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Performance of the Wind Farm Parameterization Scheme Coupled with the Weather Research and Forecasting Model under Multiple Resolution Regimes for Simulating an Onshore Wind Farm


doi: 10.1007/s00376-018-8028-3

  • We use the Wind Farm Parameterization (WFP) scheme coupled with the Weather Research and Forecasting model under multiple resolution regimes to simulate turbulent wake dynamics generated by a real onshore wind farm and their influence at the local meteorological scale. The model outputs are compared with earlier modeling and observation studies. It is found that higher vertical and horizontal resolutions have great impacts on the simulated wake flow dynamics. The corresponding wind speed deficit and turbulent kinetic energy results match well with previous studies. In addition, the effect of horizontal resolution on near-surface meteorology is significantly higher than that of vertical resolution. The wake flow field extends from the start of the wind farm to downstream within 10 km, where the wind speed deficit may exceed 4%. For a height of 150 m or at a distance of about 25 km downstream, the wind speed deficit is around 2%. This indicates that, at a distance of more than 25 km downstream, the impact of the wind turbines can be ignored. Analysis of near-surface meteorology indicates a night and early morning warming near the surface, and increase in near-surface water vapor mixing ratio with decreasing surface sensible and latent heat fluxes. During daytime, a slight cooling near the surface and decrease in the near-surface water vapor mixing ratio with increasing surface sensible and latent heat fluxes is noticed over the wind farm area.
    摘要: 利用耦合了风电场拖曳参数化(WFP)方案的WRF模式, 探究不同水平与垂直分辨率下模式对昌邑风电场湍流尾流动力过程的模拟表现, 以及对局地天气尺度系统的影响. 结果表明: 空间分辨率对尾流模拟效果影响较大, 其中水平分辨率对近地面气象要素的影响显著高于垂直分辨率, 高分辨率模拟得到的风速损耗和湍流动能与前人研究更为吻合; 沿风传播方向, 距风机组不同距离风速损耗不同, 其中10 km内尾流造成的总损耗可超过4%, 25km内总损耗降至2%, 说明风机尾流效应的影响范围在25km以内; 70 m风机的尾流影响高度在150m以下; 尾流动力过程导致夜晚至次日凌晨近地面气温升高, 地表感热通量和潜热通量减小, 水汽混合比增加; 白天, 随着地表感热通量和潜热通量的增大, 近地面温度略微下降, 水汽混合比减小.
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Manuscript received: 27 January 2018
Manuscript revised: 29 August 2018
Manuscript accepted: 25 September 2018
通讯作者: 陈斌, bchen63@163.com
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Performance of the Wind Farm Parameterization Scheme Coupled with the Weather Research and Forecasting Model under Multiple Resolution Regimes for Simulating an Onshore Wind Farm

    Corresponding author: Zhenhai GUO, gzh@mail.iap.ac.cn
  • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. Nansen-Zhu International Research Centre, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

Abstract: We use the Wind Farm Parameterization (WFP) scheme coupled with the Weather Research and Forecasting model under multiple resolution regimes to simulate turbulent wake dynamics generated by a real onshore wind farm and their influence at the local meteorological scale. The model outputs are compared with earlier modeling and observation studies. It is found that higher vertical and horizontal resolutions have great impacts on the simulated wake flow dynamics. The corresponding wind speed deficit and turbulent kinetic energy results match well with previous studies. In addition, the effect of horizontal resolution on near-surface meteorology is significantly higher than that of vertical resolution. The wake flow field extends from the start of the wind farm to downstream within 10 km, where the wind speed deficit may exceed 4%. For a height of 150 m or at a distance of about 25 km downstream, the wind speed deficit is around 2%. This indicates that, at a distance of more than 25 km downstream, the impact of the wind turbines can be ignored. Analysis of near-surface meteorology indicates a night and early morning warming near the surface, and increase in near-surface water vapor mixing ratio with decreasing surface sensible and latent heat fluxes. During daytime, a slight cooling near the surface and decrease in the near-surface water vapor mixing ratio with increasing surface sensible and latent heat fluxes is noticed over the wind farm area.

摘要: 利用耦合了风电场拖曳参数化(WFP)方案的WRF模式, 探究不同水平与垂直分辨率下模式对昌邑风电场湍流尾流动力过程的模拟表现, 以及对局地天气尺度系统的影响. 结果表明: 空间分辨率对尾流模拟效果影响较大, 其中水平分辨率对近地面气象要素的影响显著高于垂直分辨率, 高分辨率模拟得到的风速损耗和湍流动能与前人研究更为吻合; 沿风传播方向, 距风机组不同距离风速损耗不同, 其中10 km内尾流造成的总损耗可超过4%, 25km内总损耗降至2%, 说明风机尾流效应的影响范围在25km以内; 70 m风机的尾流影响高度在150m以下; 尾流动力过程导致夜晚至次日凌晨近地面气温升高, 地表感热通量和潜热通量减小, 水汽混合比增加; 白天, 随着地表感热通量和潜热通量的增大, 近地面温度略微下降, 水汽混合比减小.

