A method for determining the spacing between wind farm turbines considering the influence of thermal stability

Abstract

This invention discloses a method for determining the spacing between wind turbine units in a wind farm, taking into account the influence of thermal stability. The method includes: 1) determining the target flow field inhomogeneity factor for each wind turbine unit spacing based on the wind farm parameter set; 2) determining the corrected geostrophic drag coefficient based on atmospheric boundary layer parameters; 3) determining the average velocity value at the hub height of the entire wind farm under the construction layout using an analytical model of the wind farm; 4) determining the power generation per unit area of ​​the wind farm under the current construction layout based on the wind turbine unit spacing and the average velocity value at the hub height; 5) determining the unit cost power generation of the wind farm under the current construction layout based on the cost coefficient and the power generation per unit area; 6) changing the spacing between the wind turbine units and repeating steps 1) to 5) until the unit cost power generation under all spacings is traversed, and finally determining the turbine unit spacing that maximizes the economic benefits of the wind farm.

Description

Technical Field

[0001] This disclosure relates to the field of wind power generation technology, specifically to a method for determining the spacing between wind farm turbines considering the influence of thermal stability. Background Technology

[0002] Wind energy is one of the fastest-growing clean energy sources in the world. With the rapid development of wind energy technology, wind farms are trending towards larger scale. In wind farms, wind turbines are arranged closely together. The wake effect of upstream turbines can significantly reduce downstream wind speeds and increase turbulence intensity, leading to reduced power output and increased fatigue loads on downstream turbines. The wake effect is a crucial factor to consider when designing wind farm turbine layouts. A well-planned layout can not only improve the overall power output of the wind farm but also extend the lifespan of the wind turbines. This is particularly important for enhancing the efficiency of large-scale wind farms.

[0003] During the layout of wind farm units, it is necessary to repeatedly calculate the overall power generation of the wind farm under various atmospheric conditions and layouts. At this point, computational fluid dynamics (CFD) numerical simulation methods, which consume large amounts of computational resources and have lengthy calculation times, are no longer feasible. Instead, engineering analytical models, which offer higher computational efficiency and lower computational costs, must be used. In determining the spacing between wind farm units, equivalent roughness models of the wind farm are commonly used, such as double logarithmic law models and triple logarithmic law models. However, these models do not consider the influence of thermal stability, leading to a discrepancy between the predicted results of the analytical model and the actual power generation of the wind farm under real atmospheric conditions.

[0004] When planning the layout of wind farm units, to achieve the maximum economic return, in addition to considering the overall power generation efficiency of the wind farm, the equipment cost of the wind turbines and the land cost occupied by them should also be taken into account. Too dense a distribution of wind turbines will lead to a significant reduction in power generation efficiency and an increase in wake-induced fatigue loads, thereby shortening the lifespan of the turbines and increasing equipment maintenance costs. Conversely, too sparse a distribution will reduce power generation density and increase the installation and transportation costs of electrical equipment.

[0005] To achieve greater economic benefits, it is essential to comprehensively consider both the power generation efficiency and operating costs of wind farms. This necessitates a more accurate and computationally efficient analytical model for wind farms, along with a suitable cost function, to accurately determine the turbine spacing corresponding to the maximum unit cost power generation efficiency. This approach allows wind farms to achieve the highest possible power generation efficiency while also mitigating their own operating costs, thereby improving overall economic efficiency.

[0006] In the process of realizing the present invention, the inventors discovered that the related technology has at least the following problems: the related technology does not consider the impact of thermal stability on power generation when laying out wind farm units, which results in poor accuracy in predicting the overall power generation of the wind farm at different unit spacings, and thus cannot accurately obtain the unit spacing corresponding to the maximum unit cost power generation efficiency. Summary of the Invention

[0007] In view of this, embodiments of this disclosure provide a method for determining the spacing between wind farm turbines considering the influence of thermal stability, including:

[0008] Step 1: Determine the target flow field non-uniformity factor for each wind turbine spacing based on the wind farm parameter set. The wind farm parameter set includes the surface roughness height of the wind farm, the wind turbine hub height, the wind turbine thrust coefficient, the lateral spacing between wind turbines, the flow direction spacing between wind turbines, the lateral staggered spacing between wind turbines, and the wind turbine rotor diameter.

[0009] Step 2: Determine the corrected geostrophic drag coefficient based on atmospheric boundary layer parameters;

[0010] Step 3: For each of the above wind turbine spacings, based on the above target flow field inhomogeneity factor and the above corrected geostrophic drag coefficient in the atmospheric boundary layer, use the analytical model of the wind farm to determine the average velocity value at the hub height of the wind farm under the above wind turbine spacing under the construction layout.

