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.     

Application of Bayesian model averaging in modeling long-term wind speed distributions

Accurate estimation of wind speed distribution is critical to the assessment of wind energy potential, the site selection of wind farms, and the operations management of wind power conversion systems. This paper proposes a new approach for deriving more reliable and robust wind speed distributions than conventional statistical modeling approach. This approach combines Bayesian model averaging (BMA) and Markov Chain Monte Carlo (MCMC) sampling methods. The derived BMA probability density function (PDF) of the wind speed is an average of the model PDFs included in the model space weighted by their posterior probabilities over the sample data. MCMC method provides an effective way for numerically computing marginal likelihoods, which are essential for obtaining the posterior model probabilities. The approach is applied to multiple sites with high wind power potential in North Dakota. The wind speed data at these sites are the mean hourly wind speeds collected over two years. It is demonstrated that indeed none of the conventional statistical models such as Weibull distribution are universally plausible for all the sites. However, the BMA approach can provide comparative reliability and robustness in describing the long-term wind speed distributions for all sites, while making the traditional model comparison based on goodness-of-fit statistics unnecessary.     

Wind energy potential assessment in Uttara Kannada district of Karnataka, India

Availability of wind energy and its characteristics at Kumta and Sirsi in Uttara Kannada District of Karnataka has been studied based on primary data collected at these sites for a period of 24 months. Wind regimes at Karwar (1952–1989), Honnavar (1939–1989) and Shirali (1974–1989) have also been analysed based on data collected from India Meteorological Department (IMD) of respective meterological observatories. Wind energy conversion systems would be most effective in these taluks during the period May to August. The monthly frequency distributions of wind speed have been analysed for Kumta and Sirsi where hourly wind speed recording is available. It is shown that two parameter Weibull distribution is a good representation of the probability density function for the wind speed. Energy Pattern Factor (EPF) and Power Densities are computed for sites at Kumta and Sirsi. With the knowledge of EPF and mean wind speed, mean power density is computed for Karwar, Honnavar and Shirali. Our analyses show that the coastal taluks such as Karwar and Kumta have good wind potential. This potential, if exploited would help local industries and coconut and areca plantations. Premonsoon availability of wind energy would help in irrigating these orchards and makes the wind energy a desirable alternative.     

Wind characteristics and wind energy potential in Morocco

The wind characteristics of 11 sites in the windy regions in Morocco have been analysed. The annual average wind speed for the considered sites ranged from 5 m/s to 10 m/s and the average power density from 100 W/m² to 1000 W/m², which might be suitable for electrical power production by installing wind farms. On an annual scale the observations of the distribution of hourly wind speed are better fitted by the Weibull hybrid distribution in contrast to the Weibull distribution.The wind power is estimated to be 1817 MW, that is to say, the exploitable wind energy is 15198 GWh, which represents theoretically 11% of the total consumed energy in Morocco in 1994.     

The influence of the Weibull assumption in monthly wind energy estimation

An estimation of the monthly wind energy output for the period 1999–2003 at five wind farms in northeastern Spain was evaluated. The methodology involved the calculation of wind speed histograms and the observed average wind power versus wind relation obtained from hourly data. The energy estimation was based on the cumulated contribution of the wind power from each wind speed interval. The impact of the Weibull distribution assumption as a substitute of the actual histogram in the wind energy estimation was evaluated. Results reveal that the use of a Weibull probability distribution has a moderate impact in the energy calculation as the largest estimation errors are, on average, no larger than 10% of the total monthly energy produced. However, the evaluation of the goodness of fit through the χ² statistics shows that the Weibull assumption is not strictly substantiated for most of the sites. This apparent discrepancy is based on the partial cancellation of the positive and negative departures of the Weibull fitted and the actual wind frequency distributions. Further investigation of the relation between the χ² and the error contribution exposes a tendency of the Weibull distribution to underestimate (overestimate) the observed histograms in the lower and upper (intermediate) wind speed intervals. This fact, together with the larger wind power weight over the highest winds, results in a systematic total wind energy underestimation. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of wind power density at different heights in the Gelibolu peninsula of Turkey

This study aims to determine the wind characteristics and wind power potential of the Gelibolu peninsula in the Çanakkale region of Turkey. For this purpose, hourly average wind data observed at the Gelibolu meteorological station were used. The Weibull probability density functions and Weibull parameters of time-series of wind speed, mean wind speed, and mean wind power potential were determined for different heights as 10, 20, 30, 40, and 50 m. According to the results obtained at 10- and 50-m heights above the ground level, the annual wind speed varied from 6.85 to 8.58 m/s in this region, respectively. The annual wind power potential of the site was determined as 407 and 800 W/m² for 10- and 50-m heights, respectively. These results indicate that the investigated site has a reasonable wind power potential for generating electricity.     

