the whole field and the whole domain; and on the basis of the inflow velocity and wake velocity loss at the complex terrain, obtaining the full-field and full-domain wake velocity of the wind power plant. By comprehensively considering factors such as complex terrain, wake flow yaw and wake flow interaction, high-precision prediction of the wake flow speed of the wind power plant is realized.

Description

Technical Field

[0001] The present application relates to the technical field of wind turbine wake calculation, and more specifically, to a wind farm full-field and full-domain wake analysis method based on yaw control. Background Art

[0002] In order to promote the realization of the "dual carbon" goal, new energy industries such as wind power are experiencing rapid development. During the operation of wind turbines, due to the extraction of incoming kinetic energy, a low-speed wake zone is formed downstream. In large wind farms, due to the large number of wind turbines, downstream wind turbines are inevitably operated in the low-speed wake zone, resulting in a large power loss of wind turbines, which seriously affects the operating efficiency of wind farms.

[0003] Based on active yaw control technology, the wake is offset by controlling the yaw angle of the upstream wind turbine, reducing the negative impact of the wake on the downstream unit, thereby effectively improving the operating efficiency of the wind farm. The realization of this technology depends on the accurate prediction of the wake of the yawed wind turbine. An efficient and accurate wake prediction method can become an effective tool for precise control of wind farms and improving operating efficiency.

[0004] Currently, a series of models for yawed wind turbine wake prediction have been proposed in relevant literature. For example, wake models such as BP, QI, Shen, and Zhang (see Existing Literature 1: Bastankhah, M., Portt-Agel, F., 2016. Experimental and theoretical study of wind turbine wakes in yawed conditions. Journal of Fluid Mechanics 806, 506 - 541; Existing Literature 2: Qian, G.W., Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energies 11(3), 665; Existing Literature 3: Shen, W.Z., Lin, J.W., Jiang, Y.H., Feng, J., Cheng, L., Zhu, W.J., 2023. A novel yaw wake model for wind farm control applications. Renewable Energy 218, 11946; Existing Literature 4: Zhang, Z.Y., Huang, P., Bitsuamlak, G., Cao, S.Y., 2024. Analytical solutions for yawed wind-turbine wakes with application to wind-farm power optimization by active yaw control. Ocean Engineering 304, 117691). However, there are certain deficiencies in the applicable range and prediction accuracy of existing models. Among existing models, most models such as BP, Shen, and Zhang can only be used for the prediction of far-field wakes. Although the QI model can be used for the prediction of near-field and far-field wakes, it cannot reflect the characteristics of the skewed distribution of yawed wakes, which affects the prediction accuracy of the model. In addition, the above models are all only applicable to predicting the wake distribution of a single wind turbine on flat terrain. Due to the influence of terrain effects in mountainous areas, the wind acceleration effect at the mountaintop provides richer wind resources. Conducting wake prediction for wind farms in complex terrains with high wind energy potential poses higher requirements for the applicability of wake analysis models.

[0005] Therefore, it is of great significance to propose a wake analysis method with wide applicability and high accuracy, considering the influence of yaw control of wind turbine wakes and terrain effects in complex terrains, and having the ability to efficiently predict the wake velocity of the entire field in a wind farm, for guiding the construction and operation of wind farms. Summary of the Invention

[0006] This application provides a full-field and global wake analysis method for a wind farm based on yaw control to solve the technical problems that existing prediction models can only be used for the prediction of far-field wakes, cannot reflect the characteristics of the skewed distribution of yawed wakes, and cannot meet the requirements for wake prediction in complex terrains with high wind energy potential.

[0007] The technical solution provided by this application is as follows:

[0008] A full-field and global wake analysis method for a wind farm based on yaw control includes:

[0009] Obtain the wind turbine parameters, terrain feature parameters, and inflow parameters of the wind farm to determine the equivalent thrust coefficient C′ generated when the wind turbine yaws T , the initial wake diffusion coefficient k 0 , the initial yaw angle θ 0 , the initial wake radius r 0 , the wake radius r at the downstream position d , and the initial offset δ 0 ; the wind turbine parameters include the rotor diameter D, the hub height z h , the yaw angle γ, and the thrust coefficient C T ; the terrain feature parameters include the surface roughness length z 0 , the terrain shape parameter b, the terrain slope s, and the maximum terrain height h, and the inflow parameters include the turbulence intensity I 0 , the inflow wind speed u on flat terrain 0f , and the inflow wind speed u on complex terrain 0c ;

