In this study, wind energy potential of Siirt University campus area is statistically examined by using the mean hourly wind speed data between 2014 and 2015 years which are measured by Vantage Pro2 device, located at the roof of the Engineering Faculty building with 6 m altitude. Weibull distribution function and Rayleigh distribution function are used as statistical approach to evaluate the wind data. Weibull distribution function is examined by using two different methods that are maximum likelihood estimation and Rayleigh method. The determination coefficient (R2) and Root Mean Square Error (RMSE) values of these methods are compared. According the error analysis, it is indicated that the Rayleigh method gives better results. Wind speed and wind power density are calculated in pursuance of Weibull distribution parameters. The results are evaluated as monthly and annually. Hence, this preliminary study is made to determine the wind energy potential of Siirt University campus area.

1. DETERMINATION OF WIND ENERGY
POTENTIAL OF CAMPUS AREA OF SIIRT
UNIVERSITY
Nihat Bükün*, Mehmet Şahin+
*, +
Department of Electrical and Electronics Engineering, Siirt University, 56100 Siirt, Turkey
(*nbukun@gmail.com, +
msahin@siirt.edu.tr)
Abstract- In this study, wind energy potential of Siirt
University campus area is statistically examined by
using the mean hourly wind speed data between 2014
and 2015 years which are measured by Vantage Pro2
device, located at the roof of the Engineering Faculty
building with 6 m altitude. Weibull distribution
function and Rayleigh distribution function are used
as statistical approach to evaluate the wind data.
Weibull distribution function is examined by using
two different methods that are maximum likelihood
estimation and Rayleigh method. The determination
coefficient (R2
) and Root Mean Square Error (RMSE)
values of these methods are compared. According the
error analysis, it is indicated that the Rayleigh method
gives better results. Wind speed and wind power
density are calculated in pursuance of Weibull
distribution parameters. The results are evaluated as
monthly and annually. Hence, this preliminary study
is made to determine the wind energy potential of
Siirt University campus area.
Keywords-Weibull distribution, Rayleigh distribution,
maximum likelihood estimation, wind speed, wind
power density.
I. INTRODUCTION
Electrical energy requirement tends to increase
depending on the rapidly advancing technology.
Due to the limited amount of available fossil fuels
used in electricity production and due to the fact
that they will eventually run out, the ways to
conserve electric energy and the use of renewable
energy sources are constantly being studied on. One
of those studies is harvesting wind energy to
generate electric energy which has shown great
development in recent years, especially in Europe.
Turkey is a country with high potential regarding
wind energy. In 2007, Wind Energy Potential Map
of Turkey (REPA) was published [1]. In this map,
wind energy potential of Turkey was provided in
detail for each city. In scope of this study, wind
energy potential of Siirt campus area was studied
and evaluated using the Vantage Pro2 device
located at the roof of Block C of Engineering and
Architecture Faculty, measuring the average hourly
wind speeds between years 2014 and 2015 for a
total of 12 months from 6 meters of altitude. For the
evaluation of wind data, Weibull and Rayleigh
distribution functions were used as statistical
approaches. These two distribution functions are
widely used to determine the wind energy potential
in many studies either in Turkey and other countries
[2]. It is a known fact that wind data usually
matches with Weibull distribution [2-4]. However,
in some areas, wind data does not match with the
two parameter Weibull distribution. But mostly,
Weibull distribution is the method which is used to
represent the wind distribution in many regions
throughout the world. The reason for its use is
because it fits perfectly with the wind distribution
and also has a flexible distribution structure, also,
its parameters can easily be determined and very
few parameters are required. Its parameters can also
easily be estimated for different altitudes, once one
altitude parameters is determined [2].
Wind measurements are usually performed in
the range of 10-30 meters, however, today's large
and powerful wind turbines' hub height is much
higher than this level. Thus, in order to deduct the
value of wind speed in any particular altitude, for
any spot which was measured for just one altitude,
wind power profile law is being used. Weibull
distribution function parameters have been analyzed
using two different methods which are maximum
likelihood estimation (MLE) and Rayleigh method.
Both methods have been compared with coefficient
of determination (R2
) and root mean square error
(RMSE) analysis. Average speed and wind power
density have been statistically determined
depending on the Weibull distribution parameters.
II. WEIBULL DISTRIBUTION
Weibull distribution is used to calculate wind
energy potential in many studies. Wind data is
known to usually fit to this type of distribution.