A wind energy analysis of Grenada: an estimation using the ‘Weibull’ density function

The Weibull density function has been used to estimate the wind energy potential in Grenada, West Indies. Based on historic recordings of mean hourly wind velocity this analysis shows the importance to incorporate the variation in wind energy potential during diurnal cycles. Wind energy assessments that are based on Weibull distribution using average daily/seasonal wind speeds fail to acknowledge that wind speed probabilities can vary significantly during day and night. In particular where wind energy estimation is linked to electricity loads neglecting diurnal wind patterns can result in significant under/overestimation of wind power potential.     

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.     

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.     

Comparison between the bivariate Weibull probability approach and linear regression for assessment of the long-term wind energy resource using MCP

A detailed investigation of a measure–correlate–predict (MCP) approach based on the bivariate Weibull (BW) probability distribution of wind speeds at pairs of correlated sites has been conducted. Since wind speeds are typically assumed to follow Weibull distributions, this approach has a stronger theoretical basis than widely used regression MCP techniques. Building on previous work that applied the technique to artificially generated wind data, we have used long-term (11 year) wind observations at 22 pairs of correlated UK sites. Additionally, 22 artificial wind data sets were generated from ideal BW distributions modelled on the observed data at the 22 site pairs. Comparison of the fitting efficiency revealed that significantly longer data periods were required to accurately extract the BW distribution parameters from the observed data, compared to artificial wind data, due to seasonal variations. The overall performance of the BW approach was compared to standard regression MCP techniques for the prediction of the 10 year wind resource using both observed and artificially generated wind data at the 22 site pairs for multiple short-term measurement periods of 1–12 months. Prediction errors were quantified by comparing the predicted and observed values of mean wind speed, mean wind power density, Weibull shape factor and standard deviation of wind speeds at each site. Using the artificial wind data, the BW approach outperformed the regression approaches for all measurement periods. When applied to the real wind speed observations however, the performance of the BW approach was comparable to the regression approaches when using a full 12 month measurement period and generally worse than the regression approaches for shorter data periods. This suggests that real wind observations at correlated sites may differ from ideal BW distributions and hence regression approaches, which require less fitting parameters, may be more appropriate, particularly when using short measurement periods.     

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.     

Data efficient measure-correlate-predict approaches to wind resource assessment for small-scale wind energy

The feasibility of predicting the long-term wind resource at 22 UK sites using a measure-correlate-predict (MCP) approach based on just three months onsite wind speed measurements has been investigated. Three regression based techniques were compared in terms of their ability to predict the wind resource at a target site based on measurements at a nearby reference site. The accuracy of the predicted parameters of mean wind speed, mean wind power density, standard deviation of wind speeds and the Weibull shape factor was assessed, and their associated error distributions were investigated, using long-term measurements recorded over a period of 10 years. For each site, 120 wind resource predictions covering the entire data period were obtained using a sliding window approach to account for inter-annual and seasonal variations. Both the magnitude and sign of the prediction errors were found to be strongly dependent on the season used for onsite measurements. Averaged across 22 sites and all seasons, the best performing MCP approach resulted in mean absolute and percentage errors in the mean wind speed of 0.21 ms⁻¹ and 4.8% respectively, and in the mean wind power density of 11 Wm⁻² and 14%. The average errors were reduced to 3.6% in the mean wind speed and 10% in the mean wind power density when using the optimum season for onsite wind measurements. These values were shown to be a large improvement on the predictions obtained using an established semi-empirical model based on boundary layer scaling. The results indicate that the MCP approaches applied to very short onsite measurement periods have the potential to be a valuable addition to the wind resource assessment toolkit for small-scale wind developers.     

