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Wind Energy potential Estimation Using Weibull and Rayleigh

Distribution Models and surface measured data at Debre Birehan,

Ethiopia

Tegenu Argaw Woldegiyorgis1, Eninges Asmare Terefe

2

1Department of physics, College of Natural Science, Wollo University, Dessie, Ethiopia.

2Department of physics, College of Natural Science, Wollo University, Dessie, Ethiopia.

Corresponding author. E-mail :argawtegenu3@gmail.com&eningesiwnm@gmail.com

Received 13 Aug 2020, Revised 20 Sep 2020, Accepted 28 Sep 2020

Abstract

There is a vital need for clean and accessible energy in the Ethiopia, particularly, Debre Berhan sites.

Ethiopia possesses a potential of renewable energy, such as wind energy, solar energy and, geothermal

energies. Wind energy is one of the fastest growing renewable energy technologies of electricity generation

in the world. In this study, the wind speed that measured at a height of 2.5 m was used to calculate the

monthly mean wind speed and monthly mean wind power density of the sites at heights of 10.0 m and 50.0

m numerically. The energy pattern method was used to obtain wind Weibull distribution parameters. The

monthly average values of the Weibull shape parameter and Weibull scale parameters are varies from 3.52

to 4.07 and 1.97 m/s to 3.79 m/s respectively at height of 10.0 m. On the other hand, the monthly average

values of Weibull shape parameter and Weibull scale parameter are varies from 4.29 to 4.49 and 4.05 m/s

to 5.72 m/s respectively for a height of 50.0 m. Weibull distribution and Rayleigh distribution models were

used for assessment of wind power density of the study sites. The monthly mean wind power density was

observed to be highest in the month of February (26.68 W/m2 ) and lowest in the month of August (3.77

W/m2 ) and with the corresponding mean wind speeds were 3.44 m/s and 1.79 m/s respectively at a height

of 10.0 m. In addition, at height of 50.0 m the highest and lowest the monthly mean wind power densities

was also occurred in the month of February (111.60 W/m2) and in the month of August (39.33 W/m

2) with

corresponding mean wind speeds were 5.59 m/s and 3.95 m/s. The results reveal that the Weibull

distribution model is more accurate and efficient model for determining wind power density of Debre

Berhan, Ethiopia, than Rayleigh distribution model according to statistical performance error at heights of

10.0 m and 50.0 m: power density error(PDE), correlation coefficient(R2) and root mean square

error(RMSE) (for Rayleigh: PDE10 = 0.68, R2

10 = -1.1 and RMSE10 =11.08, for Weibull: PDE10 = 0.17 ,

R2

10 = 0.86 and RMSE10 = 2.82) as well as at height of 50.0 m: (for Rayleigh: PDE50 = 0.38, R2

50 = -0.7 and

RMSE50 = 30.8, for Weibull: PDE50 = -0.06 , R250 = 0.96 and RMSE50 = 4.63 ). Therefore, the wind power

density of Debre Berhan, Ethiopia was classified under class 1 according to the results of the study. This

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paper provides information of wind characteristics and wind power potential of the sites, which helps in

selecting suitable wind turbines to fulfill the energy needs especially in remote and rural areas.

Keywords : Wind power density, Weibull distribution model, Rayleigh distribution model, Debre Berhan,

Ethiopia.

1. Introduction

The world is moving toward renewable energies as the important sources of energy because of the limited

resources of fossil fuels and substantial demands for energy resources. The population of the world has

increased drastically after the industrial revolution, and it is directly proportional to energy consumption.

In order to fulfill the requirements of approximately seven billion humans using the conventional energy

methodology has caused excess CO2, NOx, and particulate pollutants in the air. The new age technology

and the industrial processes have been major contributors to global warming, and air and ocean pollution

[1].

Renewable energy systems are rapidly becoming more efficient and cheaper and their share of total energy

consumption is increasing [2]. As of 2019 worldwide, more than two-thirds of all new electricity capacity

installed was renewable [3]. Growth in consumption of coal and oil could end by 2020 due to increased

uptake of renewable and natural gas [4]. Today, the use of wind energy technology has been developing

very fast. Given that modern turbines have become an appropriate technique for extracting wind energy.

Wind energy is economical, sustainable, renewable and a clean energy [2, 5].The assessment of available

wind resources in a given location and time period is based on the calculated wind power density, which

can be obtained by several methods. In Puala-Andrea et al., (2014) the wind power density is calculated

from wind speed data as a time function. To obtain confident wind power density results, this

methodrequires wind speed data measurements, which not always are available. Another is based on the

wind probability distribution function (PDF), which is used to calculate the Wind Power Density

Distribution (WPDD). A comparison of the relative error between the WPDD obtained from the PDF and

the WPDD obtained from wind data is considered when making a decision if a wind PDF is a good

representation of the wind behavior [7].