However, in some areas, wind data does not
conform to the two-parameter Weibull distribution.
Various methods have been developed in order to
calculate the figure (k) and scale (c) parameters.
The methods that we used for Siirt campus area are
the maximum likelihood estimation (MLE) and
Rayleigh method. Likelihood density function of
two parameter Weibull distribution is expressed
with eq.(1).
( ) = ( ) ( ) (1)
Where the wind speed (m/s), k and c are
dimensionless figure and scale parameters,
respectively. The accumulation of Weibull
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2. distribution (cumulative) likelihood density
function is as in eq.(2) [5].
( ) = 1 − ( ) (2)
Weibull cumulative likelihood density function
gives us the likelihood of the wind speed being
actualized either smaller or equal to a specific v
value. The average wind speed is calculated using
the eq.(3) [5].
= 1 +
1
(3)
Weibull distribution is a function and this
function has a peak spot. Finding this peak means
finding the most probable speed, thus, finding the
maximum wind speed. It is the (y) gamma function
in eq.3 [2].
= (
− 1
) (4)
The speed value which contributes the most to
the energy flow is given in eq.(5) [2]
= (
+ 2
) (5)
The average power density was shown in eq.(6)
[3].
=
1
2
(1 +
3
) (6)
Where, "ρ" is the air density value and in
calculations it was taken as an average of 1,226
kg/m³ for Siirt campus area.Figure parameter (k) is
a parameter indicating the frequency of the wind. If
the wind speed does not show much fluctuation in
an area, and if the wind is blowing with an
approximate constant speed (low or high), it k
parameter is greater. Scale parameter (c) indicates
the relative cumulative wind speed frequency. In
simple words, c parameter changes depending on
the average speed. If the average speed is higher, c
parameter is also higher [3]. Wind speed
measurements are usually made in between an
altitude range of 10 to 30 meters. However,
nowadays, the hubs of wind turbines are much
higher than this level. Therefore, in order to deduct
the wind speed value of any particular altitude of
any location, wind power profile law is being used
together with the measured wind speed data of that
location [6]. Speed values for different altitude are
measured using eq.(7).
( ) = (
ℎ
ℎ
) (7)
In eq.(7), v1 represents the measured wind
speed, v2 represents the desired wind speed, h1
represents the altitude that the v1 speed was
measured, h2 represents the altitude that v2 speed is
demanded to be determined, α represents the
Hellman coefficient and is dependent on the
specifications of the location of the wind speed
measurement is made.
( ) = (
ℎ
ℎ
) (8)
If the power level in the reference altitude can
be found using eq.(8), the power density in the
desired altitude can be calculated also. In the
equation, h1 is the reference altitude, and if the
power density in this altitude is P1 and the power
density in the desired altitude (h2) is represented
with P2.
III. MAXIMUM LIKELIHOOD
ESTIMATION
Maximum likelihood estimation is one of the
methods to find the k and c values which are the
figure and scale parameters of Weibull distribution.
In maximum likelihood estimation, wind data shall
be organized as v1, v2, v3,...........vn, which will form
a set with n number of elements. The likelihood of
any data to be v=vi is proportional with f(vi;k ,c).
Similarly, the likelihood of V=V1…. V= Vn
occurrence of all the data can also be expressed.
These events are independent from each other.
Thus, the likelihood of the occurring of events can
be defined as a likelihood function as in eq.(9) [7].
1 ( ; , )n
iL f V k c  (9)
The scale parameter can be obtained using
eq.(10).
=
∑ ( ) (10)
Figure parameter can be calculated using
eq.(11).
=
∑ ln( )
∑ ( )
−
∑ ln( )
(11)
The likelihood function can be used to find the
value that will make the highest likelihood function,
for the k and c parameters calculated using above
given equations. Here, the equation for Vi=0 which
is used for k figure parameter can not be solved.
Therefore, the value of 0 should be removed from
the dataset [2].
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3. IV. RAYLEIGH DISTRIBUTION
The change and distribution of the wind in a
specific period is very important for energy
production evaluations. Turbine designers need
such information like wind distribution and change
in order to make improvements on turbines and to
reduce the costs to a minimum. If in any location,
the only known data is the average wind speed
(Vm); using Rayleigh distribution function, it should
be possible to find the percentage of any specific
wind speed (V) blowing time (hr). The wind speed
values derived from such calculations are a
distribution of likelihood density. When this
distribution is schematically depicted, the region
which is below this distribution equals to 1.
