Some statistical characteristics of monthly average wind speed at various heights

The article, which is a segment of a complex wind energy examination, uses statistical methods to analyze the time series of monthly average wind speed in the period between 1991 and 2000 measured on seven Hungarian meteorological stations. Empirical distribution of measured monthly average wind speeds is approximated by theoretical distributions to claim that certain distributions are universal, i.e. independent of orography. We used one of them, the Weibull distribution, to generate the distribution of monthly average wind speeds on levels different from anemometer altitude as well, then we calculate the averages for the entire period and we fit a power function on them. Thus we can demonstrate a correlation between Hellmann's wind profile law and the Weibull distribution.     

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.     

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.     

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.     

Dynamic models of wind farms with fixed speed wind turbines

The increasing wind power penetration on power systems requires the development of adequate wind farms models for representing the dynamic behaviour of wind farms on power systems. The behaviour of a wind farm can be represented by a detailed model including the modelling of all wind turbines and the wind farm electrical network. But this detailed model presents a high order model if a wind farm with high number of wind turbines is modelled and therefore the simulation time is long. The development of equivalent wind farm models enables the model order and the computation time to be reduced when the impact of wind farms on power systems is studied. In this paper, equivalent models of wind farms with fixed speed wind turbines are proposed by aggregating wind turbines into an equivalent wind turbine that operates on an equivalent wind farm electrical network. Two equivalent wind turbines have been developed: one for aggregated wind turbines with similar winds, and another for aggregated wind turbines under any incoming wind, even with different incoming winds.The proposed equivalent models provide high accuracy for representing the dynamic response of wind farm on power system simulations with an important reduction of model order and simulation time compare to that of the complete wind farm modelled by the detailed model.     

Short-term forecasting of wind speed and related electrical power

Wind speed and the related electrical power of wind turbines are forecasted. The work is focused on the operation of power systems with integrated wind parks. Artificial neural networks models are proposed for forecasting average values of the following 10 min or 1 h. Input quantities for the prediction are wind speeds and their derivatives. Also, spatial correlation of wind speeds and its use for forecasting, are investigated. The methods are tested using data collected over seven years at six different sites on islands of the South and Central Aegean Sea in Greece.     

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.     

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.     

Operation and coordinated control of fixed and variable speed wind farms

This paper will describe the possibilities of coordinated control and management for different wind farm concepts to guarantee that operational set points of active and reactive power, specified by the Spanish transmission system operator (TSO), are reached. This coordinated control has been designed and implemented by a hierarchical and robust control structured from a central control level to each wind farm control board and finally to an individual wind turbine level. This article will demonstrate that both technologies, fixed and variable speed based wind farms can contribute to power and voltage control. In particular, this paper will deal with the use of under-load tap changing transformers in the point of common coupling of the wind farm with the grid, and the reactive power compensation by means of convectional mechanical switched capacitors enhancing the integration of the fixed speed wind farms in the power system.     

Stochastic generation of hourly mean wind speed data

Use of wind speed data is of great importance in civil engineering, especially in structural and coastal engineering applications. Synthetic data generation techniques are used in practice for cases where long wind speed data are required. In this study, a new wind speed data generation scheme based upon wavelet transformation is introduced and compared to the existing wind speed generation methods namely normal and Weibull distributed independent random numbers, the first- and second-order autoregressive models, and the first-order Markov chain. Results propose the wavelet-based approach as a wind speed data generation scheme to alternate the existing methods.     

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.     

A novel method based on Weibull distribution for short-term wind speed prediction

Wind speed prediction (WSP) is essential in order to predict and analyze efficiency and performance of wind-based electricity generation systems. More accurate WSP may provide better opportunities to design and build more efficient and robust wind energy systems. Precious short-term prediction is difficult to achieve; therefore several methods have been developed so far. We notice that the statistics of the alterations, which occur between sequential values of the predicted wind speed data, may differ significantly from observed wind statistics. In this study, we investigate these alterations and compare them and, accordingly, propose a novel method based on Weibull and Gaussian probability distribution functions (PDF) for short-term WSP. The proposed method stands on an algorithm, which examines comparison of the statistical features of the observed and generated wind speed in order to achieve more accurate estimation. We have examined this method on the wind speed data set observed and recorded in Ankara in 2013 and in 2014. The obtained results show that the new algorithm provides better wind speed prediction with an enhanced wind speed model.     

Extrapolating wind speed time series vs. Weibull distribution to assess wind resource to the turbine hub height: A case study on coastal location in Southern Italy

Increasing knowledge on wind shear models to strengthen their reliability appears as a crucial issue, markedly for energy investors to accurately predict the average wind speed at different turbine hub heights, and thus the expected wind energy output. This is particularly helpful during the feasibility study to abate the costs of a wind power project, thus avoiding installation of tall towers, or even more expensive devices such as LIDAR or SODAR.The power law (PL) was found to provide the finest representation of wind speed profiles and is hence the focus of the present study. Besides commonly used for vertical extrapolation of wind speed time series, the PL relationship between “instantaneous” wind profiles was demonstrated by Justus and Mikhail to be consistent with the height variation of Weibull distribution. Therefore, in this work a comparison is performed between these two different PL–based extrapolation approaches to assess wind resource to the turbine hub height: (i) extrapolation of wind speed time series, and (ii) extrapolation of Weibull wind speed distribution. The models developed by Smedman–Högström and Högström (SH), and Panofsky and Dutton (PD) were used to approach (i), while those from Justus and Mikhail (JM) and Spera and Richards (SR) to approach (ii). Models skill in estimating wind shear coefficient was also assessed and compared.PL extrapolation models have been tested over a flat and rough location in Apulia region (Southern Italy), where the role played by atmospheric stability and surface roughness, along with their variability with time and wind characteristics, has been also investigated. A 3-year (1998–2000) 1–h dataset, including wind measurements at 10 and 50 m, has been used. Based on 10–m wind speed observations, the computation of 50–m extrapolated wind resource, Weibull distribution and energy yield has been made. This work is aimed at proceeding the research issue addressed within a previous study, where PL extrapolation models were tested and compared in extrapolating wind resource and energy yield from 10 to 100 m over a complex–topography and smooth coastal site in Tuscany region (Central Italy). As a result, wind speed time series extrapolating models proved to be the most skilful, particularly PD, based on the similarity theory and thus addressing all stability conditions. However, comparable results are returned by the empirical JM Weibull distribution extrapolating model, which indeed proved to be preferable as being: (i) far easier to be used, as z₀–, stability–, and wind speed time series independent; (ii) more conservative, as wind energy is underpredicted rather than overpredicted.     

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.     

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.     

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.