Weibull Distribution for Estimating the Parameters

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a novel approach based on Weibull distribution to determine the capacity of wind turbine generators (WTGs) using capacity factor (CF), normalized average power (<formula formulatype="inline"><tex> $P_{N}$</tex> </formula>), and the product of CF and <formula formulatype="inline"><tex>$P_N$</tex> </formula> under different values of tower height and rated wind speed. Five locations for installation of WTG in Taiwan are practically examined. The proposed Weibull distribution is employed to represent probability distribution of wind speed variation, while the important relationships among mean wind speed (MWS), standard deviation of wind speed, and both scale and shape parameters of the Weibull distribution are also derived. The cost of energy (COE) and capital costs of WTG under different tower heights and various locations are also determined. It can be concluded from the simulation results of five installation locations of WTG in Taiwan that suitable values for both shape parameter and scale parameters of Weibull distribution as well as wind turbine capacity are identically important for selecting locations of installing WTG. The scale parameter of Weibull distribution also significantly affects COE, and it is important to determine whether a wind farm is good or not. </para>

The intent of the study reported in this paper is to make analysis of the wind speed data and annual wind energy potential at Abomsa Metehara and Ziway in Ethiopia. The wind speed data was collected from National Metrology Agency of Ethiopia, and then monthly and annual mean wind speed, wind power potential, wind energy potential and Weibull distribution parameters for these three sites have been analyzed and assessed. In the results, the monthly mean wind speeds, the measured and Weibull estimated of most probable monthly wind velocity, wind velocity carrying maximum energy, monthly wind power and wind energy density for these three sites at site locations have been estimated. Based on monthly and annually mean wind speeds at stations, annually and monthly mean wind velocities at 40 m, 60 m, 80 m, 100 m and 120 m heights via wind shear law have been extrapolated. At these heights, annual mean wind velocity carrying maximum energy, annual most probable wind velocity, annual mean wind power and annual wind energy density for these sites have been estimated. Additionally, the annual cumulative distribution function and probability density function of wind speed for the selected sites have been obtained using the Weibull distribution functions.KeywordsMean wind speedWind power densityWeibull parametersWind-driven water pump

We report an analysis of trends in 850 hPa wind speed, as manifest in the NCEP–NCAR reanalysis fields, over the Baltic region during the latter half of the 20th century. The results indicate that annual mean wind speeds over the Baltic significantly increased over the period 1953–99 with the majority of the increase being associated with increases in the upper quartile of the wind speed distribution. Accordingly, much of the change is focused on the winter season. The trends in annual and seasonal mean wind speeds are greatest in relative and absolute sense in the southwest of the Baltic basin, where they are in excess of 0.25 m s−1 per decade for the annual mean. The extremes of the wind‐speed distribution also increased by up to 5 m s−1 over the study period for the wind speed with a 50 year return period, again with the largest magnitude changes in the southwestern Baltic. These changes in wind speed are strongly linked to changes in the synoptic‐scale circulation. The majority of the increase in wintertime wind speeds is attributable to an increase in westerly anticyclonic, westerly cyclonic and northwesterly cyclonic circulation types as manifest in the Grosswetterlagen catalogue, which are in turn related to the recent prevalence of the positive phase of the North Atlantic oscillation. Copyright © 2003 Royal Meteorological Society

ABSTRACTThe present article utilizes wind measurements from three buoys data collection stations in Ionian Sea to study the wind speed and power characteristics using the Weibull shape and scale parameters. Specifically, the site dependent, annual, and monthly mean patterns of mean wind speed, Weibull parameters, frequency distribution, most probable wind speed, maximum energy carrying wind speed, wind power density and wind energy density characteristics have been analyzed. The Weibull distribution was found to represent the wind speed distribution with more than 90% accuracy, in most of the cases. Moreover, the correlation between the percentages of times the wind speed was above cut-in-speed and the measured mean wind speed for the three selected sites, as the correlation between the aforementioned percentages and the scale parameter c were examined and were found linear. At all these sites, no definite increasing or decreasing trends in annual mean wind speed values could be detective over the data reporting period. The mean values of wind speed, scale parameter, most probable wind speed, maximum energy carrying wind speed, wind power and wind energy density values showed higher values during winter time and lower in summer time in Pylos and Zakynthos. Moreover, Pylos and Zakynthos were found to be the best sites from wind power harnessing point of view.

