Statistical scrutiny of Weibull parameters for wind energy potential appraisal in the area of northern Ethiopia
 K. Shiva Prashanth Kumar^{1}Email author and
 Satyanarayana Gaddada^{2}
https://doi.org/10.1186/s4080701500140
© Kumar and Gaddada. 2015
Received: 1 July 2015
Accepted: 28 September 2015
Published: 26 October 2015
Abstract
Paramount twoparameter Weibull function has been extensively used to assess the wind energy potential. The performance contrast of four statistical methods, i.e., energy pattern factor method, least squares regression method, method of moments and mean standard deviation method in estimating extensively used Weibull parameters for wind energy application at four selected locations of northern Ethiopia has been studied. The contrast of statistical methods is compared through relative percentage error, root mean square error, mean percentage error, mean absolute percentage error, Chisquare error and analysis of variance (or) efficiency of the methods used. Test results evidently revealed that, least squares regression method presents better performance than other methods selected in the investigation. The least efficient methods to fit the Weibull distribution curves for the assessment of wind speed data especially for four selected locations are energy pattern factor method, method of moments and mean standard deviation. From the actual data analysis, it is found that if wind speed distribution matches well with the Weibull function, the above three methods are applicable, but if not, least squares regression method can be considered based on the cross checks including energy potential and cumulative distribution function.
Keywords
Wind energy Weibull distribution Probability distribution function (PDF) Cumulative distribution function (CDF) Shape parameter (k) Scale parameter (c)Background
Wind is one of the unlimited renewable energy resources which can provide with significant units of energy to bear the requirements of a nation. It is renowned that wind energy has stood out as the most precious and promising choice for generation of electricity. Earlier studies have proved that the installation of a number of wind turbine generators can effectively reduce environmental pollution, fossil fuel consumption, and the costs of overall electricity generation (Paritosh 2011). Though wind is only the sporadic source of energy which can represent a reliable energy resource from a longterm energy policy among the diverse renewable energy resources, wind energy is one of the most admired energy resources around the globe.
In Africa, Ethiopia is among the least developed countries on the globe with a total access to electricity not exceeding 16 %. The country is endowed with all sources of energy such as hydro, solar, wind, biomass, natural gas, geothermal, etc., and has not been able to develop, transform and utilize these resources for optimal economic development. It has a capacity of generating electricity of more than 5000 MW from geothermal and 10,000 MW from wind (Ethiopian Electric Power Corporation (EEPCo) 2011) and an average potential of 5.26 kWh per square meter per day from high solar energy (Ministry of Water and Energy (MoWE) 2011). Wind power is growing globally at the rate of 30 % annually, with an installed capacity increased from 196,653 MW in 2010 to 239,000 MW at the end of 2011 (World Wind Energy Association (WWEA) 2015). The Ethiopian government is devoted to improving its energy production capacity as quickly as possible by constructing new power plants, expanding the national grid and has planned to reach 10,000 MW of installed capacities by 2015 (Ethiopian Electric Power Corporation (EEPCo) 2011). Lack of reliable wind data covering the entire country has been one of the reasons for limited application of wind energy in Ethiopia, but lately studies have shown that it has substantial potential to generate electricity from wind, geothermal and hydropower sources. Considering the substantial wind energy resource in the country, government has committed itself to generate power from wind plants by constructing eight wind farms with total capacity of 1116 MW together with a number of hydropower plants over the 5 year Growth and transformation plan (GTP) period from 2011 to 2015. This development of wind power is a part of the current energy sector policy of the country that aims at five time’s increase in renewable energy production by the end of 2015 (Mulugeta et al. 2013). Based on the theoretical cubic relationship for wind power estimation, it was found that the simplified approach may provide significantly lower estimates of wind power potential by 42–54 % (Yong et al. 2012). A feasibility study has been proven that the basic needs of the community are served by small Hydro/PV/Wind hybrid system for offgrid rural electrification in Ethiopia (Getachew and Getnet 2012). The analysis of solar energy potential and design of a hybrid stand alone electric energy supply system that includes a wind turbine, PV, diesel generator and battery (Bekele and Palm 2009).
Wind energy has intrinsic variances and hence it can be expressed by distribution functions. The Weibull distribution is an important distribution especially for reliability and maintainability analysis. Twoparameter Weibull distribution function has been commonly used in many folds which includes wind energy assessment, rainfall and water level prediction, sky clearness index classification, life length analysis of material, etc., for representing the picture of energy potential and feasibility of installing wind turbine systems (Abernethy 2002; Weibull 1939, 1951). Extreme transitions in wind speed characterization require specific efforts in investigating spatial, temporal and directional variation of wind speeds, which render rather difficult the characterization and classification of an area as of high or low wind potential, in the majority of cases (Bagiorgas et al. 2008). In recent times, it became a reference delivery in commercial wind energy software’s resembling Wind Atlas Analysis and Application Program (Carta et al. 2009).
Enlargement of upgraded and innovative techniques for accurately assessing the wind energy potential of a site is gaining augmented importance. This is because of the fact that planning and establishment of a wind energy system depend upon factors like variation of wind speed distribution, mean wind speed, standard deviation, and characteristic operational speeds of turbine viz. cutin velocity, rated velocity, and cutout velocity. It is mandatory to amend the wind speed characteristics of a particular location to establish certain wind turbines for generation of electricity. Among the methods suggested by the prior researchers, it is bringing to crucial findings that the maximum likelihood method performs better than the popularly used graphical method in determining Weibull parameters; but the graphical method’s performance can be enhanced as the bin size of wind speed is reduced (Seguro and Lambert 2000). The empirical method provides more accurate prediction of average wind speed and power density than the graphical method (Jowder 2009). Chi square method gave better estimations for Weibull parameters than the moment and graphical methods, based on the Kolmogorov–Smirnov statistics (Dorvlo 2002). The performances of maximum entropy principle (MEP) derived probability density functions (PDFs) in fitting wind speed data varies from site to site. Also, the results demonstrate that MEP—derived PDFs are flexible and have the potential to capture other possible distribution patterns of wind speed data (Junyi et al. 2010). A little difference in terms of adjusted R ^{2} and root mean square error (RMSE) values in modeling wind direction with angularlinear (AL) and Farlie–Gumbel–Morgenstern (FGM) approaches using bivariate statistical models for representing both wind direction and speed (Erdem and Shi 2011). Excellent fitting can be achieved for wind speed using conventional univariate probability distribution functions, but it is found that accurately fitting air density distribution of the North Dakota site can only be obtained using bimodal distributions (Xiuli and Jing 2010). All the geometric methods mentioned are based on the fact that wind speed data follow the Weibull probability distribution. However the wind data actually observed is not necessary with the Weibull distribution. For a given data set, widely used statistical methods such as moment method, least square regression method, standard deviation method, maximum likelihood method, modified maximum likelihood method and energy pattern factor method can be applied to estimate the Weibull parameters (Lai and Lin 2006; Zhou et al. 2006; Akpinar and Akpinar 2004; Celik 2003; Ucar and Balo 2009; Chang et al. 2003; Kwon 2010; Thiaw et al. 2010; Akdag and Dinler 2009).
The evaluation of Weibull parameters is so vital in wind energy application at a desired location. However, the precision of four statistical methods mentioned has been discussed in this current research. A very few studies have been performed to investigate the characteristics and pattern of wind speed across Ethiopia, less attention has been given to the sites principally in Northern Ethiopia. The main intention of this study is, therefore, to verify the performance of four statistical methods to analyze the Weibull parameters for wind energy applications at four selected locations (i.e., Chercher, Maychew, Mekele and Senkata) in the Northern Tigray region of Ethiopia.
Data measurement
Geographical coordinates of selected experimental locations
S. no  Stations  Longitude  Latitude  Altitude (m)  Measurement period 

