Yaw control based wind farm global wake analysis method

Abstract

The application relates to the technical field of wind turbine wake calculation, in particular to a wind farm full-field full-domain wake analysis method based on yaw control, which comprises the following steps: acquiring wind turbine parameters and terrain and inflow parameters of an operating environment in a wind farm, including the position of the wind turbine, the rotor diameter, the hub height, the yaw angle and the thrust coefficient, the flat terrain inflow wind speed, the complex terrain inflow wind speed and the turbulence intensity; calculating the lateral offset of the wake generated by the yaw of the wind turbine based on the law of conservation of momentum and the law of conservation of mass; calculating the wake width downstream of the wind turbine based on the inflow parameters and the lateral offset of the wake, and determining the range of the wake area; calculating the initial speed loss of the full-field full-domain wake based on the law of conservation of mass and the cosine distribution function; and obtaining the full-field full-domain wake speed of the wind farm based on the inflow speed and the wake speed loss at the complex terrain. Through comprehensive consideration of factors such as complex terrain, wake yaw and wake interaction, high-precision prediction of the wake speed of the wind farm is realized.

Description

A method for full-field, global wake analysis of wind farms based on yaw control Technical Field

[0001] This application relates to the field of wind turbine wake calculation technology, and more specifically, to a method for full-field, full-domain wake analysis of wind farms based on yaw control. Background Technology

[0002] To promote the achievement of "dual carbon" goals, new energy industries such as wind power are experiencing rapid development. During operation, wind turbines extract kinetic energy from incoming currents, creating a low-speed wake downstream. In large wind farms, due to the large number of turbines, downstream turbines inevitably operate in this low-speed wake, resulting in significant power losses and severely impacting the operational efficiency of the wind farm.

[0003] Active yaw control technology reduces the negative impact of wake ducts on downstream turbines by controlling the yaw angle of upstream wind turbines, thereby effectively improving the operating efficiency of wind farms. This technology relies on accurate prediction of the wake ducts from yaw-driven wind turbines. An efficient and accurate wake prediction method can be an effective tool for precise control of wind farms and improving their operational efficiency.

[0004] Currently, a series of models for predicting the wake of yaw wind turbines have been proposed in relevant literature, such as the wake models of 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, GW, Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energys 11(3), 665; Existing literature 3: Shen, WZ, Lin, JW, Jiang, YH, Feng, J., Cheng, L., Zhu, WJ, 2023. A novel yaw wake model for wind farm control applications. Renewable Energy 218, 11946; Existing literature 4: Zhang, ZY, Huang, P., Bitsuamlak, G., Cao, SY, 2024. Analytical solutions foryawed wind-turbine wakes with application to wind-farm power optimization by active yaw control. Ocean Engineering 304, 117691). However, existing models have certain shortcomings in terms of applicability and prediction accuracy. Among the existing models, most models such as BP, Shen, and Zhang can only be used for far-field wake prediction. Although the QI model can be used for near-field and far-field wake prediction, it cannot reflect the characteristics of the skewed distribution of yaw wake, affecting the prediction accuracy of the model. In addition, the above models are only suitable for 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 top of the mountain provides richer wind resources. In the case of wind farm wake prediction in complex terrain with high wind energy potential, higher requirements are placed on the applicability of wake analysis models.

[0005] Therefore, a wake analysis method with wide applicability and high accuracy is proposed, which takes into account the influence of wind turbine wake yaw control and topographic effects in complex terrain. It has the ability to efficiently predict the wake velocity of the entire wind farm, which is of great significance for guiding the construction and operation of wind farms. Summary of the Invention

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

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

[0008] A method for full-field, global wake analysis of wind farms based on yaw control includes:

[0009] Obtain 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 Initial wake diffusion coefficient k0, initial deflection angle θ0, initial wake radius r0, and wake radius r at the downstream location. d and initial offset δ0; the wind turbine parameters include rotor diameter D, hub height z h Yaw angle γ and thrust coefficient C T The terrain feature parameters include surface roughness length z0, terrain shape parameter b, terrain slope s, and maximum terrain height h; the inflow parameters include turbulence intensity I0 and inflow wind speed u on flat terrain. 0f and inflow wind speed u in complex terrain 0c ;

[0010] According to the equivalent thrust coefficient C′ T The initial wake diffusion coefficient k0, the initial deflection angle θ0, and the wake radius r at the downstream position. d And the initial offset δ0, determine the lateral offset δ of the wake generated by the wind turbine yaw;

[0011] Based on the yaw angle γ, the initial wake radius r0 and the wake radius r at the downstream position are... d The correction is made, and the horizontal distribution range of the wake region at the hub height is determined by combining the lateral offset δ of the wake.