1. Introduction
  • Wind power is a growing industry all over the world. Currently, it supplies more than 4% of the world's electricity demand (Global Wind Energy Council, 2018), with a target to supply 15%-18% by 2050 (IEA, 2013). China is the leading country, with an installation capacity of 188 232 MW, accounting for more than 4% of the national electrical energy demand (Global Wind Energy Council, 2018), with a target to meet 17% of the national electricity consumption by the end of 2050 (IEA, 2011).

    Despite the debate concerning the likely possible effects of wind farms on regional and global meteorology (Zhou et al., 2012), observation and modeling studies indicate that they can potentially influence local meteorology by turbulence enhancement and wind speed deficit within and downstream of the wind farm. Currently, however, the ability to know the spatial behavior and scope of their impact is limited by a lack of sufficient direct observations. Moreover, these perturbations are likely to differ substantially with vegetation, topography, atmospheric stability conditions, and the type of wind turbine (Fitch et al., 2013a; Vanderwende et al., 2016). Therefore, modeling techniques have become a valuable research tool to examine the impacts of wind farms at local and regional levels.

    Earlier studies used three different methods to numerically represent wind farms in atmospheric models. In all approaches, wind farms are parameterized as subgrid-scale features due to the complex nature of wake flow dynamics induced by wind turbine rotor blades while the spatial grid spacing of numerical models is too coarse (Baidya Roy, 2011). The first method includes the representation of the wind farm as an increasing surface roughness length within the grid cells of global climate models (Ivanova and Nadyozhina, 2000; Adams and Keith, 2007; Kirk-Davidoff and Keith, 2008; Wang and Prinn, 2010, Wang and Prinn, 2011). The main challenge of this method is the choice of a suitable value of the aerodynamic surface roughness length for a wind farm.

    The second method to simulate wind farms involves large-eddy simulation (LES). This method has been used to study the influence of the stability condition on the wake flow induced by wind farms (Lu and Porté-Agel, 2011; Aitken et al., 2014), the impact of wind farm wake flow on surface fluxes (Calaf et al., 2011), wake turbulence dynamics (Jiménez et al., 2007), and the Generalized Actuator Disk wind turbine parameterization scheme (Mirocha et al., 2014). Despite the fact that LES is effective in the complex interaction of individual wind turbines and the atmospheric boundary layer, it is currently too computationally expensive to be used to model a large wind farm and its consequent turbulent wake flow far downstream from the wind farm (Churchfield et al., 2012; Fitch et al., 2013a).

    The third method involves representing wind farms as elevated momentum sinks and turbulent kinetic energy (TKE) sources within the model grid cells, and has recently gained popularity. In this technique, the elevated drag forces and turbulence generation are quantified using the power curve. TKE is either directly added by the parameterization scheme (Blahak et al., 2010; Fitch et al., 2012) or indirectly induced by vertical shear within the wind turbine rotor disc (Baidya Roy et al., 2004; Jacobson and Archer, 2012; Abkar and Porté-Agel, 2015).

    The Wind Farm Parameterization (WFP) scheme was created using the third technique by (Fitch et al., 2012) and is publicly available in the Weather Research and Forecasting (WRF) model. A wind farm in WFP is handled as an elevated sink of the resolved atmospheric momentum in the vertical levels of the wind turbine rotor region. This scheme has been used in the past to perform research related to wind power generation (Eriksson et al., 2015; Jiménez et al., 2015; Lee and Lundquist, 2017) and its meteorological impact on local and regional levels (Fitch et al., 2013a, Fitch et al., 2013b; Vanderwende et al., 2016).

    Despite WFP having wide applications, few validations of the model outputs have been carried out (Eriksson et al., 2015; Jiménez et al., 2015; Lee and Lundquist, 2017). The cause for limited validation studies can be attributed to the difficulty in obtaining observational data from operational wind farms (Vanderwende et al., 2016). Measurement coverage is needed over the whole wind farm, as big wind farms can have distinctive features not found in small arrays. For this reason, different studies have drawn different conclusions from the application of WFP. For instance, (Cervarich et al., 2013), in their assessment of WRF-WFP with satellite data on surface temperature, showed that WFP can reproduce the spatial patterns of the wake effects, but that they are weaker in magnitude. However, in contrast, a study of large wind farm simulations by WFP with neutral LES conducted by (Abkar and Porté-Agel, 2015) revealed that WFP is able to accurately represent wakes generated from several wind turbine configurations.

    Several modeling studies have indicated that the degree of capturing the magnitude and rate of recovery of simulated turbulent wakes and its resulting meteorological impact can vary significantly with grid spacing (Eriksson et al., 2015; Jiménez et al., 2015; Vanderwende et al., 2016). By using data from the CWEX-13 campaign, (Lee and Lundquist, 2017) evaluated WFP in a range of atmospheric conditions and the role of vertical resolutions. However, little attention has been paid regarding the role of the horizontal resolution, and the behavior of the model in simulating the wake far downstream of the wind farm. Here, we use WFP coupled with the WRF model to simulate the turbulent wake dynamics generated by wind turbines and their influence on local meteorology for a real wind farm located in Changyi, China. In contrast with (Lee and Lundquist, 2017), we employ the effect of both horizontal and vertical resolution and account for the wake effects far downstream of the wind farm. The model is run with different vertical and horizontal resolutions to assess the performance of WFP at multiple resolution regimes. The obtained model outputs are compared with earlier modeling and observation studies to achieve a qualitative evaluation.