Ethiopia is one of the African counties making a transition to the level of middle-income countries. In

such a journey, access to reliable and adequate electricity will be vital. As stated by Mondal et al., (2016),

the final consumption of energy in Ethiopia is estimated to be 40,000 GWh. Out of that consumption; 92%

goes to domestic appliances, 3% to industries while 4% to the transportation sector. Mostly, the supply of

energy is covered by hydro power. Ethiopia as a state has been endowed with sources of renewable energy

which include hydro, geothermal, wind, solar and biomass [9, 10]. Ethiopia has very good amount of clean

and diversified energy resources; the identified potential includes 45 GW from hydropower, 7 GW from

geothermal power, 1,350 GW from wind power and 5.5 kWh/m2/day (annual average daily radiation)

from solar source [11, 12].

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A number of few studies have been conducted on the use of probability density function such Weibull and

Rayleigh for modeling of the wind speed (wind energy potential) in some selected location in Ethiopia.

According to G. D, Nage the Weibull distribution is better in fitting the measured probability density

distributions than the Rayleigh distribution for the whole years in the study sites (Hawasa and Dire Dawa).

[14] was evaluated the most effective method among Moment method (MM), Empirical method (EM) and

Energy Pattern Method (EPM) to estimate Weibull parameters. The results showed that energy pattern

method was the most efficient and effective method for determining the shape parameter (k) and scale

parameter (c) of Weibull distribution. In this study Rayleigh model recommended than Weibull model for

assessing wind energy potential through Weibull parameters at Wereilu, South Wollo, Ethiopia. In

[15]Weibull distribution function was used to analyze five years daily wind speed for assessment of wind

power potential of six sites in southern Ethiopia. However, there is no finding that have been done before

at Debre Berhan, Ethiopia to estimate wind energy potential using Weibull and Rayleigh distribution

models. Moreover, the researchers are interested to study the characteristics of wind speed and wind

energy potential for the site as well as to select appropriate distribution model to the sites. Therefore, the

main goal of this paper were i) to evaluate the wind energy potential at Debre Berhan sites, Ethiopia, ii) to

select the better distribution model for the sites. Hence, this paper was focused on the use of daily wind

speed data that obtained from Kombolcha Meteorological agency for a period of 5 years (2014-2018) to

estimate monthly average wind energy potential of Debre birehan sites, Amhara region, Ethiopia.

The lowest monthly mean wind power density value at height of 10.0 m was detected in August with a

value of 39.33 W/m2 and the corresponding wind speed was 1.79 m/s. On the other hand, 26.68 W/m

2 was

the highest monthly mean wind power density value calculated in February with corresponding wind

speed of 3.44 m/s. The lowest and the highest monthly mean wind power density at height of 50.0 m for

Debre Berhan was occurred at the months of August and February with values 39.33 W/m2and 111.60

W/m2

respectively with corresponding speeds of 3.95 m/s and 5.59 m/s. The effectiveness of the proposed

models (Weibull and Rayleigh) for predicting monthly mean wind power density was done using

statistical tests such as: power density error (PDE), correlation coefficient (R2) and root mean square error

(RMSE). Therefore, the statistical tests for Rayleigh model at height of 10.0 m and 50.0 m: (PDE10 = 0.68,

R2

10= -1.1, RMSE10=11.08 and PDE50= 0.38, R2

50= -0.7, RMSE50 = 30.8) respectively as well for Weibull

model at height of 10.0 m and 50.0 m: (PDE10= 0.17, R210 = 0.86, RMSE10 = 2.82 and PDE50= -0.06, R

250=

0.96, RMSE50 = 4.63) respectively. According to these statistical tests evaluation, Weibull distribution

model is recommended than Rayleigh distribution model to estimate monthly mean wind power density

for the sites. For this study latest computing MATLAB software and excel spread sheet has been used for

the entire analysis. By considering the results, the site of Debre Berhan, Ethiopia could be suitable for the

installation of off grid of small wind turbines and stand-alone activities since it is under wind power class.

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2. Material and Method

Study Area

This study looks Debre Berhan, which is found with latitude of 9.6767 0N and longitude of 39.533

0E.

Debra-Berhan is a city and woreda in central Ethiopia that located in the Semien Shewa Zone of the

Amhara Region, about 120 kilometers north east of Addis Ababa with an elevation of 2,840 meters. It was

an early capital of Ethiopia and afterwards, with Ankober and Angolalla, was one of the capitals of the

kingdom of Shewa. Today, it is the administrative center of the Semien Shewa Zone of the Amhara

Region. The daily wind speed data used in this study was obtained from the Kombolcha meteorological

agency, Ethiopian for the period of five years (2014-2018). Based on these data, the wind speeds were

analyzed using excels sheet and MATLAB software to estimate the monthly wind power density of the

study site.