[0011] Step 4: Based on the spacing between each of the above-mentioned wind turbine units and the average speed value at the hub of the entire field, determine the power generation per unit area of ​​the above-mentioned wind farm under the above-mentioned wind turbine unit spacing in the construction layout.

[0012] Step 5: Based on the power generation per unit area under the above wind turbine spacing and the construction cost of the above wind farm, determine the output power per unit cost corresponding to the above construction layout;

[0013] Step 6: Iterate through all the wind turbine spacing parameters in the wind farm, repeating steps 1 to 5 until the unit cost power generation of the wind farm under all the above wind turbine spacing under all construction layouts is determined, and the turbine spacing corresponding to the highest unit cost power generation efficiency is determined as the first target turbine spacing.

[0014] According to embodiments of this disclosure, in step 1 above, the target flow field non-uniformity factor for each wind turbine spacing is iteratively solved based on the wind farm parameter set. The iterative steps include:

[0015] The first step is to determine the target wake velocity among multiple wind turbines based on the initial wake recovery rate and the target wind turbine wake model.

[0016] Step 2: Based on the target wake velocity deficit, the first integration region L, and the second integration region Ω, determine two average velocity relationships. These two average velocity relationships characterize the average velocity U at the wind turbine rotor. d Average speed U at the height of the wind turbine hub h The first integration region L is determined based on the plane of the wind turbine rotor and the plane where the wind turbine hub is located, and the second integration region Ω is determined based on the ground area occupied by the wind turbine.

[0017] Step 3: Determine the non-uniformity factor of the transition flow field based on the two average velocity relationships shown below:

[0018]

[0019] Step 4: Determine the equivalent roughness height z of the wind farm based on the above-mentioned transition flow field inhomogeneity factor. 0,2 ;

[0020] Step 5: Based on the equivalent roughness height of the wind farm, the surface roughness height, and the atmospheric boundary layer height mentioned above, determine the average velocity transition formula, where the average velocity transition formula characterizes the average velocity U at the wind turbine hub height. * h The average speed U at the hub height compared to when there is no wind turbine ∞ The ratio of, where It is only related to the recovery rate of the wake;

[0021] Step 6: Based on the average velocity transition relationship shown below and the target wind turbine wake model above, solve for the transition wake recovery rate:

[0022]

[0023] Step 7: If the difference between the transition wake recovery rate and the initial wake recovery rate is greater than a preset threshold, the transition wake recovery rate is determined as the new initial wake recovery rate so that the new transition wake recovery rate can be recalculated based on the new initial wake recovery rate.

[0024] If the difference between the transition wake recovery rate and the initial wake recovery rate is less than or equal to the preset threshold, the transition wake recovery rate is determined as the target wake recovery rate, and the transition flow field inhomogeneity factor at this time is determined as the target flow field inhomogeneity factor.

[0025] According to the embodiments of this disclosure, in step 2 above, the atmospheric boundary layer parameters include gravitational acceleration, inversion layer temperature gradient, atmospheric reference temperature, and Coriolis force parameters.

[0026] The revised geostrophic drag coefficients are characterized by A(Zi) and B(Zi), where Zi is the Zilitinkevich constant. g is the gravitational acceleration, Γ is the temperature gradient of the inversion layer; θ0 is the reference temperature, f is the Coriolis force parameter; the specific expressions for A(Zi) and B(Zi) are:

[0027] A(Zi)=1.54+0.18ln(Zi), B(Zi)=1.74+0.011Zi..

[0028] According to an embodiment of this disclosure, in step 3 above, the analytical model of the wind farm is as follows:

[0029]

[0030] Where κ represents the von Kármán constant; G represents the geostrophic velocity; u *,1 u *,2 These respectively characterize the surface friction velocity and the equivalent friction velocity of the wind farm; z 0,1 Characterizing the known surface roughness height; z 0,2 The equivalent roughness height of the unknown wind farm is represented by A(Zi) and B(Zi), which are both corrected geostrophic drag coefficients. h Characterizing the height of the wind turbine hub; U h β represents the average velocity at the hub height across the entire field; β represents the non-uniformity factor of the target flow field; c ft =πC T / (4s x s y ), C T Characterizing the thrust coefficient of a wind turbine; s x =S x / D,S x The airflow spacing between wind turbine units is represented by D, and the rotor diameter of the wind turbine is represented by s. y =S y / D,S y The empirical constant a represents the lateral spacing between wind turbine units. u =4.3, where f is the Coriolis force parameter;

[0031] By iteratively solving the analytical model, the average velocity value at the hub height of the wind farm under the above wind turbine spacing is determined.