1  Chercher  N12°53′  E39°76′  1767  2013–2014 
2  Maychew  N12°47′  E39°32′  2479  
3  Mekele  N13°29′  E39°28′  2084  
4  Senkata  N14°13′  E39°34′  2480 
Methods for appraising Weibull parameters
In the modern past, numerous statistical models have been developed and used for scrutiny of wind speeds for assessing energy potential at a location. Former studies have also been showed that a very few statistical methods such as Weibull and Rayleigh distribution models can also be equally used (Akpinar and Akpinar 2005). Among these methods, paramount twoparameter Weibull probability distribution function is one of the most appropriate, conventional and suggested method for wind speed analysis owing to a better fit for measured monthly probability density distributions, than other statistical functions (Akdag et al. 2010). Moreover, the Weibull parameters at known heights can also be used to estimate wind parameters at a new height (Mathew 2006).
The entire distributions can be used to resolve the probability of occurrence affects the shape of probability curve and wind regime. The cumulative curve probability nature typically fits to the Weibull distribution function. Copious methods for estimation of Weibull parameters are originated in the literature are furnished below.
Energy pattern factor method (EPFM)
Leastsquares regression method (LSRM)
The relationship between ln(v) against ln[−ln[1 − F(v)]] represents a straight line with slope k and the intersection point with Weibull line gives the value of scale parameter (c) in meters per second.
Method of moments (MOM)
Mean standard deviation method (MSDM)
Statistical inaccuracy analysis/goodness of fit
To find the best method for analysis, several statistical tools were used by the previous researchers to analyze the efficiency of abovementioned methods. The following tests are as follows (Mohammadi and Mostafaeipour 2013; Costa Rocha et al. 2012; Justus and Mikhail 1976):
 (a)
Relative percentage of error (RPE)
$${\text{RPE}} = \left( {\frac{{x_{i, w}  y_{i, m} }}{{y_{i,m} }}} \right) \times 100 \; \%$$(17)  (b)
Rootmean square error (RMSE)
$${\text{RMSE}} = \left[ {\frac{1}{N}\mathop \sum \limits_{i = 1}^{n} \left( {y_{i,m}  x_{i,w} } \right)^{2} } \right]^{{\frac{1}{2}}}$$(18)  (c)
Mean percentage error (MPE)
$${\text{MPE}} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{n} \left( {\frac{{x_{i,w}  y_{i,m} }}{{y_{i,m} }}} \right) \times 100 \; \%$$(19)  (d)
Absolute mean percentage error (AMPE)
$${\text{AMPE}} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{n} \left {\frac{{x_{i,w}  y_{i,m} }}{{y_{i,m} }}} \right \times 100 \; \%$$(20)  (e)
Chisquare error
$$\chi^{2} = \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {y_{i,m}  x_{i,w} } \right)^{2} }}{{x_{i,w} }}$$(21)  (f)
Kolmogorov–Smirnov test
$$Q_{95} = \frac{1.36}{\sqrt N }$$(22)  (g)
Analysis of variance (or) regression coefficient
$$R^{2} = \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {y_{i,m}  z_{{i, \bar{\nu }}} } \right)^{2}  \mathop \sum \nolimits_{i = 1}^{n} \left( {y_{i,m}  x_{i,w} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {y_{i,m}  z_{{i,\bar{\nu }}} } \right)^{2} }}$$(23)
Coefficient of variation (COV)
Wind energy potential
Results and discussion
Expressive statistics for observed wind speed data at Chercher
Months  Data observations  Wind speed range (m/s)  Mean (m/s)  Standard deviation (m/s)  Skewness  Kurtosis  Power Density (W/m^{2})  Q _{95} 