[0010] Based on the equivalent thrust coefficient C′ T , the initial wake diffusion coefficient k 0 , the initial yaw angle θ 0 , the wake radius r at the downstream position d , and the initial offset δ 0 , determine the wake lateral offset δ generated by the yaw of the wind turbine;

[0011] Based on the yaw angle γ, correct the initial wake radius r 0 and the wake radius r at the downstream position d , and combine the wake lateral offset δ to determine the horizontal distribution range of the wake area at the hub height;

[0012] According to the corrected wake radius r′ d calculate the wake correction points r i inside and outside the wind turbine and the corrected lateral position r′ to determine the global initial velocity deficit df ;

[0013] According to the global initial velocity deficit d f , the flat terrain inflow wind speed u 0f and the complex terrain inflow wind speed u 0c , the full-field global wake velocity u of the wind farm is calculated.

[0014] In one possible implementation, the equivalent thrust coefficient C′ generated when the wind turbine yaws is determined T , expressed as:

[0015] C′ T = C T cos 3 γ

[0016] wherein, the thrust coefficient C T is expressed as

[0017]

[0018] In the formula, F is the wind turbine thrust; ρ is the air density; A0 is the wind turbine area.

[0019] The initial yaw angle θ is determined 0 , expressed as:

[0020]

[0021] In the formula, γ is the yaw angle; C′ T is the equivalent thrust coefficient.

[0022] In one possible implementation, the initial wake diffusion coefficient k is determined 0 , expressed as:

[0023] k 0 = 0.5 / ln(z h / z 0 )

[0024] In the formula, z 0 is the surface roughness length; z h is the hub height.

[0025] In one possible implementation, the initial wake radius r is determined 0 , expressed as:

[0026]

[0027] In the formula, D is the wind turbine diameter; C′ T is the equivalent thrust coefficient;

[0028] The wake radius r at the downstream position is determinedd , expressed as:

[0029] r d = k 0 x + 0.4k 0 C T D / I 0 + r 0 In the formula, x is the flow direction distance from the downstream position of the wind turbine.

[0030] In one possible implementation, the initial offset δ 0 , expressed as:

[0031]

[0032] In the formula, x 0 is the flow direction distance when reaching the initial offset, expressed as:

[0033]

[0034] In the formula, r d0 is the wake radius at x 0 , expressed as:

[0035]

[0036] In one possible implementation, according to the equivalent thrust coefficient C′ T , the initial wake diffusion coefficient k 0 , the initial yaw angle θ 0 , the wake radius r at the downstream position d and the initial offset δ 0 , determine the wake lateral offset δ caused by the yaw of the wind turbine, expressed as:

[0037]

[0038] Among them,

[0039] In one possible implementation, the corrected initial wake radius r′ 0 is expressed as:

[0040]

[0041] The corrected wake radius r′ d is expressed as:

[0042] r′ d = k 0 x + 0.4k 0 C T D / I 0 + r′0

[0043] Combined with the wake lateral offset δ, determine the horizontal distribution range r of the wake area at the hub height, expressed as:

[0044] δ - r′ d <r<δ + r′ d 。

[0045] In one possible implementation, according to the corrected wake radius r′ d Calculate the wake correction points r inside and outside the wind turbine i and the corrected lateral position r′, including:

[0046] The wake correction points inside and outside the wind turbine are expressed as:

[0047] r i =2[arccos(2 / π)]r′ d / π

[0048] The corrected lateral position r′ is expressed as:

[0049]

[0050] In the formula, d i is the near - and far - field wake correction point, determined by the wind turbine diameter D;

[0051] The determination of the global initial velocity deficit d f , including:

[0052] Based on the wake correction points r inside and outside the wind turbine i and the corrected lateral position r′, determine the velocity deficit d caused by the i - th wind turbine in the wind farm fi , expressed as:

[0053]

[0054] In the formula, α is the shape parameter, and the parameter value is determined by the magnitude of the yaw angle; d′ is the full - field deficit coefficient corrected by the cosine function, expressed as:

[0055]

[0056] In the formula, a is the axial induction factor of the wind turbine, expressed as

[0057] According to the velocity deficit d fi Determine the global initial velocity deficit, expressed as:

[0058]

[0059] In the formula, n is the total number of wind turbines within the wake range in the wind farm.

