- Email: [email protected]
Investigation of Wind Characteristics in the Southern Region of Algeria
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 36 (2013) 707 – 713
TerraGreen 13 Interrnational Coonference 2013 2 - Advaancements inn Renewablle Energy and Clean Environmen E nt
Investiigation of o wind characte c eristics in n the souuthern reegion of Alggeria M. F. F Benatalllah*, M.Chegaar L.O.C., Departtment of Physics, Faculty of Sciencces, Ferhat Abbass University, 190000, Setif, Algeriaa m ail.com, [email protected] Email : mbenatallah@gma
Abstract
Before an investment i inn wind turbinnes takes placce in a given n site, it is im mportant to kknow severall fundamentall properties suuch as wind behavior, avaailability, conttinuity, and probability p in the proposed d region. To make m decisionns with those properties, p stattistical and dy ynamic characcteristics of wiind of the sitee should be foound out usingg wind observvations and sttatistical wind d evaluation. In this paper a preliminary y examinationn of wind poteential of two sites in the souuthern region of o Algeria is dealt d with. W Wind measured d data of a period of 18 yeaars are collectted from these two weatherr stations. Wiind speed is sttudied to find d d whhich fits the best b the measu ured data. By performing p the F 2 test wee the adequatee probability distribution find that the Weibull disstribution funnction is the most adapted d. The corresponding parameters weree a the quick and a the least squares s methoods. Althoughh that the firstt estimated ussing two methhods. These are method is more m practicaal, the obtaineed results by both method ds can be useed to estimatee the Weibulll parameters for f both sites and a good agreeement is obtaained with thee measured datta. e Authors. Pubblished by ElsLtd. evier Ltd. © 2013The TheAuthors. © 2013 Published by Elsevier Selection and/or peer-review underunder responsibility of the TerraGreen Academy Selection annd/or peer-reviiew respponsibility off the TerraGree en Academy. Keywords: Winnd characteristics, Weibull, Algeriia.
1. Introducttion The orientattion to renewaable energies was a quick response to th he energy crissis in the 19770s [1], which h influenced inn great part thhe developed countries, c todday and due to the climate change, c all thee countries aree concerned to t take the decision d in order o to preseerve clean, healthy h and stable s future for the nextt generations.. This decisioon could not be done withhout giving more m importannce to renew wable energiess resources over o fossil fuuels. The tradditionally knoown as oil producing p couuntries are eexploring and d
*
Corresponnding author. E-m mail address: [email protected]
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the TerraGreen Academy doi:10.1016/j.egypro.2013.07.082
708
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
developing their renewable energy sources [1-9] to reduce their dependence on fossil sources and also to reduce local energy bill in profit of international market. Algeria is not an exception. The objective of this study is to determine which distribution law fits the measured wind speed data in the region of Bechar and Tamanrasset. Gamma, Lognormal, Normal and Weibull, have been used to fit the data so it is easy to predict the power density in this area. 2. Wind data source Wind speed data are collected from the stations of the National Meteorological Office available on the sites of Bechar and Tamanrasset. The records for both sites are from 1987 to 2002 (18 years data). The measurements are made at 10 meters high. The minimum speed recorded should be equal or above 0.5 m/s and wind speed is averaged over three hours. 3. Probability distributions 3.1 Normal density function The probability density function for the normal distribution with mean P and standard deviation V is generally written as: 2 2 1 f ( x, P , V 2 ) e ( x P ) / 2 V (1) 2SV 2 3.2 Normal density function The probability density function of a log-normal distribution is: f ( x; P , V )
1 xV 2S
e (ln x P )
2 / 2V 2
,x
(2)
0
This follows by applying the change-of-variables rule on the density function of a normal distribution.
