Joint probability design of marine environmental elements for wind turbines

Decommission platforms can be used as the foundation of offshore wind turbines. In order to reduce the costs of wind power, the joint probability method is applied in the joint design of marine environmental elements. Based on copulas and univariate maximum entropy margins, multivariate maximum entropy distributions are constructed. Sample data of annual maximum significant wave height and corresponding wind speed and current velocity at Point 2 in Lianyungang Harbour of China is applied to testify the efficiency of trivariate maximum entropy distributions. The marginal fittings of univariate maximum entropy distributions and the trivariate data fitting based on normal copula fit the data well. The method of conditional probability can present a joint design of significant wave height and corresponding wind speed and current velocity.     

The creation of a comprehensive metocean data set for offshore wind turbine simulations

A database of meteorological and ocean conditions is presented for use in offshore wind energy research and design. The original data are from 23 ocean sites around the USA and were obtained from the National Data Buoy Center run by the National Oceanic and Atmospheric Administration. The data are presented in a processed form that includes the variables of interest for offshore wind energy design: wind speed, significant wave height, wave peak‐spectral period, wind direction and wave direction. For each site, a binning process is conducted to create conditional probability functions for each of these variables. The sites are then grouped according to geographic location and combined to create three representative sites, including a West Coast site, an East Coast site and a Gulf of Mexico site. Both the processed data and the probability distribution parameters for the individual and representative sites are being hosted on a publicly available domain by the National Renewable Energy Laboratory, with the intent of providing a standard basis of comparison for meteorological and ocean conditions for offshore wind energy research worldwide. Copyright © 2015 John Wiley & Sons, Ltd.     

Environmental contours for circular‐linear variables based on the direct sampling method

Environmental contours are often used in the design of engineering structures to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common application of environmental contours is for wave climate variables such as significant wave height and wave period. However, for the design of wind energy installations, the joint distribution of wind speed and wind direction may be equally important. In this case, joint modelling of linear (wind speed) and circular (wind direction) variables are needed, and methods for establishing environmental contours for circular‐linear variables will be required. In this paper, different ways of establishing environmental contours for circular‐linear variables will be presented and applied to a joint distribution model for wind speed and wind direction. In particular, the direct sampling approach to environmental contours will be modified to the case where one of the variables is cyclic. In addition, contours based on exceedance planes in polar coordinates will be established, and circular‐linear contours will also be calculated based on the inverse FORM (I‐FORM) approach.     

Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment

Knowing about wind speed distribution for a specific site is very essential step in wind resource utilizations. In this paper, a probability density function with the maximum entropy principle is derived using different algorithm from previous studies. Its validity considering various numbers of moment constraints is tested and compared with the conventional Weibull function in terms of computation accuracy. Judgment criterions include the Chi-square error, root mean square error, maximum error in cumulative distribution function as well as the relative error of wind power density between theoretical function and observation data. Wind sample data are observed at four wind farms having different weather conditions in Taiwan. The results show that the entropy quantities reveal a negative correlation with the number of constraints used, regardless of station considered. For a specific site experiencing more stable weather condition where wind regimes are not too dispersive, the conventional Weibull function may accurately describe the distribution. While for wind regimes having two humps on it, the maximum entropy distributions proposed outperform a lot the Weibull function, irrespective of wind speed or power density analyzed. For the consideration of computation burden, using four moment constraints in calculating maximum entropy parameters is recommended in wind analysis.     

考虑风速风向联合概率分布的风电塔筒结构风致疲劳寿命评估

针对风向对风力机塔筒疲劳产生影响的问题,基于实测数据对考虑风速风向联合概率分布的风电塔筒结构的风致疲劳寿命展开研究。首先结合甘肃安西地区37 a的实测风速风向数据,给出风速风向联合概率分布。然后利用主S-N曲线法分别对不同风向和不同风速下风力机塔架结构法兰及门洞区域的响应规律进行分析。最后考虑风速风向联合概率分布,对风电塔筒结构风致疲劳寿命展开研究。结果表明：门洞朝向与风轮朝向的夹角变化和风速的改变均对风电塔筒的风致疲劳寿命有一定影响,其中门洞朝向与风轮朝向夹角为225°时疲劳寿命最长,风速为10~14 m/s时疲劳寿命变化幅度最大;考虑风速风向联合概率分布能更准确地计算风力机结构的风致疲劳寿命,且以此为依据对门洞朝向进行调整可延长其疲劳寿命,因此建议对风电塔架进行设计时,应考虑风电场所在地区的风速风向联合概率分布。     

