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A statistical analysis of wind power density based on the Weibull and Rayleigh models at
the southern region of Turkey
Ali Naci Celik
Mechanical Engineering Department, Mustafa Kemal University, School of Engineering and Architecture, 31024, Antakya, Hatay, Turkey
Received 21 April 2003; accepted 27 July 2003
Abstract
The electric generating capacity of Turkey must be tripled by 2010 to meet Turkey’s elec- tric power consumption, if the annual 8% growth in electric power consumption continues.
Turkey has to make use of its renewable energy resources, such as wind and solar, not only to meet the increasing energy demand, but also for environmental reasons. Studies show that Iskenderun (36v350N; 36v100E) located on the Mediterranean coast of Turkey is amongst the possible wind energy generation regions. In the present study, the wind energy potential of the region is statistically analyzed based on 1-year measured hourly time-series wind speed data. The probability density distributions are derived from time-series data and distribu- tional parameters are identified. Two probability density functions are fitted to the measured probability distributions on a monthly basis. The wind energy potential of the location is studied based on the Weibull and the Rayleigh models.
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1. Introduction
According to the Turkish Ministry of Energy and Natural Resources (MENR), the electric generating capacity of Turkey as of 1999 was 26 226 MWe [1]. Tur- key will have to treble its installed generating capacity, to a total of 65 GWe by 2010, if Turkey’s electric power consumption continues to grow at approximately 8% per year as estimated. As of 2000, electricity generation in Turkey is mainly
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doi:10.1016/j.renene.2003.07.002
hydroelectric (40%) and conventional thermal power plants (60%, coal, natural gas, fuel oil and diesel powered). The current 4000 MWe gas-fuelled generation capacity of Turkey will reach approximately 18 500 MWe by the year 2010 with the proposed new power plants currently under construction or in the planning stage. This, however, will increase dependency on imported natural gas, since only a tiny fraction of the natural gas consumed in Turkey is met by indigenous sources.
With the ultimate aim of deriving 2% of its electricity from wind power, in 2000 the Turkish Government had offered a tender for up to 390 MWe of electricity from wind power [1]. Within this wind power program, a total of 25 sites for a possible wind energy project underwent evaluation. However, the tender had to be cancelled due to International Monetary Fund-induced economic policy changes, which were accepted as a result of the economic crisis of 2000. Turkey is encour- aging the construction of built-own-transfer (BOT) wind power plants by private power developers[1]. The total installed wind power generation capacity of Turkey is 19.1 MWe in three wind power stations. The first wind power facility in Turkey, which is located on the Aegean Sea coast town of Cesme and owned by a private
Nomenclature
q Air density (kg/m3) r Standard deviations (m/s) C Gamma function
c Weibull scale factor (m/s) f(v) Probability density function
fj Frequency of occurrence of each speed class fR(v) Rayleigh probability density function fW(v) Weibull probability density function FR(v) Rayleigh cumulative distribution function FW(v) Weibull cumulative distribution function k Weibull shape factor
n Number of wind speed classes
N Number of hours in the period of time considered P(v) Power of the wind per unit area (W/m2)
Pm Mean power density (W/m2)
Pm,R Reference mean power density (W/m2)
PR Mean power density calculated from the Rayleigh function (W/m2) PW Mean power density calculated from the Weibull function (W/m2) PW,R Mean power density calculated either from the Weibull or Rayleigh
function used in calculation of the error (W/m2) R2 Correlation coefficient
v Wind speed (m/s) vm Mean wind speed (m/s)
company, started operations in February 1998. The wind farm consists of three wind turbines of 1.7 MWe total capacity. The second wind power facility started to operate in November 1998, which incorporates 12 wind turbines of a total capacity of 7.2 MWe. The third wind power generation utility, in operation since June 2000, has a total installed capacity of 10.2 MWe (17 wind turbines) and is located in Bozcaada, C¸ anakkale.
Turkey has to make use of its renewable resources, such as wind, solar and geo- thermal, not only to meet the increasing energy demand, but also for environmen- tal reasons. Turkey is seeking admission to the European Union (EU) and is trying to meet EU environmental standards, as well as the standards of non-govern- mental environmental organizations and many international environmental agree- ments, including the Air Pollution and the Antarctic Treaty.
