A joint probability density function of wind speed and direction for wind energy analysis

A very flexible joint probability density function of wind speed and direction is presented in this paper for use in wind energy analysis. A method that enables angular–linear distributions to be obtained with specified marginal distributions has been used for this purpose. For the marginal distribution of wind speed we use a singly truncated from below Normal–Weibull mixture distribution. The marginal distribution of wind direction comprises a finite mixture of von Mises distributions. The proposed model is applied in this paper to wind direction and wind speed hourly data recorded at several weather stations located in the Canary Islands (Spain). The suitability of the distributions is judged from the coefficient of determination R².

The conclusions reached are that the joint distribution proposed in this paper: (a) can represent unimodal, bimodal and bitangential wind speed frequency distributions, (b) takes into account the frequency of null winds, (c) represents the wind direction regimes in zones with several modes or prevailing wind directions, (d) takes into account the correlation between wind speeds and its directions. It can therefore be used in several tasks involved in the evaluation process of the wind resources available at a potential site. We also conclude that, in the case of the Canary Islands, the proposed model provides better fits in all the cases analysed than those obtained with the models used in the specialised literature on wind energy.     

Characterization of wind speed data according to wind direction

Knowledge of the wind speed distribution and the most frequent wind directions is important when choosing wind turbines and when locating them. For this reason wind evaluation and characterization are important when forecasting output power. The data used here were collected from eleven meteorological stations distributed in Navarre, Spain. We obtained data for the period extending from 1992 to 1995, with each datum encompassing 10 minutes of time. Wind speed data of each station were gathered in eight directional sectors, each one extended over 45 degrees according to the direction from which the wind blows. The stations were grouped in two blocks: those under the influence of the Ebro valley and those in mountainous areas. For each group the Weibull parameters were estimated, (according to the Weibull probability paper because the Weibull distribution gives the best fit in this region). Kurtosis and skewness coefficients were estimated as well. The Weibull parameters, especially the scale parameter c, depend strongly on the direction considered, and both Weibull parameters show an increasing trend as the direction considered moves to the more dominant direction, while both kurtosis and skewness show a corresponding decreasing trend.     

ARMA based approaches for forecasting the tuple of wind speed and direction

Short-term forecasting of wind speed and direction is of great importance to wind turbine operation and efficient energy harvesting. In this study, the forecasting of wind speed and direction tuple is performed. Four approaches based on autoregressive moving average (ARMA) method are employed for this purpose. The first approach features the decomposition of the wind speed into lateral and longitudinal components. Each component is represented by an ARMA model, and the results are combined to obtain the wind direction and speed forecasts. The second approach employs two independent ARMA models – a traditional ARMA model for predicting wind speed and a linked ARMA model for wind direction. The third approach features vector autoregression (VAR) models to forecast the tuple of wind attributes. The fourth approach involves employing a restricted version of the VAR approach to predict the same. By employing these four approaches, the hourly mean wind attributes are forecasted 1-h ahead for two wind observation sites in North Dakota, USA. The results are compared using the mean absolute error (MAE) as a measure for forecasting quality. It is found that the component model is better at predicting the wind direction than the traditional-linked ARMA model, whereas the opposite is observed for wind speed forecasting. Utilizing VAR approaches rather than the univariate counterparts brings modest improvement in wind direction prediction but not in wind speed prediction. Between restricted and unrestricted versions of VAR models, there is little difference in terms of forecasting performance.     

Variogram time-series analysis of wind speed

Fluctuations of wind-power production are a significant hindrance to its high penetration in power systems. System operators have to provide complementary power and relevant control strategies to smooth out the fluctuations when large-scale wind power ones is injected into the grid. To better smooth the fluctuations, the change rate of the wind speed is a critical piece of information. In this study, the variogram function is introduced to measure the change rate of the wind speed. Based on the variogram time-series, some statistical analyses are conducted. These results contribute to a better understanding of the characteristics of the change rate of the wind speed, such as the chronological variation pattern of the change rate on a day, whether the future change rate can be forecasted, and whether there is a relationship between the change rate and wind speed.     