[0032] According to an embodiment of this disclosure, step 5 above, after determining the power generation per unit area, further includes:

[0033] Based on the power generation per unit area under the above wind turbine spacing and the construction cost of the above wind farm, the unit cost output power corresponding to the above construction layout is determined, wherein the above construction cost includes the equipment cost of each wind turbine and the land cost occupied by each wind turbine, wherein one of the above construction layouts corresponds to one wind turbine spacing.

[0034] The determination of the unit cost output power corresponding to the above construction layout, based on the above-mentioned power generation per unit area under the above-mentioned wind turbine spacing and the above-mentioned construction cost of the wind farm, includes:

[0035] Based on the swept area of ​​the wind turbine rotor and the construction cost of each wind turbine, the cost coefficient of each wind turbine is determined; based on the cost coefficient, the corrected wind turbine thrust coefficient, the spacing between wind turbine units, and the power generation per unit area, the output power per unit cost is determined.

[0036] According to embodiments of this disclosure, step 6 above includes:

[0037] Iterate through all the wind turbine spacings under the above construction layout, repeat steps 1 to 5, obtain the corresponding multiple unit cost output powers, and construct the first power generation efficiency curve; based on the above first power generation efficiency curve, determine the wind turbine spacing corresponding to the maximum unit cost output power as the above first target wind turbine spacing.

[0038] According to embodiments of this disclosure, the first step described above includes:

[0039] The wake velocity of a single wind turbine in the aforementioned wind farm is determined using the target wind turbine wake model. To characterize; then, the target wake velocity among multiple wind turbines is determined by the wake velocity of a single wind turbine, using... To characterize, the initial wake recovery rate is determined based on the wind turbine hub height, the target wind turbine wake model is determined based on the wake area correction parameter and the Jensen model, and the method for determining the target wake velocity among multiple wind turbines by using the wake velocity of a single wind turbine is as follows:

[0040]

[0041] Where (x,y) are the coordinates of the wind turbines in the wind farm, x t Let U be the current wind turbine's direction coordinates, where U ∞ The average speed at the hub height when there is no wind turbine is denoted by , and T is the number of upstream wind turbines and the number of upstream mirror wind turbines with the ground as the plane of symmetry.

[0042] According to embodiments of this disclosure, a power output model for a wind farm considering thermal stability and turbine arrangement factors is constructed by combining the target flow field inhomogeneity factor for each turbine spacing determined by the wind farm parameter set with the geostrophic drag coefficient corrected by atmospheric boundary layer parameters. This allows for the determination of the power generation per unit area for the turbine spacing corresponding to the construction layout. Furthermore, based on the construction cost of the wind farm, the power generation per unit cost for the turbine spacing corresponding to the construction layout is determined. Since the influence of thermal stability is fully considered in calculating the power generation per unit cost for wind farms with different turbine spacings, the power generation per unit area for different turbine spacings can be predicted more accurately. This improves upon the problems in related technologies where the overall power generation accuracy of wind farms with different turbine spacings is poor due to the lack of consideration for thermal stability, and the inability to accurately determine the turbine spacing corresponding to the maximum power generation efficiency per unit cost. Attached Figure Description

[0043] The above and other objects, features and advantages of this disclosure will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0044] Figure 1 A flowchart illustrating a method for determining wind farm turbine spacing considering thermal stability according to an embodiment of the present disclosure is shown schematically.

[0045] Figure 2 A schematic top view of a wind turbine arrangement according to an embodiment of the present disclosure is shown.

[0046] Figure 3 A schematic diagram illustrating the setup of a mirrored wind farm according to an embodiment of the present disclosure is shown.

[0047] Figure 4 A schematic diagram of the integration region of a wind farm according to an embodiment of the present disclosure is shown.

[0048] Figure 5 This schematic diagram illustrates a construction layout of an aligned wind farm according to an embodiment of the present disclosure;

[0049] Figure 6 A schematic diagram illustrating the variation curve of the flow field non-uniformity factor in an aligned wind farm according to an embodiment of the present disclosure is shown.

[0050] Figure 7 The diagram illustrates a comparison between the unit cost output power of an aligned wind farm according to an embodiment of the present disclosure and the prediction results of large eddy simulation.

[0051] Figure 8 The diagram illustrates the relationship between the optimal and suboptimal spacing of wind turbines and the cost coefficient under aligned arrangement according to embodiments of the present disclosure.

[0052] Figure 9 The diagram illustrates a construction layout of an alternating wind farm according to an embodiment of the present disclosure.

[0053] Figure 10 This schematic diagram illustrates the unit cost output power of a wind farm under an alternating arrangement according to an embodiment of the present disclosure. Detailed Implementation

[0054] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0055] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0056] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0057] When using expressions such as "at least one of A, B, and C", they should generally be interpreted in accordance with the meaning that is commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B, and C, etc.).