[0012] Based on the corrected wake radius r′ d Calculate the wake correction points r on the inner and outer sides of the wind turbine. i The corrected lateral position r′ is used to determine the global initial velocity deficit d. f ;

[0013] Based on the global initial velocity loss d f The inflow wind speed u in the flat terrain 0f and the inflow wind speed u in the complex terrain 0cThe wake velocity u of the entire wind farm was calculated.

[0014] In one possible implementation, the equivalent thrust coefficient C′ generated during wind turbine yaw is determined. T , is represented as:

[0015] C′ T =C T cos 3 γ

[0016] Wherein, the thrust coefficient C T Represented as

[0017]

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

[0019] The initial deflection angle θ0 is determined as follows:

[0020]

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

[0022] In one possible implementation, the initial wake diffusion coefficient k0 is determined as follows:

[0023] k0 = 0.5 / ln(z) h / z0)

[0024] In the formula, z0 is the surface roughness length; z h This refers to the wheel hub height.

[0025] In one possible implementation, the initial radius r0 of the wake is determined as follows:

[0026]

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

[0028] Determine the wake radius r at the downstream location d , is represented as:

[0029] r d =k0x+0.4k0C T In the formula D / I0+r0, x is the flow distance from the downstream location of the wind turbine.

[0030] In one possible implementation, the initial offset δ0 is determined as follows:

[0031]

[0032] In the formula, x0 is the flow distance when the initial offset is reached, expressed as:

[0033]

[0034] In the formula, r d0 Let x0 be the wake radius, expressed as:

[0035]

[0036] In one possible implementation, based on the equivalent thrust coefficient C′ T The initial wake diffusion coefficient k0, the initial deflection angle θ0, and the wake radius r at the downstream position. d And the initial offset δ0, the lateral offset δ of the wake generated by the wind turbine yaw is determined as follows:

[0037]

[0038] in,

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

[0040]

[0041] Corrected wake radius r′ d Represented as:

[0042] r′ d =k0x+0.4k0C T D / I0+r′0

[0043] Based on the lateral offset δ of the wake, the horizontal distribution range r of the wake region at the hub height is determined as follows:

[0044] δ-r′ d <r<δ+r′ d .

[0045] In one possible implementation, based on the corrected wake radius r′ d Calculate the wake correction points r on the inner and outer sides of the wind turbine. i And the corrected lateral position r′, including:

[0046] The wake correction points on the inner and outer sides of the wind turbine are represented as follows:

[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 The near-field and far-field wake correction points are determined by the rotor diameter D.

[0051] The determination of the global initial velocity loss d f ,include:

[0052] Based on the wake correction points r on the inner and outer sides of the wind turbine i Based on the corrected lateral position r′, determine the velocity loss d caused by the i-th wind turbine in the wind farm. fi , is represented as:

[0053]

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

[0055]

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

[0057] According to the speed loss d fi The initial velocity deficit across the entire domain is determined as follows:

[0058]

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

[0060] In one possible implementation, based on the global initial velocity loss d f The inflow wind speed u in the flat terrain 0f and the inflow wind speed u in the complex terrain 0c The calculated global wake velocity u of the wind farm includes:

[0061] Based on the inflow velocity in complex terrain, determine the wake velocity deficit d under the influence of complex terrain. c , is represented as:

[0062]

[0063] According to the aforementioned wake velocity loss d c The wake velocity u across the entire wind farm is obtained and expressed as:

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

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

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

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

[0068]

[0069] In the formula, d h The horizontal distance between the wind turbine and the maximum elevation h of the terrain; z h L is the height of the wind turbine hub; L1 is the terrain feature length, expressed as L1=h / (2s); L is the position feature length, which is determined by the relative position of the wind turbine and the shape of the terrain.