[0060] In one possible implementation, according to the global initial velocity deficit d f , the flat terrain inflow wind speed u 0f and the complex terrain inflow wind speed u 0c , the full-field global wake velocity u of the wind farm is calculated, including:

[0061] Based on the complex terrain inflow velocity, determine the wake velocity deficit d c , expressed as:

[0062]

[0063] According to the wake velocity deficit d c , the full-field global wake velocity u of the wind farm is obtained, expressed as:

[0064] u = u 0c (1 - d c ).

[0065] In one possible implementation, the complex terrain inflow wind speed is obtained by a wind measurement device or calculated through a formula, expressed as:

[0066] u 0c = (1 + bsc)u 0f

[0067] In the formula, u 0c is the complex terrain inflow wind speed; u 0f is the flat terrain inflow wind speed; b is the terrain shape parameter; s is the terrain slope; c is the terrain influence parameter, expressed as:

[0068]

[0069] In the formula, d h is the horizontal distance at the maximum height h of the wind turbine and the terrain; z h is the hub height of the wind turbine; L 1 is the terrain characteristic length, expressed as L 1 = h / (2s); L is the position characteristic length, determined by the relative position of the wind turbine and the terrain shape.

[0070] Compared with the prior art, the technical solution provided by this application has the following beneficial effects:

[0071] The technical solution provided by the embodiment of the present application uses a terrain influence formula to calculate the inflow velocity of each wind turbine in a wind farm under complex terrain. Compared with the traditional wind profile model, it can more accurately and reasonably reflect the influence of terrain factors on the wind speed, thereby providing a more scientific basis for the layout of wind turbines and wake analysis during operation. At the same time, based on the laws of conservation of momentum and mass conservation, the lateral offset of the wake is calculated, breaking through the limitations of relying on experimental or numerical data fitting empirical formulas in the past. It not only has a wider application range but also higher prediction accuracy, effectively improving the ability to grasp wake behavior.

[0072] In addition, a cosine distribution function is used to describe the wake distribution of yawed wind turbines, accurately capturing the characteristics of the skewed wake distribution. Compared with the Gaussian function model, it further improves the prediction accuracy and makes the simulation of the wake distribution closer to the actual situation. Through multi-function coupling and considering wake interaction, it can comprehensively reflect the wake velocity distribution of the entire wind farm. It not only has a much wider application range than models that are only applicable to the prediction of the far-field wake velocity of a single wind turbine, but also shows higher accuracy in predicting the near-field wake velocity, providing strong support for the overall performance evaluation and optimization of the wind farm.

[0073] Secondly, the explicit calculation method is used in each step of the present application. Compared with the implicit analysis method that requires the use of computational fluid dynamics or iterative solution, the analysis efficiency is greatly improved, and the calculation task can be quickly completed, which is particularly suitable for high-efficiency analysis and calculation in the process of wind farm layout optimization and coordinated control. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a flowchart of a method for analyzing the full-field and global wake of a wind farm based on yaw control provided by Embodiment 1 of the present application;

[0075] Figure 2 is a flowchart of another method for analyzing the full-field and global wake of a wind farm based on yaw control provided by Embodiment 2 of the present application;

[0076] Figure 3 is a curve graph showing the lateral offset of the hub-height wake provided by Embodiment 2 of the present application;

[0077] Figure 4 is a wake velocity distribution diagram of the hub-height horizontal plane at different positions downstream of the wind turbine provided by Embodiment 2 of the present application;

[0078] Figure 5 is a wake velocity distribution diagram of the hub-height horizontal plane at different positions downstream of the wind turbine provided by Embodiment 3 of the present application;

[0079] Figure 6 is a graph showing the velocity deficit Δu and the inflow wind speed u at the wake center at different positions downstream of the wind turbine provided by Embodiment 4 of the present application0f Curve graph of the ratio;

[0080] Figure 7 This is the curve graph of the ratio of the wake velocity u to the inflow wind speed u at the hub height horizontal plane of each wind turbine position provided in the fifth embodiment of the present application. Qf Curve graph of the ratio. Specific implementation manners

[0081] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0082] Embodiment 1

[0083] Refer to Figure 1 , which is a flowchart of a full-field and global wake analysis method for a wind farm based on yaw control provided in Embodiment 1 of the present application. As Figure 1 shown in, the specific implementation steps of the above method include:

[0084] S101. Obtain the wind turbine parameters, terrain feature parameters, and inflow parameters of the wind farm. Among them, the above wind turbine parameters include the wind wheel diameter D, the hub height z h , the yaw angle γ, and the thrust coefficient C T . The above terrain feature parameters include the surface roughness length z 0 , the terrain shape parameter b, the terrain slope s, and the maximum terrain height h. The above inflow parameters include the turbulence intensity I 0 , the inflow wind speed u 0f on flat terrain, and the inflow wind speed u 0c on complex terrain.