2. Regional wind energy potential of Turkey
Oztopal et al.[2]prepared various maps based on 42 wind velocity measurement stations in Turkey and showed the regional variations of wind resource from the available data. According to the maps, the Aegean Sea coast is singled out, having the richest wind energy potential. Another potential wind region is the south-west- ern part of Turkey along the Mediterranean Sea, such as Iskenderun. Another map showing the measurement heights of wind energy potentials identifies five main locations as potential sites, Iskenderun being one of these five locations. The remaining four locations are shown in Table 1, with the geographic, topographic information and the wind characteristics. Oztopal et al. [2]make a generalization that the sea coasts provide significant wind energy potential, whereas inland sites are poor regions for wind energy generation.
Durakand Sen [3]presented the wind power potential areas in Turkey from the morphological and air mass movement prespective. The wind energy generation potential is exemplified for Turkey in Akhisar, which lies within the most wind power potential area of Turkey, the Aegean Sea region. According to the outcome of a study mentioned in Ref. [3], in 10 areas that lie in the Aegean region of
Table 1
The most favorable wind locations in Turkey Location Region in Turkey Latitude
(N)
Longitude (E)
Altitude (m)
Average wind speed (m/s)
Average power density (W/m2) at 5 m at 50 m Gokceada Northern Aegean Sea 40v120 25v540 72 3.5 5.5 70 Bandirma Southern Marmara Sea
coast
40v210 27v580 58 5.8 6.9 301
Sinop North 42v020 35v100 32 3.6 5.1 84
Diyarbakir South-western 37v540 40v140 677 – – –
Source: Oztopal et al.[2].
Turkey offer a possible 319 MW wind power generation facility. It is also stated in Ref.[3]that in the eastern Mediterranean region at the vicinity of Iskenderun bay there are suitable locations for wind power generation.
Sahin [4] studied 68 wind speed measurement stations in Turkey and produces wind velocity exceedence maps over 10, 12, 15, and 20 m/s, and the necessary interpretations were given. These maps showed that especially the western part of Turkey and, particularly, coastal areas are risky locations for structural stability and wind erosion.
3. Distributional parameters of the wind data used
In the present study, hourly time-series wind speed data in Iskenderun (36v350N;
36v100E) measured for the year 1996, have been statistically analyzed. The wind speed data were recorded at a height of 10 m, continuously by R. Fuess type of anemograph at the Iskenderun synoptical station (located on the Mediterranean Sea coast, with 2 m altitude) of the Turkish State Meteorological Service. The con- tinuously recorded wind speed data were averaged over 1 h and stored as hourly values. The monthly-mean wind speed values and the standard deviations calcu- lated for the available time-series data using Eqs. (1) and (2) are presented in Table 2. It is seen in Table 2 that the highest wind speeds occur in the summer months of June and July. February and September have little wind as indicated by the small monthlyvmvalues of 1.62 and 2.87 m/s, respectively.
vm¼ 1 N
XN
i¼1
vi
" #
ð1Þ
r¼ 1 N1
XN
i¼1
ðvivmÞ2
" #1=2
: ð2Þ
Table 2
Distributional parameters on monthly basis, calculated from the measured hourly time-series wind speed data of Iskenderun
vm(m/s) r(m/s) c(m/s) k
January 2.71 1.69 3.04 1.66
February 1.62 1.12 1.80 1.49
March 2.14 1.60 2.35 1.37
April 2.28 1.97 2.41 1.17
May 2.22 1.85 2.37 1.21
June 3.38 2.37 3.73 1.46
July 3.35 2.41 3.69 1.42
August 2.74 2.51 2.84 1.10
September 1.87 1.53 2.00 1.23
October 2.43 1.82 2.66 1.36
November 1.91 1.12 2.15 1.79
December 2.07 1.16 2.34 1.89
Alternatively, the mean wind speed can be determined from vm¼
ð1 0
v fðvÞdv ð3Þ
if the probability density function is known.
4. Wind speed probability distributions
The wind speed data in time-series format is usually arranged in the frequency distribution format since it is more convenient for statistical analysis. Therefore, the available time-series data were translated into frequency distribution format.
This process is illustrated for an example month in Table 3. The wind speed is grouped into classes (bins) as given in the second column of Table 3. The mean wind speeds are calculated for each speed class intervals (the third column). The fourth column gives the frequency of occurrence of each speed class. The prob- ability density distribution is presented in the fifth column. The monthly prob- ability density and the cumulative distributions derived from the time-series data of Iskenderun are presented inFigs. 1 and 2, respectively. The yearly probability den- sity and the cumulative distributions are seen inFig. 3.
