Joint Model of Wind Speed and Corresponding Direction Based on Wind Rose for Wind Energy Exploitation

As a common and extensive datum to analyze wind,wind rose is one of the most important components of the meteorological elements.In this study,a model is proposed to establish the joint probability distribution of wind speed and direction using grouped data of wind rose.On the basis of the model,an algorithm is presented to generate pseudorandom numbers of wind speed and paired direction data.Afterward,the proposed model and algorithm are applied to two weather stations located in the Liaodong Gulf.With the models built for the two cases,a novel graph representing the continuous joint probability distribution of wind speed and direction is plotted,showing a strong correlation to the corresponding wind rose.Moreover,the joint probability distributions are utilized to evaluate wind energy potential successfully.In cooperation with Monte Carlo simulation,the model can approximately predict annual directional extreme wind speed under different return periods under the condition that the wind rose can represent the meteorological characters of the wind field well.The model is beneficial to design and install wind turbines.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

Joint Return Value Estimation of Significant Wave Heights and Wind Speeds with Bivariate Copulas

The joint design criteria of significant wave heights and wind speeds are quite important for the structural reliability of fixed offshore platforms.However,the design method that regards different ocean environmental variables as independent is conservative.In the present study,we introduce a bivariate sample consisting of the maximum wave heights and concomitant wind speeds of the threshold by using the peak-over-threshold and declustering methods.After selecting the appropriate bivariate copulas and univariate distributions and blocking the sample into years,the bivariate compound distribution of annual extreme wave heights and concomitant wind speeds is constructed.Two joint design criteria,namely,the joint probability density method and the conditional probability method,are applied to obtain the joint return values of significant wave heights and wind speeds.Results show that(28.5±0.5)m s^(-1)is the frequently obtained wind speed based on the Atlantic dataset,and these joint design values are more appropriate than those calculated by univariate analysis in the fatigue design.

Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution

The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed , the variance of v around and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v2 f(v) and v3 f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed , the variance σ2 of the wind speed v;around the mean speed and the average wind power density.

Extreme Values of Wind Speed over the Kara Sea Based on the ERA5 Dataset

Extreme values of wind speed were studied based on the highly detailed ERA5 dataset covering the central part of the Kara Sea. Cases in which the ice coverage of the cells exceeded 15% were filtered. Our study shows that the wind speed extrema obtained from station observations, as well as from modelling results in the framework of mesoscale models, can be divided into two groups according to their probability distribution laws. One group is specifically designated as black swans, with the other referred to as dragons (or dragon-kings). In this study we determined that the data of ERA5 accurately described the swans, but did not fully reproduce extrema related to the dragons;these extrema were identified only in half of ERA5 grid points. Weibull probability distribution function (PDF) parameters were identified in only a quarter of the pixels. The parameters were connected almost deterministically. This converted the Weibull function into a one-parameter dependence. It was not clear whether this uniqueness was a consequence of the features of the calculation algorithm used in ERA5, or whether it was a consequence of a relatively small area being considered, which had the same wind regime. Extremes of wind speed arise as mesoscale features and are associated with hydrodynamic features of the wind flow. If the flow was non-geostrophic and if its trajectory had a substantial curvature, then the extreme velocities were distributed according to a rule similar to the Weibull law.

Multi-hazard joint probability distribution model for wind speed,wind direction and rain intensity

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures.However,most existing studies ignored the dependence structure between them,as well as the effect of wind direction.From the dimension of the engineering sector,this paper introduces the vine copula to model the joint probability distribution(JPD)of wind speed,wind direction and rain intensity based on the field data in Yangjiang,China during 1971–2020.First,the profiles of wind and rain in the studied area are statistically analyzed,and the original rainfall amounts are converted into short-term rain intensity.Then,the marginal distributions of individual variables and their pairwise dependence structures are built,followed by the development of the trivariate joint distribution model.The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed,wind direction and rain intensity.Meanwhile,the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction,thus the effect of wind direction cannot be neglected.The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

An advanced wind vector retrieval algorithm for the rotating fan-beam scatterometer

