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本文选取广东某已运行的海上风电场Z开展分析工作,该风电场最北边界距离北侧岛屿约10 km,距离西侧岛屿约10 km,距离东北侧横琴岛约为15 km,距离东侧小万山岛约20.5 km。场内共布置55台相同机型的机组,相邻风机间距离大于等于3D,相邻两排为不等间距排布,机位布置与场址范围如图1所示。
图 1 广东某海上风电场位置与排布与测风塔的位置
Figure 1. Location and arrangement of offshore wind farm in Guangdong and the location of anemometer tower
本文使用的气象数据主要为ERA5,SCADA数据和该风场建设前安装的测风塔所观测的数据。ERA5再分析数据是欧洲中期天气预报中心所发布的第五代全球再分析资料数据集,相较于上一代的资料集,ERA5同化了更多观测数据,空间分辨率提高到0.25°,时间分辨率到达1 h,增加了新的变量[16],在本文中驱动中尺度数值天气模型的数据的空间分辨率为0.25°,时间分辨率为3 h。
SCADA(Supervisory Control and Data Acquisition)系统数据,即数据采集与监视控制系统,安装于风电机组中便于监测机组运行和记录风场内风速风向的变化。该风场投入运营后,利用SCADA记录2022~2023年的测风数据,并且对各机位点处机舱高度的测风数据进行检验后,进行修正,排除冗余数据,得到55个机位的测风数据,本文主要使用2022年06月24日的SCADA数据。
测风塔数据主要源于场内的1座海上专用型测风塔,位于风电场址南部(如图1所示),高度为100 m,收录2019年01月至2020年01月的气象要素数据。
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PALM(Parallelized Large-Edge Simulation Model)是由德国汉诺莱布尼兹大学开发的一款用于研究大气边界层区域内的湍流过程的大涡模拟模型,已经应用于各种大气边界层内的流场模拟超过15 a[17],并已经应用于大规模并行计算。
本文使用的是PALM最新版本,即PALM version 6.0[18],模式基于Boussinesq近似的非流体静力学,对经滤波处理后,不可压缩形式的Navier-Stokes方程进行求解。下面式(1)~式(5)的方程组经离散后,在笛卡尔网格上求解平均值,因此可以隐式地实现目标分辨率尺度和次网格尺度(Sub-Grid Scale, SGS)中湍流模式的分离,其中,次网格尺度的建立是基于Deardorff(1980)提出的方法[19]。
$$ \begin{split} &\dfrac{\partial {u}_{i}}{\partial t}=-\dfrac{\partial {u}_{i}{u}_{j}}{\partial {x}_{j}}-{\varepsilon }_{ijk}{f}_{i}{u}_{k}+{\varepsilon }_{i3j}{f}_{3}{u}_{{\mathrm{g}},j}-\dfrac{1}{{\rho }_{0}}\frac{\partial {\pi }^{*}}{\partial {x}_{i}}+\\&g\frac{{\theta }_{{\mathrm{v}}}-\left\langle {{\theta }_{{\mathrm{v}}}} \right\rangle}{\left\langle {{\theta }_{{\mathrm{v}}}} \right\rangle }{\delta }_{i3}-\dfrac{\partial }{\partial {x}_{j}}\left(\overline{{{u}_{i}^{''}}{u_{j}^{''}}}-\dfrac{2}{3}e{\delta }_{ij}\right) \end{split} $$ (1) $$ \dfrac{\partial {u}_{j}}{\partial {x}_{j}}=0 $$ (2) $$ \dfrac{\partial \theta }{\partial t}=-\dfrac{\partial {u}_{j}\theta }{\partial {x}_{j}}-\dfrac{\partial }{\partial {x}_{j}}\left(\overline{{u}_{j}^{''}{\theta }^{''}}\right)-\dfrac{{L}_{{\mathrm{v}}}}{{C}_{{\mathrm{p}}}\Pi }{\varPsi }_{{\mathrm{qv}}} $$ (3) $$ \dfrac{\partial {q}_{v}}{\partial t}=-\dfrac{\partial {u}_{j}{q}_{v}}{\partial {x}_{j}}-\dfrac{\partial }{\partial {x}_{j}}\left(\overline{{u}_{j}^{''}{q}_{{\mathrm{v}}}^{''}}\right)-{\varPsi }_{{\mathrm{qv}}} $$ (4) $$ \dfrac{\partial s}{\partial t}=-\dfrac{\partial {u}_{j}s}{\partial {x}_{j}}-\dfrac{\partial }{\partial {x}_{j}}\left(\overline{{u}_{j}^{''}{s}^{''}}\right)-{\varPsi }_{{\mathrm{s}}} $$ (5) 式中:
$ i\mathrm{、}j\mathrm{、}k $ ——维度下标号,可取$ \left\{1,\mathrm{ }2,\mathrm{ }3\right\} $;
$ {u}_{i} $ ——速度分量,$ {u}_{1}=u,{u}_{2}=v,{u}_{3}=w $,$ {x}_{i} ({x}_{1}= x, {x}_{2}=y,{x}_{3}=z) $;
$ t $ ——时间;
$ {f}_{i} $ ——不同纬度位置上的科氏力(地转偏向力);
$ {u}_{{\mathrm{g}},{k}} $ ——地转风分量(m/s);
$ {\rho }_{0} $ ——空气密度(kg/m3);
$ {\pi }^{*} $ ——订正后的气压扰动(hPa);