Jan  248  1.850  2.425  0.474  −0.270  −0.393  8.730  0.086 
Feb  224  1.810  2.786  0.468  0.570  0.962  13.238  0.091 
Mar  248  2.310  2.931  0.539  0.230  0.498  15.422  0.086 
Apr  240  2.110  3.147  0.551  0.076  −0.954  19.097  0.088 
May  248  2.910  2.471  0.814  0.861  −0.388  9.240  0.086 
June  240  1.500  2.827  0.390  −0.253  −0.591  13.842  0.088 
July  248  2.260  3.096  0.536  0.337  −0.191  18.173  0.086 
Aug  248  2.190  2.626  0.669  0.038  −1.158  11.091  0.086 
Sep  240  1.860  1.905  0.524  0.913  0.169  4.234  0.088 
Oct  248  1.750  1.889  0.396  1.347  2.126  4.126  0.086 
Nov  240  1.360  2.452  0.341  0.258  −0.291  9.031  0.088 
Dec  248  2.230  2.463  0.507  1.907  4.264  9.149  0.086 
Feb–Apr  712  2.077  2.955  0.519  0.292  0.169  15.798  0.051 
May–July  736  2.223  2.798  0.580  0.315  −0.390  13.416  0.050 
Aug–Oct  736  1.933  2.140  0.530  0.766  0.379  6.001  0.050 
Nov–Jan  736  2.002  2.446  0.441  0.631  1.193  8.969  0.050 
Annual  5840  3.010  2.585  0.517  0.501  0.338  135.372  0.087 
Expressive statistics for observed wind speed data at Maychew
Months  Data observations  Wind speed range (m/s)  Mean (m/s)  Standard deviation (m/s)  Skewness  Kurtosis  Power Density (W/m^{2})  Q _{95} 

