A new probabilistic method to estimate the long-term wind speed characteristics at a potential wind energy conversion site

This paper proposes the use of a new Measure-Correlate-Predict (MCP) method to estimate the long-term wind speed characteristics at a potential wind energy conversion site. The proposed method uses the probability density function of the wind speed at a candidate site conditioned to the wind speed at a reference site. Contingency-type bivariate distributions with specified marginal distributions are used for this purpose. The proposed model was applied in this paper to wind speeds recorded at six weather stations located in the Canary Islands (Spain). The conclusion reached is that the method presented in this paper, in the majority of cases, provides better results than those obtained with other MCP methods used for purposes of comparison. The metrics employed in the analysis were the coefficient of determination (R²) and the root relative squared error (RRSE). The characteristics that were analysed were the capacity of the model to estimate the long-term wind speed probability distribution function, the long-term wind power density probability distribution function and the long-term wind turbine power output probability distribution function at the candidate site.     

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.     

Heterogeneous mixture distributions for modeling wind speed,application to the UAE

Heterogeneous mixture distributions (HTM) have not been employed for wind speed modeling of the Arabian Peninsula. In order to improve our understanding of wind energy potential in the Arabian Peninsula, HTM should be tested for the frequency analysis of wind speed. The aim of the current study is to assess the suitability of HTMs and identify the most appropriate probability distribution to model wind speed data in the UAE. Hourly mean wind speed data were used in the current study. Ten homogeneous and heterogeneous mixture distributions were used and constructed by mixing the four following probability distributions: Gamma, Weibull, Extreme value type-one, and Normal distributions. The Weibull and Kappa distributions were also employed as representatives of the conventional non-mixture distributions. Maximum Likelihood, Expectation Maximization algorithm, and Least Squares methods were employed to fit the mixture distributions. Results indicate that mixture distributions give the best fit to wind speed data for all stations. Wind speed data of five stations show strong mixture distributional characteristics. Applications of HTMs show a significant improvement in explaining the whole wind speed regime. The Weibull-Extreme value type-one mixture distribution is considered the most appropriate distribution for wind speed data in the UAE.     

Statistical bivariate modelling of wind using first-order Markov chain and Weibull distribution

This paper studies the statistical features of the wind at Oran (Algeria). The data used are the wind speed and wind direction measurements collected every 3 h at the meteorological station of Es Senia (Oran), during the 1982/92 period. The eight directions of the compass card have been considered to build the frequency distribution of the wind speed for each month of the year and each direction. The three-hourly wind data have been modelled by means of Markov chains. First-order nine-state Markov chains are found to fit well the wind direction data, whereas the related wind speed data are well fitted by first-order three-state Markov chains. The Weibull probability distribution function has also been considered and found to fit the monthly frequency distributions of wind speed measurements. Two methods of wind data retrieval are thus made available. In fact, two models of chronological bi-series are obtained describing wind speed and wind direction.     

Joint probability design of marine environmental elements for wind turbines

Decommission platforms can be used as the foundation of offshore wind turbines. In order to reduce the costs of wind power, the joint probability method is applied in the joint design of marine environmental elements. Based on copulas and univariate maximum entropy margins, multivariate maximum entropy distributions are constructed. Sample data of annual maximum significant wave height and corresponding wind speed and current velocity at Point 2 in Lianyungang Harbour of China is applied to testify the efficiency of trivariate maximum entropy distributions. The marginal fittings of univariate maximum entropy distributions and the trivariate data fitting based on normal copula fit the data well. The method of conditional probability can present a joint design of significant wave height and corresponding wind speed and current velocity.     

Estimating wind speed probability distribution based on measured data at Burla in Odisha,India

In this work, the wind speed probability distribution is estimated for Burla location in the state of Odisha in the east coast of India. For this purpose, 10 min averaged wind speed data collected over one year period at Burla is utilized. Specifically, Weibull, Gamma, Lognormal, Inverse Gaussian distributions; mixture distributions such as Weibull-Weibull, Gamma-Weibull, Normal-Weibull, and Normal-Normal are examined to evaluate their suitability to represent the measured wind speed. The non-parametric kernel density method is also used to represent the measured wind speed wherever the parametric distributions are not suitable. Chi-square test and Kolmogorov-Smirnov goodness-of-fit tests are used to evaluate the suitability of each of the above distributions.     

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.     

Assessing the suitability of wind speed probabilty distribution functions based on wind power density

Three functions have so far predominantly been used for fitting the measured wind speed probability distribution in a given location over a certain period of time, typically monthly or yearly. In the literature, it is common to fit these functions to compare which one fits the measured distribution best in a particular location. During this comparison process, parameters on which the suitability of the fit is judged are required. The parameters that are mostly used are the mean wind speed or the total wind energy output (primary parameters). It is, however, shown in the present study that one cannot judge the suitability of the functions based on the primary parameters alone. Additional parameters (secondary parameters) that complete the primary parameters are required to have a complete assessment of the fit, such as the discrepancy between the measured and fitted distributions, both for the wind speed and wind energy (that is the standard deviation of wind speed and wind energy distributions). Therefore, the secondary statistical parameters have to be known as well as the primary ones to make a judgement about the suitability of the distribution functions analysed. The primary and secondary parameters are calculated from the 12-month of measured hourly wind speed data and detailed analyses of wind speed distributions are undertaken in the present article.     