Statistical analysis of wind energy in Chile

Bearing in mind the current and pressing need for an update of the existing Chilean power supply system – which has been remarkably influenced by new requirements – the search for new energy supply sources has become a top priority.The wind resource, vis-à-vis its associated mature technology features and its apparent availability throughout Chile, comes forward as a feasible option likely to play a more important role in any future national energy generation matrix.With a view to understanding the local wind resource, this document surveys a sample set of wind profiles available in the northern Chile area, thus becoming the first public survey of this kind. It also tackles theoretical energy production and capacity factors. Those became the basis of the wind modelling we undertook for Chile’s participation in COP15. This paper shows wind generation is a suitable option for curbing down Greenhouse Gas Emissions (GHG) in Chile.     

考虑风速、风向变化及尾流效应的风电场建模

对风电场建模过程中,确立准确的输入风速模型至关重要。风电场中机组排列密集,风机之间存在尾流效应使得各台风机的输入风速不可能完全相同,尾流效应的强弱与很多因素有关,如:风速、风向、机组的排列布置等。利用MATLAB程序实现在不同风速、风向、风机排列情况下输入风速的计算,模拟实现对风速、风向变化情况下风电场的快速建模。可以较准确地描述出当风速、风向变化时风电场功率输出的变化。通过仿真验证了此方法的正确性,该方法的可移植性高,可用于各种规模风电场输入风速模型的计算。     

Effect of direction on wind speed estimation in complex terrain using neural networks

A method of estimating the annual average wind speed at a selected site using neural networks is presented. The method proposed uses only a few measurements taken at the selected site in a short time period and data collected at nearby fixed stations.The neural network used in this study is a multilayer perceptron with one hidden layer of 15 neurons, trained by the Bayesian regularization algorithm. The number of inputs that must be used in the neural network was analyzed in detail, and results suggest that only wind speed and direction data for a single station are required. In sites of complex terrain, direction is a very important input that can cause a decrease of 23% in root mean square (RMS).The results obtained by simulating the annual average wind speed at the selected site based on data from nearby stations are satisfactory, with errors below 2%.     

Trivariate maximum entropy distribution of significant wave height,wind speed and relative direction

A trivariate maximum entropy distribution of significant wave height, wind speed and the relative direction is proposed here. In this joint distribution, all the marginal variables follow modified maximum entropy distributions, and they are combined by a correlation coefficient matrix based on the Nataf transformation. The methods of single extreme factors and of conditional probability are presented for the joint design of trivariate random variables. The corresponding sampling data about significant wave heights, wind speeds and the relative directions from a location in the North Atlantic is applied for statistical analysis, and the results show that the trivariate maximum entropy distribution is sufficiently good to fit the data, and method of conditional probability can reduce the design values efficiently.     

Performance evaluation of cup-anemometers and wind speed characteristics analysis

The objective of the present work is to study the performance of cup-anemometers installed at different heights on a 40 m tall wind mast over an approximate period of 55 months between September 13, 2005 and May 09, 2010. The performance of co-located cup anemometers has been analyzed by calculating the annual mean, median, standard deviation, tower distortion factor (TDF), scatter factor (SCF), and developing linear correlations between the co-located sensors. The study showed that the performance of sensors did not deteriorate much with time but slightly higher values of TDF were obtained with passage of time. The annual mean wind speeds, the median values and the standard deviations were almost the same during different years and were comparable with co-located sensors at each height. The SCF values were found to be increasing with decreasing height of wind speed measurements. Finally, a total of 16 wind turbines of 2 MW rated capacity each were used to find the most suitable wind turbine for the location under investigation.     

低风速风力发电机轮毂强度与疲劳寿命分析

利用ANSYS有限元软件,对正常运行工况和危险工况下的低风速风力发电机轮毂进行了有限元分析,得到了轮毂的应力分布状况。利用ANSYS的Fatigue模块对轮毂进行了疲劳寿命计算,并进行了强度校核,危险工况下的应力分析表明,轮毂满足强度的要求,安全系数为2.1,轮毂的疲劳寿命为8.8 a。     