Jan  248  1.110  1.619  0.249  0.769  1.401  2.597  0.086 
Feb  224  0.580  1.649  0.174  −0.088  −1.087  2.744  0.091 
Mar  248  0.670  1.755  0.191  −0.701  −0.366  3.309  0.086 
Apr  240  0.720  1.567  0.212  0.147  −1.196  2.356  0.088 
May  248  1.030  1.906  0.225  −0.120  0.990  4.244  0.086 
June  240  2.390  2.339  0.648  0.935  −0.062  7.840  0.088 
July  248  4.960  4.110  1.443  0.062  −0.812  42.516  0.086 
Aug  248  4.240  2.919  0.992  0.861  1.148  15.230  0.086 
Sep  240  0.890  1.552  0.205  1.279  1.767  2.288  0.088 
Oct  248  0.610  1.588  0.165  −0.151  −1.014  2.451  0.086 
Nov  240  0.820  1.545  0.157  1.488  4.554  2.257  0.088 
Dec  248  0.560  1.537  0.128  0.436  0.532  2.225  0.086 
Feb–Apr  712  0.657  1.657  0.192  −0.214  −0.883  2.785  0.051 
May–July  736  2.793  2.785  0.772  0.292  0.039  13.233  0.050 
Aug–Oct  736  1.913  2.019  0.454  0.663  0.633  5.044  0.050 
Nov–Jan  736  1.939  1.567  0.178  0.898  2.162  2.356  0.050 
Annual  5840  5.450  2.007  0.399  0.410  0.488  90.058  0.087 
Expressive statistics for observed wind speed data at Mekele
Months  Data observations  Wind speed range (m/s)  Mean (m/s)  Standard deviation (m/s)  Skewness  Kurtosis  Power Density (W/m^{2})  Q _{95} 

Jan  248  0.620  1.582  0.200  −0.406  −1.112  2.427  0.086 
Feb  224  0.490  1.514  0.145  0.080  −0.935  2.124  0.091 
Mar  248  1.280  1.629  0.359  0.975  0.246  2.648  0.086 
Apr  240  1.010  1.649  0.246  0.088  −0.032  2.749  0.088 
May  248  0.530  1.481  0.167  0.293  −1.112  1.989  0.086 
June  240  0.400  1.337  0.131  1.799  1.691  1.465  0.088 
July  248  0.620  1.329  0.135  2.937  9.582  1.438  0.086 
Aug  248  0.540  1.398  0.238  2.264  5.453  1.674  0.086 
Sep  240  0.370  1.337  0.086  1.796  4.043  1.462  0.088 
Oct  248  0.520  1.458  0.158  0.611  −0.775  1.897  0.086 
Nov  240  0.560  1.481  0.169  0.736  −0.481  1.989  0.088 
Dec  248  1.040  1.420  0.241  2.681  7.293  1.755  0.086 
Feb–Apr  712  0.927  1.597  0.250  0.381  −0.240  2.497  0.051 
May–July  736  0.517  1.382  0.144  1.676  3.387  1.618  0.050 
Aug–Oct  736  0.477  1.397  0.160  1.557  2.907  1.672  0.050 
Nov–Jan  736  0.538  1.495  0.204  1.004  1.900  2.045  0.050 
Annual  5840  1.310  1.468  0.190  1.155  1.989  23.618  0.018 
Expressive statistics for observed wind speed data at Senkata
Months  Data observations  Wind speed range (m/s)  Mean (m/s)  Standard deviation (m/s)  Skewness  Kurtosis  Power Density (W/m^{2})  Q _{95} 