[0058] Figure 1 A flowchart illustrating a method for determining the spacing between wind farm turbines according to an embodiment of the present disclosure is shown. Figure 2 A schematic top view of a wind turbine arrangement according to an embodiment of the present disclosure is shown.

[0059] like Figure 1 As shown, a method for determining the spacing between wind farm turbines considering the influence of thermal stability may include operations S101 to S106.

[0060] In operation S101, the target flow field non-uniformity factor for each wind turbine spacing is determined based on the wind farm parameter set. The wind farm parameter set includes the surface roughness height of the wind farm, the wind turbine hub height, the wind turbine thrust coefficient, the lateral spacing between wind turbines, the flow direction spacing between wind turbines, the lateral staggered spacing between wind turbines, and the wind turbine rotor diameter.

[0061] In this embodiment, a wind turbine refers to a wind turbine generator. The wind farm parameter set includes the surface roughness height z of the wind farm. 0,1 Wind turbine hub height z h Wind turbine thrust coefficient C T Lateral spacing s between wind turbine units y D. Flow spacing s between wind turbine units y D. Lateral staggered spacing between wind turbine units (s) ye D and the rotor diameter of the wind turbine. The spacing between wind turbine units can refer to the directional spacing, lateral spacing, and lateral staggered spacing between multiple wind turbines in a wind farm. directional spacing refers to the distance between two adjacent rows of wind turbines along the wind direction; lateral spacing is perpendicular to the directional spacing in the horizontal plane and refers to the distance between two adjacent rows of wind turbines; lateral staggered spacing is in the same direction as the lateral spacing and refers to the lateral spacing between two adjacent rows of wind turbines in the same row. Figure 2 As shown, Figure 2 The arrangement shown is for illustrative purposes only and is not intended to limit the construction layout of this disclosure to only one type. Figure 2 The arrangement shown is as follows. One construction layout corresponds to one wind turbine spacing.

[0062] In this embodiment, the target flow field inhomogeneity factor needs to be solved iteratively, and the specific operations include:

[0063] The first step is to determine the target wake velocity among multiple wind turbines based on the initial wake recovery rate and the target wind turbine wake model. First, the wake velocity of an individual wind turbine in the wind farm needs to be determined using the target wind turbine wake model.

[0064]

[0065]

[0066] Where r0 is the radius of the wind turbine rotor, and (x,y) are the coordinates of the wind turbine in the wind farm, x t Let y be the current wind turbine's direction coordinate. t This represents the horizontal coordinate of the current wind turbine. This represents the width of the wake at the current position; wake loss beyond this width is considered zero. ∞γ represents the average velocity at the hub height when there is no wind turbine, and γ is the wake area correction parameter. The target wind turbine wake model refers to the corrected Jensen wake model. The initial wake recovery rate k0 in the first iteration can be estimated as:

[0067] k0=κ / ln(z h / z 0,1 )

[0068] Among them, z h For the height of the wind turbine hub, z 0,1 This refers to the surface roughness height of the wind farm.

[0069] Then, using the sum of squares and the wake loss superposition method, the target wake velocity among multiple wind turbines is determined by the wake velocity of a single wind turbine and the spacing between wind turbine units:

[0070]

[0071] Where T represents the number of upstream wind turbines and the number of upstream mirror wind turbines symmetrical about the ground, and the arrangement of the mirror wind turbines is as follows: Figure 3 As shown.

[0072] The second step is to determine two average velocity relationships based on the target wake velocities among multiple wind turbines:

[0073]

[0074]

[0075] Among them, U d U represents the average velocity at the rotor of the wind turbine. h Let L be the average velocity at the hub height of the wind turbine, L be the boundary line between the rotor plane and the xy section at the hub height, and Ω be the area occupied by a single wind turbine. The integration region is as follows: Figure 4 As shown.

[0076] Thirdly, based on the two average velocity relationships, we can obtain the non-uniformity factor β of the transition flow field. * :

[0077]

[0078] The fourth step is based on the transition flow field inhomogeneity factor β. * Determine the equivalent roughness height z of the wind farm under the current wind turbine spacing. 0,2 :

[0079]

[0080]

[0081]

[0082] in This is the estimated eddy viscosity coefficient of the wind turbine wake layer.

[0083] Fifth, based on the equivalent roughness height of the wind farm, the surface roughness height, and the atmospheric boundary layer height, determine the average velocity transition formula:

[0084]

[0085] Where δ is the height of the atmospheric boundary layer, for example, it can be 400 to 1000 m.

[0086] Step 6: Based on the average velocity transition relationship and the average velocity relationship among multiple wind turbines, the transition wake recovery rate is solved inversely.