3.3 Gamma density function The probability density function of the gamma distribution can be expressed in terms of the gamma function parameterized in terms of a shape parameter Į and scale parameter. The equation defining the probability density function of a gamma-distributed random variable x is f ( x; D , O )
1
1
OD * D
x
D 1
e
x
O
, for : x
0 and Į, Ȝ,
Where Į and Ȝ are respectively the shape and scale parameters
0
(3)
709
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
3.4 Weibull density function Weibull probability function is the most used distribution in wind energy studies. However in this paper we use more than one distribution. The Weibull function is two parameter functions used to estimate wind speed frequency distribution. It is defined as [4]:
f (v )
(k / c)(v / c) k 1 exp[(v / c) k ]
(4)
Where f (v) is the Weibull probability density function with the probability of having a wind speed of Ȟ.
k : is the shape factor is (dimensionless), and c (m/s): is the scale factor. The mean speed is given by [2]:
v
c *(1 1 / k )
(5)
* : is the gamma function 4. Methodology and analysis 4.1 Weibull parameter estimation using least squares parameter estimation: After arranging the data from smallest to largest we obtain their median rank plotting position by [1]:
F (vi ) |
i 0.3 N 0.4
Now by plotting different values of Yi and intercept x
x
(6)
ln{ ln[1 F (vi )]} against ln v , a straight line with slope k
k ln c is obtained, using least squares. We can find:
The Weibull shape parameter (k)[1]: § N ·§ N · ln( v ) ¦ i ¨ ¸ ¨ ¦ Yi ¸ N ©i1 ¹© i 1 ¹ ln( v ) Y ¦ i i N i 1 k 2 § N · ln( ) v i ¸ ¨¦ N 2 ¹ ln( vi ) © i 1 ¦ N i 1
(7)
The Weibull shape parameter (c)[1]:
c
e
§a· ¨ ¸ ©k¹
Where the parameter (a) is calculated using:
(8)
710
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713 N
¦Y
i
a
i 1
k
§ N · ¨ ¦ ln(vi ) ¸ ¸ k¨ i 1 N ¨ ¸ ¨ ¸ © ¹
(9)
4.2 Weibull parameter estimation using “the Quick Method”: From multiple observations we have found that for a large sample of wind speed measurements the shape and scale parameters can be estimated very accurately if we compare the estimation with the result that can be obtained using the more complicated and robust method of maximum likelihood estimators (MLE) [1]. The “quick method” requires first to calculate the arithmetic mean wind speed, for a given large sample of wind measurements using [1]: N
¦v
i
v
i 1
(10)
N
Then calculate the sample standard deviation using [1]:
V
1 N (v i v ) 2 ¦ N 1 i 1
(11)
Where vi is the actual wind speed measurement i, N is the total number of wind speed measurements and v is the arithmetic mean wind speed. The shape parameter (k) can be calculated as [1]:
k
§V · ¨ ¸ ©v¹
1.086
(12)
The scale parameter (c) is calculated as [1]:
c
v § 1· *¨1 ¸ © k¹
(13)
4.3 Weibull parameter estimation using maximum likelihood estimators Maximum likelihood estimation works by developing a likelihood function based on the available data and finding the values of the parameter estimates that maximize the likelihood function. The basic concept is to obtain the most likely values of the distribution parameters that best describe a given data. This can be achieved by taking the partial derivatives of the likelihood function with respect to the parameters, setting the resulting equations equal to zero, and solving simultaneously to determine the values of the parameter estimates.
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
The software MATLAB has a built-in function that easily calculates the Weibull parameters using maximum likelihood estimation. The function “weibfit” estimates the parameters for a given input data vector [1]. After identifying the parameters of each probability distribution, it is easy to draw curves showing predicted wind speed distribution against real values (Fig.1 and Fig.2), but simple visual examination will not lead to an objective conclusion of which law gives good agreement so it is mandatory to pass to quantified criteria which is in this case the Ȥ2 test. 5. Results and discussion Wind characteristics of Bechar and Tamanrasset have been analyzed statistically. Wind speed data were collected for a period of eighteen years. The probability density distributions and power density distributions were derived from the time series data. Four probability density functions have been fitted to the measured probability distributions on a monthly basis, based on the Weibull, lognormal, gamma law and normal models. The Weibull distribution gives a good fit to the observed wind speed data. The number of days the wind power density is more than the annual mean wind power density is about 31.4% of the year.
