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.     

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.     

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.     

Worldwide wind energy status and the characteristics of wind energy in Iran,case study: the province of Sistan and Baluchestan

In this paper, the recent trend of the worldwide wind energy utilisation is reviewed and the recent activities in using renewable energy sources in Iran are explained. As a case study, the wind characteristics of the province of Sistan and Baluchestan are statistically analysed. The wind characteristics such as the monthly mean wind speed and the wind power density of each station are presented. The monthly variation of the wind direction is presented and also the dominant wind direction is shown in a wind rose diagram. The values of turbulence intensity at different heights are calculated. The results show that the stations of Khash and Nosratabad are more suitable for limited off-grid utility applications. Lootak with the average annual wind power density of 388?W?m^?2 at the height of 40?m and constant wind direction is recommended for large-scale grid-connected wind turbines.     

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.     

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.     

Probabilistic analysis of weather data for a hybrid solar/wind energy system

In this paper, a procedure for the probabilistic treatment of solar irradiance and wind speed data is reported as a method of evaluating, at a given site, the electric energy generated by both a photovoltaic system and a wind system. The aim of the proposed approach is twofold: first, to check if the real probability distribution functions (PDFs) of both clearness index and wind speed overlap with Hollands and Huget and Weibull PDFs, respectively; and then to find the parameters of these two distributions that best fit the real data. Further, using goodness‐of‐fit tests, these PDFs are compared with another set of very common PDFs, namely the Gordon and Reddy and Lognormal functions, respectively. The results inform the design of a pre‐processing stage for the input of an algorithm that probabilistically optimizes the design of hybrid solar wind power systems. In this paper, the validity of the proposed procedure was tested using long‐term meteorological data from Acireale (Italy). Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation on wind power potential on Hong Kong islands—an analysis of wind power and wind turbine characteristics

This paper discusses the potential for electricity generation on Hong Kong islands through an analysis of the local weather data and typical wind turbine characteristics. An optimum wind speed, u_op, is proposed to choose an optimal type of wind turbine for different weather conditions. A simulation model has been established to describe the characteristics of a particular wind turbine. A case study investigation allows wind speed and wind power density to be obtained using different hub heights, and the annual power generated by the wind turbine to be simulated. The wind turbine's capacity factor, being the ratio of actual annual power generation to the rated annual power generation, is shown to be 0.353, with the capacity factor in October as high as 0.50. The simulation shows the potential for wind power generation on the islands surrounding Hong Kong.     

Viability and economic analysis of wind energy resource for power generation in Johannesburg,South Africa

In this study, wind characteristics and wind power potential of Johannesburg are investigated using 5-min average time series wind speed collected between 2005 and 2009 at anemometer height of 10 m. The statistical distribution that best fits the empirical wind speed data at the site of study is first determined based on the coefficient of determination and root mean square error criteria. The statistical parameters and wind power density based on this model are estimated for different months of the year using standard deviation method. Economic analyses of some wind turbines are also carried out. Some of the key results show that the site is only suitable for small wind turbines in a standalone application. A 10 kW wind turbine with cut-in wind speed of 3.5 m/s, rated wind speed of 9 m/s, and cut-out wind speed of 25 m/s seems most appropriate in Johannesburg with the lowest cost that varies from 0.25 to 0.33 $/kWh.     

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.     

LiDAR‐based characterization of mid‐altitude wind conditions for airborne wind energy systems

Engineers and researchers working on the development of airborne wind energy systems (AWES) still rely on oversimplified wind speed approximations and coarsely sampled reanalysis data because of a lack of high‐resolution wind data at altitudes above 200 m. Ten‐minute average wind speed LiDAR measurements up to an altitude of 1100 m and data from nearby weather stations were investigated with regard to wind energy generation and impact on LiDAR measurements. Data were gathered by a long‐range pulsed Doppler LiDAR device installed on flat terrain. Because of the low overall carrier‐to‐noise ratio, a custom‐filtering technique was applied. Our analyses show that diurnal variation and atmospheric stability significantly affect wind conditions aloft which cause a wide range of wind speeds and a multimodal probability distribution that cannot be represented by a simple Weibull distribution fit. A better representation of the actual wind conditions can be achieved by fitting Weibull distributions separately to stable and unstable conditions. Splitting and clustering the data by simulated surface heat flux reveals substate stratification responsible for the multimodality. We classify different wind conditions based on these substates, which result in different wind energy potential. We assess optimal traction power and optimal operating altitudes statistically as well as for specific days based on a simplified AWES model. Using measured wind speed standard deviation, we estimate average turbulence intensity and show its variation with altitude and time. Selected short‐term data sets illustrate temporal changes in wind conditions and atmospheric stratification with a high temporal and vertical resolution.     

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.     

A simplified model for estimating the monthly performance of autonomous wind energy systems with battery storage

This paper presents a simplified algorithm to estimate the monthly performance of autonomous small-scale wind energy systems with battery storage. The novel model is drawn based on the simulation results, using eight-year long hour-by-hour measured wind speed data from five different locations throughout the world. An hourly constant load profile is used. The renewable energy simulation program (ARES) of the Cardiff School of Engineering is used. The ARES simulates the battery state of voltage (SoV) and is able to predict the system performance.The monthly performance values obtained from the simulations are plotted against increasing energy to load ratios for varying battery storage capacities to obtain performance curves. The novel method correlates the monthly system performance with the parameters of the Weibull distribution function, thus offering a universal use. The monthly performance curves are mathematically represented using a 2-parameter function. The novel method is validated by comparing the simulated performance values with those estimated from the simplified algorithm. The standard errors calculated in estimation of the system performance using the simplified algorithm are further presented for each battery capacity.     