    We illustrate the simulation method and model configuration in section 2. In section 3, we discuss the results of the turbulent wake flow dynamics, the impacts of wind farms based on the simulations of WRF-WFP, and the influence of horizontal and vertical resolution on their magnitudes. Finally, the main conclusions of the study are summarized in section 4.

2. Experimental method
  • The WFP scheme was developed by (Fitch et al., 2012) as an extension of the work done by (Blahak et al., 2010). The main difference is that the kinetic energy (KE) harvested from the atmosphere by the rotor blades is computed by the thrust coefficient (C T) which depends on wind speed, rather than the sum of the power coefficient (C P) and the estimated loss factor in Blahak's work. The KE harvested from the atmosphere by the turbine rotor disc is distributed into electrical energy as a quantification of the C P of the turbine, and the remainder is distributed into TKE. The wind turbines are considered to be perpendicular to the airflow, which is exactly the case for most recent turbines. In that case, only the horizontal motion, V=(u,v), is affected by the turbine's drag during the interaction with the atmospheric flow.

    The simplest form of the Reynolds-averaged Navier-Stokes (RANS) momentum equation, which includes the drag force induced by turbines, is given by \begin{eqnarray} \label{eq1} \frac{\partial\langle\bar {u}_i\rangle}{\partial t}+\langle\bar {u}_j\rangle\frac{\partial\langle\bar {u}_i\rangle}{\partial x_j} &=&-\frac{1}{\langle\rho\rangle}\frac{\partial\langle\bar {p}\rangle}{\partial x_i}-2\varepsilon_{i,j,k}\Omega_j\langle\bar {u}_k\rangle-\delta_{i,3}g-\nonumber\\ &&\frac{\partial\langle \overline{u'_iu'_j}\rangle}{\partial x_j}+\langle \overline{f_{\rm wt}}\rangle , \ \ (1)\end{eqnarray} where i,j and k are indices of summation notation (each can take a value of 1, 2 or 3 in x,y and z Cartesian coordinates), the angle brackets denote the volume-average of the variables; ρ, $\bar p$, $\bar u$, and $\overline{u'_iu'_j}$ represent the mean air density, mean pressure, mean velocity components and Reynolds stress components, respectively; Ωj and g are Earth's rotational vector and gravitational acceleration, respectively; εi,j,k and δi,3 are the symbols of Levi-Civita and Kronecker delta, respectively; and $\overline{f_{wt}}$ is the mean forcing term exerted by the action of turbines that act only in the horizontal direction. The Reynolds stress components in Eq. (2) are parameterized by a planetary boundary layer (PBL) scheme as \begin{equation} \label{eq2} \overline{u'_iu'_j}=-K_{\rm m}\frac{\partial\bar {u}_i}{\partial x_j} , \ \ (2)\end{equation} where K m is the eddy diffusivity term, which is quantified by the TKE per unit mass, stability function, and turbulence length scale (Volker et al., 2015). The most general form of the TKE equation is given by \begin{equation} \label{eq3} \frac{\partial\langle\bar {e}\rangle}{\partial t}=-\langle\overline{T_{\rm t}}\rangle- \langle\overline{T_\in}\rangle+\langle\overline{T_{\rm s}}\rangle+\langle\overline{T_{\rm b}}\rangle +\langle\overline{T_{\rm wt}}\rangle , \ \ (3)\end{equation} where $\partial\bar e/\partial t$ denotes the local storage of TKE, $\overline{T_\rm t}$ represents the transport term, $\overline{T_\in}$ represents the dissipation term, $\overline{T_\rm s}$ represents the shear term, $\overline{T_\rm b}$ represents the buoyancy term, and $\overline{T_{wt}}$ represents the TKE induced by the turbine rotor. The WFP scheme coupled with WRF can be used to solve the $\langle\overline{f_{wt}\rangle}$ and $\langle\overline{T_{wt}}\rangle$ induced by wind turbines within the wind farm. The computation of the forcing term and TKE term in WFP is described in detail by (Fitch et al., 2012).

  • The Advanced Research version of the WRF model (ARW) is a dynamical solver of the WRF model consisting of nonhydrostatic and compressible Euler equations discretized on an Arakawa staggered C-grid. As described by (Skamarock et al., 2008), version 3.8.1 of ARW is used to simulate a real onshore wind farm located at (37.093°N, 119.518°E). The wind farm is located on grassland along the coastline of the Bohai Sea in Changyi, China. The altitude of the site is between 0 and 3 m above sea level. The maximum difference in elevation between the wind farm site and its surrounding terrain is less than 10 m. Following (Manwell et al., 2002), for a non-flat terrain, the elevation differences should be greater than 60 m anywhere within 11.5 km diameter around the wind farm. Hence, the terrain of the wind farm in our study can be classified as flat.

    Strong summer low-level jets (LLJs) is a common feature of the Bohai and Yellow seas in eastern China (Li et al., 2018). This feature means the region and its surrounding area is of great importance in terms of wind energy production (Gutierrez et al., 2014). Recently, there has been huge growth in the construction of wind farms along the entire eastern coastline of China. The wind farm in this study is among those constructed along the coastline of the Bohai Sea in Changyi. However, little is known about the influence of these wind farms on the atmospheric boundary layer around the regions they are located. In the absence of field data, the modeling approach is an important tool to study the interaction of wind farms with the atmospheric boundary layer, which may serve as a basis for measurements in the future.