Because the likelihood of the wind blowing in any
speed including zero is equal to 100%. Rayleigh
density function is as it was shown in eq.(12) [2, 5-
10].
( ) =
2
( ) −
2
( ) (12)
Rayleigh cumulative distribution function can
be represented as in eq.(13)
( ) = 1 − −
4
( ) (13)
The biggest advantage of Rayleigh
distribution is that the distribution can be
determined with just using the average wind speed.
In Rayleigh distribution, calculations are done
considering that the k scale parameter equals to 2.
Because the calculations are made over a single
parameter, it is a simpler method compared to
Weibull distribution. Its validity in wind studies
have been shown in many references [2-5].
V. ERROR ANALYSIS
Error analysis shall be done in order to find out
which of the figure and scale parameters calculated
using Weibull distribution, MLE and Rayleigh are
the most suitable ones for the real data. The
methods used in this study have been analyzed
using two different error analysis methods. The first
of these is R2
(determining coefficient) and it can be
expressed as in eq.(14) [2, 8,9].
= 1 −
∑ ( − )
∑ ( − )
(14)
The other error analysis method is root mean
square error (RMSE), and it has been represented in
eq.(15).
=
1
( − )
.
(15)
Where, n is the number of observations, y are
real values, x are values calculated using Weibull
distribution and average real values. The fact that
R2
value is the largest and RMSE value is the
smallest shows that this distribution function is the
best one [2, 8, 9].
VI. RESULTS AND DISCUSSION
In the estimation of the parameters of Weibull
distribution and Rayleigh function, hourly wind
speed data measured in 6 meters of altitude for 12
months between 2014 and 2015 in Siirt campus
area was used. Then the results for 40 meters of
altitude were calculated using Hellmann coefficient.
Table 1. Weibull parameter, speed and power estimates for 2014-2015 data of Siirt campus area
Table 1 shows the analysis of hourly wind
data in Siirt campus. Calculations were performed
with hourly measurements made at an altitude of 6
meters. Then, using Helmann coefficient, wind
power density was calculated for the altitude of 40
meters. As seen in table 1, the highest average
k c
vm
(m/s)
σ
(m/s)
ƒw(ν) Fw(ν)
Vmostlikely
(m/s)
Vmax E
(m/s)
P/A
(w/m2
)
6m
P/A
(w/m2
)
40m
JULY-2014
1.2269 1.9318 1.8002 1.4808 0.6020 0.2489 0.4882 4.2488 3.6179 8.9892
AUGUST 1.1412 1.6777 1.6003 1.4055 0.2620 0.6123 0.2689 4.0741 2.5122 6.2419
SEPTEMBER 1.2241 1.7396 1.6282 1.3371 0.2757 0.6024 0.4345 3.8375 2.6460 6.5744
OCTOBER 1.3019 1.2766 1.1787 0.9131 0.4042 0.5940 0.4154 2.6094 1.0039 2.4943
NOVEMBER 1.1994 1.1068 1.0413 0.8718 0.4227 0.6052 0.2480 2.5080 0.6920 1.7193
DECEMBER 1.7899 0.7339 0.6528 0.3772 0.9882 0.5556 0.4647 1.1160 0.1705 0.4236
JANUARY 2015 1.1195 1.1532 1.1065 0.9901 0.3718 0.6151 0.1563 0.8305 0.8305 2.0685
FEBRUARY 1.1919 1.4217 1.3397 1.1285 0.3265 0.6061 0.3071 3.2491 1.4740 3.6623
MARCH 1.1853 1.5221 1.4364 1.2164 0.3029 0.6069 0.3180 3.5047 1.8168 4.5141
APRIL 1.1440 1.9039 1.8147 1.5902 0.2316 0.6119 0.3110 4.6074 3.6636 9.1065
MAY 1.3280 2.0167 1.8548 1.4103 0.2618 0.5913 0.7036 0.5913 3.9118 9.7195
JUNE 1.3406 2.4522 2.2515 1.6968 0.2177 0.5901 0.8823 4.8456 6.9960 17.3827
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4. speed and power density in Siirt Campus took place
in June. But these two data distributions are not
sufficient for energy investments, it is necessary to
examine the distributions of other data as well.