Jan  248  0.850  1.921  0.206  0.014  −0.104  4.342  0.086 
Feb  224  1.470  2.152  0.332  −0.249  0.063  6.101  0.091 
Mar  248  1.470  2.348  0.440  0.597  −0.564  7.931  0.086 
Apr  240  2.570  3.119  0.667  0.805  −0.187  18.582  0.088 
May  248  3.200  2.446  0.822  1.435  1.789  8.960  0.086 
June  240  1.960  2.251  0.668  0.130  −1.743  6.983  0.088 
July  248  1.170  1.672  0.299  0.771  0.794  2.862  0.086 
Aug  248  1.770  1.666  0.333  2.366  9.132  2.833  0.086 
Sep  240  1.770  2.068  0.563  0.504  −1.073  5.418  0.088 
Oct  248  2.720  2.522  0.712  0.947  0.424  9.826  0.086 
Nov  240  1.940  2.173  0.471  0.292  −0.037  6.282  0.088 
Dec  248  2.200  2.051  0.543  1.442  1.491  5.285  0.086 
Feb–Apr  712  1.837  2.540  0.480  0.384  −0.229  10.032  0.051 
May–July  736  2.110  2.123  0.597  0.779  0.280  5.858  0.050 
Aug–Oct  736  2.087  2.085  0.536  1.272  2.828  5.555  0.050 
Nov–Jan  736  1.682  2.048  0.407  0.583  0.450  5.263  0.050 
Annual  5840  3.420  2.199  0.505  0.754  0.832  85.405  0.087 
Middling values of monthly mean Weibull parameters estimated from four methods at selected locations
Chercher  Maychew  Mekele  Senkata  

k  c (m/s)  k  c (m/s)  k  c (m/s)  k  c (m/s)  
Jan  4.282  2.580  5.229  1.907  6.173  1.865  7.090  2.119 
Feb  4.856  2.860  7.242  1.904  7.881  1.793  5.197  2.334 
Mar  4.511  2.987  7.055  1.990  3.871  1.941  4.422  2.513 
Apr  4.702  3.163  5.820  1.857  5.367  1.930  3.976  3.172 
May  2.769  2.676  6.556  2.115  6.825  1.778  2.709  2.659 
Jun  5.738  2.868  3.203  2.547  7.764  1.657  3.034  2.478 
Jul  4.739  3.120  2.673  4.088  7.494  1.652  4.592  1.960 
Aug  3.447  2.775  2.704  3.061  4.797  1.736  4.174  1.964 
Sep  3.221  2.185  5.946  1.843  11.462  1.634  3.251  2.319 
Oct  4.030  2.148  7.325  1.856  7.089  1.757  3.153  2.703 
Nov  5.694  2.565  7.486  1.820  6.758  1.778  3.926  2.384 
Dec  4.089  2.621  8.983  1.802  4.797  1.754  3.312  2.303 
Annual  4.340  2.712  5.852  2.232  6.690  1.773  4.070  2.409 
In statistical analysis, for judgment of statistical methods to each other and to find out the efficiency of the methods, six statistical tools, i.e., relative percentage error (RPE), root mean square error (RMSE), mean percentage error (MPE), mean absolute percentage error (MAPE), Chi square error (χ ^{2}), and analysis of variance or efficiency of the method (R ^{2}) were used. Many researchers have already been used the methods at different geographical locations for wind energy estimation (Lun and Lam 2000). In general, only one column is required to rank the statistical methods, since the above all approaches gave identical virtual results. For more precise diagnosis, authors used these six statistical tools to rank the methods.
Efficiency of statistical methods used at Chercher
Method  k  c (m/s)  RPE  RMSE  MPE  MAPE  χ ^{2}  R ^{2} 

EPFM  3.900  2.858  0.108145  0.146590  0.013447  0.000025  13.563  0.802 
LSRM  1.346  2.424  0.040660  0.054781  0.005040  0.000026  4.227  0.972 
MOM  6.077  2.783  0.140325  0.204084  0.017467  0.000023  16.522  0.602 
MSDM  6.036  2.784  0.139926  0.203193  0.017417  0.000024  14.715  0.605 
Efficiency of statistical methods used at Maychew
Method  k  c (m/s)  RPE  RMSE  MPE  MAPE  χ ^{2}  R ^{2} 

EPFM  4.087  2.221  0.155112  0.237382  0.019259  0.000029  20.393  0.401 
LSRM  1.356  2.428  0.048056  0.070872  0.005960  0.000027  5.496  0.952 
MOM  9.036  2.140  0.249320  0.434901  0.031003  0.000028  6.889  0.542 
MSDM  8.929  2.141  0.270923  0.476823  0.033704  0.000025  11.666  0.786 
Efficiency of statistical methods used at Mekele
Method  k  c (m/s)  RPE  RMSE  MPE  MAPE  χ ^{2}  R ^{2} 

