Assessment of Wind Speed Statistics in Samaria Region

1. Introduction

During the last decade, wind characteristics and wind power potential have been studied in many countries worldwide [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,61,63,64,65], demonstrating that despite the prolonging global economic crisis, the worldwide wind power ascent continues. The world’s wind power capacity added 38.6 GW in 2009, growing by 32%/year and 38.1 GW in 2010 (24%/year growth), demonstrating 110% growth in three years, to extend total installations up to 197.0 GW. A huge part of this capacity was installed in China with 22.7% of the world wind energy yield (about third of the world year’s additions) and USA with 20.4%, while Germany, Spain and India installing cumulative capacity of 30.9% together [48].

Wind energy became a significant player in the world’s energy market. Global market worth of wind turbine installations in 2009 was around 63 billion US$. About half a million people are now employed, corresponding to GWEC estimates, by the wind industry around the world [49]. Main markets of the wind energy are situated in Asia, North America, and Europe, each of which adds more than 10 GW capacity a year.

Considering the Israeli energy market, the desire to add to the natural gas found, which is a nonrenewable local energy resource has also motivated the state to devote various efforts to the ‘green’ energy research and development, primarily in the area of solar energy. Recently, wind energy drew attention of energy initiatives as well. Yet the wind power amount produced in Israel is diminutive comparing to the continuously growing global market; however, the last steps undertaken by the state are destined to improve the situation.

Israel currently operates a single wind farm in Asanyia Hill in the Golan Heights, with total installed capacity of 6 MW (consisting of ten 600 kW turbines), satisfying the consumption of about 5 thousand families. The wind farm operates around 97% of the time and yields revenue of ~1 million US $ a year. Indeed, wind energy potential of Israel is restricted because of surplus of moderate- or poor-wind velocities’ areas and is limited to the areas with sufficiently constant wind, some of which are being opposed by green groups on landscape conservation grounds. Nevertheless, the state continues efforts for bringing into operation of two more farms with a 50 MW capacity [50].

It is emphasized in the Israel Knesset document that an improved estimate, based on the wind turbines’ technological development, gives a value much more than 500 MW of the Israeli potential wind energy capacity [51]. One of perspective areas for efficient wind technology development, considering its climatic characteristics, is the Samaria region.

It is well known that energy yield of a wind turbine mainly depends on wind energy characteristics and turbine power curve [52,53]. In this paper, statistical characteristics of the wind speed behavior in Ariel (located in Samaria) are derived and investigated, relying on data collected be meteorological station located in Ariel University campus.

2. Materials and Methods

Eleven years of meteorological data (2001-2011), acquired by Ariel Meteorological Station and supplied by the Israeli Meteorological Service were processed. Measurement samples were taken at 10-meter height above the ground and were available at 10 minutes intervals. The city of Ariel is located at 32° 6′ 21.6″ N, 35° 11′ 16.43″ E, in the center of Israel (Figure 1). Ariel Meteorological Station is located inside Ariel University campus at eastern part of the city (Figure 2), residing at 700 m above sea level.

The wind speed data was provided by meteorological station as raw matrix of wind speed ad azimuth versus time at 10 m height, sampled at 10 minutes. In reality, the sample time is much higher than stated and the available data sample is actually an average of tens to thousands of faster samples. An example of monthly wind speed raw data in Ariel represented by 10 minutes samples is shown in Figure 3.

The raw vector is used to extract mean and standard deviation parameters and then can be either transformed into a histogram (discrete probability distribution function – PDF) or fitted to a known PDF, typically of Weibull type, as shown in Figure 4. When creating a histogram, the bins are typically chosen to be 1 m∙s^-1 wide to match the resolution of the manufacturer provided turbine power curve data, resulting in the following discrete PDF,

$$f_{HST}(v)=f(v_i),v_i-0.5\le v<v_i+0.5$$

(1)

where $f\left(v_i\right)$ is the magnitude of the histogram bin, centered at $v_i$.

Weibull PDF is defined by two parameters: shape or Weibull modulus (k, dimensionless), and scale (c, m/s for wind speed). The general form of the Weibull PDF is given by:

$$f_{WBL}(v)=\frac{k}{c}{(\frac{v}{c})}^{k-1}{e}^{-{(\raisebox{1ex}{$v$}\!\left/ \!\raisebox{-1ex}{$c$}\right.)}^k}$$

(2)

for positive wind speeds (v > 0) with parameters c and k = related to the site wind speed mean μ_v and standard deviation σ_v as [54]:

$${\mu }_v=c\Gamma \left(1+\frac{1}{k}\right)$$

(3)

And

$${\sigma }_v=c\sqrt{\Gamma \left(1+\frac{2}{k}\right)-{\Gamma }^2\left(1+\frac{1}{k}\right)}$$

(4)

respectively, where:

$$\Gamma (x)={\displaystyle \underset{0}{\overset{\infty }{\int }}{t}^{x-1}{e}^{-t}dt}$$

(5)

is the complete Gamma function. In case the wind raw data of a site is unavailable, but the mean and standard deviation of the wind speed are given, Weibull PDF is usually assumed, and its parameters are extracted from (4) and (5). In general, several ways to extract Weibull parameters from raw data exist [55]; MATLAB function wblfit was used in this work.