Determination of Weibull parameters for wind energy analysis of İzmir,Turkey

In this study, the two Weibull parameters of the wind speed distribution function, the shape parameter k (dimensionless) and the scale parameter c (ms^?1), were computed from the wind speed data for ?zmir. Wind data, consisting of hourly wind speed records over a 5‐year period, 1995–1999, were measured in the Solar/Wind‐Meteorological Station of the Solar Energy Institute at Ege University. Based on the experimental data, it was found that the numerical values of both Weibull parameters (k and c) for ?zmir vary over a wide range. The yearly values of k range from 1.378 to 1.634 with a mean value of 1.552, while those of c are in the range of 2.956–3.444 with a mean value of 3.222. The average seasonal Weibull distributions for ?zmir are also given. The wind speed distributions are represented by Weibull distribution and also by Rayleigh distribution, with a special case of the Weibull distribution for k=2. As a result, the Weibull distribution is found to be suitable to represent the actual probability of wind speed data for ?zmir (at annual average wind speeds up to 3 ms^?1). Copyright © 2002 John Wiley & Sons, Ltd.     

Wind shear coefficients and energy yield for Dhahran, Saudi Arabia

This study presents calculated values of wind shear coefficients (WSE) using measured values of wind speed at 20, 30, and 40 m above ground level (AGL), for Dhahran, Saudi Arabia. The study also includes the air density estimated using measured air temperature and surface pressure and effect of wind shear coefficient on energy yield from a wind farm of 60 MW installed capacity developed using 40 wind turbines of 1500 kW size. The data used in the determination of wind shear coefficient covered a period of almost 5 years between 4 October 1995 and 30 November 2000.The study suggests a value of 0.189 of wind shear coefficient for the calculation of wind speed at different heights if measured values are known at one height. No regular seasonal trend was observed in the values of wind shear coefficients. In case of diurnal variation, higher values were observed during nighttime and early hours of the day and comparatively smaller values during day light hours. The air density, calculated using measured temperature and pressure was found to be 1.18 kg/m³. The energy yield obtained using RetScreen software, showed that the actual wind shear coefficient presented in this paper produced around 11–12% more energy compared to that obtained using 1/7 power law. Accordingly, 2–3% higher plant capacity factors were achieved using actual site-dependent wind shear coefficient instead of 1/7th wind power law exponent for the calculation of wind speed at hub-height.     

A novel method for reliability and risk evaluation of wind energy conversion systems considering wind speed correlation

This paper investigates an analytical approach for the reliability modeling of doubly fed induction generator (DFIG) wind turbines. At present, to the best of the authors’ knowledge, wind speed and wind turbine generator outage have not been addressed simultaneously. In this paper, a novel methodology based on the Weibull- Markov method is proposed for evaluating the probabilistic reliability of the bulk electric power systems, including DFIG wind turbines, considering wind speed and wind turbine generator outage. The proposed model is presented in terms of appropriate wind speed modeling as well as capacity outage probability table (COPT), considering component failures of the wind turbine generators. Based on the proposed method, the COPT of the wind farm has been developed and utilized on the IEEE RBTS to estimate the well-known reliability and sensitive indices. The simulation results reveal the importance of inclusion of wind turbine generator outage as well as wind speed in the reliability assessment of the wind farms. Moreover, the proposed method reduces the complexity of using analytical methods and provides an accurate reliability model for the wind turbines. Furthermore, several case studies are considered to demonstrate the effectiveness of the proposed method in practical applications.     

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.     

Wind energy potential assessment for the offshore areas of Taiwan west coast and Penghu Archipelago

The average wind speed and wind power density of Taiwan had been evaluated at 10 m, 30 m and 50 m by simulation of mesoscale numerical weather prediction model (MM5). The results showed that wind energy potential of this area is excellent. Taiwan has offered funds to encourage the founding of offshore wind farms in this area. The purpose of this study is to make a high resolution wind energy assessment for the offshore area of Taiwan west coast and Penghu archipelago by using WAsP. The result of this study has been used to the relative financial planning of offshore wind farm projects in Taiwan. The basic inputs of WAsP include wind weather data and terrain data. The wind weather data was from a monitoring station located on a remote island, Tongi, because that all of weather stations in the area of Taiwan west coast are affected by urbanization. SRTM was selected to be used as terrain data and downloaded from CGIAR-CSI for voids problem. The coverage of considered terrain area in this assessment work is about 300 km × 400 km that made some difficulties to run wind energy assessment of the whole area with a high resolution of 100 m. So the interested area of this study is divided into 19 areas for the wind energy assessment and mapping. The assessment results show the Changhua area has best wind energy potential in the area of Taiwan west coast which power density is above 1000 W/m² height and the areas of Penghu archipelago are above 1300 W. These results are higher than the expected from NWP. 180 of 3 MW wind turbines were used in the study of micro sitting in the Changhua area.The type and number of the wind turbines and the layout of the wind farm is similar to the prior study of Taipower Company for demonstrating the reliability of this study. The assessment result of average net annual energy production (AEP) of the wind farm is about 11.3 GWh that is very close to the prior study. The terrain effect is also studied. The average net annual energy production will decrease about 0.7 GWh if the wind turbines were moved eastward 3600 m closer to the coast because of terrain effect. As the same reason, the average net annual energy production would be increased to 11.392 GWh if the wind farm is moved westward 3600 m away from the coast.