A Multivariate and Multimodal Wind Distribution model

This paper presents a new methodology to accurately characterize and predict the annual variation of wind conditions. The estimate of the distribution of wind conditions is necessary to quantify the available energy (power density) at a site, and to design optimal wind farm configurations. A smooth multivariate wind distribution model is developed to capture the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind Distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the joint distribution of wind speed and wind direction (bivariate); and (iii) the joint distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Both onshore and offshore wind distributions are estimated using the MMWD model. Recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN) and the National Data Buoy Center (NDBC), is used in this paper. The coupled distribution was found to be multimodal. A strong correlation among the wind condition parameters was also observed.     

Ultra short‐term probability prediction of wind power based on LSTM network and condition normal distribution

Considering the inevitable prediction errors in the traditional point predictions of wind power, in this paper, a new ultra short‐term probability prediction method for wind power is proposed, in which the long short‐term memory (LSTM) network, wavelet decomposition (WT), and principal component analysis (PCA) are combined together for ultra short‐term probability prediction of wind power, a conditional normal distribution model that is developed to describe the uncertainty of prediction errors. First, WT and PCA are jointly used to smooth the original time series, then the point prediction model for subsequence data based on LSTM network is proposed. It is worth pointing out that the input matrix of the model includes many features, such as wind power and wind speed, which will be helpful for improving prediction performance. After optimizing the index of the ultra short‐term probability prediction interval (PI) of wind power by particle swarm optimization (PSO), the conditional normal distribution model of prediction errors is developed. Thus, the ultra short‐term PIs for wind power are obtained. Finally, based on the data of two wind farms in China, simulation results are provided to illustrate the usefulness of the proposed prediction model. It follows from those results that the proposed method can improve the accuracy of prediction, and the reliability of probability prediction for wind power is also improved.     

Estimation of wind energy potential using different probability density functions

In addition to the probability density function (pdf) derived with maximum entropy principle (MEP), several kinds of mixture probability functions have already been applied to estimate wind energy potential in scientific literature, such as the bimodal Weibull function (WW) and truncated Normal Weibull function (NW). In this paper, two other mixture functions are proposed for the first time to wind energy field, i.e. the mixture Gamma–Weibull function (GW) and mixture truncated normal function (NN). These five functions will be reviewed and compared together with conventional Weibull function. Wind speed data measured from 2006 to 2008 at three wind farms experiencing different climatic environments in Taiwan are selected as sample data to test their performance. Judgment criteria include four kinds of statistical errors, i.e. the max error in Kolmogorov–Smirnov test, root mean square error, Chi-square error and relative error of wind potential energy. The results show that all the mixture functions and the maximum entropy function describe wind characterizations better than the conventional Weibull function if wind regime presents two humps on it, irrespective of wind speed and power density. For wind speed distributions, the proposed GW pdf describes best according to the Kolmogorov–Smirnov test followed by the NW and WW pdfs, while the NN pdf performs worst. As for wind power density, the MEP and GW pdfs perform best followed by the WW and NW pdfs. The GW pdf could be a useful alternative to the conventional Weibull function in estimating wind energy potential.     