EPFM  4.326  1.615  0.130576  0.254938  0.016291  0.000108  19.846  0.162 
LSRM  1.352  2.420  0.036178  0.086152  0.004485  0.000101  7.027  0.853 
MOM  10.611  1.528  0.245858  0.614909  0.030568  0.000083  4.717  0.163 
MSDM  10.470  1.529  0.244792  0.605580  0.030435  0.000103  1.277  0.551 
Efficiency of statistical methods used at Senkata
Method  k  c (m/s)  RPE  RMSE  MPE  MAPE  χ ^{2}  R ^{2} 

EPFM  3.740  2.440  0.124385  0.169483  0.015435  0.000023  20.368  0.723 
LSRM  1.340  2.417  0.050517  0.066387  0.006275  0.000024  5.072  0.960 
MOM  5.599  2.390  0.160906  0.235879  0.020002  0.000024  15.513  0.380 
MSDM  5.599  2.390  0.160906  0.235879  0.020002  0.000024  15.513  0.380 
Standings of the methods by statistical test results
S. no  Statistical methods  Chercher  Maychew  Mekele  Senkata  Recommendation 

1  EPFM  Second  Fourth  Fourth  Second  – 
2  LSRM  First  First  First  First  First preference 
3  MOM  Fourth  Third  Third  –  – 
4  MSDM  Third  Second  Second  –  – 
Conclusions
In this paper, the scrutiny of four statistical methods in deriving Weibull parameters for wind energy application has been scientifically compared at selected locations in Northern Ethiopia. Statistical diagnosis of the best Weibull distribution methods for wind data analysis is discussed and presented. From the analysis of test results evidently revealed that LSRM presents better performance than other methods. The accuracy of four methods enhances more data numbers. Other methods such as EPFM, MOM and MSDM are the least efficient methods to fit the Weibull distribution curves for the assessment of wind speed data especially for these four selected locations. The maximum regression coefficient noticed at Chercher. The poor class wind power has been noticed in all selected locations. Furthermore, energy density and total energy intensity per unit area has been analyzed by numerical iteration methods. This study offers a new pathway on how to evaluate feasible locations for wind energy assessment which is applicable at any windy sites in any country in the world.
Nomenclature
Symbols
 \(\overline{{\nu^{3} }}\) :

mean of wind speed cubes, m^{3}/s^{3}
 \(\bar{\nu }\) :

mean wind speed, m/s
 c :

scale parameter of Weibull distribution function, m/s
 COV:

coefficient of variation
 EPF:

energy pattern factor, dimensionless
 E _{w} :

wind energy per unit area by Weibull function, kW h/m^{2}
 f(v):

Weibull pdf
 F(v):

cumulative Weibull function
 k :

Weibull shape parameter, dimensionless
 N :

total no. of wind speed observations
 R ^{2} :

regression coefficient or analysis of variance
 T :

time period, h
 v :

wind speed, m/s
 x _{ iw } :

the frequency of Weibull or ith calculated value from the Weibull distribution
 y _{ i,m } :

the frequency of observation or ith calculated value from measured data
 z _{ i,v } :

the mean of ith calculated value from measured data
 χ ^{2} :

Chisquare error
Greek letters
 σ :

standard deviation of wind speed, m/s
 Γ( ):

gamma function
 ρ :