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

[0071] The technical solution provided in this application uses a terrain influence formula to calculate the inflow velocity of each wind turbine in a wind farm under complex terrain. Compared with traditional wind profile models, it can more accurately and reasonably reflect the influence of terrain factors on wind speed, thus providing a more scientific basis for wake analysis of wind turbine layout and operation. Simultaneously, it calculates the lateral wake offset based on the laws of momentum and mass conservation, breaking through the limitations of previous methods that relied on fitting empirical formulas with experimental or numerical data. This not only has a wider range of applications but also higher prediction accuracy, effectively improving the ability to understand wake behavior.

[0072] Furthermore, using the partial cosine distribution function to describe the wake distribution of yaw wind turbines accurately captures the characteristics of skewed wake distribution, further improving prediction accuracy compared to Gaussian function models and making the simulation of wake distribution more realistic. Through multi-function coupling and consideration of wake interactions, it can comprehensively reflect the wake velocity distribution across the entire wind farm, not only extending its applicability far beyond models applicable only to far-field wake velocity prediction for a single wind turbine, but also demonstrating higher accuracy in near-field wake velocity prediction, providing strong support for the overall performance evaluation and optimization of wind farms.

[0073] Secondly, this application uses explicit calculation methods in each step, which greatly improves the analysis efficiency compared with implicit analysis methods that require computational fluid dynamics or iterative solutions. It can quickly complete the calculation task and is particularly suitable for efficient analysis and calculation in the process of wind farm layout optimization and collaborative control. Attached Figure Description

[0074] Figure 1 is a flowchart of a wind farm wake analysis method based on yaw control provided in Embodiment 1 of this application;

[0075] Figure 2 is a flowchart of another wind farm wake analysis method based on yaw control provided in Embodiment 2 of this application;

[0076] Figure 3 is a graph representing the lateral offset of the wheel hub height wake provided in Embodiment 2 of this application;

[0077] Figure 4 is a diagram showing the wake velocity distribution at different locations downstream of the wind turbine at the hub height level in Embodiment 2 of this application.

[0078] Figure 5 is a diagram showing the wake velocity distribution at different locations downstream of the wind turbine at the hub height level in Embodiment 3 of this application;

[0079] Figure 6 shows the velocity deficit Δu and inflow wind speed u at different locations downstream of the wind turbine wake center, as provided in Embodiment 4 of this application. 0f A graph of the ratio;

[0080] Figure 7 shows the wake velocity u and inflow wind velocity u on the horizontal plane representing the hub height of each wind turbine position, as provided in Embodiment 5 of this application. Qf A graph showing the ratio. Detailed Implementation

[0081] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the embodiments of this application. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0082] Example 1

[0083] Referring to Figure 1, this is a flowchart of a wind farm full-field wake analysis method based on yaw control provided in Embodiment 1 of this application. As shown in Figure 1, 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 these, the wind turbine parameters include the rotor diameter D and the hub height z. h Yaw angle γ and thrust coefficient C T The aforementioned topographic features include surface roughness length z0, topographic shape parameter b, topographic slope s, and maximum topographic height h. The aforementioned inflow parameters include turbulence intensity I0 and inflow wind speed u for flat terrain. 0f and inflow wind speed u in complex terrain 0c .

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

[0086]

[0087] In the formula, F is the wind turbine thrust; ρ is the air density; A0 is the wind turbine area; and γ is the yaw angle, determined by the right-hand rule.

[0088] The inflow wind speed in complex terrain is obtained by wind measuring equipment or calculated using the following formula (2), and is expressed as:

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

[0090] In the formula, u 0c For inflow wind speed in complex terrain; u 0f denoted as denoted as inflow wind speed on flat terrain; b is the terrain shape parameter, taken as 4.0 for hilly terrain and 1.6 for sloping terrain; s is the terrain slope; c is the terrain influence parameter, expressed as:

[0091]

[0092] In the formula, d h The horizontal distance between the wind turbine and the maximum elevation h of the terrain; z hL is the height of the wind turbine hub; L1 is the terrain feature length, expressed as L1 = h / (2s); L is the position feature length. When the wind turbine is upstream of the maximum height, L = L1; when the wind turbine is downstream of the maximum height and b is 4.0, L = L1; when the wind turbine is downstream of the maximum height and b is 1.6, L = 2L1. In other words, the value of the position feature length L is determined by the relative position of the wind turbine and the shape of the terrain.