[0085] Specifically, the value of the above thrust coefficient C T is determined by the following formula (1), expressed as:

[0086]

[0087] In the formula, F is the wind wheel thrust; ρ is the air density; A 0 is the wind wheel area; γ is the yaw angle, which is determined by the right-hand rule.

[0088] The inflow wind speed on complex terrain is obtained by a wind measurement device or calculated by the following formula (2), expressed as:

[0089] u 0c =(1 + bsc)u 0f (2)

[0090] In the formula, u 0c is the inflow wind speed of complex terrain; u 0f is the inflow wind speed of flat terrain; b is the terrain shape parameter, taking 4.0 for hill terrain and 1.6 for slope terrain; s is the terrain slope; c is the terrain influence parameter, expressed as:

[0091]

[0092] In the formula, d h is the horizontal distance between the wind turbine and the maximum height h of the terrain; z h is the hub height of the wind turbine; L 1 is the terrain characteristic length, expressed as L 1 = h / (2s); L is the position characteristic length. When the wind turbine is upstream of the maximum height, L = L 1 , when the wind turbine is downstream of the maximum height and b takes 4.0, L = L 1 , when the wind turbine is downstream of the maximum height and b takes 1.6, L = 2L 1 . That is to say, the value of the position characteristic length L is determined by the relative position of the wind turbine and the terrain shape.

[0093] Step 102: According to the above wind turbine parameters, terrain characteristic parameters and inflow parameters, determine the equivalent thrust coefficient C′ T , initial wake diffusion coefficient k 0 , initial deflection angle θ 0 , wake initial radius r 0 , wake radius r d at the downstream position and initial offset δ 0 .

[0094] Among them, the equivalent thrust coefficient C′ T generated when the wind turbine yaws is expressed as:

[0095] C′ T = C T cos 3 γ (4)

[0096] The above initial wake diffusion coefficient k 0 , is expressed as:

[0097] k 0 = 0.5 / ln(z h / z 0 ) (5)

[0098] In the formula, z 0 is the surface roughness length.

[0099] The above initial deflection angle θ 0, expressed as:

[0100]

[0101] The above-mentioned initial wake radius r 0 , expressed as:

[0102]

[0103] According to the above-mentioned initial wake radius r 0 Determine the wake radius r at the above-mentioned downstream position d , expressed as:

[0104] r d = k 0 x + 0.4k 0 C T D / I 0 + r 0 (8)

[0105] In the formula, x is the flow direction distance from the downstream position of the wind turbine.

[0106] The above-mentioned initial offset δ 0 Expressed as:

[0107]

[0108] In the formula, x 0 The flow direction distance when reaching the above-mentioned initial offset, which is calculated by the following formula (10) and expressed as:

[0109]

[0110] Among them, r d0 Is the wake radius at x 0 Expressed as:

[0111]

[0112] Step 103. Based on the momentum conservation and mass conservation theorems, according to the above-mentioned equivalent thrust coefficient C′ T , the above-mentioned initial wake diffusion coefficient k 0 , the above-mentioned initial deflection angle θ 0 , the above-mentioned wake radius r at the downstream position d And the above-mentioned initial offset δ 0 , determine the wake lateral offset δ generated by the yaw of the wind turbine.

[0113] Specifically, the wake lateral offset δ is expressed as:

[0114]

[0115] In the formula, the function f(r d / D) is calculated using the following formula (13) and is expressed as:

[0116]

[0117] The function f(r d0 / D) is calculated in the same way as the above f(r d / D), that is, substituting the above formula (11) into the above formula (13), and f(r d0 / D) can be obtained, which is expressed as:

[0118]

[0119] Step 104. Based on the yaw angle γ, correct the above initial wake radius r 0 and the wake radius r d at the downstream position.

[0120] Among them, the corrected initial wake radius r′ 0 is expressed as:

[0121]

[0122] The corrected wake radius r′ d is expressed as:

[0123] r′ d = k 0 x + 0.4k 0 C T D / I 0 + r′ 0 (16)

[0124] In the formula, x is the flow direction distance from the downstream position of the wind turbine.

[0125] Step 105. According to the corrected initial wake radius r′ 0 and the corrected wake radius r′ d , combined with the calculated wake lateral offset δ, determine the horizontal distribution range of the wake area at the hub height.