兆瓦级风力机结构系统可靠性分析的样本分数阶矩最大熵方法

以兆瓦级风力机塔架和叶片极限载荷的概率外推模型为基础,结合载荷动态响应峰值的独立同分布假设和三参数威布尔模型,外推获取了正常湍流和极端湍流强度条件下风力机关键部件长期服役载荷概率分布;进一步通过无量纲极值统计量定义系统失效的结构可靠性状态函数,结合样本分数阶矩和最大熵理论提出兆瓦级风力机关键部件结构可靠性分析的数值方法,对比湍流模型对兆瓦级风力机关键部件结构失效概率的影响。计算结果表明：样本分数阶矩最大熵方法能有效重构结构可靠性状态函数的概率分布;基于无量纲极值统计量的系统可靠性建模方法能有效表征风力机关键部件耦合相关失效问题,结合该文方法可获得系统失效概率的准确预测结果;湍流模型对风力机结构失效概率影响较大,难以预先判定何种模型将得到结构失效概率的保守预估结果,需结合IEC 61400-1标准中的设计载荷工况细致分析后才能确定。     

可调式喷嘴雾化液滴粒径分布预测

阐述并推导了构建喷嘴雾化液滴粒径分布模型的三种方法:经验法、最大熵法和离散概率函数法.将最大熵法模型应用于可调式机械-空气喷嘴雾化中,计算出的液滴体积分布与累积体积分布结果与实验结果、R-R分布拟合结果吻合较好.     

中小流域洪峰流量与水位联合分布的设计洪水分析

针对库岸堤坝防洪设计中洪峰流量与相应洪峰水位的联合分布研究的不足,采用Archimedean Gumbel-Hougaard Copula函数和Kendall分布函数分析洪峰流量和洪峰水位联合分布的重现期水平。以罗坝水流域结龙湾水文站1958～2013年的洪峰流量和相应洪峰水位为例,计算了二者联合分布下的"或"重现期、"且"重现期和Kendall重现期及其最可能的设计值。结果表明,洪峰流量和洪峰水位的遭遇条件概率显示存在多种防洪设计标准;对比"或"联合重现期和"且"重现期,Kendall重现期更准确地反映了洪峰流量和洪峰水位组合的风险率;以出现最大概率原理推算的不同洪峰流量和水位遭遇概率组合的Kendall重现期设计值为多种防洪标准选择与风险管理提供了更多的参考依据。     

A comparison between wind speed distributions derived from the maximum entropy principle and Weibull distribution. Case of study; six regions of Algeria

The knowledge of the probability density function of wind speed is of paramount importance in many applications such as wind energy conversion systems and bridges construction. An accurate determination of the probability distribution of wind speed allows an efficient use of wind energy, thus rendering wind energy conversion system more productive. In the present paper, the maximum entropy principle (MEP) is used to derive a family of pre-exponential distributions in order to fit wind speed distributions. Using averaged hourly wind speed of six different regions in Algeria, it has been found that the proposed pre-exponential distributions fit the wind speed distributions better than the conventional Weibull distributions in terms of root mean square error. However, it has been found also that MEP based distributions have shown some practical limitations such as the choice of pre-exponential order and interval of definition.     

Quality of wind speed fitting distributions for the urban area of Palermo,Italy

This study investigates the wind speed characteristics recorded in the urban area of Palermo, in the south of Italy, by a monitoring network composed by four weather stations. This article has two main objectives: the first one, to describe with clarity and simplicity the numerical procedures adopted to perform a preliminary statistical analysis of wind speed data, providing at the same time, the necessary mathematical tools useful to perform this analysis also without special software. The second objective is to verify if there are more suitable probability distributions able to better represent the original data respect the traditional ones. After a preliminary statistical analysis, in which the wind speed time series are split and analysed for each month and season, seven probability density functions are employed to describe wind speed frequency distributions: Weibull, Rayleigh, Lognormal, Gamma, Inverse Gaussian, Pearson type V and Burr. Shape and scale parameters for each weather station, period and distribution are provided. Their estimation is performed using the maximum likelihood method and the maximum likelihood estimators for each probability density function are provided. The quality of the data-fit is assessed by the classic statistical test Kolmogorov–Smirnov. The statistical test is used to rank the selected distributions in order to identify the distribution better fitting with the wind speed data measured in the urban area of Palermo. The Burr probability density function seems to be the most reliable statistical distribution.     