3.Theoretical Analysis

3.1 Weibull Distribution

Various distribution functions have been used to analyze the wind data, but the two-parameter Weibull

distribution is found to be the most effective. Besides its many advantages, the Weibull function has a

limitation: it cannot precisely represent the probabilities of zero or very low wind speeds. Probability

density function and cumulative density function were used to read the wind speed variation, which

indicates and compares the average speed data. The probability density function, f(v), gives the probability

for a given speed v, while the cumulative density function, F(v), gives the probability for the velocity equal

to or less than v. It has two parameters, scale factor (c), with the same units as wind speed and shape factor

(k) dimensionless [16-24]. Weibull distribution is given by;

(

)

(

)

(1)

is the probability density function(PDF); v is the wind speed (m/s). The Weibull distribution

expression is valid for k >1 and c > 0.

By integrating the Weibull probability distribution, Weibull cumulative distribution is obtained [25, 26]

and it is expressed as;

∫ dv (

)

(2)

Where v represents the highest wind speed under consideration and it changes according to the site.

A special case of the Weibull distribution with a parameter value of k = 2 is the Rayleigh distribution,

defined by [27-29]

(

) (

)

(3)

Rayleigh's cumulative distribution function is given by:

(

)

(4)

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The parameters for Weibull distribution can be calculated using different methods. In this paper, according

to [15, 26, 30] energy pattern method (Epf) is used to calculate the shape and scale parameters and can be

calculated as follows;

pf

∑

(

∑

)

(

)

(

) (5)

Where

( pf)

(

)

Where “ ” is known as the gamma function and it is defined as;

∫

dx

3.2 Wind Power Density

Wind power density is measure of capacity of wind resources in specified site. Wind Power density can be

measured based on many approaches [29, 31, 32, 33]. It is well known that the power of wind that flows at

(v) through a blade swept area (A = 1) increases as the cube of its velocity and is given by;

(6)

Many researchers have used mean velocity to calculate wind power density. Because the wind power is

proportional to cube of velocity, root mean cube of wind speed gives better result and is defined as [31,

34]:

rmc √

∑

(7)

The wind power density is considered to be a better indicator of wind resource as it takes into account the

frequency distribution of the wind speed, the air density and the cube of wind velocity. Thus, it can be

assessed using the following equation [35, 36].

∫

dv

(

) (8)

From Rayleigh distribution, power density can be calculated by [31, 37];

(

)

(9)

Where is air density at the site. The air density is calculated using the following expression [38, 39];

(

)

Where Z is the elevation and T is the temperature at a considered site.

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3.3 Most Probable Wind Speed and Wind Speed Carrying Maximum Energy

The wind speeds that are most possible or probable (vmp) and carry the highest (maximum) energy (vmaxE)

are necessary for approximating wind power. The two wind speeds are obtained from the scale and shapes

factors, as expressed in Equations below [40, 41].

mp (

)

max (

)

(10)

3.4 Wind Speed Variation (Extrapolation of Wind speed)

The power law is used to determine the vertical profile of the wind which is proposed by [42, 43]

*

+

(11)

Where, is the wind speed measured at reference height, ho , v is the speed that must be calculated at

height, h, is the surface roughness coefficient and lies in the range 0.05–0.5 and calculated by:

n

n(

) (12)

4. Distribution Models Evaluation

Many statistical methods have been used to compute the performance of the distribution models. Therefore,

in this study the prediction accuracy of the models in the estimation of the wind energy with respect to the

actual values was evaluated based on the following performance tests:

4.1 Power density error (PDE)

The relative error between the wind power density calculated from actual time-series data and that from

theoretical probability function is expressed as (yearly average error value in calculating the power density)

[44, 45];

∑ [

]

(13)

Where Pm,R is the wind power density for the probability density distribution, derived from measured

values and is given as:

ts

rmc

(14)

PW,R is the mean power density calculated from either the Weibull or Rayleigh function used in the

calculation of the error and is given by

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tp

∫ dv

(15)

4.2 Correlation coefficient

The correlation coefficient whose ideal value is one (1) gives the correlation between the predicted or

expected (in order to measure goodness of fit of Weibull distribution and Rayleigh distribution with

observed values) and observed data [46, 47].It is given by the relation;

∑ ∑

∑

(16)

Where yi = actual wind power values

xi = wind power calculated from Weibull or Rayleigh models

z = mean of actual wind power values.