[0126] Specifically, the horizontal distribution range of the wake area at the hub height can be expressed as:

[0127] δ - r′ d < r < δ + r′ d (17)

[0128] Step 106. Based on the mass conservation theorem and the partial cosine distribution function, calculate the wake correction points r d inside and outside the wind turbine according to the corrected wake radius r′ iand the corrected lateral position r′ for determining the velocity deficit d fi .

[0129] Specifically, the inner and outer wake correction points r i are expressed as:

[0130] r i = 2[arccos(2 / π)]r′ d / π (18)

[0131] The corrected lateral position r′ is expressed as:

[0132]

[0133] where d i is the near and far field wake correction point, determined by the wind turbine diameter D. By way of example, in this embodiment, 3D is taken.

[0134] Further, based on the above inner and outer wake correction points r i and the corrected lateral position r′ of the wind turbine, the velocity deficit d fi caused by the i-th wind turbine in the wind farm is determined, and is expressed as:

[0135]

[0136] where α is a shape parameter, and the parameter value is determined by the magnitude of the yaw angle. When the yaw angle γ is negative, α takes 1; when the yaw angle γ is positive, α takes -1; when the yaw angle γ is 0 or at a position within the near field wake, α takes 0.

[0137] d′ is the full field deficit coefficient corrected by the cosine function, and is expressed as:

[0138]

[0139] where a is the axial induction factor of the wind turbine, and is expressed as

[0140] Step 107, according to the above velocity deficit d fi determine the global initial velocity deficit df, which is expressed as:

[0141]

[0142] where n is the total number of wind turbines within the wake in the wind farm.

[0143] Step 108, according to the above global initial velocity deficit d f , the above flat terrain inflow wind speed u 0f and the above complex terrain inflow wind speed u 0c calculate the full field global wake velocity u of the wind farm.

[0144] Specifically, first, based on the inflow velocity of complex terrain and the above-mentioned global initial velocity deficit d f , determine the wake velocity deficit d c under the influence of complex terrain, expressed as:

[0145]

[0146] According to the above-mentioned wake velocity deficit d c , determine the wake velocity u of the entire wind farm, expressed as:

[0147] u = u 0c (1 - d c ) (24)

[0148] Compared with the prior art, the technical solution provided in the first embodiment of the present application has the following beneficial effects:

[0149] The technical solution provided in the embodiment of the present application uses a terrain influence formula to calculate the inflow velocity of each wind turbine in a wind farm under complex terrain. Compared with the traditional wind profile model, it can more accurately and reasonably reflect the influence of terrain factors on wind speed, thus providing a more scientific basis for wake analysis during wind turbine layout and operation. At the same time, based on the conservation laws of momentum and mass, the wake lateral offset is calculated, breaking through the limitations of relying on experimental or numerical data fitting empirical formulas in the past. It not only has a wider application range but also higher prediction accuracy, effectively improving the ability to grasp wake behavior.

[0150] In addition, using the cosine distribution function to describe the wake distribution of yawed wind turbines accurately captures the characteristics of the skewed wake distribution. Compared with the Gaussian function model, it further improves the prediction accuracy and makes the simulation of wake distribution closer to the actual situation. Through multi-function coupling and considering wake interaction, it can comprehensively reflect the wake velocity distribution of the entire wind farm. It not only has a much wider application range than the model that is only applicable to the far-field wake velocity prediction of a single wind turbine but also shows higher accuracy in near-field wake velocity prediction, providing strong support for the overall performance evaluation and optimization of the wind farm.

[0151] Secondly, the explicit calculation method is used in each step of the present application. Compared with the implicit analysis method that requires computational fluid dynamics or iterative solution, the analysis efficiency is greatly improved, and the calculation task can be quickly completed, which is especially suitable for high-efficiency analysis and calculation in the process of wind farm layout optimization and coordinated control.

