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.     

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.     

Assessment of wind characteristics and wind turbine characteristics in Taiwan

Wind characteristics and wind turbine characteristics in Taiwan have been thoughtfully analyzed based on a long-term measured data source (1961–1999) of hourly mean wind speed at 25 meteorological stations across Taiwan. A two-stage procedure for estimating wind resource is proposed. The yearly wind speed distribution and wind power density for the entire Taiwan is firstly evaluated to provide annually spatial mean information of wind energy potential. A mathematical formulation using a two-parameter Weibull wind speed distribution is further established to estimate the wind energy generated by an ideal turbine and the monthly actual wind energy generated by a wind turbine operated at cubic relation of power between cut-in and rated wind speed and constant power between rated and cut-out wind speed. Three types of wind turbine characteristics (the availability factor, the capacity factor and the wind turbine efficiency) are emphasized. The monthly wind characteristics and monthly wind turbine characteristics for four meteorological stations with high winds are investigated and compared with each other as well. The results show the general availability of wind energy potential across Taiwan.     

Reliably model of microwind power energy output under real conditions in France suburban area

Micro-wind turbine are now specially designed for rural or urban environment and one of the main advantages of such turbine is that it can be propelled by a wind speed as low as 3 m/s. However, due to terrain roughness in urban environments wind flow is reduced compared to open spaces reducing power output and increasing payback time on capital investment. Well mounting turbines in urban areas may provide the perfect opportunity for onsite generation from wind power. In this paper, we investigate the performance of a micro-wind turbine in a complex urban area and show that due to long time period and very subtile onsite measurements the ideal position for the wind turbine can be determined. Well measured data, wind speed, power output at this particular location are approximated by the Weibull function. The considered model is tested and validated at an urban landscape location in Metz City, France, where an anemometry is positioned at adjacent to the turbine and the instrumentation is positioned specific to its surrounding location and, record wind turbine data thanks to real time wireless communications. Technical data including wind speed and output power were analyzed and reported allowing to provide an reliable estimation of the wind energy potential in an urban location.     

Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application

Two-parameter Weibull function has been widely applied to evaluate wind energy potential. In this paper, six kinds of numerical methods commonly used for estimating Weibull parameters are reviewed; i.e. the moment, empirical, graphical, maximum likelihood, modified maximum likelihood and energy pattern factor method. Their performance is compared through Monte Carlo simulation and analysis of actual wind speed according to the criterions such as Kolmogorov–Smirnov test, parameter error, root mean square error, and wind energy error. The results show that, in simulation test of random variables, the graphical method’s performance in estimating Weibull parameters is the worst one, followed by the empirical and energy pattern factor methods, if data number is smaller. The performance for all the six methods is improved while data number becomes larger; the graphical method is even better than the empirical and energy pattern factor methods. The maximum likelihood, modified maximum likelihood and moment methods present relatively more excellent ability throughout the simulation tests. From analysis of actual data, it is found that if wind speed distribution matches well with Weibull function, the six methods are applicable; but if not, the maximum likelihood method performs best followed by the modified maximum likelihood and moment methods, based on double checks including potential energy and cumulative distribution function.     

Implications of seasonal and diurnal variations of wind velocity for power output estimation of a turbine: a case study of Grenada

This case study highlights the importance of taking into consideration diurnal variations of wind velocity for wind energy resources assessment. Previous studies of wind energy distribution that are based on the two-parameter Weibull density function have so far neglected to consider time of day fluctuations in wind speed, instead concentrating primarily on seasonal deviations. However, this has serious implications where such a wind energy model is the underpinning of calculations for the potential power production from a wind turbine and in particular where the timing of the energy output is essential to meet electricity loads. In the case of Grenada the energy output from a wind turbine during the day is approximately two times the output at night thereby fluctuating enormously around the seasonal mean distribution. When this is not taken into account the economic and technological viability of a wind turbine project may be overestimated or not even be identified. This work shows how a wind energy resources assessment based on the Weibull distribution model can be done and how the power output of a horizontal axis turbine is calculated. An analysis of the recorded wind data confirms the application of the Weibull density function as a suitable tool for modelling wind regimes. Copyright © 2003 John Wiley & Sons, Ltd.     