4.3 Root mean square error (RMSE)

Root mean square error (RMSE) provides a term-by-term comparison of the actual deviation between

observed probabilities and predicted probabilities. A lower value of RMSE indicates a better distribution

[48].

M *

∑ ic

+

(17)

Where, yi is the actual value at time stage i, yic is the value computed from correlation expression for the

same stage, and n is the number of data.

5. Discussion and Results

Data for wind speed that measured at height of 2.50 m used in this study was obtained during the period

2014-2018 from the Kombolcha meteorological agency, Ethiopia. Based on these data, the wind speeds

were analyzed using excels sheet and MATLAB software to estimate the monthly wind power density of

Debre Berhan, Ethiopia at height of 10.0 m and 50.0 m.

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Table 1: Monthly characteristics of average wind speed from NASA (Vnasa) and extrapolated wind speed

(Vextra) of Debre Berhan at height of 10 m.

2014 2015 2016 2017 2018

Month Vnasa Vextr Vnasa Vextr Vnasa Vext Vnasa Vextr Vnasa Vextr

Jan. 2.61 3.45 2.81 3.16 2.39 3.27 2.88 2.93 2.74 2.92

Feb. 2.51 3.18 2.91 3.36 2.85 3.55 2.65 3.90 2.58 3.22

Mar. 2.74 3.47 3.05 3.62 2.62 3.23 2.45 3.48 2.73 3.29

April 2.80 3.64 3.59 2.85 2.00 2.51 2.99 3.52 2.07 2.36

May 2.63 3.12 2.81 3.04 1.94 2.70 2.16 2.79 2.68 4.71

June 2.40 3.07 2.02 2.86 2.05 2.70 2.38 3.06 2.16 2.45

July 1.85 2.31 2.03 2.31 1.64 1.96 1.92 2.15 1.95 1.92

Aug. 1.52 1.93 1.89 1.79 1.84 1.88 1.70 1.73 1.64 1.61

Sept. 1.69 1.82 2.12 1.84 1.74 2.02 1.80 2.01 2.22 2.29

Oct. 2.72 1.99 3.38 2.24 2.54 2.07 2.81 2.28 3.03 2.06

Nov. 3.11 2.46 3.22 2.55 2.77 2.67 3.01 2.42 2.74 2.59

Dec. 2.81 2.88 2.90 3.51 3.12 3.67 2.74 3.16 2.85 3.19

As indicated in table:1, the minimum monthly characteristics of average wind speed from NASA and that

extrapolated wind speed at height of 10.0 m was occurred in the month of August. Also the monthly

average maximum wind speed of the site was occurred in the month of February from the year of 2014 to

2018.

Table 2: Monthly average of the maximum energy carries of wind speed from NASA and that

extrapolated at height of 10.0 m of Debre Berhan from 2014 to 2018.

2014 2015 2016 2017 2018

Month NASA Extra NASA Extra NASA Extra NASA Extra NASA Extra

Jan. 4.41 4.15 5.11 3.86 3.84 4.17 5.08 3.54 4.71 3.62

Feb. 3.92 3.81 4.95 4.08 4.83 4.25 4.60 4.71 4.48 4.13

Mar. 4.49 4.30 5.14 4.41 4.25 3.98 4.05 4.25 4.42 4.06

Apr. 4.75 4.70 6.05 3.45 3.52 3.05 4.94 4.36 3.93 2.90

May 4.76 3.91 5.28 3.81 3.84 3.41 4.31 3.53 4.97 3.80

June 4.44 3.82 4.03 3.68 3.84 3.41 4.72 3.78 3.95 3.00

July 3.36 2.87 3.33 2.78 3.10 2.43 3.44 2.62 3.33 2.38

Aug. 2.85 2.41 3.44 2.21 3.16 2.30 3.13 2.10 2.93 1.96

Sept. 3.30 2.24 4.02 2.29 3.30 2.57 3.57 2.50 4.20 2.87

Oct. 4.51 2.39 5.49 2.73 4.24 2.52 4.73 2.80 4.96 2.53

Nov. 4.89 2.95 5.26 3.15 4.51 3.29 4.88 2.98 4.45 3.15

Dec. 4.57 3.53 4.68 3.64 5.28 3.71 4.70 3.27 4.83 3.23

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As shown in table: 2, the wind speed from NASA that carries the maximum energy in the year 2014 was

occurred at of November, in the year of 2015 was occurred at month of April, in the year of 2016 was

occurred at month of February, in the year of 2017 was occurred at the month of January and in 2018 was

occurred at the month of October (4.89 m/s, 6.05 m/s, 4.83 m/s, 5.08 m/s and 4.96 m/s respectively). From

extrapolated height of 10.0 m, the wind speed that carries the maximum energy in the year of 2014 was

occurred at the month of April, in the year of 2015 was occurred at the month of March, in the year of 2016

to 2018 was occurred at the month of February (4.70 m/s, 4.41 m/s, 4.25 m/s, 4.71 and 4.13 m/s

respectively).

