Accurate energy calculations are critical in wind power engineering. Improving the precision of output estimation can help to improve the precision of investment return expectations. Wind resource engineers must select a suitable wake model based on the characteristics of different wind farm terrain environments when calculating energy, and when the wake model performs simulation calculations of energy, ground roughness is a very dependent parameter. As a result, in the same simulation environment, a high-precision land cover map can improve the wake model’s calculation accuracy.
The Yingchen wind farm, which has been connected to the grid, is chosen as the actual measurement project in this paper. According to this project’s feasibility study report (FSR), the Openwind [
35] wind farm design software is also used for modeling, the WindMap [
36] wind flow model is used to calculate the wind flow field, and the Eddy-Viscosity wake model is used to calculate energy. The initial data uses the same wind measurement data, surveying and measured topographic map, and the same uncertainty table. On this basis, the roughness length is calculated using EAS land cover data, and the energy is calculated using the Deep Array EV wake model and the ASM-EV wake model. It should be noted that the wake model’s general parameters use the same settings, while the non-general parameters use the default parameters without modification. The experiment’s energy data is compared to the wind farm feasibility study report data and the wind farm’s actual operation data. On one hand, it confirms that WorldCover data can be used in the wind power industry. On the other hand, it compares the errors of different wake models. The flowchart process will be used for verification in this paper (
Figure 4).
3.1. Wake Model
The Eddy-Viscosity wake model (EV) [
37] is a linear CFD calculation that calculates the wake of an axisymmetric structure wind turbine using the time-averaged Navier–Stokes equations (RANS). The model employs cylindrical coordinates and assumes incompressible airflow.
The Eddy-Viscosity wake model automatically observes mass and momentum conservation in the wake. The average Eddy-Viscosity of each downstream wake segment is used to calculate the wind-turbulence interaction. The wake in the Eddy-Viscosity model has a Gaussian distribution, and its recovery depends on the turbulence intensity. The more turbulence there is, the more the wake wind mixes with the free wind around it, and the wake travels and recovers faster [
33]. Its equation for calculation is as follows:
where
represents the average free stream wind speed,
v represents the wind speed at a distance r from the wake centerline,
represents the initial wind speed attenuation at the wake centerline, and b represents the wake width parameter, and the equation is as follows:
where
is related to thrust coefficient
and turbulence intensity, the expression is as follows:
where
is the ambient turbulence intensity (%).
The Eddy-Viscosity wake model was used to calculate the energy in the feasibility study.
Figure 5 depicts the Eddy-Viscosity wake model simulating the wake behind a single wind turbine, which employs a Gaussian distribution to improve the prediction of the wake velocity deficit, and is run by Openwind. The X-axis in the figure is a multiple of the wind turbine impeller’s diameter(D), and the background free wind speed is 10 m/s, which is displayed in red. The legend assumes that the background wind speed is 1(100%), and different colors correspond to different multiples of that speed.
The Deep Array Eddy-Viscosity wake model (DAWM-EV) [
38] is a modification and improvement of the Eddy-Viscosity wake mode, a coupling model based on Sten Frandsen’s theory. Deep Array and Eddy-Viscosity are separately modeled in the DAWM model and combined by taking the maximum value of roughness influence and basic wake influence (background roughness is obtained by reading the imported rough map).
An infinite array of wind turbines is represented as a uniform region of high surface roughness in Frandsen’s theory. The roughness drags on the atmosphere, causing changes in the structure of the planetary boundary layer (PBL) downstream, most notably a decrease in free-stream wind speed at turbine hub height. According to this theory, the equivalent roughness of the wind farm is:
where
is the hub height,
k is the von Karman constant (about 0.4),
is the ambient roughness between turbines, and
is the distributed thrust coefficient,
where
is the thrust coefficient,
is the mean downwind spacings in rotor diameters and
is the mean crosswind spacings in rotor diameters.
Assume that each wind turbine occupies a distinct area that contributes to increased surface roughness. Increased roughness creates the internal boundary layer as the wind reaches the wind turbine. The wind width line or shear in this internal boundary layer is defined by the wind turbine roughness rather than the ambient roughness, and the velocity at the top of the internal boundary layer must immediately match the velocity above it. After the wind has passed through the wind turbine, a second internal boundary layer will form to indicate the transition back to the environment’s surface. Both internal boundary layers grow with downstream distance, according to the following equation.
In this equation, represents the height of the internal boundary layer, x represents the distance generated by the internal boundary layer, and represents the downstream roughness (wind turbine roughness for the first internal boundary layer and ambient roughness for the second internal boundary layer). The downstream wind turbine produces its own internal boundary layer under the upstream wind turbine.
Once the equivalent roughness is defined, the meteorological theory is used to estimate the impact on the hub-height wind speed deep within the array (i.e., where the PBL has reached equilibrium with the array roughness) under the assumption of a constant geostrophic wind speed G and a neutral logarithmic profile throughout the PBL. Taking only the first turbine’s IBL pair and assuming that both IBLs have grown to exceed hub height, the equation for hub-height speed is as follows:
is the wind speed of the wind turbine hub height downstream of the wind farm, is the wind speed of the upstream wind turbine hub height, h1 and h2 are the heights of the first and second internal boundary layers, respectively, and and are the roughness of the wind turbine and the environment (background).
Figure 6 depicts the wake behind a single wind turbine as simulated by the Deep Array EV wake model, which predicts wake velocity deficits using a Gaussian distribution in the near-wake region and a linear extension in the far-wake region, and it is run by Openwind. The X-axis in the figure is a multiple of the wind turbine impeller’s diameter(D), and the background-free wind speed is 10 m/s, which is displayed in red. The legend assumes that the background wind speed is 1(100%), and different colors correspond to different multiples of that speed.
The Area Slowdown Eddy-Viscosity wake model (ASM-EV) [
39] considers the wind farm as a whole. The wind farm is related to the inversion layer at the top of the atmospheric boundary layer as additional surface roughness and as a gravity wave generator, which means that even though the wind speed of the atmospheric boundary layer above the wind field is uniform, it is very sensitive to the decrease of the lower wind speed and the decrease of energy, so there will be changes in the pressure gradient and the generation of gravity waves. The model calculates the interaction force between the atmosphere and wind farm based on the conservation of kinetic energy and the above-influencing factors, which is a top-down simulation method of fluid kinetic energy. The basic equation is:
where
is the free wind speed of the upstream wind turbine at hub height,
v is the wind speed of the downstream wind turbine at hub height.
where z is PBL’s height, h is wind turbine hub height,
= z − h,
is the friction velocity.
The ASM EV wake model’s single wake wind speed is depicted in the figure below (
Figure 7), which ran by Openwind. The X-axis in the figure is a multiple of the wind turbine impeller’s diameter(D), and the background free wind speed is 10 m/s, which is displayed in red. The legend assumes that the background wind speed is 1 (100%), and different colors correspond to different multiples of that speed.