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.     

Statistical wind direction modeling for the analysis of large scale wind power generation

Understanding the effects of large‐scale wind power generation on the electric power system is growing in importance as the amount of installed generation increases. In addition to wind speed, the direction of the wind is important when considering wind farms, as the aggregate generation of the farm depends on the direction of the wind. This paper introduces the wrapped Gaussian vector autoregressive process for the statistical modeling of wind directions in multiple locations. The model is estimated using measured wind direction data from Finland. The presented methodology can be used to model new locations without wind direction measurements. This capability is tested with two locations that were left out of the estimation procedure. Through long‐term Monte Carlo simulations, the methodology is used to analyze two large‐scale wind power scenarios with different geographical distributions of installed generation. Wind generation data are simulated for each wind farm using wind direction and wind speed simulations and technical wind farm information. It is shown that, compared with only using wind speed data in simulations, the inclusion of simulated wind directions enables a more detailed analysis of the aggregate wind generation probability distribution. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Copula-based joint distribution analysis of wind speed and wind direction: Wind energy development for Hong Kong

Accurate and reliable assessment of wind energy potential has important implication to the wind energy industry. Most previous studies on wind energy assessment focused solely on wind speed, whereas the dependence of wind energy on wind direction was much less considered and documented. In this paper, a copula-based method is proposed to better characterize the direction-related wind energy potential at six typical sites in Hong Kong. The joint probability density function (JPDF) of wind speed and wind direction is constructed by a series of copula models. It shows that Frank copula has the best performance to fit the JPDF at hilltop and offshore sites while Gumbel copula outperforms other models at urban sites. The derived JPDFs are applied to estimate the direction-related wind power density at the considered sites. The obtained maximum direction-related wind energy density varies from 41.3 W/m² at an urban site to 507.9 W/m² at a hilltop site. These outcomes are expected to facilitate accurate micro-site selection of wind turbines, thereby improving the economic benefits of wind farms in Hong Kong. Meanwhile, the developed copula-based method provides useful references for further investigations regarding direction-related wind energy assessments at various terrain regions. Notably, the proposed copula-based method can also be applied to characterize the direction-related wind energy potential somewhere other than Hong Kong.     

Hourly wind speed analysis in Sicily

The hourly average wind speed data recorded by CNMCA (Centro Nazionale di Meteorologia e Climatologia Aeronautica) have been used to study the statistical properties of the wind speed at nine locations on Sicily. By grouping the observations month by month, we show that the hourly average wind speed, with calms omitted, is represented by a Weibull function. The suitability of the distribution is judged by the discrepancies between the observed and calculated values of the monthly average wind speed and of the standard deviation.     

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.     

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.     

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.     

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.     

Short‐term spatio‐temporal prediction of wind speed and direction

This paper aims to produce a low‐complexity predictor for the hourly mean wind speed and direction from 1 to 6 h ahead at multiple sites distributed around the UK. The wind speed and direction are modelled via the magnitude and phase of a complex‐valued time series. A multichannel adaptive filter is set to predict this signal on the basis of its past values and the spatio‐temporal correlation between wind signals measured at numerous geographical locations. The filter coefficients are determined by minimizing the mean square prediction error. To account for the time‐varying nature of the wind data and the underlying system, we propose a cyclo‐stationary Wiener solution, which is shown to produce an accurate predictor. An iterative solution, which provides lower computational complexity, increased robustness towards ill‐conditioning of the data covariance matrices and the ability to track time‐variations in the underlying system, is also presented. The approaches are tested on wind speed and direction data measured at various sites across the UK. Results show that the proposed techniques are able to predict wind speed as accurately as state‐of‐the‐art wind speed forecasting benchmarks while simultaneously providing valuable directional information. Copyright © 2013 John Wiley & Sons, Ltd.     

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.