The rotating fan-beam scatterometer （RFSCAT） is a new type of satellite scatterometer that is proposed approximately 10 a ago. However, similar to other rotating scatterometers, relatively larger wind retrieval errors occur in the nadir and outer regions compared with the middle regions of the swath. For the RFSCAT with the given parameters, a wind direction retrieval accuracy decreases by approximately 9 in the outer regions compared with the middle region. To address this problem, an advanced wind vector retrieval algorithm for the RFSCAT is presented. The new algorithm features an adaptive extension of the range of wind direction for each wind vector cell position across the whole swath according to the distribution histogram of a retrieved wind direction bias. One hundred orbits of Level 2A data are simulated to validate and evaluate the new algorithm. Retrieval experiments demonstrate that the new advanced algorithm can effectively improve the wind direction retrieval accuracy in the nadir and outer regions of the RFSCAT swath. Approximately 1.6 and 9 improvements in the wind direction retrieval are achieved for the wind vector cells located at the nadir and the edge point of the swath, respectively.

集中绕组模块组合式定子结构对低速大功率永磁电机性能影响

针对集中绕组模块组合式定子结构对低速大功率直驱永磁同步电机性能的影响进行研究。首先介绍了模块化定子的分块规则和分块数。基于绕组函数法推导了单个定子单元模块在不同拆分方式下的绕组函数和电感表达式。基于有限元仿真先分析了仅绕组分块对电机性能影响;然后分析了冲片和绕组都分块对电机性能影响。通过对比空载和负载性能,总结出各种定子模块化拆分方案的优缺点,为大功率低速直驱永磁同步电机的模块化设计与制造建立了基础。

考虑输出约束及外部干扰的柔性航天器振动控制

针对具有输出约束及外部干扰的柔性航天器系统,提出一种直接关节力矩输入的振动控制方法。利用哈密顿原理,系统动力学特性由偏微分方程(PDE)和常微分方程(ODE)耦合组成的分布参数模型来描述。设计了非线性干扰观测器补偿外界干扰,并基于正切型障碍李雅普诺夫函数解决了航天器姿态角度误差和振动误差的多输出约束问题。利用扩展的拉塞尔不变集原理和半群理论证明了系统的渐近稳定性。不仅实现了姿态角的位置控制,还抑制了柔性航天器的弹性振动。通过对比仿真验证了所提方法的有效性。

考虑相干性海洋结构风-浪联合作用力一种计算方法

随机风、浪环境要素之间存在较强相干性,该相干性影响风、浪联合传播过程中脉动风速与波浪形态,进而影响海洋结构风-浪联合作用力及结构响应。为准确计算结构随机风-浪联合作用力,基于已建立的描述随机风、浪联合传播相干性的风-浪相干函数,计算获取海洋结构来流脉动风速与入射随机波面之间互相关谱,建立包括风速自谱、风速互谱、波浪谱及风-浪互谱在内的结构随机风-浪联合功率谱矩阵。基于联合谱矩阵的Cholesky分解矩阵,利用谐波合成方法生成风、浪相互作用下的结构来流脉动风速时程,进而结合结构水上部分风阻系数生成结构脉动风作用力时程;基于联合谱矩阵的Cholesky分解矩阵,通过谐波合成计算式中引入结构随机波浪作用水动力传递函数的方式,生成风、浪相互作用下的结构随机波浪作用力时程。联立生成的随机风、浪作用力时程即可建立结构随机风-浪联合作用力同步时程。以直立圆柱风-浪联合作用力计算为例,开展了以上算法的算例应用分析。