    Simulations are run at multiple resolutions, for which each simulation is labeled accordingly. Five experiments are conducted for the period 0000 UTC 5 July to 0000 UTC 26 July 2014. The first two days are used to allow the model to spin up; the output during this period is excluded from the analysis. Therefore, only the results from 0000 UTC 7 July to 0000 UTC 26 July 2014 are used in the analysis. In each experiment, the onshore wind farm is simulated by WRF-WFP, which we refer to as the Wind Farm (WF) simulation. Another similar simulation, but without including the turbines within the wind farm area, is conducted and referred to as the No-Wind-Farm (NWF) simulation. The model-runs in all experiments are performed for three one-way nested domains. The outer domains serve to capture synoptic scale events and to realize the flow from the boundary data region with a coarser grid resolution towards the inner domain, which covers the entire wind farm area (Fig. 1). A spectral nudging technique, described by (Von Storch et al., 2000) and used by (Telford et al., 2008), (Bowden et al., 2012), (Uhe and Thatcher, 2015) and (Ma et al., 2016), is also used in this study. The nudging is applied to horizontal wind components and potential temperature. The choice of which prognostic variables to nudge is an important aspect of the experimental design. For simplicity, we choose to nudge horizontal wind components and potential temperature for consistency with the nudging approach used by (Telford et al., 2008) and (Uhe and Thatcher, 2015). The nudging adjustment is only applied above the PBL, with a nudging frequency of 0.0003 s-1. The wave number used for all experiments in the zonal and meridional directions is set to a constant value of 3 (Bowden et al., 2012, Liu et al., 2012). The first experiment is performed with 51 vertical levels, 17 of which are below 500 m above the ground and 4 intersect the rotor disc of the turbine, and a 1 km horizontal grid spacing for the innermost nested domain. This experiment is referred to as the control simulation (CNTR). Four additional experiments are also conducted. For the first two experiments, we halve and double the horizontal resolution of CNTR, referred to as HR0.5 and HR2, respectively. The last two experiments have the same horizontal resolution as CNTR, but 81 vertical levels; below 500 m above the ground level there are 27 levels, 6 of which intersect the rotor disc of the turbine. The other experiment has 29 vertical levels; 10 of the levels are under 500 m, 2 of which intersect the rotor disc. These two experiments are referred to as VR6 and VR2, respectively. More configuration details of the domain parameters are summarized in Table 1, and an illustration of the vertical grid resolution in all experiments is presented in Fig. 2.

    Figure 1.  WRF model domains of simulations on the right, with the wind farm area enclosed in the innermost domain. The zoomed Google map on the left-hand side shows the wind farm layout within the wind farm site.

    Figure 2.  Illustration of the three vertical grids chosen: four vertical levels within rotor diameter for CNTR; six vertical levels within rotor diameter for VR6; and two vertical levels within rotor diameter for VR2. HR0.5 and HR2 have the same vertical grids as CNTR. The upper and lower dashed black lines show the upper and lower tips of the rotor disc, respectively.

    The turbines used in this study are based on the C T of SINOVEL SL1500 turbines, with a nominal power output of 1.5 MW, 70 m hub-height, 89.42 m rotor diameter, 3 m s-1 cut-in, 20 m s-1 cut-out, and 11.5 m s-1 rated wind speeds.

    The rotor disc for the wind turbines used in this study span from the height of 25.29 to 114.71 m. A total of 72 wind turbines are present at the wind farm, which covers an area of about 7.4 km × 7.4 km. NCEP Final Analysis reanalysis data are used as an input at the boundaries (Banks et al., 2016). The dataset has a 1°× 1° grid resolution prepared operationally four times a day with 6-h time steps. The data fields are distributed over 26 vertical levels, with the lowest and highest levels at 1000 hPa and 10 hPa, respectively.

    The Mellor-Yamada-Nakanishi-Niino (MYNN) level 2.5 PBL scheme is used (Fitch et al., 2012; Cervarich et al., 2013). This scheme supports TKE advection and active coupling to radiation. The shortwave radiative process is parameterized with the Dudhia scheme, which involves a simple downward integration allowing for efficient cloud and clear-sky absorption and scattering. The longwave radiative transfer is parametrized with the RRTMG scheme, which uses look-up tables accounting for multiple bands, trace gases and microphysical species (de Andrade Campos et al., 2017). All other physical parameterizations used in the study are summarized in Table 2.