Table 3: Monthly characteristics of average wind speed from NASA (Vnasa) and extrapolated wind speed

(Vextra) of Debre Berhan at height of 50 m.

Month 2014 2015 2016 2017 2018

Vnasa Vextr Vnas Vnasa Vnasa Vextr Vnasa Vextr Vnasa Vextr

Jan 5.05 5.65 5.52 5.39 4.38 5.46 5.42 5.18 5.41 5.16

Feb 4.82 5.42 5.37 5.56 5.45 5.74 5.02 5.82 4.95 5.40

March 5.09 5.65 5.51 5.78 4.63 5.45 4.69 5.68 5.06 5.31

April 5.32 5.70 6.59 5.11 4 4.77 5.28 5.69 4.26 4.62

May 5.17 5.33 5.72 5.26 4.10 4.94 4.64 5.02 5.34 5.17

June 5.01 5.30 4.44 5.07 4.35 4.93 5.09 5.29 4.45 4.70

July 4.04 4.56 4.07 4.57 3.80 4.18 4.19 4.39 4.26 4.13

Aug 3.19 4.02 4.05 3.97 3.82 4.09 3.74 3.92 3.79 3.76

Sept 3.70 4.01 4.45 4.04 3.63 4.22 3.86 4.23 4.58 4.53

Oct 4.90 4.22 6.07 4.49 4.66 4.31 5.18 4.53 5.38 4.29

Nov 5.42 4.73 5.72 4.92 5.05 4.92 5.34 4.66 4.89 4.85

Dec 5.34 5.13 5.11 4.99 5.65 5.10 5.31 4.82 5.14 4.89

As shown in table:3, the maximum monthly characteristics of average wind speed at height of 50.0 m for

Debre Berhan was occurred at different month since wind speed is variable. Therefore, the maximum

monthly average extrapolated wind speed at height of 50.0 m were found in the year of 2017 at month of

February, in the year of 2014 at the month April, in the year of 2015 at March, in the year of 2016 at

month February, in the year of 2018 at month February, which were 6.61 m/s, 6.58 m/s, 6.39 m/s, 6.26 m/s

and 6.16 m/s respectively. The maximum monthly average of wind speed at height of 50.0 m for Debre

Berhan from NASA were occurred in the year of 2015 at month of April, in the year of 2016 at month of

December in the year of 2014 at month of November, in the year of 2017 at month of January, in the year

of 2018 at month of January,which were 6.59 m/s, 5.65 m/s, 5.42 m/s, 5.42 m/s and 5.41 m/s respectively.

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Table 4: Monthly average of the most probable wind speed of Debre Berhan at height 10.0 m and 50.0 m

from 2014-2018.

Month Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec.

Vmp-10(m/s) 3.32 3.6 3.51 3.22 2.99 2.89 2.51 2.16 2.34 2.48 2.8 3.04

Vmp-50(m/s) 5.17 5.41 5.40 5.02 4.99 4.88 4.19 3.82 4.06 4.16 4.62 4.84

The monthly average of the most probable wind speed for Debre Berhan at height of 10.0 m and 50.0 m

from 2014 to 2018 were found in the month of February, March and January (for10.0 m: 3.6 m/s, 3.51 m/s

and 3.32 m/s and for 50.0 m: 5.41 m/s, 5.40 m/s and 5.17 m/s respectively).

Table 5: The Weibull shape parameter (k) and scale parameter(c) values at height of 10.0 m and 50.0 m

from 2014-2018.

Month Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

k-10 m 3.94 4.07 3.91 3.83 3.52 3.66 3.93 3.91 3.68 4.05 4.01 4.02

c-10.m 3.48 3.79 3.78 3.29 3.24 3.14 2.35 1.97 2.21 2.35 2.80 3.14

k-50 m 4.45 4.48 4.49 4.4 4.29 4.34 4.45 4.44 4.34 4.37 4.47 4.31

c-50.m 5.47 5.72 5.71 5.32 5.31 5.18 4.43 4.05 4.32 4.42 4.89 5.15

The value of Weibull shape parameter (k) varies from 3.52 to 4.07 at height of 10.0 m as well as at

height of 50.0 m varies from 4.29 to 4.49. The Weibull scale parameter (c) value varies from 1.97 m/s

to 3.79 and varies from 4.05 to 5.72 m/s for 10.0 m and 50.0 m height respectively.

Figure 1: Monthly average of wind speed that extrapolated at height of 10.0m and from NASA of

Debre Berhan from 2014 to 2018.