基于Nakagami分布的风速概率分布拟合研究

准确拟合风速概率分布对估算潜在风场所蕴含的风能具有重要作用。引入二参数Nakagami分布对美国西部涵盖沿海、海岛和内陆的八个站点风速数据进行拟合,并对比瑞丽分布、伽马分布、威布尔分布、对数正态分布、广义极值分布以及JohnsonSB分布,使用决定系数、均方根误差、误差平方和以及Kolmogorov-Smirnov四个拟合指标进行校验。与参数较少的瑞丽分布、伽马分布、对数正态分布以及威布尔分布精度进行比较,Nakagami分布在八个站点的四个拟合指标均值中取得最优的拟合精度。与三参数的广义极值分布以及四参数JohnsonSB分布进行拟合对比,Nakagami分布在四个站点获得最优精度。根据风速数据的统计结果,当站点的平均风速低于3 m/s时,Nakagami比其它分布获得了更高的拟合精度。综合考虑Nakagami简便的计算及较高的拟合精度,其在拟合风速概率分布领域更具优势。

基于三种不同分布函数的西藏东部地区极大风速估算研究

基于西藏东部地区9个站点40~67 a的长期观测数据(最早自1953年起)与61个站点2014年后的短期观测数据,利用三种不同概率密度分布函数,估算西藏东部地区极大风速并研究其时空分布情况。结果表明:长期来看,西藏东部地区位于西风带与季风共同影响区域,主要以西北风(频率达27%)为主,99%的样本风速不超过9.0 m/s,风速超过15.0 m/s的仅占万分之1.6;对实测极大风速分别进行极值Ⅰ型、极值Ⅱ型和极值Ⅲ型分布函数拟合,发现不同时期数据拟合后的参数无显著差异;利用最小二乘法进行检验订正,可使估算的极大风速的平均绝对偏差和均方根误差大幅降低,观测数据时间序列越长整体估算效果越好;基于极值Ⅱ型函数估算的西藏东部地区极大风速分布能更好地表征该地区实际极大风速的空间分布,极大风速变化范围为13.2~30.9 m/s。

基于机组与测风塔数据的机舱风速传递函数关系建模方法比对研究

基于某风电场机组SCADA数据和测风塔实测数据构建机舱风速传递函数(NTF)。选择线性方法(标准方法、VR、VS、SS)、由风速分布特点衍生的曲线方法(WBL)、时间矩阵方法(MTS),共计三类方法,6种函数模型,探究不同函数模型的拟合效果,并将拟合后的结果数据与激光雷达实测数据进行对比验证,同时与国际电工委员会(IEC)提出的方法进行比对。验算结果表明:线性分析模型中,相比于IEC标准推荐的函数模型,VR、SS函数模型从总体数据出发,考虑到风速散点图中的偏离点,其拟合效果会较为优异;对于WBL模型,基于风速风特性角度,其函数分布特点能够涵盖住样本散点图中的偏离数据点。因此在实际工程项目中,可考虑优先应用WBL模型进行仿真计算,线性模型中推荐VR、SS函数模型。

Simulating Temporally and Spatially Correlated Wind Speed Time Series by Spectral Representation Method

In this paper,it aims to model wind speed time series at multiple sites.The five-parameter Johnson mdistribution is deployed to relate the wind speed at each site to a Gaussian time series,and the resultant-Z(t)dimensional Gaussian stochastic vector process is employed to model the temporal-spatial correlation of mwind speeds at different sites.In general,it is computationally tedious to obtain the autocorrelation functions Z(t)(ACFs)and cross-correlation functions(CCFs)of Z(t),which are different to those of wind speed times series.In order to circumvent this correlation distortion problem,the rank ACF and rank CCF are introduced to Z(t)characterize the temporal-spatial correlation of wind speeds,whereby the ACFs and CCFs of can be analytically obtained.Then,Fourier transformation is implemented to establish the cross-spectral density matrix Z(t)mof,and an analytical approach is proposed to generate samples of wind speeds at different sites.Finally,simulation experiments are performed to check the proposed methods,and the results verify that the five-parameter Johnson distribution can accurately match distribution functions of wind speeds,and the spectral representation method can well reproduce the temporal-spatial correlation of wind speeds.