Uncertainty analysis of wind energy potential assessment

This study presents a framework to assess the wind resource of a wind turbine using uncertainty analysis. Firstly, probability models are proposed for the natural variability of wind resources that include air density, mean wind velocity and associated Weibull parameters, surface roughness exponent, and error for prediction of long-term wind velocity based on the Measure–Correlate–Predict method. An empirical probability model for a power performance curve is also demonstrated. Secondly, a Monte-Carlo based numerical simulation procedure which utilizes the probability models is presented. From the numerical simulation, it is found that the present method can effectively evaluate the expected annual energy production for different averaging periods and confidence intervals. The uncertainty, which is 11% corresponding to the normalized average energy production in the present example, can be calculated by specifically considering the characteristics of the individual sources in terms of probability parameters.     

Wind power potential and characteristic analysis of the Pearl River Delta region, China

Wind power potentials of the Pearl River Delta (PRD) region have been statistically analyzed based on the hourly measured wind speed data in four islands. The hourly and monthly wind speed and wind power density are assessed to have remarkable variations, and the Weibull distribution function has been derived from the available data with its two parameters identified. The wind power and operating possibilities of these locations have been studied based on the Weibull function. The wind power potentials of these sites were found to be encouraging; however, the wind power at different site varies significantly, so attention should be paid to the wind conditions as well as the site terrains in choosing the wind farm sites.     

Potential wind power generation in the State of Kuwait

The wind characteristics of six locations in the State of Kuwait have been assessed. The annual average wind speed for the considered sites ranged from 3.7 to 5.5 m/s and a mean wind power density from 80 to 167 W/m² at standard height of 10 m. The Weibull parameters and power density of each station have been determined using Weibull distribution. The wind data at heights 15, 20, 25 and 30 m were obtained by extrapolation of the 10 m data using the Power-Law. The potential wind energy at different heights was estimated using Weibull parameters. Maximum power density is found at 30 m height which varies between 130 and 275 W/m² with 70% increase from the standard height indicating fairly potential wind energy especially in the northern part of the country. The highest potential wind power was found during the summer season which is the peak demand season of electricity in Kuwait.     

Performance evaluation of pairing between sites and wind turbines

This paper presents a simple method for determination of pairing between sites and wind generators. It requires six parameters to describe the matching between turbine models and site characteristics, and the energy output performance can thus be easily estimated and used as the index of pairing effectiveness. To describe a Weibull model of wind speed distribution, the shape parameter and the scale parameter are necessarily required. Besides, four other parameters are chosen to specify the characteristics of the power curve of a wind generator: the cut-in speed, the rated speed, the cut-off speed and the nominal power. By combining these six parameters, the average power output of some particular wind turbine at a specific site can be practically and quickly approximated as a reference for turbine siting consideration. An example is also shown to demonstrate the utilization of the proposed method to choose between a group of wind sites and a list of commercial wind turbines.     

Investigation of wind characteristics and wind energy potential in Kirklareli, Turkey

Utilization of wind energy as an energy source has been growing rapidly in the whole world due to environmental pollution, consumption of the limited fossil fuels and global warming. Although Turkey has fairly high wind energy potential, exploitation of the wind energy is still in the crawling level. In the current study, wind characteristics and wind energy potential of Kırklareli province in the Marmara Region, Turkey were analyzed taking into account the wind data measured as hourly time series. The wind data used in the study were taken from Electrical Power Resources Survey and Development Administration (EIEI) for the year 2004. The measured wind data were processed as annual, seasonal and monthly. Weibull and Rayleigh probability density functions of the location are calculated in the light of observed data and Weibull shape parameter k and scale parameter c are found as 1.75 and 5.25 m/s for the year 2004. According to the power calculations done for the site, annual mean power density based on Weibull function is 138.85 W/m². The results indicate that investigated site has fairly wind energy potential for the utilization.     

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.     

A new semi-empirical wind turbine capacity factor for maximizing annual electricity and hydrogen production

The capacity factor is an important wind turbine parameter which is ratio of average output electrical power to rated electrical power of the wind turbine. Another main factor, the AEP, the annual energy production, can be determined using wind characteristics and wind turbine performance. Lower rated power may lead to higher capacity factor but will reduce the AEP. Therefore, it is important to consider simultaneously both the capacity factor and the AEP in design or selecting a wind turbine. In this work, a new semi-empirical secondary capacity factor is introduced for determining a rated wind speed at which yearly energy and hydrogen production obtain a maximum value. This capacity factor is expressed as ratio of the AEP for wind turbine to yearly wind energy delivered by mean wind speed at the rotor swept area. The methodology is demonstrated using the empirical efficiency curve of Vestas-80 2 MW turbine and the Weibull probability density function. Simultaneous use of the primary and the secondary capacity factors are discussed for maximizing electrical energy and hence hydrogen production for different wind classes and economic feasibility are scrutinized in several wind stations in Kuwait.     