[0152] Embodiment Two

[0153] In the second embodiment of this application, the experimental data measured in the wind tunnel of the Wind Energy Engineering and Renewable Energy Laboratory of the Swiss Federal Institute of Technology in Lausanne (derived from the existing literature 1: Bastankhah, M., Porté-Agel, F., 2016. Experimental and theoretical study of wind turbine wakes in yawed conditions. Journal of Fluid Mechanics 806, 506-541) is used to test the prediction effect of the method provided in the embodiment of this application. In the experiment, the rotor diameter D of the wind turbine model is 0.15 m, and the hub height z h = 0.125 m, and the wind turbine is installed at the position of x = 0). In the two yaw conditions, the yaw angles γ of the wind turbine are -10° and -20° respectively, and the thrust coefficients C r are 0.81 and 0.83 respectively. The inflow wind speed u 0f = u 0c = 4.88 m / s, the turbulence intensity I 0 = 7.7%, and the surface roughness length z 0 = 0.022×10 -3 m. As shown in Figure 2 , the prediction steps are as follows:

[0154] Step 1: Obtain the parameters of the wind turbines in the wind farm, the terrain of the operating environment, and the inflow parameters, including: the position of the wind turbine, the rotor diameter D, the hub height z h , the yaw angle γ, and the thrust coefficient C T , the inflow wind speed u 0f at the hub height of the wind turbine on flat terrain, the inflow wind speed u 0c in complex terrain, and the turbulence intensity I 0 as well as the terrain characteristic parameters.

[0155] Step 2: Based on the momentum conservation and mass conservation theorems, calculate the wake lateral offset δ generated by the yaw of the wind turbine.

[0156] Specifically, first, the equivalent thrust coefficient C′ is determined by the yaw angle γ and the thrust coefficient C T through C′ T = C T cos 3 γ. The initial wake diffusion coefficient k is determined by the hub height z T and the surface roughness length z h through formula (5). The initial deflection angle is calculated by formula (6). Then, the initial wake radii r 0 and r 0 are calculated by formulas (7) and (8) respectively. Then, the initial wake radii r 0 and r d0, calculate x according to formulas (10) and (9) 0 and the initial offset δ 0 , calculate the wake radius r respectively according to formulas (8), (13), and (14) d and the function f(r d / D), f(r d0 / D). Finally, use formula (12) to calculate the wake lateral offset δ.

[0157] Step 3: Based on the inflow parameters and the yaw wake lateral offset, calculate the wake width r′ downstream of the wind turbine d , determine the wake region range δ ± r′ d .

[0158] Specifically, first use formula (15) to calculate the corrected initial wake radius r′ 0 . Then calculate the corrected wake width r′ through formula (16) d . Finally, determine the wake region range as δ - r′ d <r<δ + r′ d .

[0159] Step 4: Based on the mass conservation theorem and the partial cosine distribution function, calculate the initial velocity deficit d of the entire wake field f .

[0160] Specifically, to calculate the initial velocity deficit d of the wake f first, it is necessary to calculate the axial induction factor of the wind turbine and the inner and outer wake correction points r i = 2[arccos(2 / π)]r′ d / π. Then calculate the corrected lateral position r′ and the corrected deficit coefficient d′ respectively by formulas (19) and (21). Finally, when the yaw angle γ is negative, take α = 1, and use formula (22) to calculate the initial velocity deficit d f .

[0161] Step 5: Based on the inflow velocity at the complex terrain, calculate the wake velocity deficit d under the influence of the complex terrain c , and obtain the wake velocity u of the entire wind farm

[0162] Such as Figure 3 and Figure 4As shown, they are respectively the lateral offset of the wake at hub height and the wake velocity distribution at the hub height horizontal plane at different positions downstream of the wind turbine. The solid lines in the figure are the prediction results based on the method provided in the embodiments of the present application, and the dashed lines are the prediction results of the model proposed by Qian and Ishihara (see the existing literature 2: Qian, G.W., Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energies 11(3), 665). It can be seen from the comparison in the figure that the present application can better predict the lateral offset of the wake and the wake velocity, and the cosine distribution applied in the present application better reflects the velocity distribution characteristics of the yawed wake.

[0163] Embodiment III

[0164] In Embodiment III of the present application, the data of a wind turbine with a rotor diameter D = 0.57 m and a hub height z h = 0.7 m obtained by numerical simulation using the Reynolds stress model (derived from the existing literature 2: Qian, G.W., Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energies 11(3), 665) is used to test the prediction effect of the present application. In the two yawed operating conditions simulated, the yaw angles γ of the wind turbine are 8° and 16° respectively, the thrust coefficient C T is 0.84, and the wind turbine is installed at the position of x = 0. The incoming flow velocity u 0f = u 0c , the turbulence intensity I 0 = 3.5%, and the surface roughness length z 0 = 0.1×10 -3 m.

[0165] The calculation steps are the same as those in Embodiments I and II. Figure 5 As shown in the figure, it is the wake velocity distribution at the hub height horizontal plane at different positions downstream of the wind turbine. It can be seen from the results shown in the figure that the present application can not only better predict the wake velocity in the whole range including the near field and the far field, but also better reflect the characteristics of the skewed distribution of the yawed wake velocity.