When we examine the seasonal data, we can see
that the highest average speed and power density
happens to be in summer and late spring months.
Fig.1 shows the power density values calculated in
the years 2014-2015 for Siirt Campus area.
Fig.1. Power densities calculated using MLE for years in between 2014-2015
Depending on the altitude, wind speed and its
power density varies. Parameter values in different
altitudes were deducted from the revised data
obtained for the altitude of 6 meters and by
adapting it to 40 meters of altitude.
Table 2. Rayleigh parameter, speed and power estimates for 2014-2015 data of Siirt campus area
c Vm (m/s)
σ
(m/s)
ƒw(ν) Fw(ν)
Vmostlikely
(m/s)
Vmax E
(m/s)
P/A
(w/m2
)
6m
P/A
(w/m2
)
40m
JULY-2014 2.3422 2.0757 0.7900 0.1508 0.9356 1.6562 3.3124 10.4710 26.0162
AUGUST 2.1796 1.9316 0.7352 0.2027 0.9070 1.5412 3.0824 8.4378 20.9646
SEPTEMBER 2.1141 1.8735 0.7131 0.2263 0.8930 1.4949 2.9897 7.6993 19.1297
OCTOBER 1.5322 1.3578 0.5168 0.4738 0.6908 1.0834 2.1668 2.9309 7.2821
NOVEMBER 1.4548 1.2893 0.4907 0.5049 0.6529 1.0287 2.0574 2.5089 6.2336
DECEMBER 0.7592 0.6728 0.2561 0.5691 0.2504 0.5369 1.0737 0.3566 0.8860
JANUARY 2015 1.6483 1.4607 0.5560 0.4237 0.7429 1.1655 2.3310 3.6490 9.0663
FEBRUARY 1.8286 1.6205 0.6168 0.3436 0.8121 1.2930 2.5860 4.9894 12.3967
MARCH 1.9776 1.7526 0.6671 0.2798 0.8585 1.3984 2.7968 6.3028 15.6599
APRIL 2.4870 2.2040 0.8389 0.1129 0.9546 1.7585 3.5171 12.5343 31.1427
MAY 2.3389 2.0728 0.7889 0.1517 0.9351 1.6539 3.3077 10.4264 25.9054
JUNE 2.7890 2.4717 0.9407 0.0571 0.9795 1.9721 3.9443 17.6790 43.9552
Table 2 shows the analysis according to
Rayleigh distribution of the hourly wind speed data
for Siirt campus area for years 2014-2015.
According to the calculations, the highest power
density was recorded in June and the lowest was
recorded in December.
0
2
4
6
8
10
12
14
16
18
20
PowerDensity(W/m2)
Months
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5. Fig.2. Power densities calculated using Rayleigh for years in between 2014-2015
Fig. 2 shows the power density data calculated
using Rayleigh distribution for Siirt campus area
for years 2014-2015. As can be seen in the figure,
the highest power density was recorded in June and
the lowest was recorded in December. The
coefficient of determination (R2
) is valued either 0
or 1, as the measurement of the power of estimation
of any model. The closer the coefficient of
determination to 1, the higher the power of
estimation of the model used. The smaller the
RMSE value gets, the better that particular
distribution function becomes.
Table 3. The comparison of likelihood distributions calculated using Rayleigh and Weibull distributions
MONTHS METHOD R2 RMSE
July-2014 Weibull 0.87348 0.02658
Rayleigh 0.98975 0.02431
August Weibull 0.90545 0.03017
Rayleigh 0.97552 0.02986
September Weibull 0.92778 0.02653
Rayleigh 0.98993 0.01749
October Weibull 0.99543 0.00994
Rayleigh 0.98847 0.00106
November Weibull 0.91022 0.02452
Rayleigh 0.94961 0.02957
December Weibull 0.91665 0.01065
Rayleigh 0.90463 0.01893
January-2015 Weibull 0.90956 0.03654
Rayleigh 0.90077 0.03012
February Weibull 0.92849 0.02986
Rayleigh 0.91199 0.02901
March Weibull 0.92654 0.02536
Rayleigh 0.99123 0.02014
April Weibull 0.95457 0.03541
Rayleigh 0.98656 0.03210
May Weibull 0.95465 0.02312
Rayleigh 0.99645 0.02017
June Weibull 0.94712 0.03789
Rayleigh 0.99223 0.02875
0
5
10
15
20
25
30
35
40
45
50
PowerDensity(W/m2)
Months
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6. The data obtained from Weibull and Rayleigh
distributions for Siirt campus area for 2014-2015
was presented in Table 3. When the table is
examined, it can be seen that a statistical
comparison of Weibull and Rayleigh distributions
was made according to R2
and RMSE criteria. If
these comparisons are examined, it can be seen that
the use of Rayleigh distribution is more suitable for
that particular region. This can also be seen in Fig.