[0087]

[0088]

[0089] Step 7: Determine if the wake recovery rate converges. If the difference between the transition wake recovery rate and the initial wake recovery rate is greater than a preset threshold, the transition wake recovery rate is determined as the new initial wake recovery rate. Repeat steps 1 to 6 above to recalculate the new transition wake recovery rate based on the new initial wake recovery rate. If the difference between the transition wake recovery rate and the initial wake recovery rate is less than or equal to a preset threshold, the transition wake recovery rate is determined as the target wake recovery rate, and the new transition flow field inhomogeneity factor is determined as the target flow field inhomogeneity factor. The preset threshold can be set according to the construction location of the wind farm; for example, it can be set to 10. -5 .

[0090] In operation S102, the corrected geostrophic drag coefficient is determined based on atmospheric boundary layer parameters.

[0091] In this embodiment, the atmospheric boundary layer parameters characterize the gravitational acceleration g, the temperature gradient Γ of the inversion layer, the atmospheric reference temperature θ0, and the Coriolis force parameter f; the corrected geostrophic drag coefficients refer to A(Zi) and B(Zi), and their specific expressions are as follows:

[0092] A(Zi)=1.54+0.18ln(Zi), B(Zi)=1.74+0.011Zi.

[0093] This is the Zilitinkevich constant.

[0094] In operation S103, for each type of wind turbine spacing, based on the target flow field inhomogeneity factor and the corrected geostrophic drag coefficient in the atmospheric boundary layer, the average velocity value at the hub height of the wind farm under the wind turbine spacing of the construction layout is determined using the analytical model of the wind farm.

[0095] In this embodiment, the analytical model of the wind farm refers to:

[0096]

[0097] Where κ represents the von Kármán constant; G represents the geostrophic velocity; u *,1 u *,2 These respectively characterize the surface friction velocity and the equivalent friction velocity of the wind farm; z 0,1 Characterizing the known surface roughness height; z 0,2 The equivalent roughness height of the unknown wind farm is represented by A(Zi) and B(Zi), which are both corrected geostrophic drag coefficients. h Characterizing the height of the wind turbine hub; U h β represents the average velocity at the hub height across the entire field; β represents the non-uniformity factor of the target flow field; c ft =πC T / (4s x s y ), C T Characterizing the thrust coefficient of a wind turbine; s x =S x / D,S x The airflow spacing between wind turbine units is represented by D, and the rotor diameter of the wind turbine is represented by s. y =S y / D,S y The empirical constant a represents the lateral spacing between wind turbine units. u =4.3, where f is the Coriolis force parameter. Where (u *,1 ,u *,2 ,z 0,2 U h The variable is denoted as , and the others are input parameters. By iteratively solving the four equations in the analytical model of the wind farm, the average velocity at the hub height across the entire wind farm, based on the turbine spacing, can be determined. The `fsolve` function in Matlab can be used to iteratively solve the analytical model of the wind farm.

[0098] In operation S104, the power generation per unit area of ​​the wind farm under the wind turbine spacing is determined based on the spacing between each type of wind turbine and the average speed value at the hub of the entire field.

[0099] In this embodiment, the average velocity U at the wind turbine rotor can be determined based on the average velocity at the hub, the axial flow induction factor of the wind turbine, and the target flow field non-uniformity factor.d :

[0100] U d =β(1-a)U h ,

[0101] In the embodiment, based on the average speed U at the wind turbine rotor d Earth rotation speed G, wind turbine spacing s x D、s y Given D and the footprint S of the wind turbines, determine the power generation per unit area P of the wind farm under the given wind turbine spacing and construction layout. + :

[0102]

[0103] Where ρ is the air density, C' T Corrected wind turbine thrust coefficient:

[0104]

[0105] In operation S105, the unit cost output power corresponding to the construction layout is determined based on the unit area power generation under the spacing of wind turbine units and the construction cost of the wind farm.

[0106] In this embodiment, the construction cost of a wind farm may include the equipment cost and land cost for each wind turbine. The equipment cost may include, but is not limited to, the purchase cost and installation cost of the wind turbine. The land cost may include, but is not limited to, the price of the land itself and the cost of building materials.

[0107] Based on the swept area of ​​the wind turbine rotor and the construction cost of each wind turbine, the cost coefficient α for each wind turbine is determined:

[0108]

[0109] A = πD 2 / 4,

[0110] Among them, cost T Cost represents equipment cost. L A represents the land cost, A represents the swept area of ​​the wind turbine rotor, α is the cost coefficient, and D is the diameter of the wind turbine rotor.

[0111] Based on the cost coefficient α and the corrected wind turbine thrust coefficient C' T Wind turbine spacing s x s y Power generation per unit area P at the spacing of wind turbine units + Determine the unit cost output power P * :

[0112]

[0113] S = s x s y D 2 ,

[0114] Where S is the footprint of a single wind turbine, s x D and s y D represents the flow spacing and the lateral spacing, respectively; P + U is the power generation per unit area. d G is the average speed at the rotor of the wind turbine, and G is the Earth's rotation speed.