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.     

Practical ways of evaluating wind speed persistence

Wind speed persistence is a measure of the mean wind speed duration over a given period of time at any location. This definition implies that wind speed persistence means a positive serial correlation in time series. The wind speed persistence provides useful information about the general climatological characteristics of the wind persisting at a given location. Therefore, wind speed persistence should be taken into account in many studies such as weather forecast, site selection for wind turbines and synthetic generation of the wind speed data. On the other hand, if wind direction information is considered together with the wind speed then this type of persistence can be used for additional purposes such as forest fires, dispersion of the air pollutants, building ventilation, etc. In this study, three different methods with some modifications of the previous methods have been applied to the wind speed data obtained from the meteorology stations located at the northwest part of Turkey. These methods are based on autocorrelation function, conditional probability and the wind speed duration curves. It has been shown that the proposed methods clearly reflect the persistence properties of the wind speed in the study area.     

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.     

Analysis of wind potential and characteristics in North Aegean, Greece

Wind data for the years 2000 and 2001 were analyzed to evaluate the wind potential of the Mikra–Thessaloniki, region in northern Greece. The objective of the analysis was the establishment of the required criteria to answer the question: “are the renewable energy sources capable to maintain the operation of a desalination pilot unit?” The polar diagrams of the wind (wind speed, frequency, direction), the mean monthly and annual wind speed profile and the Weibull distributions for the years 2000 and 2001 are presented.     

Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean

The statistical characteristics of wind speed data recorded at nine buoys, located in Ionian and Aegean Sea (Eastern Mediterranean) are analyzed in this paper, in order to present a more accurate method for estimation of wind speed characteristics, according to the suitability of the probability distribution functions (pdf). This article has focussed on wind regimes that present nearly zero percentages of null wind speeds. The selected distributions for examination are the typical two-parameter Weibull wind speed distribution (W-pdf) and the two-component mixture Weibull distribution (WW-pdf), involving five parameters (two shape parameters, two scale parameters, and one proportionality parameter).     

Extraction of synoptic pressure patterns for long-term wind speed estimation in wind farms using evolutionary computing

In this paper we present an evolutionary approach for the problem of discovering pressure patterns under a quality measure related to wind speed and direction. This clustering problem is specially interesting for companies involving in the management of wind farms, since it can be useful for analysis of results of the wind farm in a given period and also for long-term wind speed prediction. The proposed evolutionary algorithm is based on a specific encoding of the problem, which uses a dimensional reduction of the problem. With this special encoding, the required centroids are evolved together with some other parameters of the algorithm. We define a specific crossover operator and two different mutations in order to improve the evolutionary search of the proposed approach. In the experimental part of the paper, we test the performance of our approach in a real problem of pressure pattern extraction in the Iberian Peninsula, using a wind speed and direction series in a wind farm in the center of Spain. We compare the performance of the proposed evolutionary algorithm with that of an existing weather types (WT) purely meteorological approach, and we show that the proposed evolutionary approach is able to obtain better results than the WT approach.     

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.     

An M‐Rice wind speed frequency distribution

Several known statistical distributions can describe wind speed data, the most commonly used being the Weibull family. In this paper, a new law, called ‘M‐Rice’, is proposed for modeling wind speed frequency distributions. Inspired by recent empirical findings that suggest the existence of some cascading process in the mesoscale range, we consider that wind speed can be described by a seasonal AutoRegressive Moving Average (ARMA) model where the noise term is ‘multifractal’, i.e. associated with a random cascade. This leads to the distribution of wind speeds according to the M‐Rice probability distribution function, i.e. a Rice distribution multiplicatively convolved with a normal law. A comparison based on the estimation of the mean wind speed and power density values as well as on the different goodness‐of‐fit tests (the Kolmogorov–Smirnov test, the Kuiper test and the quantile–quantile plot) was made between this new distribution and the Weibull distribution for 35 data sets of wind speed from the Netherlands and Corsica (France) sites. Accordingly, the M‐Rice and Weibull distributions provided comparable performances; however, the quantile–quantile plots suggest that the M‐Rice distribution provides a better fit of extreme wind speed data. Beyond these good results, our approach allows one to interpret the observed values of Weibull parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

A comparison between wind speed distributions derived from the maximum entropy principle and Weibull distribution. Case of study; six regions of Algeria

The knowledge of the probability density function of wind speed is of paramount importance in many applications such as wind energy conversion systems and bridges construction. An accurate determination of the probability distribution of wind speed allows an efficient use of wind energy, thus rendering wind energy conversion system more productive. In the present paper, the maximum entropy principle (MEP) is used to derive a family of pre-exponential distributions in order to fit wind speed distributions. Using averaged hourly wind speed of six different regions in Algeria, it has been found that the proposed pre-exponential distributions fit the wind speed distributions better than the conventional Weibull distributions in terms of root mean square error. However, it has been found also that MEP based distributions have shown some practical limitations such as the choice of pre-exponential order and interval of definition.