$ {p}^{*} $ ——气压扰动;
$ e $ ——次网格内的湍流能量(J)。
位势温度定义为:
$$ \theta =\dfrac{T}{\mathrm{\Pi }} $$ (6) $$ \mathrm{\Pi }={\left(\dfrac{p}{{p}_{0}}\right)}^{\tfrac{{R}_{{\mathrm{d}}}}{{C}_{{\mathrm{p}}}}} $$ (7) 式中:
$ {R}_{{\mathrm{d}}} $ ——干空气气体常数[J/(kg·K)];
$ \theta $ ——位势温度(K);
$ T $ ——温度(K);
$ p $ ——气压(hPa)。
应用在PALM中的风力发电机模型(Wind Turbine Model)是基于一般性圆盘模型(Actuator Disk Model, ADM)方法建模而成的,即将风力发电机抽象成具有一定厚度的圆盘,且由气流产生的阻力和动量作用在这个虚拟的圆盘上(如图2所示)。
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本文将对关注的风电场区域采用中尺度数值天气WRF模型进行关注时间段内环境风场时空变化的模拟。WRF模式是美国大气研究中心、美国国家海洋和大气管理局以及天气预报系统实验室等研究机构和相关院校合作开发的高时空分辨率、考虑大气非静力平衡的中尺度数值天气模型[20]。本文使用的是WRF 4.2版本。
针对本文关注风电场的位置在WRF中模拟区域如图3所示。在研究区域内采用双重嵌套,最外层区域格点分辨率为9 km,最里面区域的格点分辨率为3 km。采用的物理参数化方案(表1)选用广东海域最优参数化方案[21],在边界层底部(离地300 m)的到海平面进行模式垂直方向上的细分,使得模式能再现到海上风电资源评估中需要关注的风场剖面变化和相关天气系统过程。选取Z风电场2022年6月24日12时~15时作为模拟时段,结合该风场的SCADA系统收集的数据进行评估和验证。
表 1 WRF参数化方案
Table 1. WRF parameterized schemes
参数化方案 简称 微物理参数化方案 Milbrandt 2-mon 大气边界层方案 YSU-revised 近地层物理参数化方案 MM5 Monin-Obukhov 短波辐射方案 RRTMG 长波辐射方案 RRTMG -
PALM模式留有接入外部中尺度模式模拟结果的数据接口[18],该接口允许用户提供netCDF数据格式的动态驱动文件作为PALM的模式输入,该动态驱动文件包括大气边界层的气象强迫和由中尺度模式的模拟结果所提供的初始大气状态变量剖面。因此,WRFinPALM用于将输入的WRF模拟结果转换为能驱动PALM的动态输入(表2),程序结构如图4所示。
表 2 PALM动态驱动变量需求
Table 2. PALM dynamic drive variable requirements
变量名 变量描述 Init_soil_t 初始土壤温度/K Init_soil_m 初始土壤湿度/(kg·kg−1) Init_atmosphere_x Pt ——位势温度/K Qv——绝对湿度/(kg·kg−1) U ——经度方向风速/(m·s−1) V ——纬度方向风速/(m·s−1) W ——垂直速度/(m·s−1) Ls_forcing_left_x 西边界条件 Ls_forcing_right_x 东边界条件 Ls_forcing_north_x 北边界条件 Ls_forcing_south_x 南边界条件 Ls_forcing_ug 径向地转风分量 Ls_forcing_vg 纬向地转风分量 Surface_forcing_surface_pressure 外部大尺度气压对表面的影响/Pa -
本文使用皮尔逊相关系数来描述模拟结果和风电场观测数据之间的相关性,公式如下:
$$ R=\dfrac{\dfrac{1}{N-1}\cdot \displaystyle \sum_{n=1}^{N}\left({{\mathrm{model}}}_{n}-\overline{{\mathrm{model}}}\right)\cdot \left({{\mathrm{ob}}}_{n}-\overline{{\mathrm{ob}}}\right)}{{\sigma }_{{\mathrm{model}}}\cdot {\sigma }_{{\mathrm{ob}}}} $$ (8) $$ {\mathrm{RMSE}}=\sqrt{\dfrac{\displaystyle \sum _{n=1}^{N}{\left({{\mathrm{ob}}}_{n}-{{\mathrm{model}}}_{n}\right)}^{2}}{N}} $$ (9) $$ {\mathrm{Bias}}=\dfrac{1}{N}\cdot \displaystyle \sum _{n=1}^{N}\left({{\mathrm{ob}}}_{n}-{{\mathrm{model}}}_{n}\right) $$ (10) 式中:
N ——关系观测样品数;
$ {{\mathrm{model}}}_{n} $ ——模式结果;
$ \overline{{\mathrm{model}}} $ ——模式均值;
$ {{\mathrm{ob}}}_{n} $ ——站点观测值;
$ \overline{{\mathrm{ob}}} $ ——观测均值;
$ {\sigma }_{{\mathrm{model}}} $ ——模式的标准差;
$ {\sigma }_{{\mathrm{ob}}} $ ——观测的标准差。
在评估模式模拟值和站点观测观测值之间的误差,本文使用均方根误差(RMSE)和偏差(Bias)2个统计量来评价模式与观测的平均接近程度,数值越小,表示模型模拟值越接近实际观测。
Refined Wind Simulation Based on Large Eddy Simulation and Mesoscale Numerical Weather Model
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摘要:
目的 结合中尺度模型与大涡模拟模型,考虑大气边界层变化,开展了亚公里级的项目机组排布的数值模拟,给海上风机项目在选址排布阶段提供发电效能高的排布方案。 方法 将中尺度数值天气模拟结果转换为大涡模拟模型输入的边界条件,并在大涡模拟模型中引入实际风电场运行的模型参数,进行考虑实际大气边界层变化下的风电场空间的环境风场数值模拟试验,基于风电场收集的观测数据,对本风场精细化模拟方案的结果进行评估。 结果 模拟结果表明:将中尺度天气模型的模拟结果转换为大涡模拟模型能读取的动态驱动并基于该模型对风电场所处的风场进行模拟,其模拟结果能再现在实际风电场中,外部风场流经风电场后,外部风场的变化和在风电机群内所产生的尾流及其对于风电场内部风场的影响,且在风机轮毂处的风速模拟值的均方根误差为1.54 m/s。 结论 该考虑中尺度气象要素变化和风电场对环境风场影响的风场精细化模拟方案可为实际项目设计阶段提供相应的指导。 Abstract:Introduction Combining mesoscale numerical model and large eddy simulation (LES) model, numerical sumulation of sub-kilometer-scale project unit placement is carried out, which takes into account atmospheric boundary layer changes. It provides offshore wind turbine projects with high-efficiency power generation placement schemes. Method This study converted the mesoscale numerical weather simulation results into boundary conditions for the input of the LES model and introduced model parameters reflecting the operation of an actual wind farm into the LES simulation. The numerical sumulation experiments of the ambient wind field in the wind farm region was carried out under the consideration of the change of the actual atmospheric boundary layer, and the results of the refined simulation scheme of this wind field were evaluated based on the observation data collected from the wind farm. Result The simulation results indicate that by converting the results of the mesoscale weather model into the dynamic drive which is read by the LES model and simulating the wind field where the wind farm is located based on the model, the simulation results are able to replicate the changes in the external wind field after passing through the wind farm and the wake generated within the wind turbine fleet, as well as its impact on the internal wind field of the wind farm. The root mean square error of wind speed simulation at the hub of wind turbines is 1.54 m/s. Conclusion The refined wind field simulation scheme, which takes into account the variation of mesoscale meteorological elements and the impact of wind farms on the ambient wind field, can provide guidance for the design phase of actual projects. -
Key words:
- mesoscale numerical weather model /
- large eddy simulation /
- wake effect /
- wind turbine /
- real time data
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表 1 WRF参数化方案
Tab. 1. WRF parameterized schemes
参数化方案 简称 微物理参数化方案 Milbrandt 2-mon 大气边界层方案 YSU-revised 近地层物理参数化方案 MM5 Monin-Obukhov 短波辐射方案 RRTMG 长波辐射方案 RRTMG 表 2 PALM动态驱动变量需求
Tab. 2. PALM dynamic drive variable requirements
变量名 变量描述 Init_soil_t 初始土壤温度/K Init_soil_m 初始土壤湿度/(kg·kg−1) Init_atmosphere_x Pt ——位势温度/K Qv——绝对湿度/(kg·kg−1) U ——经度方向风速/(m·s−1) V ——纬度方向风速/(m·s−1) W ——垂直速度/(m·s−1) Ls_forcing_left_x 西边界条件 Ls_forcing_right_x 东边界条件 Ls_forcing_north_x 北边界条件 Ls_forcing_south_x 南边界条件 Ls_forcing_ug 径向地转风分量 Ls_forcing_vg 纬向地转风分量 Surface_forcing_surface_pressure 外部大尺度气压对表面的影响/Pa -
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