Daily wind speed harmonic analysis for Marmara region in Turkey

Presently exploited rates of fossil fuels are expected to deplete resources within the next 40–50 years, and consequently, human beings seek alternative energy resources that are clean, friendly to the environment and sustainable. Accumulation of carbon dioxide in the lower layers of the atmosphere may cause climate change and consequent occurrence of floods, intensive rainfalls and droughts. In order to reduce such dangerous effects all countries have to try to improve their energy resources quality and, if possible, to replace fossil fuels, such as coal, with the renewable alternatives of wind, solar and solar-hydrogen energies. Among these, wind power has a priori significance for Turkey. Wind time series depend very much on meteorological measurements of wind direction and velocity. Unfortunately, in many parts of the world, it is difficult to obtain such data for wind speed time series assessments.In this study, harmonic analysis is used to model the daily wind speed values recorded at ten stations in the Marmara region, Turkey, with distinct meteorological conditions from 1993 to 1997. The coefficients, amplitude, variance and phase angle, of each harmonic are calculated for the months of January, April, July and October, leading to total variance maps for spatial interpolations. It is seen that up to the 9th harmonic more than 80% of the total variance can be presented. The western and eastern parts of the Marmara region have different wind pattern characteristics. The contributions of each harmonic to the total variance are calculated, and then regional variance maps are evaluated.     

Transient analysis of variable-speed wind turbines at wind speed disturbances and a pitch control malfunction

As wind power generation undergoes rapid growth, new technical challenges emerge: dynamic stability and power quality. The influence of wind speed disturbances and a pitch control malfunction on the quality of the energy injected into the electric grid is studied for variable-speed wind turbines with different power-electronic converter topologies. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with permanent magnet synchronous generators. The performance of disturbance attenuation and system robustness is ascertained. Simulation results are presented and conclusions are duly drawn.     

Dynamic behavior and transient stability analysis of fixed speed wind turbines

This paper analytically investigates the dynamic behavior of fixed speed wind turbines (FSWTs) under wind speed fluctuations and system disturbances, and identifies the nature of transient instability and system variables involved in the instability. The nature of transient instability in FSWT is not similar to synchronous generators in which the cause of instability is rotor angle instability. In this paper, the study of dynamic behavior includes modal and sensitivity analysis, dynamic behavior analysis under wind speed fluctuation, eigenvalue tracking, and using it to characterize the instability mode, and investigating possible outcomes of instability. The results of theoretical studies are verified by time domain simulations. It is found that the instability occurs due to the mechanical dynamics and the instability is closely related to increasing of generator slip.     

Load flow analysis for variable speed offshore wind farms

A serial AC?DC integrated load flow algorithm for variable speed offshore wind farms is proposed. It divides the electrical system of a wind farm into several local networks, and different load flow methods are used for these local networks sequentially. This method is fast, more accurate, and many factors such as the different wind farm configurations, the control of wind turbines and the power losses of pulse width modulation converters are considered. The DC/DC converter model is proposed and integrated into load flow algorithm by modifying the Jacobian matrix. Two iterative methods are proposed and integrated into the load flow algorithm: one takes into account the control strategy of converters and the other considers the power losses of converters. In addition, different types of variable speed wind turbine systems with different control methods are investigated. Finally, the method is demonstrated using an 80-MW offshore wind farm.     

Simulation of hourly wind speed and array wind power

Statistical summaries of wind speed are sufficient to compute many characteristics of turbine-generated power, such as the mean, variance and reliability of various power levels. However, a wind speed time series is necessary to produce a sequence of power values as used for investigating load matching and storage requirements. Since a long historical record of wind speed may not be available at a wind turbine candidate site, it is desirable to be able to generate a simulated numerical sequence of hourly wind speed values. Two such approximate procedures are developed in this paper. One procedure generates sequential wind speed values at a site based on the Weibull parameters of hourly wind speed and the lag-one autocorrelation of hourly wind speed values. Comparison with historical data at a site is made. The second procedure generates sequential hourly wind power values for a regional array of wind turbines. It utilizes the typical site wind characteristics, the spatial and lag-one cross correlation and autocorrelation of hourly wind speed values and an equivalent linearized relationship between array average wind speed and array power. Comparison with results for six different wind turbines in three different regional arrays indicates good agreement for wind power histograms, autocorrelation function and mean persistence.     