Fig.1. Weibull distribution for Bechar (adjustment at 10 m)
711
712
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
T (adju ustment at 10 m) Fig.2. Weibull distribution for Tamanrasset
Table 1. Values of Ȥ2 test Distributtion function G Gamma Loggnormal N Normal W Weibull
Bechar Ȥ2 306.31 44096 117.9 106.48
Tabble 2. Weibull parrameters calculateed by three methoods Quick method Least squares method Location C C(m/s) K(-) C(m/s) K(-) Bechar 4 4.4746 2.9819 4.4747 2.9932 Tamanrasset 3 3.7697 2.0506 3.7727 1.9917
Tamanrasset Ȥ2 499.07 98789 246.32 119.03
maximum likelihood method C((m/s) K(-) 4.4 4749 2.9662 3.7 7688 2.0285
Tabble 3. Weibull disttribution parametters and estimatedd wind power den nsity Numberr of days Stattion Annuall wind Sensor Data source Mean wind pow wer speed (m/s) Density[MWPD D] where WPD D>MWPD Height 2 (m) (W/m ) (day//year) Becchar 3.99947 10 ONM 56.659 1332 Tamannrasset 3.33395 10 ONM 42.143 1008
Peeriod of rrecord 1980-1997 1980-1997
6. Conclusiion The most im mportant outcoomes of the study s can be summarized s as a follows: Thhe average winnd speeds forr Bechar, Tam manrasset werre found to raange betweenn 3 and 4m/s. The values of o shape paraameter, k, and d scale param meter, c, at Bechar/Tamanr B rasset sites were w examineed and found to be 2.9819/2.0506 and d
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
4.4746/3.7697, respectively. Empirical correlations were also developed to estimate distribution parameters. The Weibull distribution is fitting the measured probability density distributions better than the other three distributions for the whole period. The Weibull distribution provides better power density estimation. The number of days the wind power density is above the annual mean wind power density is about 31.4% of the year. This work is just a preliminary study in order to estimate wind energy analysis of the region. Deeper investigation is required for industrial purpose. References: [1] Ulgen K. and Hepbasli A. Determination of Weibull parameters for wind energy analysis of Izmir, Turkey international Journal of Energy Research, 26, 2002, 495-506. [2] Carlos Antonio Ramos Robles, Determination of favorable conditions for the development of wind power Farm in Puerto Rico. University of Puerto Rico, 2005, 32-41. [3] Abdullah H.A., Wind energy potential in Aden-Yemen, Renewable energy, 13, 1998, 255-260. [4] Adrian I. and Ed M., Wind potential assessment of Quebec Province, Renewable energy, 28, 2003, 1881-1897. [5] Walker J.F. and Jenkins N., ‘Wind Energy Technology’, 1st Ed. Chichester John Wiley and Sons, 1997. [6] Pneumatikos J.D., ‘An experimental study of the empirical formulae commonly used to represent wind speed profiles near the ground’, Renewable energy, 1, 1999, 623 – 628. [7] Cheremisinoff N.P., ‘Fundamentals of wind energy’, 2nd Ed. Ann Arbor, MI, Ann Arbor, Science Publisher Inc, 1979. [8] Youm I., Sarr J., Sall M. and Kane M.M., ‘Renewable Energy Activities in Senegal–a Review’, Renewable and Sustainable Energy Reviews, 4, 2000, 75-89. [9] Adekoya L.O. and Adewale A.A., ‘Wind energy potential of Nigeria’, Renewable Energy, 2, 1992, 35-39.