3. Results and discussion
  • In this section, we discuss the turbulent wake flow and the impact of wind farms based on WRF-WFP with different horizontal and vertical resolutions. All the results in this study are represented as an average of the 19-day simulation period. The first two days are considered to be a model spin-up period, and therefore excluded from the analysis. Figure 3 indicates frequent south-southwesterly (SSW) winds in both experiments, which account for more than 27% of the proportion for CNTR, 26% for HR0.5, 28% for VR6, 28% for VR2, and 25% for HR2. (Gao et al., 2015) conducted an assessment along the coastline of China (including the Bohai Sea, where the wind farm in this study is located), and showed that the prevaling winds in summer for the entire coast of China are southerly. They used a period of 40-62 years from 12 meteorological sites in their study. (Hainbucher et al., 2004) and (Wang et al., 2008) reported that the Bohai coastline is controlled by eastern Asian monsoon circulation, in which the prevailing wind direction during winter is from north to northwest and during the summer is between SSW and southeasterly. The presence of seasonal LLJs around the Bohai and Yellow seas has been reported by (Li et al., 2018). The LLJs around that region is strong during the summer period, with a wind speed ranging from 10-16 m s-1 and prevailing wind directions between southerly and southwesterly. The slight difference in our results compared with the above-mentioned studies can be attributed to the experimental period used in our study, and therefore it might be affected by the general circulations and synoptic weather systems. To examine the turbulent wake flow properties at different resolutions, we study the cases with winds within the 202.5°±11° sector, which correspond to SSW. Only the wind speeds that range from 8-12 m s-1 are selected, to avoid changes in wind speed patterns that can be found in different experiments.

    Figure 3.  The 15-min average wind rose at hub-height from (a) CNTR, (b) HR0.5, (c) VR6, (d) VR2, and (e) HR2. Both results are averaged over the entire innermost domain of the NWF simulation for the 19-day simulation period. The first two days are excluded as model spin-up.

    The wake flows within and downstream of the wind farm for all experiments at hub-height are plotted from the WF simulation and presented in Fig. 4. The influence of the wind farm on the atmospheric boundary layer is captured in all experiments, i.e. the wake's effects can be seen clearly except for the HR2 experiment. The wake spreading along the north-northeast direction and a 0.5-2 m s-1 wind speed deficit is noted within and downstream of the wind farm for different experiments. The wake's influence varies at different resolutions, although significant wake effects extend much further downstream in HR0.5 than in other experiments. The increase in vertical resolution in VR6 reduces the downstream propagation distance of the noticeable wake effects. This is caused by the increase in the vertical shear representation within the rotor disc of the wind turbines, hence facilitating turbulent mixing of the resolved momentum that acts to recover the wake within the atmosphere. The HR2 experiment shows the weakest wake effects. The wake flow within the wind farm is more complex and characterized by high turbulence and high-speed gradients, which could not be resolved well by the 2 km resolution in HR2.

    Figure 4.  Wind farm wake flow for the prevailing wind direction (SSW) for (a) CNTR, (b) HR0.5, (c) VR6, (d) VR2, and (e) HR2. All results are from the WF simulation at hub-height over the 19-day simulation period. The first two days are excluded as model spin-up. The inset dashed rectangle in the plots is the area containing the wind turbines.

    To quantify the wake effects, the wind speed deficit at the last grid cells containing the wind turbines in the direction of the wind are analyzed by comparing with the inflow wind speed. Since the prevaling winds are in the SSW direction, the upwind inflow wind speed is computed within the grid cell 1 km outside of SSW of the wind farm. The difference in wind speed upstream of the wind farm is very small in all experiments. Therefore, the upstream inflow wind speed vertical profile is computed in the WF simulation of the CNTR experiment. The vertical profile of the outflow wind speed is computed at the last grid cells containing the wind turbines for each experiment in the WF simulation and presented in Fig. 5a. The subsequent relative wind speed deficit's vertical profile, which is computed as the ratio of the difference between the outflow and inflow to the average upstream hub-height wind speed, is depicted in Fig. 5b. The horizontal dashed green line denotes the hub-height of the wind turbines and the other two dashed red lines denote the upper and lower tips of the turbines rotor disc. Results show that the inflow wind speed (red line) vertical profile is nearly an exponential distribution. However, the outflow wind speed encounters deficits due to the wake effects. It can also be noted that the vertical wake effects occur mainly below 150 m height, at which the wind speed deficit is about 1%. Moreover, as a result of the flow acceleration below the rotor disc caused by enhanced turbulent mixing and pressure perturbation, the downstream wind speed slightly surpasses the upstream wind speed (red line) below the lower tip of the rotor disc (Fig. 5a). Flow-accelerated wind speeds of around 0.4 m s-1 and 0.3 m s-1, equivalent to 2.5% and 3%, are respectively obtained below the rotor disc in HR0.5 and VR6 (Fig. 5b). Similar phenomena were reported by (Rajewski et al., 2014) and (Vanderwende et al., 2016). In addition, the maximum wind speed deficits within the wake-affected region are restricted to the upper half of the rotor disc and spread out within the whole rotor area. A similar remark was made by (Lu and Porté-Agel, 2011) and (Volker et al., 2015).

    Figure 5.  (a) Wind speed vertical profile for the upstream inflow and last grid cells containing wind turbines along the wind direction. (b) Relative wind speed deficit vertical profile. The dashed green line represents the hub-height of the wind turbines, while the upper and lower dashed red lines indicate the upper and lower boundaries of the wind turbine rotor disc, respectively. The results are averaged over a 19-day simulation period, with the first two days excluded as model spin-up.