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Table 6: Comparison of monthly average Actual power density (Pa) with average Weibull power density

(Pw) and average Rayleigh power density (Pr) of Debre berhan at height of 10.0m from 2014 to 2018.

2014 2015 2016 2017 2018

Month Pw Pa Pr Pw Pa Pr Pw Pa Pr Pw Pa Pr Pw Pa Pr

Jan. 30.35 25.94 44.41 23.85 20.37 34.53 28.25 23.88 34.53 18.72 16.00 27.33 19.30 16.42 27.54

Feb. 23.67 20.21 34.70 28.44 24.34 41.28 32.77 27.97 41.28 44.16 37.75 64.49 27.23 23.11 37.60

Mar. 32.35 27.66 46.32 35.71 30.50 51.65 25.84 22.03 51.65 32.00 27.37 46.35 28.55 23.41 39.42

Apr. 39.66 35.22 54.48 17.36 14.81 25.27 11.89 10.18 25.27 33.79 28.94 48.33 10.09 8.59 14.52

May 23.85 20.30 33.75 22.06 18.79 31.19 15.73 13.42 31.19 17.32 14.71 24.29 21.14 17.82 29.19

June 22.59 19.19 32.18 19.15 16.23 26.35 15.69 13.37 26.35 22.09 18.84 31.66 11.16 9.53 16.10

July 9.61 8.18 13.72 9.11 7.78 13.31 5.83 4.98 13.31 7.46 6.38 10.82 5.49 4.68 7.83

Aug. 5.62 4.78 7.96 4.41 3.77 6.31 5.04 4.311 6.31 3.88 3.32 5.64 3.14 2.69 4.54

Sept. 4.61 3.94 6.61 4.86 4.14 6.92 6.65 5.68 6.92 6.31 5.39 9.01 9.44 8.04 13.38

Oct. 5.82 4.97 8.51 8.47 7.23 12.27 6.71 5.73 12.27 9.05 7.73 13.05 6.69 5.72 9.64

Nov. 10.95 9.35 16.05 12.78 10.91 18.36 14.5 12.43 18.36 10.83 9.26 15.54 13.13 11.08 19.08

Dec. 18.18 15.54 26.25 19.94 17.03 28.72 21.35 18.22 28.72 14.76 12.57 21.49 13.91 11.27 20.08

From the results, the month of August was the month in which the monthly mean minimum wind power

density was occurred at height of 10.0 m and 50.0 m, which were 3.77 W/m2 and 39.33 W/m

2 respectively.

Furthermore, the monthly mean maximum wind power density of Debre Berhan, Ethiopia at height of 10.0

m and 50.0 m was occurred in the month of February, which were 26.68 W/m2 and 111.60 W/m

2

respectively from the year of 2014 to 2018.

The monthly average minimum wind speed that extrapolated at height of 10.0 m and from NASA was

occurred at month of August which were 1.79 m/s and 1.72 respectively. The monthly average of

maximum wind speed from NASA in the period of 2014 to 2018 were found at months of November,

October and December, which were 2.97 m/s, 2.80 m/s and 2.88 m/s respectively. The monthly average of

maximum wind speed that extrapolated at height of 10.0 m were occurred at the months of February,

March and January, which were 3.44 m/s, 3.42 m/s and 3.15 m/s respectively as shown in Table :1 and

Figure:1.

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Table 7: Comparison of monthly average Actual power density (Pa) with average Weibull power

density (PW) and average Rayleigh power density (Pr) of Debre Berhan at height of 50.0 m from 2014 to

2018.

Month 2014 2015 2016 2017 2018

Pa Pw Pr Pa Pw Pr Pa Pw Pr Pa Pw Pr Pa Pw Pr

Jan 111.69 102.79 151.61 97.20 90.74 133.55 102.88 100.11 146.41 86.21 79.83 117.68 85.73 81.58 119.77

Feb 98.09 89.94 132.73 107.03 99.73 146.79 116.58 106.84 157.69 135.99 125.5 185.14 100.31 98.52 143.64

Mar. 113.13 105.21 154.41 120.33 112.7 165.85 100.69 94.32 138.62 113.69 106.3 156.51 103.99 98.02 145.04

Apr. 128.29 122.24 179.27 82.60 75.29 110.97 67.32 63.97 94.14 115.71 110.0 161.41 61.24 57. 84.82

May 95.27 91.82 134.54 91.35 85.86 125.78 76.00 73.60 107.61 79.83 77.29 113.08 87.66 87.92 128.41

June 93.07 88.66 130.18 83.01 81.73 119.10 75.81 72.58 106.14 92.48 87.61 128.69 64.79 59.27 87.17