A particular (and very common) case of Weibull PDF is the case where k = 2. It is called Rayleigh PDF and is given by

$$f_{RLH}(v)=\frac{2v}{c^2}{e}^{-{(\raisebox{1ex}{$v$}\!\left/ \!\raisebox{-1ex}{$c$}\right.)}^2}$$

(6)

for positive wind speeds (v > 0) with scale parameter c related to the site mean wind speed as

$${\mu }_v=\frac{\sqrt{\pi }}{2}c$$

(7)

making (6) to be dependent on average wind speed as [56]:

$$f_{RLH}(v)=\frac{\pi v}{2{\mu }_v^2}{e}^{-{(\raisebox{1ex}{$\sqrt{\pi }v$}\!\left/ \!\raisebox{-1ex}{$2{\mu }_v$}\right.)}^2}$$

(8)

It is worth noting that wind energy resource is typically classified according to average wind speed at 10 m height as shown in Table 1 [56].

Since power in the wind increases with height [57,58], the turbine hub of medium and large-scale wind turbines is usually located a 50 – 150 m height. Therefore, statistical wind parameters must be either measured at hub height or extrapolated from measurements available at smaller heights. In case single height measurements only are available, power law is usually employed to estimate wind speed $v_1$ at height $H_1$ as

$$\left(\frac{v_1}{v_0}\right)={\left(\frac{H_1}{H_0}\right)}^{\alpha }$$

(9)

where $v_0$ is the wind speed measurement available at height $H_0$ and $\alpha$ is the surface roughness dependent friction coefficient [59,60]. Friction coefficient dependence on terrain characteristics is typically determined from Table 2 [56].

According to the above, a software simulator was created receiving meteorological data (excel format) as an input and calculating the following output. Using the wind speed raw data, mean and standard deviation (STD) vales were calculated, followed by Weibull parameters extraction, and plotting respective histograms along with resulting Weibull PDFs. The process was repeated after extrapolating the samples to 70-meter height using friction coefficient of 0.3 according to Table 2. All the results were calculated monthly, annually, and seasonally. As to wind directions, annual Rose diagrams were created for both 10 and 70 m heights.

3. Results

Table 3 and Table 4 summarize yearly and cumulative mean and STD of wind speed and azimuth at 10 and 70 m heights, respectively. It may be concluded that the wind belongs to class 2, according to Table 1.

Table 5 and Table 6 summarize monthly, yearly, and cumulative Weibull parameters of wind speed at 10 and 70 m heights, respectively. It may be concluded that winds in Ariel may be accurately assumed as Rayleigh since the cumulative k is very close to 2.

In order to validate the applicability of Weibull PDF to wind statistics in Ariel, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15 present yearly wind speed raw data histograms and Weibull PDFs at both 10 and 70 m heights. Good matching is evident at all figures.

All yearly Weibull PDFs are plotted together in Figure 16 for 10 and 70 m heights, respectively. It may be concluded that wind regime is relatively stable and hence predictable. This is supported by Figure 17, presenting statistical as well as Weibull parameters variations throughout the years at 10 m height.

Weibull parameters were estimated seasonally as well. Winter season in Israel generally takes place from November to January, autumn season - from August to October, spring season - from February and April and summer season from May to July. The results are summarized in Table 7 and Table 8 for 10 and 70 m heights, respectively. Cumulative seasonal PDF plots are given in Figure 18, Figure 19, Figure 20 and Figure 21, respectively.

Another important aspect of wind analysis is prevailing wind direction (azimuth). Eleven years wind direction polar histograms (Rose diagrams) are shown as rose diagram in Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31 and Figure 32 for both 10 and 70 m heights. Cumulative wind rose diagrams are shown in Figure 33. It may be concluded that the prevailing wind direction remains relatively stable throughout the years.

4. Wind Power Generation

The power curves of available turbines are described in [66,67], from which three examples are analyzed in this paper and are depicted in Figure 34.

Among the turbines analyzed, the largest is Enercon’s model E101/3000 turbine with a radius of 50.5 m. Hence, we will assume from now on that the hub of the turbine is 70 m. Table 9 will summarize the area and radii of the turbines under study:

For this height, we obtain a speed average of 8.8 m/s. The average of the power and the standard deviation obtained for each turbine are depicted in Table 10, we have used the Weibull distribution to calculate the average power and the power standard deviation.

Table 10 contains the annual economic value of the turbine based on the current price of energy for household consumers in Israel, which is 0.5342 SH for kW hour on January 1, 2023 (before tax), the exchange rate for the same date is 3.5190 SH for one US $. In Israel the price is determined by governmental authorities who strike a balance between the interest of other producers, the cost of transmission and distribution, and the public interest in clean energy.

5. Conclusions

In this work, statistical characteristics, and Weibull parameters of the wind speed in Samaria region have been extracted from 11 years of wind data provided by the Israeli Meteorological Service, acquired at 10 m height above the ground. The cumulative mean wind speed at measurement height was found to be 4.53 m/s with standard deviation of 2.32 m/s. Prevailing wind direction is shown to be characterized by cumulative mean azimuth of 226^o with standard deviation of 79.76^o. Weibull distribution parameters were calculated yearly, monthly, and seasonally, demonstrating good match with histogram-based statistical representations. Shape parameter of Weibull distribution was shown to reside within narrow range around 2, allowing to assume Rayleigh statistics. The results were extrapolated to 70-meter height in order to estimate wind characteristics at hub height of a medium-scale wind turbine. It was shown that both statistical parameters and wind direction distribution remain relatively constant throughout the years, indicating good prediction potential. The novelty of the current paper is related to gathering wind statistics for a certain area (Samaria), we are not aware of any published statistics regarding wind velocity and direction in this area. The data may be interesting for potential regional wind energy development in which the obtained Weibull distribution can be used in calculations of expected power generation of particular turbines with known power dependence on velocity. We also point out that the fact that realistic wind velocity statistics is well described by an analytic formula (Weibull distribution) is not trivial, and in fact the fit may have been poor.