[0093] Step 102: Based on the wind turbine parameters, terrain feature parameters, and inflow parameters mentioned above, determine the equivalent thrust coefficient C′ generated when the wind turbine yaws. T Initial wake diffusion coefficient k0, initial deflection angle θ0, initial wake radius r0, and wake radius r at the downstream location. d and the initial offset δ0.

[0094] Among them, the equivalent thrust coefficient C′ generated during wind turbine yaw T Represented as:

[0095] C′ T =C T cos 3 γ (4)

[0096] The initial wake diffusion coefficient k0 mentioned above is expressed as:

[0097] k0 = 0.5 / ln(z) h / z0) (5)

[0098] In the formula, z0 is the surface roughness length.

[0099] The initial deflection angle θ0 mentioned above is expressed as:

[0100]

[0101] The initial radius r0 of the wake mentioned above is expressed as:

[0102]

[0103] The wake radius r at the downstream position is determined based on the initial wake radius r0 mentioned above. d , is represented as:

[0104] r d =k0x+0.4k0C T D / I0+r0(8)

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

[0106] The initial offset δ0 mentioned above is expressed as:

[0107]

[0108] In the formula, the flow direction distance when x0 reaches the initial offset is calculated by the following formula (10), and is expressed as:

[0109]

[0110] Where, r d0 Let x0 be the wake radius, expressed as:

[0111]

[0112] Step 103: Based on the laws of conservation of momentum and mass, and according to the above equivalent thrust coefficient C′ T The initial wake diffusion coefficient k0, the initial deflection angle θ0, and the wake radius r at the downstream position are all mentioned above. d Based on the initial offset δ0 mentioned above, the lateral offset δ of the wake generated by the yaw of the wind turbine is determined.

[0113] Specifically, the lateral drift δ of the wake 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] function f(r) d0 The calculation method of / D) is the same as that of f(r) above. d The same applies to f(r). Substituting formula (11) into formula (13) yields f(r). d0 / D), represented as:

[0118]

[0119] Step 104: Based on the yaw angle γ, adjust the initial wake radius r0 and the wake radius r at the downstream position. d Make corrections.

[0120] The corrected initial wake radius r′0 is expressed as:

[0121]

[0122] Corrected wake radius r′ d Represented as:

[0123] r′ d =k0x+0.4k0C T D / I0+r′0(16)

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

[0125] Step 105: Based on the corrected initial wake radius r′0 and the corrected wake radius r′ d By combining the calculated lateral offset δ of the wake, the horizontal distribution range of the wake region at the hub height is determined.

[0126] Specifically, the horizontal distribution range of the wake region at the hub height can be represented 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, according to the corrected wake radius r′ d Calculate the wake correction points r on the inner and outer sides of the wind turbine. i And the corrected lateral position r′, used to determine the velocity deficit d fi .

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

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

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

[0132]

[0133] In the formula, d i The near-field and far-field wake correction points are determined by the rotor diameter D. For example, in this embodiment, 3D is used.

[0134] Furthermore, based on the aforementioned wake correction points r on the inner and outer sides of the wind turbine... i Based on the corrected lateral position r′, determine the velocity loss d caused by the i-th wind turbine in the wind farm. fi , is represented as:

[0135]

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

[0137] d′ is the cosine function-corrected total loss coefficient, expressed as:

[0138]

[0139] In the formula, a is the axial induction factor of the wind turbine, expressed as:

[0140] Step 107: Based on the above speed loss d fi The global initial velocity deficit df is determined as follows:

[0141]

[0142] In the formula, n is the total number of wind turbines in the wake range of the wind farm.

[0143] Step 108: Based on the above global initial velocity loss d f The inflow wind speed u in the aforementioned flat terrain 0f And the inflow wind speed u in the aforementioned complex terrain 0c The wake velocity u of the entire wind farm was calculated.