[0115] In operation S106, iterate through all the wind turbine spacing parameters in the wind farm parameters, repeat operations S101 to S105 until the unit cost power generation of the wind farm under all construction layouts is determined, and the turbine spacing corresponding to the maximum unit cost power generation is obtained through iteration.

[0116] In this embodiment, due to the highly efficient analytical model used, it is possible to obtain the unit cost power generation of the wind farm under all wind turbine spacings using an traversal method. A first power generation efficiency curve is constructed based on multiple unit cost output powers corresponding to different wind turbine spacings. Based on the first power generation efficiency curve, the wind turbine spacing corresponding to the maximum unit cost output power is determined as the first target wind turbine spacing.

[0117] Example 1: Determining the spacing between wind farm turbines in an aligned arrangement.

[0118] Figure 5 The diagram illustrates a construction layout of an aligned wind farm according to an embodiment of the present disclosure. Figure 6 The diagram illustrates the variation curve of the flow field non-uniformity factor in an aligned wind farm according to an embodiment of the present disclosure. Figure 7 The diagram illustrates a comparison between the unit cost output power of an aligned wind farm according to an embodiment of the present disclosure and the prediction results of large eddy simulation. Figure 8 The diagram illustrates the relationship between the optimal and suboptimal spacing of wind turbines and the cost coefficient under aligned arrangement according to embodiments of the present disclosure.

[0119] In one exemplary embodiment, for example, Figure 5 The layout of a wind farm with aligned wind turbines is optimized, assuming that the lateral spacing between wind turbines is equal to the flow spacing. x =s y =s, the lateral staggered spacing between wind turbines ye =0, wind turbine hub height z h =100m, wind turbine rotor diameter D=100m, surface roughness z0,1 =0.1m, geostrophic wind speed G = 18.68m / s, Coriolis force parameter f = 9.34×10 -5 s -1 The temperature gradient of the inversion layer is Γ = 1 K / km, and the axial flow induction factor of the wind turbine is a = 0.25.

[0120] Set the spacing s between wind turbines x ∈[3,40], initial wake recovery rate k0=κ / ln(z h / z 0,1 The initial boundary layer height δ0 = 400m. Using the method disclosed herein, the variation trend of the flow field inhomogeneity factor under different wind turbine spacings can be determined, such as... Figure 6 As shown. To improve computational efficiency, the calculated flow field non-uniformity factor is fitted, and the fitting curve is shown in formula (1):

[0121] β=1-2.719exp(-0.241(s+15.19)), (1)

[0122] Set the spacing s between wind turbines x Given ∈[3,40], and the flow field non-uniformity factor and the corrected geostrophic drag coefficient under the corresponding construction layout, we can obtain formula (2). Solving formula (2) will yield the average velocity U at the hub height of the wind turbine under different construction layouts. h :

[0123]

[0124] Based on the average velocity at the hub of the entire wind farm, the axial flow induction factor of the wind turbine, and the non-uniformity factor of the target flow field, the power generation per unit area P of the wind farm under different construction layouts is obtained. + :

[0125]

[0126] Based on the different equipment and land costs of individual wind turbines (i.e., different α), and the power generation per unit area of ​​wind farms under different construction layouts, the first power generation efficiency curve P of the wind farm's unit cost output power versus different wind turbine spacing is calculated. * =P * (s).

[0127] The unit cost output power results calculated in this disclosure were verified using the high-precision Large Eddy Simulation (LES) method, such as... Figure 7 As shown, Figure 7 In this context, "Model" refers to the unit cost output power obtained by the method of this disclosure. Figure 7It can be seen that the optimal spacing of wind farms varies significantly under different cost coefficients α. The influence of thermal stability on the optimal and suboptimal spacing s was then calculated, where the suboptimal spacing refers to the minimum spacing between wind turbine units when the unit cost power reaches 90% of the optimal power. Figure 8 As shown, Figure 8 In this context, "thermal" indicates the wind farm turbine spacing determined by the method of this disclosure after considering thermal stability, while "neutral" indicates the wind farm turbine spacing determined without considering thermal stability. With a relatively large cost coefficient α, considering only the thermal stratification effect of the atmospheric boundary layer, the optimal and second-optimal spacing of wind farms can be reduced by 10% compared to a neutral atmospheric boundary layer. This means that the size of the wind farm can be reduced by approximately 20%, allowing for denser arrangement of wind turbines, less land occupation, and lower grid connection costs and resistance losses.

[0128] Example 2: Determining the spacing between wind farm turbines in a staggered arrangement.