风向风速的联合概率结构建模

风向和风速的联合分布模型是结构工程和风能研究领域的重要参数,但两者的相关性等致使模型建立困难。基于乘法定理导出离散-连续混合联合分布模型,明确各项的物理和数学意义,并指出将风向风速离散-连续混合联合分布模型与2维连续联合分布模型建立联系的可能性。以重庆市日极值风数据为对象,导出风速条件密度变换解,计算出各风向上的数值解,并与经验累积分布函数比较验证数值解的准确性;然后引入混合概率密度函数对数值解进行拟合,建立风速条件概率密度的两分量混合模型,较单一概率分布模型有明显改善;将风速条件概率密度与风向频度函数相联合即可获得风向风速的离散-连续混合联合分布模型。为建立风向风速的2维连续联合分布模型,首先由风向频度函数和风向角概率直方图之间的联系确定风向角的概率直方图,再经拟合给出风向角的混合分布模型;类似地,由曲线拟合亦可获得风速混合模型中各参数与风向角的关系式,从而建立统一的风速条件概率密度模型;将两者结合起来,即为风向风速的2维连续联合分布模型。

基于健康监测的苏通大桥风速风向联合分布研究

为了描述苏通大桥桥址区风速风向联合分布规律,为大跨度桥梁结构的风振分析精细化研究奠定基础,基于苏通大桥结构健康监测系统开展了桥址区风速风向联合分布研究。根据该系统风速仪在主梁跨中上游、跨中下游、北塔塔顶、南塔塔顶4个关键部位记录的风特性数据,采用数理统计方法,推算了4个部位10年、100年重现期的极值风速。结果表明,苏通大桥风特性监测数据合理可靠、桥址区极值风速分布概型接近Weibull分布,考虑风向影响的极值风速总体上比不考虑风向影响时的结果要小。

上海地区风速风向联合概率密度函数的研究

根据上海地区历年来详尽的风速风向实测资料，首先利用统计方法计算出本地区离散的风速风向联合概率密度函数值；然后运用曲面拟合方法，得到简洁法实用的风速风向联合概率密度函数由面的表达式．文中同时分析了风速风向在各季节的特点．这些结果可以方便地用于上海地区结构的抗风设计及风洞试验研究．对其它地区的民极年特性分析，文中的方法及结论也可被参考使用．

计及风速与负荷相关性的配电网重构方法

风速与负荷均受多种气候因素影响,二者具有一定相关性,因此对含风力发电的配电网进行随机潮流计算和配电网重构时应计及二者相关性的影响。基于Copula函数理论,提出一种计及风速与负荷相关性的配电网随机潮流算法,并以有功功率损耗期望值最小为目标函数,建立计及风速-负荷相关性的配电网重构模型。算例结果表明,所提方法能精确描述风速与负荷的相关结构,并且二者相关性的强弱对配电网随机潮流和重构结果均有一定影响。

基于Copula函数的杭州地区多风向极值风速估计

为了合理确定建设场地的结构抗风设计风速,提出多风向极值风速估计方法.以杭州地区日极值风速风向为统计样本,采用核密度-广义帕累托混合模型来描述各风向下的极值风速边缘分布,提高了Up-crossings法估计极值风速的准确性.基于严格选择的Copula函数建立杭州地区风速风向联合分布模型.采用该联合分布模型计算得到了不同重现期下考虑风向相关性的多风向极值风速,并与不考虑风向相关性的极值风速估计值进行对比.结果表明,具有给定重现期的设计风速估计应考虑风向相关性的影响.在不考虑风向相关性的情况下,容易给出偏于风险的极值风速估计值.

上海地区台风条件风速和雨强联合概率分布统计

选取上海市崇明岛侯家镇气象站纪录的47个台风最大10min时距平均风速和最大雨强作为样本,使用不同的概率分布模型分别对风速和雨强的概率分布参数进行拟合并作拟合优度比较,提出台风条件下风速和雨强联合概率分布函数。优化结果表明,Gumbel Copula函数联合概率分布模型和极值Ⅰ型联合概率分布模型适合描述台风条件下风速和雨强联合概率分布,其中Gumbel Copula函数联合概率分布模型中风速和雨强各自的概率分布模型分别采用极值Ⅲ型概率分布模型和Gamma分布模型。