The statistical prediction of local sea surface winds from large-scale, free-tropospheric fields is investigated at a number of locations over the global ocean using a statistical downscaling model based on multiple linear regression. The predictands (the mean and standard deviation of both vector wind components and wind speed) calculated from ocean buoy observations on daily, weekly, and monthly scales are regressed on upper-level predictor fields from reanalysis products. It is found that in general the mean vector wind components are more predictable than mean wind speed in the North Pacific and Atlantic, while in the tropical Pacific and Atlantic the difference in predictive skill between mean vector wind components and wind speed is not substantial. The predictability of wind speed relative to vector wind components is interpreted by an idealized model of the wind speed probability density function, which indicates that in the midlatitudes the mean wind speed is more sensitive to the vector wind standard deviations (which generally are not well predicted) than to the mean vector winds. In the tropics, the mean wind speed is found to be more sensitive to the mean vector winds. While the idealized probability model does a good job of characterizing month-to-month variations in the mean wind speed in terms of the vector wind statistics, month-to-month variations in the standard deviation of speed are not well modeled. A series of Monte Carlo experiments demonstrates that the inconsistency in the characterization of wind speed standard deviation is the result of differences of sampling variability between the vector wind and wind speed statistics.

Large scale wind power penetration has a significant impact on the reliability of the electric generation systems. A wind farm consists of a large number of wind turbine generators (WTGs). A major difficulty in modeling wind farms is that the WTG not have an independent capacity distribution due to the dependence of the individual turbine output on the same energy source, the wind. In this paper, a model of the wind farm output power considering multi-wake effects is established according to the probability distribution of the wind speed and the characteristic of the wind generator output power: based on the simple Jenson wake effect model, the wake effect with wind speed sheer model and the detail wake effect model with the detail shade areas of the upstream wind turbines are discussed respectively. Compared to the individual wake effect model, this model takes the wind farm as a whole and considers the multi-wakes effect on the same unit. As a result the loss of the velocity inside the wind farm is considered more exactly. Furthermore, considering the features of sequentially and self-correlation of wind speed, an auto-regressive and moving average (ARMA) model for wind speed is built up. Also the reliability model of wind farm is built when the output characteristics of wind power generation units, correlation of wind speeds among different wind farms, outage model of wind power generation units, wake effect of wind farm and air temperature are considered. Simulation results validate the effectiveness of the proposed models. These models can be used to research the reliability of power grid containing wind farms, wind farm capacity credit as well as the interconnection among wind farms

Poor wind conditions in metropolitan areas can result in inadequate ventilation and degradation of the thermal environment. Several researches have demonstrated that the building ground floor elevation (BGFE) enhances the wind conditions surrounding buildings. Further investigation is required to thoroughly examine the BGFE’s impact on the wind conditions in the courtyard area. We researched how the various overhead placements affect the ventilation of a U-shaped school building’s courtyard space in different wind directions. We performed Computational Fluid Dynamics (CFD) numerical simulation experiments on 93 overhead scenarios based on field measurements and validation. The statistical analysis of the experimental data revealed that the BGFE had significant effects on reducing the mean air age (p &lt; 0.001), standard deviation of air age (p &lt; 0.01), standard deviation of wind speed (p &lt; 0.001), and mean wind speed (p &lt; 0.01) in the courtyard space. The BGFE in the northeastern zone of the U-shaped school building significantly increased the mean air age (p &lt; 0.05), while the BGFE in the middle and southwestern zones significantly decreased the mean air age (p &lt; 0.001), and the BGFE in the southeastern zone significantly decreased the mean wind speed (p &lt; 0.05). The BGFE facilitates the entry of fresh air and offers even ventilation while significantly reducing wind speed. Choose sites C and D to enhance the U-shaped courtyard’s ventilation and avoid locations B and E. This paper’s findings provide theoretical guidance for designing the elevation of courtyard space from a ventilation perspective and for the green rehabilitation of existing buildings.

Near‐surface seasonal and annual mean wind speed in Switzerland is investigated using homogenized observations, Twentieth Century Reanalysis (20CRv2c) data and raw model output of a 75 member EURO‐COoRdinated Downscaling EXperiment regional climate model (RCM) ensemble for present day and future scenarios. The wind speed observations show a significant decrease in the Alps and on the southern Alpine slopes in the period 1981–2010. However, the 20CRv2c data reveal that the recent trends lie well within the decadal variability over longer time periods and no clear signs of a systematic wind stilling can be found for Switzerland. The ensemble of RCMs shows large biases in the annual mean wind speed over the Jura mountains, and some members also show large biases in the Alps compared to station observations. The spatial distribution of the model biases varies strongly between the RCMs, while the resolution and the driving global model have less impact on the pattern of the model bias. The RCMs are mostly able to represent the seasonality of wind speed on the Plateau but miss important details in complex terrain related to local wind systems. Most models show no significant changes in near‐surface mean wind speed until the end of the 21st century. The model ensemble changes range from a 7% decrease to a 6% increase with an ensemble mean decrease of 1 to 2%. Due to model biases, the scale mismatch between model grid and station observations and the missing representation of local winds in the simulations, the changes need to be interpreted with utmost care. Future assessments might lead to major revisions even for the sign of the projected changes, in particular over complex terrain.