Bayesian adaptive combination of short-term wind speed forecasts from neural network models

Short-term wind speed forecasting is of great importance for wind farm operations and the integration of wind energy into the power grid system. Adaptive and reliable methods and techniques of wind speed forecasts are urgently needed in view of the stochastic nature of wind resource varying from time to time and from site to site. This paper presents a robust two-step methodology for accurate wind speed forecasting based on Bayesian combination algorithm, and three neural network models, namely, adaptive linear element network (ADALINE), backpropagation (BP) network, and radial basis function (RBF) network. The hourly average wind speed data from two North Dakota sites are used to demonstrate the effectiveness of the proposed approach. The results indicate that, while the performances of the neural networks are not consistent in forecasting 1-h-ahead wind speed for the two sites or under different evaluation metrics, the Bayesian combination method can always provide adaptive, reliable and comparatively accurate forecast results. The proposed methodology provides a unified approach to tackle the challenging model selection issue in wind speed forecasting.     

Analytical methods for wind persistence: Their application in assessing the best site for a wind farm in the State of Veracruz,Mexico

The properties of wind persistence are an essential parameter in carrying out a complete analysis of possible sites for a wind farm. This parameter can be defined as a measure of the mean duration of wind speed within a given interval of values for a concrete site. In this study the persistence properties are evaluated from the methods based on the autocorrelation function, conditional probability and the curves of speed duration, used satisfactorily by other authors. The statistical analysis of the series of useful persistence is also carried out to validate the results obtained. These methods have been applied to hourly data of wind speed corresponding to five Weather Stations (WS) in the State of Veracruz, Mexico in the period 1995–2006. The results obtained indicate that the coastal areas have the best properties of wind speed persistence and are, therefore, the most indicated for the generation of electricity from this renewable energy source.     

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.     

Estimation of wind power availability in Tamil Nadu

Eleven years' daily wind speed data at 21 locations in the state of Tamil Nadu, India were analysed to assess the available wind power potential using Weibull distribution under two different methods. The mean wind speed varied from 1.0 to 5.0 m/s dividing the state into four regions. Judged by mean and standard deviation of available wind power, six locations have been identified as possible sites for a wind energy system.     

Wind power analysis and site matching of wind turbine generators in Kingdom of Bahrain

In this paper, the hourly measured wind speed data for years 2003–2005 at 10 m, 30 m and 60 m height for Kingdom of Bahrain have been statically analyzed to determine the potential of wind power generation. Extrapolation of the 10 m data, using the Power Law, has been used to determine the wind data at heights of 30 m and 60 m. Weibull distribution parameters have been estimated and compared annually and on monthly bases using two methods; the graphical method and the another method, designated in this paper as approximated method, which depends on the standard deviation and average wind speed. The maximum power density for 10 m, 30 m and 60 m heights were found to be 164.33 W/m², 624.17 W/m² and 1171.18 W/m² in February, respectively while the minimum power density were 65.33 W/m², 244.33 W/m² and 454.53 W/m² in October, respectively. The average annual wind power density was found to be 114.54 W/m² for 10 m height, 433.29 W/m² for 30 m height and 816.70 W/m² for 60 m height. Weibull probability function, using Weibull parameters estimated from the approximated method, has shown to provide more accurate prediction of average wind speed and average power density than the graphical method. In addition, the site matching of wind turbine generators at 30 m and 60 m heights has been investigated by estimating the capacity factors of various commercially available wind turbines generators. The monthly and annual variation of capacity factors have been studied to ensure optimum selection of wind turbine generators.     

Wind speed time series characterization by Hilbert transform

Predictions of wind energy potential in a given region are based on on‐location observations. The time series of these observations would later be analysed and modelled either by a probability density function (pdf) such as a Weibull curve to represent the data or recently by soft computing techniques, such as neural networks (NNs). In this paper, discrete Hilbert transform has been applied to characterize the wind sample data measured on ?zmir Institute of Technology campus area which is located in Urla, ?zmir, Turkey, in March 2001 and 2002. By applying discrete Hilbert transform filter, the instantaneous amplitude, phase and frequency are found, and characterization of wind speed is accomplished. Authors have also tried to estimate the hourly wind data using daily sequence by Hilbert transform technique. Results are varying. Copyright © 2005 John Wiley & Sons, Ltd.     

The wind energy potential of Thailand

Routine wind data from meteorological stations have been used to determine seasonal wind speed distributions and mean power densities at the surface over Thailand. Analyses of hourly wind speeds at two stations show that Weibull distributions fit the data well, provided that observations of calm are excluded. The diurnal variation of the wind at these stations has also been found. Estimates of mean power densities of surface winds over the whole country are typically in the range 10–20 Wm^?2. Upper level climatic charts indicate that mean free-stream wind power densities above the surface boundary layer are typically in the range 100–600 Wm^?2. Similar power densities would be accessible to wind machines on high ground in many places, depending on mountain topography and machine siting.