[0129] Figure 9 A schematic diagram of an alternating construction layout according to an embodiment of the present disclosure is shown. Figure 10 A schematic diagram illustrating the unit cost output power according to an embodiment of the present disclosure is shown.

[0130] In another exemplary embodiment, for example, Figure 8 The layout of a wind farm with staggered wind turbines, as shown, is optimized, assuming that the lateral spacing between wind turbines is equal to the flow-direction spacing. x =s y =s, the lateral staggered spacing between wind turbine units ye =s / 2, wind turbine hub height z h =100m, wind turbine rotor diameter D=100m, surface roughness z 0,1 =0.1m, geostrophic wind speed G = 18.68m / s, Coriolis force parameter f = 9.34×10 -5 s -1 Temperature gradient of inversion layer Γ=10K / km, axial flow induction factor of wind turbine a=0.25, initial wake recovery rate k0=κ / ln(z h / z 0,1 The boundary layer height δ0 = 700m. The final predicted curve of unit cost output power as a function of different wind turbine spacing is attached. Figure 10 As shown.

[0131] During the optimization process described above, it can be seen that the thermal stratification effect of the free atmosphere has a significant impact on the power output of the wind farm. Compared with the case where the thermal stratification effect is not considered, the presence of the thermal stratification effect will significantly reduce the spacing between wind turbines in the wind farm. This allows the wind farm to be smaller in size while maintaining a high power output, the wind turbines to be arranged more densely, the land occupation to be less, and the cost of grid connection and resistance loss to be lower.

[0132] According to embodiments of this disclosure, through optimization tests of wind farm construction layouts with aligned and staggered arrangements, it was found that the method of this disclosure can simultaneously consider the thermal stratification effect of the free atmosphere, the construction layout of the wind farm, and the economic constraints faced by the wind farm during operation. The resulting wind turbine layout can take into account both the costs incurred in the early stage of wind farm construction and the economic income from the later generation of wind farm power. This not only reduces the size of the wind farm but also ensures a high power output of the wind farm, thereby improving the overall economic benefits of the wind farm.

[0133] The flowcharts and block diagrams in the accompanying drawings illustrate methods according to various embodiments of this disclosure. Those skilled in the art will understand that the features recited in the various embodiments and / or claims of this disclosure can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly stated in this disclosure. In particular, the features recited in the various embodiments and / or claims of this disclosure can be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0134] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this disclosure is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A method for determining the spacing between wind farm turbines considering the influence of thermal stability, characterized in that, include: Step 1: Determine the target flow field non-uniformity factor for each wind turbine spacing based on the wind farm parameter set, wherein the wind farm parameter set includes the surface roughness height of the wind farm, the wind turbine hub height, the wind turbine thrust coefficient, the lateral spacing between wind turbines, the flow direction spacing between wind turbines, the lateral staggered spacing between wind turbines, and the wind turbine rotor diameter. Step 2: Determine the corrected geostrophic drag coefficient based on atmospheric boundary layer parameters; Step 3: For each type of wind turbine spacing, based on the target flow field inhomogeneity factor and the corrected geostrophic drag coefficient in the atmospheric boundary layer, use the analytical model of the wind farm to determine the average velocity value at the hub height of the wind farm under the wind turbine spacing of the construction layout. Step 4: Based on the spacing between each wind turbine and the average speed at the hub of the entire wind farm, determine the power generation per unit area of ​​the wind farm under the specified wind turbine spacing in the construction layout. Step 5: Determine the unit cost output power corresponding to the construction layout based on the unit area power generation power under the wind turbine spacing and the construction cost of the wind farm; Step 6: Traverse all wind turbine spacing parameters in the wind farm, repeating steps 1 to 5 until the unit cost power generation of the wind farm under all construction layouts is determined, and the turbine spacing corresponding to the highest unit cost power generation efficiency is determined as the first target turbine spacing.