    Figure 6a represents the normalized wind speed at hub-height (WS h/WS oh) where WS h is the hub-height wind speed calculated in each grid cell upstream and within the wake region of the wind farm (within and downstream) along 202.5°±11° in the WF simulation. WS oh is the upstream inflow wind speed at hub-height. The value of WS oh is calculated from the grid cell 10 km from the first grid cell containing turbines in the SSW of the wind farm in the WF simulation. Figure 6b represents the average change in pressure over the turbine's blade tip-to-tip extension. The wind farm extension is marked with vertical dashed blue lines.

    Figure 6.  (a) Wind speed recovery rates at hub-height upstream, within, and downstream of the wind farm for all experiments, and (b) the average change in pressure upstream, within, and downstream of the wind farm over the turbine's blade tip-to-tip extension. The wind farm extension is marked by vertical dashed blue lines. The wind farm is defined from the left-hand boundary of the first turbine-containing grid cell up to the right-hand boundary of the last turbine-containing grid cell. The results are averaged over a 19-day simulation period along 202.5°±11° and passing through the wind farm.

    The wind speed deficit increases just before the ambient flow interacts with the turbines toward the inside of the wind farm, and decreases behind the wind farm to downstream (Fig. 6a). The increase in wind speed deficit before the wind farm can be explained in terms of the elevation of the pressure change just before the main flow enters the wind farm (Fig. 6b). This creates an unfavorable pressure gradient (i.e., decelerating wind speed), causing the wind speed deficit. The wind speed at the first turbine-containing grid cell is already reduced by up to 2%. A similar phenomenon was predicted by the linear model of (Smith, 2009). The decreasing pressure change within the wind farm, as seen in Fig. 6b, creates a favorable pressure gradient within the wind farm, which acts against drag forces of the wind turbines. Therefore, it acts to recover the wind speed due to the momentum sinks by the drag force of the wind turbines. This confirms that the main source of the wind speed deficit within the wind farm is the removal of momentum by the wind turbines. Downstream of the wind farm, there is an unfavorable pressure gradient, which prevents the immediate recovery of the wind speed.

    From Fig. 6a, it is apparent that the hub-height wind speed deficit is sensitive to both the horizontal and vertical resolution. Results show that the wakes are strong within and just behind the wind farm up to about 8 km downstream, within which the wind speed deficit can exceed 8%. VR6 produces the highest magnitude of the wind speed deficit on the wind farm, followed by HR0.5, CNTR, VR2, and lastly HR2. However, the rate of wind speed recovery downstream of the wind farm is faster in VR6 than in HR0.5 and in CNTR. For example, at a distance of 25 km downstream of the wind farm, around 1.5% of wind speed deficit can be noted in VR6, while around 2.7% of wind speed deficit is apparent in HR0.5 and CNTR. The wind speed deficit recovery rates within and downstream of the wind farm for each experiment are summarized in Table 3. The result for HR0.5 and VR6 matches the observations of (Christiansen and Hasager, 2005), from their study on Horns Rev and Nysted wind farms. They observed an 8%-9% wind speed deficit just behind the wind farm, and about 2% around 21 km downstream. (Fitch et al., 2012) reported a maximum 16% wind speed deficit within the wind farm, and 11% at a distance of 11 km downstream of the wind farm. The slight difference in results could be due to the difference in the size of the wind farm and specifications of the wind turbines.

    The wake flow field of the turbines within the wind farm is characterized by a wind speed deficit and high turbulent mixing, due to the action of the turbine rotor blades. It is important to understand the distribution of TKE enhancement in the near and far wakes, due to the fact that the additional TKE by the turbines can influence vertical mixing, which may facilitate the transport of momentum and scalars within and downstream of the wind farm. To obtain a better understanding of the TKE enhancement distribution in the wake region of the wind farm, we calculate the difference in TKE between the WF and NWF simulations along the wake direction in each experiment. Figures 7 and 8 present the excess TKE in vertical and horizontal cross sections, respectively, for all experiments. The cross sections are plotted along the SSW direction, the vertical cross section passing through the center of the wind farm. The horizontal cross sections are plotted at hub-height of the wind turbines and pass through the wind farm. The dashed rectangle in each contour shows the extensions of the wind farm. These figures show that the excess TKE is resolution-dependent. Strong TKE enhancement is found in HR0.5 and VR6, with a maximum value of around 0.5 m2 s-2 just behind the wind farm in both Fig. 7 and Fig. 8. However, the TKE enhancement in VR6 decays faster than in HR0.5, similar to the wind speed deficit (Fig. 6).

    The maximum TKE enhancement is found to occur behind the wind farm, and can be explained in terms of the multiple wake effects accumulated from upstream turbines. The excess TKE is highest in the central region of the wake just behind the wind farm (Fig. 8), but it decreases much more rapidly downstream of the wind farm than the wind speed deficit. Within the wind farm, TKE increases vertically from the lower to the upper model levels (Fig. 7). The maximum increase in TKE enhancement occurs at the top tip of the rotor diameter, due to the fact that——apart from the main source of TKE being explicitly added by WFP within the rotor——the shear production of TKE is higher at the top tip than the lower tip of the rotor blades. Similar behavior was reported on the LES studies conducted by (Porté-Agel et al., 2011) and (Wu and Porté-Agel, 2013). The excess TKE spread vertically up to a height of 150 m above ground level (AGL).