[0166] Embodiment IV

[0167] In Embodiment IV of the present application, for a wind turbine (D = 126 m, z h = 90 m, C T= 0.84, γ = 0) for large eddy simulation data (from the existing literature 5: Mishra, A., Arya, N., Bhattacharya, A., 2024. Wake steering of wind turbine in the presence of a two - dimensional hill. Physics of Fluids 36(4), 045125) to test the prediction effect of the technical solution provided by this application. The inflow wind speed u in the simulation 0f = 8 m / s, and the surface roughness length z 0 = 0.2 m. There is a hill terrain in the basin, and the governing equation of the terrain is:

[0168]

[0169] where the hill height H = 50 m; the characteristic length L 1 = 200 m. The wind turbine is installed at the position of x = 0. The calculation steps are as follows:

[0170] First, according to the inflow wind speed u 0f Calculate the inflow wind speed u on the hill from formulas (2) and (3), and the terrain shape parameter b = 4 in formula (2). 0c

[0171] The subsequent calculation steps are the same as those in Examples 1 and 2. Finally, the full - field wake velocity of the wind turbine is determined by formulas (23) and (24) from the initial velocity deficit and the inflow velocity at the complex terrain. Figure 6 Shown is the ratio of the velocity deficit Δu to the inflow wind speed u at the wake center at different positions downstream of the wind turbine. 0f From the results shown in the figure, it can be seen that except for the extremely close distance to the wind turbine, this application can better predict the wind turbine wake velocity distribution under complex terrain.

[0172] Example 5

[0173] Example 5 of this application uses the wind tunnel experimental data measured by Iowa State University (derived from the existing literature 6: Tian, W., Ozbay, A., Yuan, W., Sarakar, P., Hu, H., Yuan, W., 2013. An experimental study on the performances of wind turbines over complex terrain. The 51st AIAA aerospace sciences meeting induding the new horizons forum and aerospace exposition, Grapevine, Texas) to test the prediction effect of the method of the present invention. In the experiment, 5 wind turbine models (D = 0.127 m, z h = 0.225 m, γ = 0, spaced 3D apart) are arranged at equal intervals along the flow direction, the turbulence intensity I 0 = 16%, there is a hill terrain in the flow field, and the governing equation of the terrain is:

[0174]

[0175] Among them, the hill height H = 0.285 m; the characteristic length L 1 = 0.57 m, and the slope s is 0.25. The first wind turbine is installed at the position of x = -6D.

[0176] The calculation steps are the same as those in Example 4. Figure 7 Shown is the ratio of the wake velocity u to the inflow velocity u 0f at the hub height horizontal plane of each wind turbine position. It can be seen from the results shown in the figure that this application can better predict the wake velocity distribution of the entire wind farm over complex terrain.

[0177] Although the embodiments of the present application have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present application. The scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the global wake of a wind farm based on yaw control, characterized in that: include: Obtain wind turbine parameters, terrain characteristic parameters and inflow parameters of the wind farm to determine the equivalent thrust coefficient C′ generated when the wind turbine is yawed T , initial wake diffusion coefficient k0, initial deflection angle θ0, initial wake radius r0, wake radius r at downstream position d and initial offset δ0; the wind turbine parameters include rotor diameter D, hub height z h , yaw angle y and thrust coefficient C T The terrain characteristic parameters include surface roughness length z0, terrain shape parameter b, terrain slope s and terrain maximum height h, and the inflow parameters include turbulence intensity I0, flat terrain inflow wind speed u 0f and the inflow wind speed u in complex terrain 0c ; According to the equivalent thrust coefficient C′ T , the initial wake diffusion coefficient k0, the initial deflection angle θ0, the wake radius r at the downstream position d and the initial offset δ0, determining the lateral offset δ of the wake generated by the yaw of the wind turbine; The initial wake radius r0 and the wake radius r at the downstream position are determined based on the yaw angle γ. d Correction is performed, and the horizontal distribution range of the wake area at the hub height is determined in combination with the wake lateral offset δ; According to the corrected wake radius r′ d Calculate the wake correction point r inside and outside the wind turbine i and the corrected lateral position r′, used to determine the global initial velocity loss d f ; According to the global initial velocity loss d f , the flat terrain inflow wind speed u 0f and the complex terrain inflow wind speed u 0c The wake velocity u of the entire wind farm is calculated.