713
ScienceDirect Energy Procedia 36 (2013) 707 – 713
TerraGreen 13 Interrnational Coonference 2013 2 - Advaancements inn Renewablle Energy and Clean Environmen E nt
Investiigation of o wind characte c eristics in n the souuthern reegion of Alggeria M. F. F Benatalllah*, M.Chegaar L.O.C., Departtment of Physics, Faculty of Sciencces, Ferhat Abbass University, 190000, Setif, Algeriaa m ail.com, [email protected] Email : mbenatallah@gma
Abstract
Before an investment i inn wind turbinnes takes placce in a given n site, it is im mportant to kknow severall fundamentall properties suuch as wind behavior, avaailability, conttinuity, and probability p in the proposed d region. To make m decisionns with those properties, p stattistical and dy ynamic characcteristics of wiind of the sitee should be foound out usingg wind observvations and sttatistical wind d evaluation. In this paper a preliminary y examinationn of wind poteential of two sites in the souuthern region of o Algeria is dealt d with. W Wind measured d data of a period of 18 yeaars are collectted from these two weatherr stations. Wiind speed is sttudied to find d d whhich fits the best b the measu ured data. By performing p the F 2 test wee the adequatee probability distribution find that the Weibull disstribution funnction is the most adapted d. The corresponding parameters weree a the quick and a the least squares s methoods. Althoughh that the firstt estimated ussing two methhods. These are method is more m practicaal, the obtaineed results by both method ds can be useed to estimatee the Weibulll parameters for f both sites and a good agreeement is obtaained with thee measured datta. e Authors. Pubblished by ElsLtd. evier Ltd. © 2013The TheAuthors. © 2013 Published by Elsevier Selection and/or peer-review underunder responsibility of the TerraGreen Academy Selection annd/or peer-reviiew respponsibility off the TerraGree en Academy. Keywords: Winnd characteristics, Weibull, Algeriia.
1. Introducttion The orientattion to renewaable energies was a quick response to th he energy crissis in the 19770s [1], which h influenced inn great part thhe developed countries, c todday and due to the climate change, c all thee countries aree concerned to t take the decision d in order o to preseerve clean, healthy h and stable s future for the nextt generations.. This decisioon could not be done withhout giving more m importannce to renew wable energiess resources over o fossil fuuels. The tradditionally knoown as oil producing p couuntries are eexploring and d
*
Corresponnding author. E-m mail address: [email protected]
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the TerraGreen Academy doi:10.1016/j.egypro.2013.07.082
708
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
developing their renewable energy sources [1-9] to reduce their dependence on fossil sources and also to reduce local energy bill in profit of international market. Algeria is not an exception. The objective of this study is to determine which distribution law fits the measured wind speed data in the region of Bechar and Tamanrasset. Gamma, Lognormal, Normal and Weibull, have been used to fit the data so it is easy to predict the power density in this area. 2. Wind data source Wind speed data are collected from the stations of the National Meteorological Office available on the sites of Bechar and Tamanrasset. The records for both sites are from 1987 to 2002 (18 years data). The measurements are made at 10 meters high. The minimum speed recorded should be equal or above 0.5 m/s and wind speed is averaged over three hours. 3. Probability distributions 3.1 Normal density function The probability density function for the normal distribution with mean P and standard deviation V is generally written as: 2 2 1 f ( x, P , V 2 ) e ( x P ) / 2 V (1) 2SV 2 3.2 Normal density function The probability density function of a log-normal distribution is: f ( x; P , V )
1 xV 2S
e (ln x P )
2 / 2V 2
,x
(2)
0
This follows by applying the change-of-variables rule on the density function of a normal distribution.