    Figure 7.  Excess TKE computed as WF-NWF for all experiments: (a) CNTR; (b) HR0.5; (c) VR6; (d) VR2; and (e) HR2. The cross sections pass through the center of the wind farm from the upwind to downwind through the prevailing wind direction (SSW). The wind farm extension is marked by the dashed rectangles. The wind farm is defined from the left-hand boundary of the first turbine-containing grid cell up to the right-hand boundary of the last turbine-containing grid cell. The cross sections are averaged over a 19-day simulation period, with the first two days excluded as model spin-up.

    Figure 8.  Average horizontal cross section at hub-height for the excess TKE computed as WF-NWF for all experiments: (a) CNTR; (b) HR0.5; (c) VR6; (d) VR2; and (e) HR2. The wind farm extension is marked by the dashed rectangles. The wind farm is defined from the left-hand boundary of the first turbine-containing grid cell up to the right-hand boundary of the last turbine-containing grid cell. The cross sections are averaged over a 19-day simulation period, with the first two days excluded as model spin-up.

    Similar to Fitch et al. (2012, 2013b), the excess TKE is largely restricted within the wind farm area and quickly decays downstream. A maximum increase in TKE of 0.9 m2 s-2 can be seen within the wind farm, and 0.04 m2 s-2 was reported at a distance 10 km downstream by (Fitch et al., 2012). A TKE of 0.5 m2 s-2 is noticeable at a height of about 280 m AGL within the wind farm. In (Fitch et al., 2013b), a maximum TKE production of 0.5 m2 s-2 was obtained, which is slightly different to the peak TKE production seen in LES by (Lu and Porté-Agel, 2011), where a maximum of 0.6 m2 s-2 was obtained. The difference in magnitude between our results and these studies is due to the difference in the size of the wind farm and the specification of the wind turbines used. The wind farm size and the wind turbines used were relatively large compared to the one used in our study. However, the qualitative impression of the results obtained in HR0.5 and VR6 is similar to that reported in these previous studies.

  • Recently, interest has grown regarding the potential impact of wind farms on near-surface meteorology. Early studies (Baidya Roy and Traiteur, 2010; Baidya Roy, 2011) indicated that enhanced turbulent mixing due to the turbine rotors changes the vertical temperature profile in the turbine layer, thereby altering near-surface temperature, momentum and heat fluxes. To illustrate the impact of the wind farm as simulated by WRF-WFP on near-surface meteorology, Fig. 9 presents the averaged differences between WF and NWF across the wind farm area over a 19-day simulation period. Change in near-surface temperature (∆T2), change in near-surface water vapor mixing ratio (∆WVMR), change in surface sensible heat flux (∆SHF), and change in surface latent heat flux (∆LHF), are presented.

    Figure 9.  Average near-surface meteorological difference between WF and NWF within the wind farm area for different vertical and horizontal resolutions for the 19-day simulation period, with the first two days excluded as model spin-up: (a) near-surface temperature; (b) near-surface total water vapor mixing ratio; (c) surface sensible heat flux; and (d) surface latent heat flux. Local standard time=UTC+8.

    The average near-surface temperature change over the wind farm throughout the simulation period indicates near-surface warming during the night and early morning, with a maximum of around +0.2 K, and a near-surface cooling during daytime of around -0.1 K (Fig. 9a). The change in near-surface temperature obtained here is as a result of the enhanced vertical mixing due to the excess TKE added by wind turbines within the atmosphere. Figure 10 presents the average time-height cross section of the temperature and total water vapor mixing ratio from the CNTR experiment. During nighttime, the ground surface starts to cool (Fig. 10a), and a stable layer forms in the atmosphere; therefore, the near-surface air becomes cooler than that above. The spinning turbine rotor blades mix the warm air down and cool air up, as a result of increasing near-surface air temperature (Figs. 10c and e). The opposite happens during the daytime when the ground surface is warm compared to the air above.

    Figure 10.  Average time-height cross sections for temperature and total water vapor mixing ratio from the CNTR experiment over a 19-day simulation period, with the first two days excluded as model spin-up: (a) temperature from the NWF simulation; (b) total water vapor mixing ratio from the NWF simulation; (c) temperature from the WF simulation; (d) total water vapor mixing ratio from the WF simulation; (e) change in temperature [(c) minus (a)]; and (f) change in total water vapor mixing ratio [(d) minus (b)].

    A maximum near-surface temperature change is obtained in the HR0.5 experiment (green), while HR2 (red) gives the lowest magnitude of change in near-surface temperature (Fig. 9a). There is no clear difference in the magnitude of the change in surface temperature for CNTR, VR6 and VR2. This indicates that making fine vertical grids has no impact on the magnitude of the simulated near-surface temperature. Results of the change in near-surface temperature obtained in this study match well with the study by (Fitch et al., 2013b), who found a maximum nighttime warming of about 0.5 K and slight daytime cooling, as well as the observations by (Zhou et al., 2012), who found a small daytime temperature change and a warming of up to 0.72 K at night. The slight difference in magnitude of the temperature change obtained in this study compared to other studies is unsurprising because of the difference in the size of the wind farms and the specification of the wind turbines used.