[0144] Specifically, firstly, based on the inflow velocity in complex terrain and the aforementioned global initial velocity deficit d... f Determine the wake velocity deficit d under the influence of complex terrain. c , is represented as:

[0145]

[0146] Based on the aforementioned wake velocity loss d c The wake velocity u across the entire wind farm is determined as follows:

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

[0148] Compared with the prior art, the technical solution provided in Embodiment 1 of this application has the following beneficial effects:

[0149] The technical solution provided in this application uses a terrain influence formula to calculate the inflow velocity of each wind turbine in a wind farm under complex terrain. Compared with traditional wind profile models, it can more accurately and reasonably reflect the influence of terrain factors on wind speed, thus providing a more scientific basis for wake analysis of wind turbine layout and operation. Simultaneously, it calculates the lateral wake offset based on the laws of momentum and mass conservation, breaking through the limitations of previous methods that relied on fitting empirical formulas with experimental or numerical data. This not only has a wider range of applications but also higher prediction accuracy, effectively improving the ability to understand wake behavior.

[0150] Furthermore, using the partial cosine distribution function to describe the wake distribution of yaw wind turbines accurately captures the characteristics of skewed wake distribution, further improving prediction accuracy compared to Gaussian function models and making the simulation of wake distribution more realistic. Through multi-function coupling and consideration of wake interactions, it can comprehensively reflect the wake velocity distribution across the entire wind farm, not only extending its applicability far beyond models applicable only to far-field wake velocity prediction for a single wind turbine, but also demonstrating higher accuracy in near-field wake velocity prediction, providing strong support for the overall performance evaluation and optimization of wind farms.

[0151] Secondly, this application uses explicit calculation methods in each step, which greatly improves the analysis efficiency compared with implicit analysis methods that require computational fluid dynamics or iterative solutions. It can quickly complete the calculation task and is particularly suitable for efficient analysis and calculation in the process of wind farm layout optimization and collaborative control.

[0152] Example 2

[0153] Example 2 of this application uses experimental data obtained from the wind tunnel of the Wind Engineering and Renewable Energy Laboratory at the Swiss Federal Institute of Technology in Lausanne (source: 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) to test the predictive effect of the method provided in this application. In the experiment, the wind turbine model had a rotor diameter D = 0.15m and a hub height z. h =0.125m, the wind turbine is installed at the position (x=0). In the two yaw conditions, the yaw angle γ of the wind turbine is -10° and -20° respectively, and the thrust coefficient C r The values ​​are 0.81 and 0.83 respectively. Inflow velocity u 0f =u 0c =4.88 m / s, turbulence intensity I0 = 7.7%, surface roughness length z0 = 0.022 × 10-3 m. As shown in Figure 2, the prediction steps are as follows:

[0154] Step 1: Obtain wind turbine parameters and environmental parameters such as topography and inflow parameters of the wind farm, including: turbine location, rotor diameter D, and hub height z. h Yaw angle γ and thrust coefficient C T The inflow wind speed u at the height of the wind turbine hub is on flat terrain. 0f Inflow wind speed u in complex terrain 0c And turbulence intensity I0 and terrain feature parameters.

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

[0156] Specifically, firstly, the yaw angle γ and the thrust coefficient C... T Through C′ T =C T cos 3 γ determines the equivalent thrust coefficient C′ T The height of the wheel hub z h The initial wake diffusion coefficient k0 is determined by formula (5) based on the surface roughness length z0. The initial deflection angle is calculated by formula (6). Then, the initial wake radii r0 and r are calculated by formulas (7) and (8), respectively. d0 x0 and the initial offset δ0 are calculated using formulas (10) and (9), and the wake radius r is calculated using formulas (8), (13), and (14) respectively. d sum function f(r) d / D), f(r) d0 / D). Finally, the lateral offset δ of the wake is calculated using formula (12).

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

[0158] Specifically, the corrected initial wake radius r′0 is first calculated using formula (15). Then, the corrected wake width r′ is calculated using formula (16). d Finally, the wake region was determined to be δ-r′. d <r<δ+r′ d .

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

[0160] Specifically, the initial velocity deficit d of the wake is calculated. fFirst, the axial induction factor of the wind turbine needs to be calculated. and inner and outer wake correction points r i =2[arccos(2 / π)]r′ d / π. Then, the corrected lateral position r′ and the corrected loss coefficient d′ are calculated using formulas (19) and (21), respectively. Finally, since the yaw angle γ is negative, α = 1 is taken, and the initial velocity loss d is calculated using formula (22). f .

[0161] Step 5: Calculate the wake velocity deficit d under the influence of complex terrain based on the inflow velocity at the complex terrain location. c The wake velocity u of the entire wind farm is obtained.