基于Copula-vines的电机线圈发热故障状态监测研究

小型交流电机作为现代工业化的重要基础设备之一,实现对其整体运行状态的实时监测显得尤其重要。通过对电机现有基本多元监测参数构建联合分布的密度函数作为正常运行的状态标准,利用藤理论将多元参数分组分解为两两相关结构,构建最优二元联合分布的Copula函数模型实现对电机状态准确描述。以相对熵作为评价监测数据与正常数据的概率密度的分布差异。实验表明,基于多元Copula函数构建的小型交流电机状态参数联合分布的概率密度函数作为故障特征值,能在电机线圈发热初期及时预警。系统实现了基于现有监测参数对电机故障状态快速预识别,从而避免电机运行事故的发生。     

中国水库年最高水位统计特性分析（英）

对中国 1 60个水库年最高水位纪录资料的统计特性进行了分析 .研究结果表明 ,水库年最高水位为独立随机变量 ,可用三参数 (均值、Cv 和 Cs)对数正态分布描述 ,其参数与水库特性和水文地区有关 ,宜采用概率权重矩法估计。建立的多元回归方程对工程应用是有益的。在设计标准期内 ,水库年最高水位的分布可近似表示为正态分布 ,这对水库大坝结构安全设计的可靠性估计是十分有用的     

Response load extrapolation for wind turbines during operation based on average conditional exceedance rates

The paper explores a recently developed method for statistical response load (load effect) extrapolation for application to extreme response of wind turbines during operation. The extrapolation method is based on average conditional exceedance rates and is in the present implementation restricted to cases where the Gumbel distribution is the appropriate asymptotic extreme value distribution. However, two extra parameters are introduced by which a more general and flexible class of extreme value distributions is obtained with the Gumbel distribution as a subclass. The general method is implemented within a hierarchical model where the variables that influence the loading are divided into ergodic variables and time‐invariant non‐ergodic variables. The presented method for statistical response load extrapolation was compared with the existing methods based on peak extrapolation for the blade out‐of‐plane bending moment and the tower mudline bending moment of a pitch‐controlled wind turbine. In general, the results show that the method based on average conditional exceedance rates predicts the extrapolated characteristic response loads at the individual mean wind speeds well and results in more consistent estimates than the methods based on peak extrapolation. Copyright © 2011 John Wiley & Sons, Ltd.     

Copula‐based model for wind turbine power curve outlier rejection

Power curve measurements provide a conventional and effective means of assessing the performance of a wind turbine, both commercially and technically. Increasingly high wind penetration in power systems and offshore accessibility issues make it even more important to monitor the condition and performance of wind turbines based on timely and accurate wind speed and power measurements. Power curve data from Supervisory Control and Data Acquisition (SCADA) system records, however, often contain significant measurement deviations, which are commonly produced as a consequence of wind turbine operational transitions rather than stemming from physical degradation of the plant. Using such raw data for wind turbine condition monitoring purposes is thus likely to lead to high false alarm rates, which would make the actual fault detection unreliable and would potentially add unnecessarily to the costs of maintenance. To this end, this paper proposes a probabilistic method for excluding outliers, developed around a copula‐based joint probability model. This approach has the capability of capturing the complex non‐linear multivariate relationship between parameters, based on their univariate marginal distributions; through the use of a copula, data points that deviate significantly from the consolidated power curve can then be removed depending on this derived joint probability distribution. After filtering the data in this manner, it is shown how the resulting power curves are better defined and less subject to uncertainty, whilst broadly retaining the dominant statistical characteristics. These improved power curves make subsequent condition monitoring more effective in the reliable detection of faults. Copyright © 2013 John Wiley & Sons, Ltd.     

Wind turbine effect on the voltage profile of distribution networks

The operation of wind turbines in the distribution networks may affect the power quality offered to the consumers. One of the most important considerations is the effect on the voltage profile, i.e. the induced slow voltage variations, which are the subject of this paper. Two alternative approaches are presented for their evaluation. The first, adopted by many utility guides and recommendations, is deterministic, seeking to ensure that the voltage deviations always remain within certain limits. The other recognises the statistical nature of the voltage variations and conforms to latest European Norm, EN 50160. Rather than assessing the maximum deviations that can possibly appear, the probability distribution of the voltage is calculated and then the conformity to the standards is assessed. In applying the statistical method, either time series, or directly probability distributions can be used. As a study case, the methods are applied to an existing MV distribution feeder, where significant wind power is installed. Measurement data are provided for the same feeder.