    Figure 9b indicates a decrease in the near-surface water vapor mixing ratio over the wind farm area during daytime and an increase at night and in the early morning. The increase in near-surface water vapor mixing ratio in the WF simulation relative to the NWF simulation can be explained by a similar mechanism to the temperature change within the wind farm. During daytime, the near-surface air is more moist than the air above (Fig. 10b), and therefore the moist air from the near-surface is transported aloft as a result of decreasing near-surface moisture (negative ∆WVMR). The opposite is seen at night, when the air aloft is more moist than the near-surface. The ∆WVMR in Fig. 9b shows a similar pattern to the ∆T2 in Fig. 9a. While the horizontal resolution has been shown to play a major role in the magnitude of the ∆WVMR, the vertical resolution shows little impact.

    The change in near-surface temperature and water vapor mixing ratio has a direct impact on the surface heat fluxes. The extra near-surface warming during nighttime causes more heat to be taken to the ground surface within the wind farm, which results in an increase in the negative surface sensible heat flux (Fig. 9c). The reverse is the case during daytime. The latent heat flux is driven by the near-surface air moisture gradient (Baidya Roy, 2011). Thus, the latent heat flux can be seen to increase during the day (Fig. 9d), when the water vapor mixing ratio is decreasing (Fig. 9b), and tends to decrease during nighttime, when the moisture in the near-surface air increases. Similar results were reported by (Baidya Roy, 2011). At nighttime, the maximum increases in negative surface sensible and latent heat fluxes are 10 W m-2 and 5 W m-2, respectively. During daytime, the positive increases in surface sensible and latent heat fluxes are 10 W m-2 and 7 W m-2, respectively. Like the near-surface temperature, the highest and lowest magnitudes of surface sensible and latent heat fluxes are obtained in HR0.5 and HR2, respectively. The vertical resolution shows no impact on the simulated magnitude of surface heat fluxes.

    Given that the flow behavior of the wind farm can change under different stability conditions (Fitch et al., 2012; Vanderwende et al., 2016), the averaged results presented in this study may be a slight overestimation or underestimation of the magnitude of the wind speed deficit and TKE production within and downstream of the wind farm. However, compared with previous studies, our results show a similar spatial behavior in terms of the wind speed deficit, TKE production, and near-surface meteorology. Further modeling and observation research that involves a longer period of time and a wider range of atmospheric conditions is required around this area.

4. Conclusions
  • This work evaluates the performance of WRF-WFP, at multiple resolutions, in simulating a real onshore wind farm. Three experiments, at horizontal resolutions of 2 km, 1 km and 0.5 km and a constant 17 vertical levels below 500 m above the ground, with 4 levels interacting with the rotor of the turbines, are performed. Two extra experiments are then conducted, with a constant 1 km horizontal resolution. The first experiment is conducted with 27 vertical levels below 500 m above the ground, 6 of which are within the rotor region of the wind turbine. The second experiment is conducted with 10 vertical levels below 500 m above the ground, 2 of which are within the rotor of the turbine.

    Results show that high horizontal and vertical grid refinement has a considerable impact on the simulated turbulent wake flow dynamics. These results are comparable with the results from earlier modeling and observation studies. Results produced in this work reveal that the wind speed deficit in the wake region due to the wind farm is less than 12% in all experiments. Analysis of the influence of the wind farm on the surrounding environment confirms that the most affected region is the turbine rotor spanned area and just behind the wind farm. At a distance of 10 km downstream of the wind farm, the wind speed deficit is around 6%. At the height of 150 m or at a distance of 25 km downstream of the wind farm, the wind speed deficit is around 2% in all experiments. Therefore, for optimal performance of two wind farms constructed in the same area, they must be separated at least 25 km, to avoid interaction between the wakes generated by the two wind farms, which might affect the power production.

    Moreover, the turbines within the wind farm are shown to influence near-surface meteorology on a local scale. However, the impact is different for different simulation periods. Analysis of the WF and NWF simulation results shows that there is an increase in the near-surface temperature in the WF relative to the NWF simulation during the night and early morning. This indicates a slight warming over the wind farm area. An opposite scenario is simulated during the daytime. The same behavior is exhibited by the near-surface water vapor mixing ratio. The surface sensible heat and latent heat fluxes show opposite behavior to that indicated by the near-surface temperature and total water vapor mixing ratio. Results show that increasing the horizontal resolution has a considerable impact on the magnitude of the simulated near-surface meteorological variables. The vertical resolution, however, exhibits little influence on the magnitude of the simulated meteorological variables.

    As a step in applying WRF-WFP to a real onshore wind farm simulation, our results show that higher vertical and horizontal resolutions have a marked impact on the simulated wake flow dynamics, plus its corresponding wind speed deficits and TKE production, within and downstream of the wind farm. Qualitative comparisons with results from other studies indicate that the results of HR0.5 and VR6 exhibit the same behavior and comparable magnitudes in terms of TKE and wind speed deficit compared with the other experiments. This study has important implications for wind energy and land-use policies. The wakes and their corresponding impacts on the near-surface meteorological surface are likely to affect both the performance of the wind farm and economic activities, such as agriculture, for those wind farms constructed near agricultural lands. However, more simulations for a longer period of time and with a wider range of conditions are required to conclusively demonstrate this phenomenon.

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