The wind speed probability distributions and the functions representing them mathematically are the main tools used in the wind-related literature. Their use includes a wide range of applications, from the techniques used to identify the parameters of the distribution functions[5]to the use of such functions for analyz- ing the wind speed data and wind energy economics[6],[7]. Two of the commonly used functions for fitting a measured wind speed probability distribution in a given location over a certain period of time are the Weibull and Rayleigh. The prob-
Table 3
Arrangement of the measured hourly time-series data in frequency distribution format for May and the probability density distributions calculated from the Weibull, (fW(vj)), and Rayleigh (fR(vj)) functions
j vj vm,j fj f(vj) fW(vj) fR(vj)
1 0–1 0.5 195 0.262 0.316 0.153
2 1–2 1.5 231 0.310 0.261 0.334
3 2–3 2.5 127 0.171 0.178 0.294
4 3–4 3.5 74 0.099 0.112 0.159
5 4–5 4.4 52 0.070 0.067 0.057
6 5–6 5.4 30 0.040 0.038 0.014
7 6–7 6.4 17 0.023 0.021 0.002
8 7–8 7.4 8 0.011 0.012 0.000
9 8–9 8.4 6 0.008 0.006 0.000
10 9–10 9.5 1 0.001 0.003 0.000
11 10–11 10.5 1 0.001 0.002 0.000
12 11–12 11.5 1 0.001 0.001 0.000
13 12–13 12.5 – 0.001 0.000 0.000
ability density function of the Weibull distribution is given by, fWð Þ ¼v k
c v c
k1
exp v c
k
: ð4Þ
The corresponding cumulative probability function of the Weibull distribution is,
FWðvÞ ¼1exp ðv=cÞk: ð5Þ
If Eq. (3) is solved together with Eq. (4) making the substitution ofn¼ ðv=cÞkfor
Fig. 1. Monthly wind speed probability density distributions, derived from the measured hourly time- series data of Iskenderun.
Fig. 2. Monthly wind speed cumulative probability distributions, derived from the measured hourly time-series data of Iskenderun.
v, the following is obtained for the mean wind speed,
vm¼cC 1þ1 k
: ð6Þ
Note that the gamma function has the properties of CðxÞ ¼
ð1 0
nx1expðnÞdn andCð1þxÞ ¼xCðxÞ:
The Weibull parameters calculated analytically for the available data using the method given by Jamil [8]are presented in Table 2. It is seen from the table that while the scale factor varies between 1.80 and 3.73 m/s, the shape factor ranges from 1.10 to 1.89 for the location analyzed. Some advantages of the Weibull model are summarized in Ref.[9]. There are several methods presented in the literature to identify the parameters of the Weibull function, see[5],[10]and[11].
The Rayleigh model is a special and simplified case of the Weibull model. It is obtained when the shape factorcof the Weibull model is assumed to be equal to 2.
The probability density and the cumulative distribution functions of the Rayleigh model are given by,
fRð Þ ¼v p 2
v
v2m exp p 4
v v2m
" k#
ð7Þ
FRðvÞ ¼1 exp p 4
v vm
" 2#
: ð8Þ
One of the most distinct advantages of the Rayleigh distribution is that the prob- ability density and the cumulative distribution functions could be obtained from the mean value of the wind speed. The Rayleigh model has also widely been used to fit the measured probability density distribution and its validity was shown for various locations in Ref. [12–14]. The probability density distributions obtained
Fig. 3. Yearly wind speed probability density and cumulative probability distributions, derived from the measured hourly time-series data of Iskenderun.
from the monthly Weibull and Rayleigh parameters are presented in the sixth and seventh columns ofTable 3.
The monthly probability density distributions obtained from the Weibull and Rayleigh models were compared to the measured distributions to study their suit- ability. The correlation coefficient values are used as the measure of the goodness of the fit of the probability density distributions obtained from the Weibull and Rayleigh models. The correlation coefficient values are presented in Fig. 4 on a monthly basis for the Iskenderun data. The coefficient values range from 0.66 to 0.96 for the Weibull model, while they vary between 0.46 and 0.96 for the Rayleigh model. The average of the monthly values is 0.88 for the Weibull model and 0.80 for the Rayleigh model. The month to month comparison shows that the Weibull model returns higher coefficient values in seven of the months than the Rayleigh model, indicating better fit to the measured probability density distributions.