air density, kg/m^{3}
Declarations
Authors’ contributions
KSPK collected the wind data and carried out initial analysis. Wind turbine calculations were performed by STNG. “Background” section was drafted by STNG and “Results and discussion” section was jointly drafted by KSPK and STNG. Both the authors compiled and abridged. Both authors read and approved the final manuscript.
Authors’ information
KSPK is working as a Lecturer in Department of Civil Engineering, Wollega University, Nekemte, Ethiopia. He obtained bachelor’s degree in Civil Engineering from Osmania University (OU), Hyderabad, and master’s degree in Geoenvironmental Engineering from JNTUH College of Engineering, Hyderabad. STNG is Associate Professor in Department of Electrical and Computer Engineering, Wollega University, Nekemte, Ethiopia. He obtained bachelor’s degree in Science from JVR Government Degree College, Sathupally, Khammam, Telangana state, India and Doctoral Degree in Computer Science and Engineering with specialization in Data Warehousing and Data Mining.
Acknowledgements
The authors are grateful to the National Meteorological Agency (NMA), Mekele, Ethiopia, for their cooperation in providing the raw data.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 Abernethy, R. B. (2002). The new Weibull handbook (4th ed.), North Palm Beach, FloridaGoogle Scholar
 Ahmed, S., & Mahammed, H. (2012). A statistical analysis of wind power density based on the Weibull and Ralyeigh models of “Penjwen Region” Sulaimani/Iraq. Jordan Journal of Mechanical and Industrial Engineering, 6, 135–140.Google Scholar
 Akdag, S. A., Bagiorgas, H. S., & Mihalakakou, G. (2010). Use of twocomponent Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean. Applied Energy, 87, 2566–2573.View ArticleGoogle Scholar
 Akdag, S. A., & Dinler, A. (2009). A new method to estimate Weibull parameters for wind energy applications. Energy Conversion Management, 50, 1761–1766.View ArticleGoogle Scholar
 Akpinar, E. K., & Akpinar, S. (2004). Determination of the wind energy potential for Maden Elazig, Turkey. Energy Conversion Management, 45, 2901–2914.View ArticleGoogle Scholar
 Akpinar, E. K., & Akpinar, S. (2005). An assessment on seasonal analysis of wind energy characteristics and wind turbine characteristics. Energy Conversion and Management, 46, 1848–1867.View ArticleGoogle Scholar
 Bagiorgas, H. S., Mihalakakou, G., & Matthopoulos, D. (2008). A statistical analysis of wind speed distributions in the area of western Greece. International Journal of Green Energy, 5(1), 120–137.View ArticleGoogle Scholar
 Bekele, G., & Palm, B. (2009). Feasibility study for a standalone solar—wind based hybrid energy system for application in Ethiopia. Applied Energy, 87(2), 487–495.View ArticleGoogle Scholar
 Benard, A., & BosLevenbach, E. C. (1953). Het uitzetten van waarnemingen op waarschijnlijkdeidspapier (the plotting of observations on probability paper). Statististica Neerlandica, 7, 163–173.MathSciNetView ArticleGoogle Scholar
 Carta, J. A., Ramirez, P., & Velazquez, S. (2009). A review of wind speed probability distributions used in wind energy analysis case studies in the Canary Islands. Renewable Sustainable Energy Reviews, 13, 933–955.View ArticleGoogle Scholar
 Celik, A. N. (2003). A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey. Renew Energy, 29, 593–604.View ArticleGoogle Scholar
 Chang, T. J., Wu, Y. T., Hsu, H. Y., Chu, C. R., & Liao, C. M. (2003). Assessment of wind characteristics and wind turbine characteristics in Taiwan. Renewable Energy, 28, 851–871.View ArticleGoogle Scholar
 Costa Rocha, P. A., de Sousa, R. C., de Andrade, C. F., & da Silva, M. E. V. (2012). Comparison of seven numerical methods for determining Weibull parameters for wind energy generation in the northeast region of Brazil. Applied Energy, 89, 395–400.View ArticleGoogle Scholar
 Dorvlo, A. S. S. (2002). Estimating wind speed distribution. Energy Conversion Management, 43, 2311–2318.View ArticleGoogle Scholar
 Erdem, E., & Shi, J. (2011). Comparison of bivariate distribution construction approaches for analyzing wind speed and direction data. Wind Energy, 14(1), 27–41.View ArticleGoogle Scholar
 Ethiopian Electric Power Corporation (EEPCo). (2011). Strategic management and programming. Facts in brief, http://www.eepco.gov.et/files/…/RPF%20ENREP%20Main%20document.doc.
 Ethiopian Electric Power Corporation (EEPCo). (2011). Strategic plan 2011–2025, Addis Ababa. http://www.capitalethiopia.com/index.php?option=com_content&view=article&id=1078:eepcoenvisionsnext25years&catid=35:capital&Itemid=27.