Wind power energy potential at the northeastern region of Saudi Arabia

In the present study the energy potential of wind for the Eastern Province of Saudi Arabia is investigated. A suitable Weibull distribution is generated based on the data obtained for a duration of one complete year at a costal location in northeastern Saudi Arabia. Comparison of this model is made with the Rayleigh distribution of wind power densities. Two horizontal-axis type of wind energy conversion systems which operate at fixed rpm are considered and a model of quadratic power output function is used. It is found that the error in using the Rayleigh approximation will be less than 10% of the full rated power density level.     

Evaluation of hydrogen production from harvesting wind energy at high altitudes in Iran by three extrapolating Weibull methods

One of the most appropriate ways for energy storage is producing hydrogen from renewable resources. Wind energy is recognized as one of the widely used renewable energy resources. This paper investigates the use of wind energy for producing hydrogen in Iran. To achieve this, the country is divided into five major regions: center, north, south, east and west. The performance of three large-scale commercial wind turbines, ranging from 1500 kW to 3000 kW at hub height of 80 m and four large-scale wind turbine ranging from 2000 kW to 4500 kW at hub height of 120 m are evaluated for producing hydrogen in 150 wind stations in Iran. All wind data were recorded based on 10-min time intervals for more than one year at different wind mast heights. For estimating Weibull parameters, the Standard Deviation Method (SDM), Empirical Method of Lysen (EML) and Power Density Method (PDM) are used. An extrapolation method is used to determine the shape and the scale parameters of the Weibull distribution at the high attitudes of 80 m and 120 m. Then, power law and surface roughness exponents, capacity factor, annual energy production and annual hydrogen production for the wind sites are determined. The results indicate that rated power is not the only determinative parameter and the highest hydrogen production is from the GW-109/2500 wind turbine at the hub height of 80 m and from E112/4500 at the hub height of 120 m. For better assessment, the amount of hydrogen production is depicted in Geographic Information Science (GIS) maps using power production of the seven wind turbine models. Next by analyzing these GIS maps, it is found that there are significant potentials in north, north-west, east and south of Iran for producing hydrogen from wind energy.     

Optimum turbine-site matching

This paper presents a new formulation for the turbine-site matching problem, based on wind speed characteristics at any site, the power performance curve parameters of any pitch-regulated wind turbine, as well as turbine size and tower height. Wind speed at any site is characterized by the 2-parameter Weibull distribution function and the value of ground friction coefficient (α). The power performance curve is characterized by the cut-in, rated, and cut-out speeds and the rated power. The new Turbine-Site Matching Index (TSMI) is derived based on a generic formulation for Capacity Factor (CF), which includes the effect of turbine tower height (h). Using the CF as a basis for turbine-site matching produces results that are biased towards higher towers with no considerations for the associated costs. The proposed TSMI includes the effects of turbine size and tower height on the Initial Capital Cost (ICC) of wind turbines. The effectiveness and the applicability of the proposed TSMI are illustrated using five case studies. In general, for each turbine, there exists an optimal tower height, at which the value of the TSMI is at its maximum. The results reveal that higher tower heights are not always desirable for optimality.     

新疆达坂城风电场风能资源特性分析

对新疆达坂城风电场的风能资源特性进行了详细的研究。基于在达坂城风电场实测的10m和24m高程的10min平均风速数据,分析了原始风速的分布特性。根据地表风速沿高度呈风剪指数分布的特性,计算了在各个轮毂高度上的风速分布。采用最小误差逼近算法原理,计算了风速韦布尔分布的参数以及平均风速和分布方差。通过对韦布尔分布的分析,计算了各个高度上风电场的平均风功率密度、有效平均风功率密度和可利用小时数等风能资源特性参数,为当地的风能开发提供分析基础。     

A particle swarm optimization for wind energy control problem

The control problem of a wind turbine involves the determination of rotor speed and tip-speed ratio to maximize power and energy capture from the wind. The problem can be formulated as a nonlinear programming problem with the annual energy generation as the objective function. The wind speed distribution is modeled as the Weibull distribution. The Weibull shape and scale parameters are assigned to be stochastic in response to limited wind data and variability nature of the wind. It is proposed to apply particle swarm optimization to solve for optimum rotor speed under fixed-speed operation and optimum tip-speed ratio under variable-speed operation. The optimum rotor speed varies with the wind speed distribution, while the optimum tip-speed ratio does not depend on the wind speed distribution. It can be concluded from the simulation results that both the wind power and energy are more dependent of the Weibull scale parameter than the Weibull shape parameter. This implies that the wind power and energy are more dependent of the mean wind speed than the speed distribution.