5. Power density distributions and mean power density
If the power of the wind per unit area is given by PðvÞ ¼1
2 qv3 ð9Þ
the wind power density for the measured probability density distribution given in Table 3 can be calculated from the following equation, which serves as the ‘refer- ence mean power density’,
Pm;R¼Xn
j¼1
1
2 q v3m;j fðvjÞ
: ð10Þ
Fig. 4. Correlation coefficient values obtained in fitting the measured probability density distributions with the Weibull and Rayleigh functions.
The most general equation to calculate the mean wind power density is, Pm¼
ð1 0
PðvÞ!
Q
fðvÞdv: ð11ÞHowever, the mean wind power density can be calculated directly from the follow- ing equation if the mean value ofv3s, (v3)m, is already known,
PmðvÞ ¼1
2 qðv3Þm: ð12Þ
From Eq. (3), the mean value ofv3s can be determined as ðv3Þm¼
ð1 0
v3 fðvÞdv: ð13Þ
Integrating Eq. (13), the following is obtained for the Weibull function, ðv3Þm¼ Cð1þ3=kÞ
C3 ð1þ1=kÞ ðvmÞ3: ð14Þ Introducing Eqs. (6) and (14) into Eq. (12), the mean power density for the Wei- bull function becomes:
PW ¼1
2qc3C 1þ3 k
: ð15Þ
Fork¼2, the following is obtained from Eq. (6), vm¼c ffiffiffiffiffiffiffiffi
pp=4
: ð16Þ
By extracting cfrom Eq. (16) and setting k equal to 2, the power density for the Rayleigh model is found to be,
PR¼3
pqv3m: ð17Þ
The power densities calculated from the measured probability density distributions and those obtained from the models are shown inFig. 5. The power density shows a large month to month variation. The minimum power densities occur in Feb- ruary and November, with 7.54 and 9.77 W/m2, respectively. It is interesting to note that the highest power density values occur in the summer months of June, July and August, with the maximum value of 63.69 W/m2in June. The power den- sities in the remaining months are between these two groups of low and high. The errors in calculating the power densities using the models in comparison to those using the measured probability density distributions are presented in Fig. 6, using the following formula:
Errorð%Þ ¼PW;RPm;R Pm;R
: ð18Þ
The Weibull model returns smaller error values in calculating the power density when compared to the Rayleigh model. The highest error value occurs in July with 11.4% for the Weibull model. The power density is estimated by the Weibull model with a very small error value of 0.1% in April. The yearly average error value in calculating the power density using the Weibull function is 4.9%, using the follow- ing equation
Errorð%Þ ¼ 1 12
X12
i¼1
PW;RPm;R Pm;R
: ð19Þ
Fig. 5. Wind power density obtained from the measured data versus those obtained from the Weibull and Ragleigh models, on a monthly basis.
Fig. 6. Error values in calculating the wind power density obtained from the Weibull and Rayleigh mod- els, in reference to the wind power density obtained from the measured data, on monthly basis.
The monthly analysis shows that the error values in calculating the power den- sity using the Rayleigh model are relatively higher, over 50% in some months, such as August and September. Even the smallest error in the power density calculation using the Rayleigh model is 11.3%. The yearly average error value in estimating the power density using the Rayleigh model is 36.5%.
6. Conclusions
In the present study, hourly measured time-series wind speed data of Iskenderun have been statistically analyzed. The probability density distributions have been derived from the time-series data and the distributional parameters were identified.
Two probability density functions have been fitted to the measured probability dis- tributions on a monthly basis. The wind energy potential of the location has been studied based on the Weibull and the Rayleigh models. The most important out- comes of the study can be summarized as follows:
1. Even though Iskenderun is shown as one of the most potential wind energy gen- eration regions in Turkey, this particular site, where the Iskenderun synoptical station (located on the Mediterranean Sea coast, with 2 m latitude) of the Turk- ish State Meteorological Service is located, presents poor wind characteristics.
This is shown by the low monthly and yearly mean wind speed and power den- sity values.
2. As the yearly average wind power density value of 30.20 W/m2 indicates, this particular site corresponds to the wind power class of 1, since the density value is less than 100 W/m2. Therefore, this particular site is not ideal for grid-con- nected applications. This level of power density may be adequate for non-con- nected electrical and mechanical applications, such as battery charging and water pumping.
3. However, the diurnal variations of the seasonal wind speed and the wind power density have to be further studied, since the diurnal variation may show a sig- nificant difference.
4. The Weibull model is better in fitting the measured monthly probability density distributions than the Rayleigh model. This is shown from the monthly corre- lation coefficient values of the fits.
5. The Weibull model provided better power density estimations in all 12 months than the Rayleigh model.
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