عنوان مقاله [English]
Nowadays, the exploitation of the renewable energy sources such as wind plays a key role in human life. Although, Iran has a high potential for wind power generation, there is not an efficient energy planning yet. Environmental variables such as wind speed have variations according to spatial points. It seems reasonable to consider that there exists a spatial correlation between wind speed data at different locations. In geostatistics the spatial autocorrelation of data could be investigated by calculating the experimental semivariogram. The parameters of the fitted semivariogram model may be used to estimate the wind speed at unknown locations through kriging algorithms.
In order to describe the behaviour of wind speed at a particular location, the data distribution should be first fitted by a suitable distribution function. There are different wind speed distribution models used to fit the wind speed distributions over a period of time. Among them, Weibull distribution function has been found to be the best all over the world because of its great flexibility and simplicity.
The aim of this study is to simulate the daily mean and maximum wind speed probability distribution using Weibull distribution function and to investigate spatial variability of the wind speed data. This study was also aimed to interpolate the means of Weibull distribution functions of daily mean wind speed data observed at stations over Iran.
Materials and Methods
Study area and data set
The study is based on a long term (20 years) wind data recorded in 104 synoptic stations spread over Iran. The wind data are recorded at 10m above the ground level (a.g.l.) and contain daily mean and maximum wind speed (m/s).
The Weibull distribution function
For each site, the daily mean and maximum wind speed data were fitted by a two-parameter Weibull distribution, whose parameters (shape and scale) were determined through the maximum likelihood (ML) technique. The Weibull probability density function is defined as follows:
where V is wind speed (m/s), 𝑐 is the scale parameter (m/s) and 𝑘 is shape parameter (dimensionless). The high and low 𝑘 values indicate the sharpness and the broadening of Weibull peak, respectively. The Weibull probability density function curve could be displayed if the 𝑘 and 𝑐 values are obtained. This could be conducted through different ways, such as maximum likelihood method as:
where Vj is the wind speed for jth sample and n is the number of sample data. Equation (3) is an implicit equation and could be solved through an iteration method.
Two interpolation methods including inverse distance weighing and ordinary kriging were used to estimate the theoretical mean values of the previously determined Weibull distributions of the wind speed data at unsampled locations.
Inverse Distance Weighing (IDW)
In absence of data spatial autocorrelation, IDW is usually used as an alternative method for spatial estimation of random field. IDW is a weighted averaging interpolator in which data is weighted according to their distance to the estimation point such that more distant points get less weight than closer points.
Ordinary Kriging (OK)
The OK is the most popular kriging approach used in the spatial interpolation of the regionalized variables. It needs the parameters of the best fitted semivariogram model to incorporate spatial dependence of data on the estimation process. The semivariogram quantifies the dissimilarity between observations as the separation distance between them increases.
Results and Discussion
According to the obtained results, Semnan and Bandar-Abbass had the lowest and highest shape (k) factor of the fitted weibull distribution functions to the daily maximum wind speed data, respectively. For daily mean wind speed data, Nehbandan and Bandar-Abbass had the lowest and highest shape (k) factor of the fitted theoretical Weibull distributions, respectively. A high k value means less variation of the wind speed.
The annual duration of daily wind velocity exceed 4 m/s. It is also calculated for each site in order to obtain the first diagnostic sign of most promising areas in terms of wind energy potential. According to the results, the cities of Rafsanjan, Zabol, Torbate Jam, Khodabandeh, Ardebil, Bijar and Kahnouj have the highest potential in high wind speed.
The auto-correlation analysis showed that wind speed is moderately correlated in space with spatial structure model of spherical and a correlation distance of about 500 km (Figure 1 (a)). There was no apparent drift within the range of 500 km. The best semivariogram model was selected according to the cross validation results as well as the highest correlation coefficient (r) and the lowest residual sum of squares (RSS) functionally of GS+ software.
To predict the spatial distribution pattern of wind speed over Iran, Weibull mean wind speed data were interpolated over a point grid superimposed to the map of Iran using IDW and OK. The cross validation results indicated that both methods performed similarly. However, the maps generated were visually different. Besides, unlike IDW, OK represented the map of estimation error which is useful in decision-making as it provides a measure of uncertainty.
According to wind speed map generated by OK (Figure 1 (b)), eastern Iran (e.g. the cities of Zabol, Rafsanjan and Torbate Jam) and northwestern provinces (e.g. Ardebil) are the most promising areas for wind energy planning.
The spatial variability of wind speed and duration across Iran has been investigated. First, the frequency distribution of daily mean and maximum wind speed data during recent 20 years was simulated by Weibull function. Then, the mean values of the theoretical Weibull probability distribution functions are used to investigate the spatial variability and predict the spatial distribution pattern of wind speed across the country. According to the results, wind speed is moderately correlated in space with an influence range of about 500 km. The maps of wind speed at 10 m a.g.l. generated using IDW and OK encourage the utilization of wind energy on the eastern (e.g. Rafsanjan, Zabol, Torbate Jam) and northwestern (e.g. Ardebil) regions. Besides, additional measurements may be considered in the areas of highest estimation of uncertainty (e.g. center and eastern parts).
Fig. 1. Experimental semivariogram along with the best fitted model (a) and the interpolation map of mean wind speed at 10 m a.g.l. generated by OK (b)