July 59.27 56.35 82.74 58.92 54.30 80.08 45.65 43.23 63.50 52.58 47.12 69.36 44.00 41.51 60.92

Aug. 44.30 42.49 62.30 39.31 37.35 54.82 42.67 39.28 57.81 37.24 34.66 51.04 33.11 31.09 45.72

Sept. 40.30 38.20 56.09 41.22 39.27 57.64 47.94 46.95 68.48 47.42 44.17 64.79 58.35 56.28 82.49

Oct. 46.46 42.81 63.15 56.18 52.48 77.27 49.69 46.40 68.30 57.95 54.46 80.08 49.35 45.21 64.85

Nov. 65.18 65.56 96.70 69.33 63.47 93.25 74.22 70.22 103.15 63.43 58.25 85.53 70.66 65.73 96.83

Dec. 83.97 78.88 115.99 78.87 76.71 112.11 91.96 87.17 125.00 75.70 70.47 103.84 72.86 68.99 101.51

Figure2: Comparison of monthly average Wind speed from NASA (Vnasa) and Extrapolated wind speed

(Vextra) at height of 50.0 m from 2014-2018.

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As shown in Table:1 and Figure:3, the monthly average minimum wind speed of Debre Berhan at the

height of 50 m was occurred at the month of August for both values from NASA and extrapolated, which

were 3.718 m/s and 3.954 m/s respectively. The average maximum wind speed of Debre Berhan at height

of 50 m was occurred at the month of February for the values from NASA and extrapolated, which were

5.123 m/s and 5.588 m/s respectively.

Figure 3: Monthly averages of the maximum energy carriers of wind speed at height of 10.0 m and 50.0m

from NASA and extrapolated height.

The monthly average of wind speed that carries the maximum energy at the height of 10.0 m from NASA

were occurred at the months of December, November and October, which were 4.81 m/s, 4.80 m/s and 4.78

m/s respectively. The monthly average of wind speed that carries the maximum energy that extrapolated at

the height of 10.0 m were occurred at the months of March, February and January, which were 4.20 m/s,

4.19 m/s and 3.87 m/s respectively as shown in Table:2 and Figure:3.

The maximum most probable wind speed of Debre berhan at height of 10.0 m and50.0 m were occurred at

the same months February, March and January (with values of 3.60 m/s, 3.51 m/s and 3.32 m/s for 10.0 m

and 5.41m/s, 5.40 m/s and 5.17 m/s for 50.0 m). The minimum most probable wind speed of Debre Berhan

at height of 10.0 m and 50.0 m were occurred at the months of August, September and October (with

values of 2.16 m/s, 2.34 m/s and 2.48 m/s for 10.0 m and 3.82 m/s, 4.06 m/s and 4.16 m/s for 50.0 m).

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Table 4: Monthly averages of the most probable wind speed of Debre Birehan at height of 10.0 m and 50

m from 2014-2018.

Figure 5: Comparison of monthly average actual power density (Pa) with monthly average Weibull power

density (Pw) and Rayleigh power density (Pr) of Debre Berhan at height of 10.0 m from 2014-2016.

The monthly average minimum wind power densities of actual, Weibull and Rayleigh of Debre Berhan at

height of 10.0 m were occurred at the months of August, September, October and July with values of: (3.77

W/m2, 5.44 W/m

2, 6.27 W/m

2 and 6.40 W/m

2 respectively for actual power density), (4.42 W/m

2, 6.37

W/m2, 7.35 W/m

2 and 7.50 W/m

2 respectively, for Weibull power density) and (6. 35 W/m

2, 9.04 W/m

2,

10.64 W/m2 and 10.81 W/m

2 respectively for Rayleigh power density). The monthly average maximum

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258

wind power densities of actual, Weibull and Rayleigh of Debre Berhan at height of 10.0 m were found at

the months of February, March, January and April with values of: (26.68 W/m2, 26.20 W/m

2, 20.52 W/m

2

and 19.55 W/m2 respectively for actual power density), (31.25 W/m

2, 30.89 W/m

2, 24.10 W/m

2 and 22.56

W/m2 respectively for Weibull power density) and (45.22 W/m

2, 44.17 W/m

2, 34.63 W/m

2 and 31.97 W/m

2

respectively for Rayleigh power density).

Figure 6: Comparison of monthly average actual power density (Pa) with monthly average Weibull power

density (Pw) and Rayleigh power density (PR) of Debre Berhan at height of 50 m from 2014-2016.