The power generated by a wind turbine generator depends mainly on the wind speed, and varies randomly with time. It could be very useful from a practical application point of view if an approximate wind power generation model can be developed, which is relatively simple to use in a reliability study, and requires relatively little wind data for the site of interest. Large wind farms are installed in locations with good wind resources, and they need to be connected to a power system grid. This paper presents a simplified wind speed model that can generate wind speed probability distributions for multiple wind farm sites if their annual mean wind speed and standard deviation values are known. The developed wind speed model can be combined with the wind turbine generator characteristics to obtain a simplified wind farm generation model that can be further modified to incorporate the effect of the transmission line on wind power delivery. The results from reliability studies on a test system are presented. The effects on the system reliability of different system parameters, such as the system load levels, and the size and length of the transmission line are analyzed.

A wind resource assessment was conducted for Phases I and II wind farms in Santa Vitoria do Palmar, Brazil. The data used for wind analysis was taken from April 2007 to March 2008 at a meteorological mast height of 101 m. A 10-minute data set of wind speed, standard deviation, wind direction, relative humidity, environmental temperature, and pressure were measured. Analytical estimation models were used to determine the Weibull parameters required for calculating the annual average wind speed, mean power density, cumulative distribution, and probability density functions of the wind regime. The probability density function statistical results were analyzed at two different heights – the reference height of 101 m and the hub height of 80 m. The outcomes were then compared with the WAsP numerical output. The analysis showed that the energy pattern factor method has a confidence level above 97.5% with a correlation coefficient of 100%. Calculation results showed that the annual mean wind speed was 8.10 m/s at 80 m hub height, recommending the site is appropriate for GL Wind 2010 and IEC 61400-1 Ed.2 Class II wind turbine generators. The characteristic wind turbulence at 101 m reference height was IEC Subclass B. Out of the selected wind turbine generators, the HAWT-5/2.50 MW has the highest capacity factor of 44.17% but the lowest levelized energy cost of US$ 44.36/MWh. WAsP was also used to numerically calculate the given locality’s net annual energy production. Based on the proposed wind turbine arrangement, the predicted net annual energy production with wake loss effect for Phases I and II wind farms are 104.92 GWh/year and 456.89 GWh/year, respectively.

Wind power distributions: A review of their applications

The climate of Faraday, situated at the west coast of the Antarctic Peninsula (AP), is strongly influenced by the extent of sea ice cover in the Amundsen and Bellingshausen Seas (ABS). ABS sea ice cover is negatively correlated with Faraday annual mean temperature, wind speed and cloudiness, while a positive correlation was found with precipitation frequency. The amplitude of the semi-annual oscillation (SAO) and wintertime ABS sea ice extent are coupled as follows: in years with a poorly-developed SAO, the northwestward migration of the circumpolar pressure trough from April to July is suppressed, causing negative sea ice anomalies in the ABS that persist throughout the winter. The weakening of the SAO since the late 1970s has led to: an increase of annual mean wind speed and cloudiness in the region, one of the possible causes for the onset of the long-term ABS sea ice cover decrease; and changes in the annual cycles of wind speed and cloudiness such that sea ice growth in the period April-July has decreased, causing negative winter sea ice anomalies in the ABS and enhanced regional warming.

Annual and seasonal variations in mean wind speed and wind turbine energy production

Wind energy is a non polluting cost-effective renewable energy source. The science of exploration of wind power is not a new one. For the past few centuries, people have been extracting energy from the wind in various ways. One means of converting wind energy to a more useful form is through the use of windmills. Wind power technology in Bangladesh has been growning significantly in the last decade. Capacity of wind turbines has been increased significantly and at the same time, the cost of generating power from wind has come down. For the purpose of wind data, first of all the wind data of the coastal areas in Bangladesh from January to December, 2006 is to be collected and sorted in sequence in appropriate frequency. The data are further analyzed and converted into several useful parameters, like daily mean wind speed, monthly mean wind speed, and mean annual wind speed. After that, the velocity frequency bar graph, energy bar graph, velocity duration curve, etc. have been plotted and analyzed. During the analysis, it has been found that an unusual wind characteristic at sitakundu on September, 2006 with respect to other month. This unusual wind behavior further analysis for determining wind gusts and Weibull parameters. The wind speed data of a location has been fitted to Weibull function to find different parameters for that site. The value of Weibull shape factor (k) and Weibull scale factor (c) have been calculated by different methods and compared and plotted them by employing different methods. Although the peak wind velocity, the equivalent pressure on rigid bodies, and the dynamic along wind response of flexible structures are component parts of the gust buffeting problem, different procedures have been developed in the technical literature with reference to each of these subjects.

Wind power potential of Saudi Arabia