基于不同风切变指数算法的风场风速推算精度分析

文章采用内蒙古某风场测风塔3 a逐10 min风速实测数据,基于5种算法计算不同高度层间风切变指数,分别进行风速实例推算,对比分析各种算法的精度。结果表明:去除小风速数据算法(M2)较其他4种算法的变异系数小,推算风速精度总体最高;同一算法中,不同高度层间风切变指数随高度层高度和层间高度差增加而增大,非相邻层间风切变指数随高度差增加而增大;同一算法中,年平均风速推算比月平均风速推算精度更高,相邻层间风速推算较非相邻层间风速推算精度高,且相邻高度层越高精度越高,非相邻层间风速推算,高度差越小精度越高。该研究结果对风场建设可行性论证和风资源评估,及开展风场轮毂高度风速的推算、预测具有较好的指导意义。     

Small-signal model and dynamic analysis of variable speed induction machine wind farms

A unified, modular, small-signal dynamic model for an induction machine-based wind farm is presented. The proposed model can represent an arbitrary number of fixed-speed, partially variable-speed (doubly fed) and variable-speed induction machine-based wind units in a wind farm. The model represents the dynamics of (i) each wind turbine-generator electromechanical system, (ii) each converter system and the corresponding controls and (iii) the host electrical grid, within the subsynchronous frequency range (0.1?60 Hz). In contrast to the widely used state-space formulation, the proposed approach is based on developing electrical and mechanical transfer-function matrices to formulate the overall system as a multivariable feedback system. Thus, it provides significant flexibility to represent a large number of wind units and their controllers, identical or nonidentical, within a wind farm. Based on the developed model, a frequency response-based method is also introduced, as an alternative to the eigen analysis approach, for small-signal subsynchronous dynamic analysis of the wind farm and its host electrical grid. The proposed method provides a new performance robustness criterion for performance evaluation and also a design tool based on the `size? of the system transfer-function matrix. The concept of induced norm is adopted here as a measure of matrix size. As an example, applications of the model and the analysis approach to a twounit wind farm is presented and the results are validated based on time-domain simulation studies in the PSCAD/ EMTDC environment.     

A study of the wind speed and wind energy availability in Bangladesh

Characteristics of wind speed data for three recent years, recorded at 14 stations of the Bangladesh Meteorological Department, have been studied. The data have been used to compute the monthly average wind speed and the wind energy availability for the stations. Average values of monthly wind speed for 1931–1960 have been employed to obtain the energy availability from the energy pattern factor, and the two sets of results have been compared. It has been found that, for the Chittagong station, the frequency distributions have good fits of the Weibull type.     

大型恒频变速风力发电机组桨叶的建模与动态特性分析

通过计算桨叶的弯曲频率和扭转频率,采用ANSYS大型有限元软件对大型恒频变速风力发电机组桨叶进行建模,同时分析该桨叶动态特性的优缺点,并分析影响桨叶建模和动态特性的主要因素,对计算值和测量值的误差进行比较,同时对桨叶的振型进行分析,为今后更深入地研究大型恒频变速风电机组桨叶特性奠定了良好的理论基础。     

Low wind speed turbines and wind power potential in Minnesota, USA

Wind power development in Minnesota largely has been focused in the “windy” southwestern part of the state. This research evaluates the additional power that potentially could be generated via low wind speed turbines, particularly for areas of the state where there has been comparatively little wind energy investment. Data consist of 3 years (2002–2004) of wind speed measurements at 70–75 m above ground level, at four sites representing the range of wind speed regimes (Classes 2–5) found in Minnesota. Power estimates use three configurations of the General Electric 1.5-MW series turbine that vary in rotor diameter and in cut-in, cut-out, and rated speeds. Results show that lower cut-in, cut-out, and rated speeds, and especially the larger rotor diameters, yield increases of 15–30% in wind power potential at these sites. Gains are largest at low wind speed (Class 2) sites and during the summer months at all four sites. Total annual wind power at each site shows some year-to-year variability, with peaks at some sites partially compensating for lulls at others. Such compensation does not occur equally in all years: when large-scale atmospheric circulation patterns are strong (e.g., 2002), the four sites show similar patterns of above- and below-average wind power, somewhat reducing the ability of geographic dispersion to mitigate the effects of wind speed variability.