2. The method for analyzing the global wake of a wind farm based on yaw control according to claim 1 is characterized in that: Determine the equivalent thrust coefficient C′ generated when the wind turbine is yawed T , expressed as: C′ T =C′ T cos 3 c Wherein, the thrust coefficient C T Expressed as Where F is the wind rotor thrust; ρ is the air density; A0 is the wind rotor area. Determine the initial deflection angle θ0, expressed as: Where, γ is the yaw angle; C′ T is the equivalent thrust coefficient.

3. The method for wind farm wake analysis based on yaw control according to claim 1 is characterized in that: Determine the initial wake diffusion coefficient k0, expressed as: k0=0.5 / ln(z h / z0) Where z0 is the surface roughness length; z h is the wheel hub height.

4. The method for wind farm wake analysis based on yaw control according to claim 1 is characterized in that: Determine the initial wake radius r0, expressed as: Where D is the diameter of the wind wheel; C′ T is the equivalent thrust coefficient. Determine the wake radius r at the downstream location d , expressed as: r d =k0x+0.4k0C T D / I0+r0 Where x is the flow distance from the downstream position of the wind turbine.

5. The method for wind farm full-field global wake analysis based on yaw control according to claim 1 is characterized in that: Determine the initial offset δ0, expressed as: Where x0 is the flow distance when the initial offset is reached, expressed as: In the formula, r d0 is the wake radius at x0, expressed as:

6. The method for wind farm wake analysis based on yaw control according to claim 1 is characterized in that: According to the equivalent thrust coefficient C′ T , the initial wake diffusion coefficient k0, the initial deflection angle θ0, the wake radius r at the downstream position d and the initial offset δ0, the lateral offset δ of the wake generated by the yaw of the wind turbine is determined as: in, 7. The method for wind farm full-field global wake analysis based on yaw control according to claim 1 is characterized in that: The corrected initial wake radius r′0 is expressed as: Corrected wake radius r′ d It is expressed as: r′ d =k0x+0.4k0C T D / I0+r′0 Combined with the wake lateral offset δ, the horizontal distribution range r of the wake area at the hub height is determined, which is expressed as: δ-r′ d <r<δ+r′ d 。 8. The method for wind farm wake analysis based on yaw control according to claim 7 is characterized in that: According to the corrected wake radius r′ d Calculate the wake correction point r inside and outside the wind turbine i and the corrected lateral position r′, including: The inner and outer wake correction points of the wind turbine are expressed as: r i =2[arccos(2 / π)]r′ d / p The corrected lateral position r′ is expressed as: Where, d i It is the near and far field wake correction point, which is determined by the wind wheel diameter D. Determine the global initial velocity loss d f ,include: Based on the wind turbine inner and outer wake correction points r i and the corrected lateral position r′, determine the speed loss d caused by the i-th wind turbine in the wind farm fi , expressed as: Wherein, α is a shape parameter, and the parameter value is determined by the magnitude of the yaw angle; d′ is the full-field loss coefficient corrected by the cosine function, which is expressed as: Where a is the axial induction factor of the wind turbine, expressed as According to the speed loss d fi Determine the global initial velocity loss, expressed as: Where n is the total number of wind turbines within the wake range of the wind farm.

9. The method for wind farm wake analysis based on yaw control according to claim 1, characterized in that: According to the global initial velocity loss d f , the flat terrain inflow wind speed u 0f and the complex terrain inflow wind speed u 0c The global wake velocity u of the wind farm is calculated, including: Based on the inflow velocity of complex terrain, determine the wake velocity loss d under the influence of complex terrain c , expressed as: According to the wake velocity loss d c , the global wake velocity u of the wind farm is obtained, which is expressed as: u=u 0c (1-d c )。 10. The method for wind farm wake analysis based on yaw control according to claim 1, characterized in that: The inflow wind speed in complex terrain is obtained by wind measuring equipment or calculated by formula, which is expressed as: u 0c =(1+bsc)u 0f In the formula, u 0c is the inflow wind speed in complex terrain; u 0f is the inflow wind speed on flat terrain; b is the terrain shape parameter; s is the terrain slope; c is the terrain influence parameter, expressed as: Where, d h is the horizontal distance between the wind turbine and the terrain at the maximum height h; z h is the hub height of the wind turbine; L1 is the characteristic length of the terrain, expressed as L1=h / (2s); L is the position characteristic length, which is determined by the relative position of the wind turbine and the terrain shape.

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