3.3 Gamma density function The probability density function of the gamma distribution can be expressed in terms of the gamma function parameterized in terms of a shape parameter Į and scale parameter. The equation defining the probability density function of a gamma-distributed random variable x is f ( x; D , O )
1
1
OD * D
x
D 1
e
x
O
, for : x
0 and Į, Ȝ,
Where Į and Ȝ are respectively the shape and scale parameters
0
(3)
709
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
3.4 Weibull density function Weibull probability function is the most used distribution in wind energy studies. However in this paper we use more than one distribution. The Weibull function is two parameter functions used to estimate wind speed frequency distribution. It is defined as [4]:
f (v )
(k / c)(v / c) k 1 exp[(v / c) k ]
(4)
Where f (v) is the Weibull probability density function with the probability of having a wind speed of Ȟ.
k : is the shape factor is (dimensionless), and c (m/s): is the scale factor. The mean speed is given by [2]:
v
c *(1 1 / k )
(5)
* : is the gamma function 4. Methodology and analysis 4.1 Weibull parameter estimation using least squares parameter estimation: After arranging the data from smallest to largest we obtain their median rank plotting position by [1]:
F (vi ) |
i 0.3 N 0.4
Now by plotting different values of Yi and intercept x
x
(6)
ln{ ln[1 F (vi )]} against ln v , a straight line with slope k
k ln c is obtained, using least squares. We can find:
The Weibull shape parameter (k)[1]: § N ·§ N · ln( v ) ¦ i ¨ ¸ ¨ ¦ Yi ¸ N ©i1 ¹© i 1 ¹ ln( v ) Y ¦ i i N i 1 k 2 § N · ln( ) v i ¸ ¨¦ N 2 ¹ ln( vi ) © i 1 ¦ N i 1
(7)
The Weibull shape parameter (c)[1]:
c
e
§a· ¨ ¸ ©k¹
Where the parameter (a) is calculated using:
(8)
710
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713 N
¦Y
i
a
i 1
k
§ N · ¨ ¦ ln(vi ) ¸ ¸ k¨ i 1 N ¨ ¸ ¨ ¸ © ¹
(9)
4.2 Weibull parameter estimation using “the Quick Method”: From multiple observations we have found that for a large sample of wind speed measurements the shape and scale parameters can be estimated very accurately if we compare the estimation with the result that can be obtained using the more complicated and robust method of maximum likelihood estimators (MLE) [1]. The “quick method” requires first to calculate the arithmetic mean wind speed, for a given large sample of wind measurements using [1]: N
¦v
i
v
i 1
(10)
N
Then calculate the sample standard deviation using [1]:
V
1 N (v i v ) 2 ¦ N 1 i 1
(11)
Where vi is the actual wind speed measurement i, N is the total number of wind speed measurements and v is the arithmetic mean wind speed. The shape parameter (k) can be calculated as [1]:
k
§V · ¨ ¸ ©v¹
1.086
(12)
The scale parameter (c) is calculated as [1]:
c
v § 1· *¨1 ¸ © k¹
(13)
4.3 Weibull parameter estimation using maximum likelihood estimators Maximum likelihood estimation works by developing a likelihood function based on the available data and finding the values of the parameter estimates that maximize the likelihood function. The basic concept is to obtain the most likely values of the distribution parameters that best describe a given data. This can be achieved by taking the partial derivatives of the likelihood function with respect to the parameters, setting the resulting equations equal to zero, and solving simultaneously to determine the values of the parameter estimates.
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
The software MATLAB has a built-in function that easily calculates the Weibull parameters using maximum likelihood estimation. The function “weibfit” estimates the parameters for a given input data vector [1]. After identifying the parameters of each probability distribution, it is easy to draw curves showing predicted wind speed distribution against real values (Fig.1 and Fig.2), but simple visual examination will not lead to an objective conclusion of which law gives good agreement so it is mandatory to pass to quantified criteria which is in this case the Ȥ2 test. 5. Results and discussion Wind characteristics of Bechar and Tamanrasset have been analyzed statistically. Wind speed data were collected for a period of eighteen years. The probability density distributions and power density distributions were derived from the time series data. Four probability density functions have been fitted to the measured probability distributions on a monthly basis, based on the Weibull, lognormal, gamma law and normal models. The Weibull distribution gives a good fit to the observed wind speed data. The number of days the wind power density is more than the annual mean wind power density is about 31.4% of the year.