2. The method according to claim 1, characterized in that, In step 1, the target flow field non-uniformity factor for each wind turbine spacing is iteratively solved based on the wind farm parameter set. The iterative steps include: The first step is to determine the target wake velocity among the multiple wind turbines based on the initial wake recovery rate and the target wind turbine wake model; Step 2: Based on the target wake velocity deficit, the first integration region L, and the second integration region Ω, determine two average velocity relationships, where the two average velocity relationships represent the average velocity U at the wind turbine rotor. d Average speed U at the height of the wind turbine hub h The first integration region L is determined based on the plane of the wind turbine rotor and the plane where the wind turbine hub height is located, and the second integration region Ω is determined based on the ground area occupied by the wind turbine. Step 3: Determine the non-uniformity factor of the transition flow field based on the two average velocity relationships shown below: Step 4: Determine the equivalent roughness height z of the wind farm based on the aforementioned transition flow field inhomogeneity factor. 0,2 ; Step 5: Based on the equivalent roughness height of the wind farm, the surface roughness height, and the atmospheric boundary layer height, determine the average velocity transition formula, where the average velocity transition formula characterizes the average velocity U at the wind turbine hub height. * h The average speed U at the hub height compared to when there is no wind turbine ∞ The ratio of, where It is only related to the recovery rate of the wake; Step 6: Based on the average velocity transition relationship and the target wind turbine wake model shown below, solve for the transition wake recovery rate: Step 7: If the difference between the transition wake recovery rate and the initial wake recovery rate is greater than a preset threshold, the transition wake recovery rate is determined as the new initial wake recovery rate so that the new transition wake recovery rate can be recalculated based on the new initial wake recovery rate. If the difference between the transition wake recovery rate and the initial wake recovery rate is less than or equal to the preset threshold, the transition wake recovery rate is determined as the target wake recovery rate, and the transition flow field inhomogeneity factor at this time is determined as the target flow field inhomogeneity factor.

3. The method according to claim 1, characterized in that, In step 2, the atmospheric boundary layer parameters include gravitational acceleration, inversion layer temperature gradient, atmospheric reference temperature, and Coriolis force parameters. The corrected geostrophic drag coefficients are characterized by A(Zi) and B(Zi), where Zi is the Zilitinkevich constant. g is the gravitational acceleration, Γ is the temperature gradient of the inversion layer; θ0 is the reference temperature, f is the Coriolis force parameter; the specific expressions for A(Zi) and B(Zi) are: A(Zi)=1.54+0.18ln(Zi), B(Zi)=1.74+0.011Zi.

4. The method according to claim 1, characterized in that, In step 3, the analytical model of the wind farm is: Where κ represents the von Kármán constant; G represents the geostrophic velocity; u *,1 u *,2 These respectively characterize the surface friction velocity and the equivalent friction velocity of the wind farm; z 0,1 Characterizing the known surface roughness height; z 0,2 The equivalent roughness height of the unknown wind farm is represented by A(Zi) and B(Zi), which are both corrected geostrophic drag coefficients. h Characterizing the height of the wind turbine hub; U h The average velocity at the hub height across the entire field is characterized by β; the non-uniformity factor of the target flow field is characterized by β; c ft =πC T / (4s x s y ), C T Characterizing the thrust coefficient of a wind turbine; s x =S x / D,S x The airflow spacing between wind turbine units is represented by D, and the rotor diameter of the wind turbine is represented by s. y =S y / D,S y The empirical constant a represents the lateral spacing between wind turbine units. u =4.3, where f is the Coriolis force parameter; By iteratively solving the analytical model, the average velocity value at the hub height of the entire wind farm under the specified wind turbine spacing is determined.

5. The method according to claim 1, characterized in that, Step 5, after determining the power generation per unit area, further includes: Based on the power generation per unit area under the wind turbine spacing and the construction cost of the wind farm, the unit cost output power corresponding to the construction layout is determined, wherein the construction cost includes the equipment cost of each wind turbine and the land cost occupied by each wind turbine, and wherein one construction layout corresponds to one wind turbine spacing; The step of determining the unit cost output power corresponding to the construction layout based on the unit area power generation power under the wind turbine spacing and the construction cost of the wind farm includes: The cost coefficient of each wind turbine is determined based on the swept area of ​​the wind turbine rotor and the construction cost of each wind turbine; the unit cost output power is determined based on the cost coefficient, the corrected wind turbine thrust coefficient, the spacing between wind turbine units, and the power generation per unit area.

6. The method according to claim 1, characterized in that, Step 6 includes: Traverse all the wind turbine unit spacings under the construction layout, repeat steps 1 to 5 to obtain the corresponding multiple unit cost output powers, and construct a first power generation efficiency curve; based on the first power generation efficiency curve, determine the wind turbine unit spacing corresponding to the maximum unit cost output power as the first target wind turbine unit spacing.

7. The method according to claim 2, characterized in that, The first step includes: The wake velocity of a single wind turbine in the wind farm is determined using a target wind turbine wake model. To characterize; then determine the target wake velocity among multiple wind turbines by using the wake velocity of a single wind turbine, using The initial wake recovery rate is determined based on the wind turbine hub height, and the target wind turbine wake model is determined based on the wake area correction parameter and the Jensen model. The method for determining the target wake velocity among multiple wind turbines by using the wake velocity of a single wind turbine is as follows: Where (x,y) are the coordinates of the wind turbines in the wind farm, x t Let U be the current wind turbine's direction coordinates, where U ∞ The average speed at the hub height when there is no wind turbine is denoted by , and T is the number of upstream wind turbines and the number of upstream mirror wind turbines with the ground as the plane of symmetry.

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