[0162] Figures 3 and 4 show the lateral offset of the wake at the hub height and the wake velocity distribution at different locations downstream of the wind turbine, respectively. The solid lines in the figures represent the prediction results based on the method provided in this application, while the dashed lines represent the prediction results of the model proposed by Qian and Ishihara (see existing literature 2: Qian, GW, Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energys 11(3), 665). The comparison in the figures shows that this application can predict the lateral offset and wake velocity of the wake relatively well, and the partial cosine distribution applied in this application reflects the velocity distribution characteristics of the yaw wake well.

[0163] Example 3

[0164] In Embodiment 3 of this application, the Reynolds stress model is used to apply stress to a wind turbine with a diameter D = 0.57m and a hub height z. h The numerical simulation data of a wind turbine with a thrust coefficient of 0.7m (derived from existing literature 2: Qian, GW, Ishihara, T., 2018. A New Analytical Wake Model for Yawed Wind Turbines. Energys 11(3), 665) were used to verify the prediction effect of this application. In the two sets of simulated yaw conditions, the yaw angle γ of the wind turbine was 8° and 16°, respectively, and the thrust coefficient C T The velocity is 0.84, and the wind turbine is installed at x=0. The inflow velocity is u. 0f =u 0c Turbulence intensity I0 = 3.5%, surface roughness length z0 = 0.1 × 10⁻⁶ -3 m.

[0165] The calculation steps are the same as in Examples 1 and 2. Figure 5 shows the wake velocity distribution at different locations downstream of the wind turbine at the hub height level. The results in the figure show that this application can predict wake velocities well across the entire field, including both near and far fields, and also reflects the skewed distribution of yaw wake velocities well.

[0166] Example 4

[0167] Embodiment 4 of this application describes a wind turbine (D=126m, z) h =90m, C T =0.84, γ=0) Data from large eddy simulation (derived from 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) were used to verify the predictive effect of the technical solution provided in this application. The inflow wind speed u in the simulation 0f =8m / s, surface roughness length z0 = 0.2m. The watershed contains hilly terrain, and the governing equation for the terrain is:

[0168]

[0169] The hill height H = 50m; the characteristic length L1 = 200m. The wind turbine is installed at position x = 0. The calculation steps are as follows:

[0170] First, based on the inflow velocity u 0f The inflow wind speed u on the hill can be calculated using formulas (2) and (3). 0c In formula (2), the terrain shape parameter b = 4.

[0171] The subsequent calculation steps are the same as in Examples 1 and 2. Finally, the wake velocity of the wind turbine across the entire field is determined by formulas (23) and (24) based on the initial velocity deficit and the inflow velocity at complex terrain. Figure 6 shows the velocity deficit Δu and inflow wind velocity u at different locations downstream of the wind turbine wake center. 0f The ratio is shown in the figure. As can be seen from the results, except at extremely close distances to the wind turbine, this application can predict the wind turbine wake velocity distribution well under complex terrain.

[0172] Example 5

[0173] Example 5 of this application uses wind tunnel experimental data measured at Iowa State University (derived from 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 predictive effect of the method of this invention. In the experiment, five wind turbine models (D = 0.127 m, z) were arranged at equal intervals along the flow direction. h =0.225m, γ=0, interval 3D), turbulence intensity I0=16%, the watershed contains hilly terrain, and the governing equation for the terrain is:

[0174]

[0175] The hill has a height H = 0.285m, a characteristic length L1 = 0.57m, and a slope s = 0.25. The first wind turbine is installed at a position x = -6D.

[0176] The calculation steps are the same as in Example 4. Figure 7 shows the wake velocity u and inflow wind velocity u at the horizontal plane of the hub height of each wind turbine location. 0f The ratio is shown in the figure. As can be seen from the results, this application can predict the wake velocity distribution of wind farms in complex terrain relatively well.