3. If the figure is examined, it can be seen that the
highest coefficient of determination was obtained
using Rayleigh distribution.
Fig.3. The comparison of Weibull and Rayleigh distributions according to R2
criteria for Siirt campus area in between years 2014 and 2015
VII. CONCLUSIONS
For the determination of the wind potential of
any region for energy purposes, its wind speed
distribution should be known first. Depending on
the wind speed distribution data, wind power
density is calculated and after the required
economic and environmental analysis, it can be
understood if the wind farming would be beneficial
for that particular area or not. In this study, Weibull
parameters used to determine the distribution of
speed have been determined using two different
distribution methods, maximum likelihood
estimation (MLE) and Rayleigh distribution
method. As a result of the error analysis made in
Siirt campus region, and also considering the R2
and RMSE factors, it was seen that Rayleigh
distribution gave better results. The data was
obtained for 6 meters of altitude by using the device
Vantage Pro2 device, located at the roof of the
Engineering Faculty building, and using the
Hellmann coefficient, the possible wind data for the
altitude of 40 meters was calculated. Generally
speaking, when evaluated for its wind potential
throughout 2014-2015, for a period of 12 months, it
has been understood that late Spring and Summer
months had the highest potential of power density,
and the lowest power density was observed in
months of Winter and Fall. For any location to be
eligible to have a wind farm, its power density
should be over 50 W/m2
. In our measurements, we
have come to the conclusion that in order to have a
wind farm in this location, the wind turbine rotors
should be situated above 40 meters of altitude.
REFERENCES
[1] Wind Energy Potential Atlas (REPA), “Wind
energy potential in Turkey”,
http://repa.eie.gov.tr/ (25.05.2016).
[2] S.A. Akdağ ve Dinler A., ''A new method to
estimate Weibull parameters for wind energy
applications'', Energy Convers Manag, 50,
1761-1766.2009.
[3] T.P., Chang ''Performance comparison of six
numerical methods in estimating Weibull
parameters for wind energy application'', Appl
Energy, 88, 272-282.2011.
[4] A.Güngör, Eskin N., “Wind Energy as a
Sustainable Energy Source and Turkey “,
Thermodynamics, 165, 102-110, 2006.
[5] M. Kurban, F.O. Hocaoğlu, Y.M. Kantar, “The
comparative analysis of the two statistical
distributions used for wind energy potential
estimations”, Pamukkale University,
Engineering Sciences Magazine, 13, 103-109,
2007.
0,8000
0,8200
0,8400
0,8600
0,8800
0,9000
0,9200
0,9400
0,9600
0,9800
1,0000
1,0200
TheDeterminationCoefficient
Months
Weibull
Rayleigh
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7. [6] M.R.Patel, “Wind and Solar Power System
Design Analysis and Operation”, Taylor &
Francis, Raton, 2006.
[7] U. Sarıkaya, “Renewable energy source
potential of Niğde”, Master’s thesis, Niğde
University, Institute of Science, Niğde, 1-52.
2010.
[8] B.Dursun, B. Alboyacı, , ''An Evaluation of
Wind Energy Characteristics for Four
Different Locations in Balikesir'', Energy
Sources, Part A: Recovery, Utilization, and
Environmental Effects, 33(11), 1086-1103,
2011.
[9] E.K. Akpınar, S.Akpınar, ''Determination of the
wind energy potential for Maden-Elazig,
Turkey'', Energy Convers Manage, 45, 2901-
2913, 2004. [19] Patel, M.R., Wind and Solar
Power System Design Analysis and Operation,
Taylor & Francis, Raton, 2006.
[10] Z., Demirkol, “Renewable energy source
potential of Afyonkarahisar”, Master’s thesis,
Selçuk University, Institute of Science,
Konya, 1-60. 2013.
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