The minimum monthly average of wind power densities for actual, Weibull and Rayleigh of Debre Berhan

at height of 50.0 m were occurred at the months of August, September, October and July with values of:

(39.33 W/m2, 47.05 W/m

2, 51.92 W/m

2 and 52.08 W/m

2 respectively for actual power density), (36.98

W/m2, 44.97 W/m

2, 48.27 W/m

2 and 48.50 W/m

2 respectively for Weibull power density) and (54.34

W/m2, 65.90 W/m

2, 70.73 W/m

2 and 71.32 W/m

2 respectively for Rayleigh power density). The maximum

monthly average wind power densities of actual, Weibull and Rayleigh of Debre Berhan at height of 50.0

m were found at the months of February, March and January with values of: (111.60 W/m2, 110.37 W/m

2

and 96.74 W/m2 respectively for actual power density), (104.12 W/m

2, 103.33 W/m

2 and 91.01 W/m

2

respectively for Weibull power density) and (153.20 W/m2, 152.09 W/m

2 and 133.81 W/m

2 respectively for

Rayleigh power density) as displayed in table :7 and figure:6.

6. Statistical Evaluation

The Weibull and Rayleigh distribution models were compared with each other on the basis of the statistical

error indicators such as: Power density error (PDE), Root Mean Square Error (RMSE), correlation

coefficeient (R2). Statistical tests between measured mean actual wind power density and estimated mean

wind power density from Weibull and Rayleigh is given in Table: 6, Table: 7 and in Figure: 5 and Figure 6.

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The correctness of the estimated values of the wind power density was tested by calculating the PDE, Root

RMSE andR2 as given in table 8.

Table 8: tatistica tests for distribution mode s

Distribution models R2 RMSE PDE

Weibull-10 m 0.86 2.82 0.17

Rayleigh-10 m -1.1 11.08 0.68

Weibull-50 m 0.96 4.63 -0.056

Rayleigh-50 m -0.7 30.8 0.38

From statistical performance tests as indicated in the Table 8, Figure: 5 and Figure: 6 Weibull distribution

model is more suitable than Rayleigh distribution model for Debre Berhan sites, Ethiopia.

7. Conclusion

This study focus on the estimation of wind energy potential of Debre Berhan based on daily wind data that

collected from January 2014 to December 2018 from Kombolcha meteorological Agency, Ethiopia. The

weibull scale (c) and shape (k) parameters are calculated using that energy pattern method. Therefore, the

present work has proposed to evaluate the monthly average of wind energy potential in the periods of 2014-

2018. The wind energy potential of this study area is modeled using Weibull and Rayleigh distribution

models at the height of 10.0 m and 50.0 m from surface measured data. The monthly mean power density

varies between (3.77 W/m2 and 26.68 W/m

2) and (39.33 W/m

2 and 111.60 W/m

2) at height of 10.0 m and

50.0 m respectively. Five years of monthly average wind speed data at 10.0 m and 50.0 m height were

assessed and analyzed using MATLAB and excel spread sheet. The results obtained showed the following:

The monthly mean of the most probable wind speed varies between 2.34 m/s (August) to 3.60 m/s

(February) and 3.82 m/s (August) to 5.41 m/s (February) at height of 10.0 m and 50.0 m

respectively.

The monthly wind speed that carries the maximum energy at height of 10.0 m varies between 2.20

m/s (August) to 4.20 m/s (March) and for height of 50.0 m varies between 4.41 m/s (August) to

6.21 m/s (February).

The monthly average maximum wind speed that extrapolated at height of 50.0 m varies between

4.41m/s in the month of August and 6.21 m/s in the month February.

The Weibull shape parameter (k) and scale parameter(c) values at 10.0 m elevation ranged between

3.52 to 4.07 and 1.97 m/s to 3.79 m/s and values at 50.0 m elevation ranged between 4.35 to 4.45

and 4.85 m/s to 5.11 m/s respectively from 2014-2018.

Monthly mean wind speeds varies between 1.79 m/s in the month of August and 3.44 m/s in the

month of February at height of 10.0 m with corresponding wind power densities of 3.77 W/m2 and

26.68 W/m2.

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Monthly mean wind speeds varies between 3.95 m/s in the month of August and 5.59 m/s in the

month of February at height of 50.0 m with corresponding wind power densities of 39.33 W/m2

and 111.60 W/m2.

At height of 10.0 m and 50.0 m, Weibull distribution model more fit than Rayleigh Distribution model for

Debre Berhan, Amhara region, Ethiopia according to the statistical performance. The results of this paper

revealed that the site corresponds to wind power of class 1 and this wind resource is not suitable for grid

connected wind power generation, however, can run small stand-alone wind turbines and can be used for

many households, especially in remote and rural areas, where the energy demand is low.

Acknowledgment

The authors are grateful to Kombolcha Meteorological Agency, Ethiopia for their cooperation in providing

daily meteorological wind data used in this work.

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