[0177] Although embodiments of this application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for full-field, global wake analysis of wind farms based on yaw control, characterized in that, include: Obtain wind turbine parameters, terrain feature parameters, and inflow parameters of the wind farm to determine the equivalent thrust coefficient generated when the wind turbine yaws. Initial wake diffusion coefficient k0, initial deflection angle θ0, initial wake radius r0, and wake radius r at the downstream location. d and initial offset δ0; the wind turbine parameters include rotor diameter D, hub height z h Yaw angle γ and thrust coefficient C T The terrain feature parameters include surface roughness length z0, terrain shape parameter b, terrain slope s, and maximum terrain height h; the inflow parameters include turbulence intensity I0 and inflow wind speed u on flat terrain. 0f and inflow wind speed u in complex terrain 0c According to the equivalent thrust coefficient The initial wake diffusion coefficient k0, the initial deflection angle θ0, and the wake radius r at the downstream position. d And the initial offset δ0, the lateral offset δ of the wake generated by the wind turbine yaw is determined, expressed as: in, ， Based on the yaw angle γ, the initial wake radius r0 and the wake radius r at the downstream position are... d The correction is made, and the horizontal distribution range of the wake region at the hub height is determined by combining the lateral offset δ of the wake; wherein, the corrected initial radius of the wake is... Represented as: Corrected wake radius Represented as: Based on the lateral offset δ of the wake, the horizontal distribution range r of the wake region at the hub height is determined as follows: <r< Based on the corrected wake radius Calculate the wake correction points r on the inner and outer sides of the wind turbine. i and the corrected lateral position Used to determine the global initial velocity deficit d f The wake correction points on the inner and outer sides of the wind turbine are represented as follows: The corrected lateral position , is represented as: In the formula, d i The near-field and far-field wake correction points are determined by the rotor diameter D; the determination of the global initial velocity deficit d f This includes: based on the wake correction points r on the inner and outer sides of the wind turbine. i and the corrected lateral position Determine the velocity loss d caused by the i-th wind turbine in the wind farm. fi , is represented as: In the formula, α is a shape parameter, and the parameter value is determined by the magnitude of the yaw angle; The overall loss coefficient, corrected for the cosine function, is expressed as: In the formula, a is the axial induction factor of the wind turbine, expressed as: According to the speed loss d fi The initial velocity deficit across the entire domain is determined as follows: In the formula, n is the total number of wind turbines within the wake range of the wind farm; based on the global initial velocity deficit d... f The inflow wind speed u in the flat terrain 0f and the inflow wind speed u in the complex terrain 0c The wake velocity u across the entire wind farm was calculated; among which, based on the inflow velocity in complex terrain, the wake velocity deficit d under the influence of complex terrain was determined. c , is represented as: According to the aforementioned wake velocity loss d c The wake velocity u across the entire wind farm is obtained and expressed as: 。 2. The wind farm wake analysis method based on yaw control according to claim 1, characterized in that, Determine the equivalent thrust coefficient generated during wind turbine yaw. , is represented as: Wherein, the thrust coefficient C T Represented as In the formula, F is the wind turbine thrust, ρ is the air density, and A0 is the wind turbine area; the initial deflection angle θ0 is determined as follows: In the formula, γ is the yaw angle. The equivalent thrust coefficient is given.

3. The wind farm wake analysis method based on yaw control according to claim 1, characterized in that, The initial wake diffusion coefficient k0 is determined as follows: In the formula, z0 is the surface roughness length, z h This refers to the wheel hub height.

4. The wind farm wake analysis method based on yaw control according to claim 1, characterized in that, The initial radius r0 of the wake is determined as follows: In the formula, D is the diameter of the wind turbine. The equivalent thrust coefficient is given; the wake radius r at the downstream position is determined. d , is represented as: In the formula, x is the flow distance from the downstream position of the wind turbine.

5. The wind farm wake analysis method based on yaw control according to claim 1, characterized in that, The initial offset δ0 is determined as follows: In the formula, x0 is the flow distance when the initial offset is reached, expressed as: In the formula, r d0 Let x0 be the wake radius, expressed as: 。 6. The wind farm wake analysis method based on yaw control according to claim 1, characterized in that, The inflow wind speed in complex terrain is obtained by wind measurement equipment or calculated by formula, and is expressed as: In the formula, u 0c For inflow wind speed in complex terrain; u 0f denoted as: b is the inflow wind speed in flat terrain; s is the terrain shape parameter; c is the terrain slope; and c is the terrain influence parameter. In the formula, d h The horizontal distance between the wind turbine and the maximum elevation h of the terrain; z h L is the height of the wind turbine hub; L1 is the terrain feature length, expressed as L1=h / (2s); L is the position feature length, which is determined by the relative position of the wind turbine and the shape of the terrain.

Images