 Getachew, B., & Getnet, T. (2012). Feasibility study of small Hydro/PV/Wind hybrid system for offgrid rural electrification in Ethiopia. Applied Energy, 97, 5–15.View ArticleGoogle Scholar
 International Standards Organization: guide to the expression of uncertainty in measurement, 1st edition (1992). http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf.
 Johnson, N. L., & Kotz, S. (1970). Continuous univariate distributions, vol. 2. Houghton Mifflin.Google Scholar
 Jowder, F. A. L. (2009). Wind power analysis and site matching of wind turbine generators in Kingdom of Bahrain. Applied Energy, 86, 538–545.View ArticleGoogle Scholar
 Junyi, Z., Ergin, E., Gong, L., & Jing, S. (2010). Comprehensive evaluation of wind speed distribution models: a case study for North Dakota sites. Energy Conversion and Management, 51(7), 1449–1458.View ArticleGoogle Scholar
 Justus, C. G., Hargraves, W. R., Mikhail, A., & Graber, D. (1978). Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology, 17, 350–353.View ArticleGoogle Scholar
 Justus, C., & Mikhail, A. (1976). Height variation of wind speed and wind distributions statistics. Geophysical Research Letters, 3, 261–264.View ArticleGoogle Scholar
 Kwon, S. D. (2010). Uncertainty analysis of wind energy potential assessment. Applied Energy, 87, 856–865.View ArticleGoogle Scholar
 Lai, C. M., & Lin, T. H. (2006). Technical assessment of the use of a smallscale wind power system to meet the demand for electricity in a land aquafarm in Taiwan. Renew Energy, 31, 877–892.View ArticleGoogle Scholar
 Lun, I. Y. F., & Lam, J. C. (2000). A study of Weibull parameters using longterm wind observations. Renewable Energy, 20, 145–153.View ArticleGoogle Scholar
 Manwell, J. F., McGowan, J. G., & Rogers, A. L. (2010). Wind energy explained: theory, design and application (2nd ed.). Wiltshire: Wiley.Google Scholar
 Mathew, S. (2006). Wind energy: fundamentals, resource analysis and economics. Heidelberg: Springer.View ArticleGoogle Scholar
 Ministry of Water and Energy (MoWE). (2011). Energy sector mapping and database development (ESMAD), first phase report. http://ergethiopia.com/energysectormappinganddatabasedevelopmentesmad/.
 Mohammadi, K., & Mostafaeipour, A. (2013). Using different methods for comprehensive study of wind turbine utilization in Zarrineh, Iran. Energy Conversion Management, 65, 463–470.View ArticleGoogle Scholar
 Mulugeta, B. A., Aleksandar, S., Dragan, K., & Slobodan, S. (2013). Wind energy resource development in Ethiopia as an alternative energy future beyond the dominant hydropower. Renewable and Sustainable Energy Reviews, 23, 366–378.View ArticleGoogle Scholar
 Paritosh, B. (2011). Weibull distribution for estimating the parameters. Wind Energy Management, publication with In Tech, ISBN: 9789533073361. http://www.intechopen.com/books/windenergymanagement/weibulldistributionforestimatingtheparameters.
 Seguro, J. V., & Lambert, T. W. (2000). Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. Journal of Wind Energy and Industrial Aerodynamics, 85(1), 75–84.View ArticleGoogle Scholar
 Thiaw, L., Sow, G., Fall, S. S., Kasse, M., Sylla, E., & Thioye, S. (2010). A neural network based approach for wind resource and wind generators production assessment. Applied Energy, 87, 1744–1748.View ArticleGoogle Scholar
 Tian, P. C. (2011). Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application. Applied Energy, 88(1), 272–282.View ArticleGoogle Scholar
 Ucar, A., & Balo, F. (2009). Investigation of wind characteristics and assessment of wind generation potentiality in UludagBursa, Turkey. Applied Energy, 86, 333–339.View ArticleGoogle Scholar
 Weibull, W. (1939). A statistical theory of the strength of materials. Ingeniors Vetenskaps Akademiens Handlingar (Royal Swedish Institute for Engineering), 151, 1–45.Google Scholar
 Weibull, W. (1951). A statistical distribution functions of wide applicability. Journal of Applied Mechanics, Transactions of the ASME, 18, 292–297.Google Scholar
 Xiuli, Q., & Jing, S. (2010). Bivariate modeling of wind speed and air density distribution for longterm wind energy estimation. International Journal of Green Energy, 7(1), 21–37.View ArticleGoogle Scholar
 World Wind Energy Association (WWEA). (2014). http://www.wwindea.org. Accessed April 2015.
 Yong, H. O. U., Yidong, P. E. N. G., Johnson, A. L., & Jing, S. H. I. (2012). Empirical analysis of wind power potential at multiple heights for North Dakota wind observation sites. Energy Science and Technology, 4(1), 1–12.Google Scholar
 Zhou, W., Yang, H. X., & Fang, Z. H. (2006). Wind power potential and characteristic analysis of the Pearl River Delta region, China. Renew Energy, 31(6), 739–753.View ArticleGoogle Scholar