Fig.1. Weibull distribution for Bechar (adjustment at 10 m)
711
712
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
T (adju ustment at 10 m) Fig.2. Weibull distribution for Tamanrasset
Table 1. Values of Ȥ2 test Distributtion function G Gamma Loggnormal N Normal W Weibull
Bechar Ȥ2 306.31 44096 117.9 106.48
Tabble 2. Weibull parrameters calculateed by three methoods Quick method Least squares method Location C C(m/s) K(-) C(m/s) K(-) Bechar 4 4.4746 2.9819 4.4747 2.9932 Tamanrasset 3 3.7697 2.0506 3.7727 1.9917
Tamanrasset Ȥ2 499.07 98789 246.32 119.03
maximum likelihood method C((m/s) K(-) 4.4 4749 2.9662 3.7 7688 2.0285
Tabble 3. Weibull disttribution parametters and estimatedd wind power den nsity Numberr of days Stattion Annuall wind Sensor Data source Mean wind pow wer speed (m/s) Density[MWPD D] where WPD D>MWPD Height 2 (m) (W/m ) (day//year) Becchar 3.99947 10 ONM 56.659 1332 Tamannrasset 3.33395 10 ONM 42.143 1008
Peeriod of rrecord 1980-1997 1980-1997
6. Conclusiion The most im mportant outcoomes of the study s can be summarized s as a follows: Thhe average winnd speeds forr Bechar, Tam manrasset werre found to raange betweenn 3 and 4m/s. The values of o shape paraameter, k, and d scale param meter, c, at Bechar/Tamanr B rasset sites were w examineed and found to be 2.9819/2.0506 and d
M.F. Benatallah and M. Chegaar / Energy Procedia 36 (2013) 707 – 713
4.4746/3.7697, respectively. Empirical correlations were also developed to estimate distribution parameters. The Weibull distribution is fitting the measured probability density distributions better than the other three distributions for the whole period. The Weibull distribution provides better power density estimation. The number of days the wind power density is above the annual mean wind power density is about 31.4% of the year. This work is just a preliminary study in order to estimate wind energy analysis of the region. Deeper investigation is required for industrial purpose. References: [1] Ulgen K. and Hepbasli A. Determination of Weibull parameters for wind energy analysis of Izmir, Turkey international Journal of Energy Research, 26, 2002, 495-506. [2] Carlos Antonio Ramos Robles, Determination of favorable conditions for the development of wind power Farm in Puerto Rico. University of Puerto Rico, 2005, 32-41. [3] Abdullah H.A., Wind energy potential in Aden-Yemen, Renewable energy, 13, 1998, 255-260. [4] Adrian I. and Ed M., Wind potential assessment of Quebec Province, Renewable energy, 28, 2003, 1881-1897. [5] Walker J.F. and Jenkins N., ‘Wind Energy Technology’, 1st Ed. Chichester John Wiley and Sons, 1997. [6] Pneumatikos J.D., ‘An experimental study of the empirical formulae commonly used to represent wind speed profiles near the ground’, Renewable energy, 1, 1999, 623 – 628. [7] Cheremisinoff N.P., ‘Fundamentals of wind energy’, 2nd Ed. Ann Arbor, MI, Ann Arbor, Science Publisher Inc, 1979. [8] Youm I., Sarr J., Sall M. and Kane M.M., ‘Renewable Energy Activities in Senegal–a Review’, Renewable and Sustainable Energy Reviews, 4, 2000, 75-89. [9] Adekoya L.O. and Adewale A.A., ‘Wind energy potential of Nigeria’, Renewable Energy, 2, 1992, 35-39.
713