Evaluation of the cost of producing wind-generated electricity in Chad

Abstract

This paper presents an economic analysis of the electricity produced by different types of wind turbines selected for Chad. Thus, the data considered for the analysis in this study are the average monthly wind speeds at selected locations, as well as the altitude value. Statistical analysis was performed using the Weibull distribution. The same energy factor allowed determining the Weibull parameters. The results obtained show that the average annual wind speed varies from 1 m/s in Am-Timan to 4.2 m/s in N'Djamena, at a height of 10 m from the ground. Weibull statistical parameters ( k and c ) were determined at 10, 30, 50, and 70 m. These were obtained by extrapolation using a power law based on Weibull parameters. Three models of wind turbines available on the market were used in this study: Bonus 300 kW/33, Bonus 1 MW/54, and Vestas 2 MW/V80. The performance of these wind turbines was evaluated using the calculation of the capacity factor and the annual energy produced by each type of wind turbine at 12 sites. The PVC (present value) method was used to perform an economic analysis. The lowest cost of wind power generation was obtained with the Vestas 2 MW/V80 model, with a cost per kilowatt-hour (kWh) of approximately $143.08/kWh/year in Moundou and 132343$89/kWh/year in Am-Timan. Therefore, it is recommended the use of a Vestas 2 MW/80 wind turbine in Chad.

Introduction

The possibility of exploiting renewable energies for electricity generation has been considered by different researchers across the globe because of the negative effects of fossil fuels on the environment. Among the many clean sources of energy is wind energy which has developed very rapidly over the past 2 decades. Great technological progress has been made to reduce the cost of producing wind-generated electricity [ 1 ]. The turbine is free of fossil fuel energy and, hence, does not cause an environmental pollution when generating electricity [ 2 ]. Similarly, it can produce wind power near load centers, eliminating transmission loss in rural and urban landscape lines [ 3 ]. In developing countries, it is important to study and carefully understand the energy model to ensure a good standard of living and to alleviate poverty [ 4 , 5 ].

Speed, direction, continuity, and availability are the characteristics of the wind that can be developed to determine the wind energy potential of a site [ 6 , 7 ]. In many countries around the world, studies and assessments of wind characteristics and the potential of wind energy are being conducted. Countries like Hong Kong Islands have its wind analysis discussed by Lu et al. [ 8 ]. Youm et al. presented wind energy potential in Senegal and the analysis of wind data using the Weibull probability distribution [ 9 ]. Mostafaeipour et al. [ 10 ] evaluated wind energy resources for selected sites in Iran. Shaahid et al. [ 11 ] studied the economic feasibility of the development of wind power plants in coastal areas of Saudi Arabia. Dursic et al. [ 12 ] evaluated the wind energy source in the southern Banat region as a surbie. Statistical analyses focused on the measurement of wind parameters such as mean wind speed, power density, direction, and Weibull distribution parameters. A mathematical method of the sum of the least squares is used to analyze the vertical profile of the wind speed. Alami Els [ 13 ] in the Gulf of Tunis in Tunisia during their study on the potential of wind resources considered the hourly data of the wind speed and wind direction every 10 min to assess the wind potential. Worked on the evaluation of wind energy and electricity generation in the Gulf of Tunis, Tunisia. Four different methods were used to determine the Weibull parameters [ 14 ]. Worked on the energy balance of the first wind farm of Sidi Daoud in Tunisia. Thus, based on wind speed data measured over a 5-year period. The wind potential of the Sidi Daoud site is analyzed statistically using the Weibull and Rayleigh parameters [ 15 ]. Sidi Daoud [ 15 , 16 ], El-Kefregion [ 17 ], and Tunisia [ 18 , 19 ] in the literature have assessed the potential for wind power and electricity production in 2011 in BorjCedria [ 20 ]. For the long-term prediction of electrical energy consumption, they have made a study on the approach based on gene expression. To identify the most important independent variables affecting electricity demand, a sensitivity analysis was performed [ 21 ]. Conducted an optimization study based on NSGA-II and MOPSO for sizing a hybrid PV/wind/battery energy storage system. To determine the optimal number of PV panels and wind farm system, the optimized hybrid system was examined in MATLAB [ 22 ]. Worked on short-term electricity price forecasting using the hybrid backtracking algorithm and the ANFIS approach. Thus, a hybrid machine learning algorithm and a search algorithm in the learning process of the ANFIS approach have been developed to predict the price of electricity more precisely [ 23 ]. Conducted a study on solving the problem of sending non-convex economic load via an artificial algorithm for cooperative research. Thus, they used a method that is to interfere and work with feasible solutions throughout the optimization [ 24 ]. As an indication, in 2009, the population of Chad was estimated at 11,039,873 inhabitants, at a growth rate of 6% per year. As a result, current statistics estimate this population at 15,177,557. In Chad, making electricity available everywhere has always been an important socio-economic issue. However, despite the considerable efforts made by the public authorities, the population still encounters many difficulties in accessing electricity. In other words, Chad is one of the poorest-supplied countries in the Economic and Monetary Community of Central Africa (CEMAC) sub-region [ 25 ]: less than 5% of the population has access to electricity, mainly in the urban areas (2017), 80% of the country's consumption is in N'Djamena, load shedding is common, because the grid does not provide enough electricity; there is still no national interconnection of the network; domestic wood accounts for 90% of primary energy consumption. Since no study has been conducted to estimate the cost of a wind turbine in Chad, this work is on the determination of Weibull parameters in evaluating wind characteristics in Chad. Also, economic analysis of wind power generation considering three turbines models for the selected locations is carried out using present value cost (PVC) method.

Methodology

Presentation of Chad

A landlocked country in Central Africa, Chad is located between 7° and 24° north latitude and 13° and 24° east longitude (Fig. 1 ). It is bordered, in the North with Libya, in the East with Sudan, in the South with the Central African Republic, and in the West with Cameroon, Niger and Nigeria (countries with which it shares Lake Chad). The nearest port, Douala, is 1700 km from N'Djamena, the capital. The Chadian population is estimated at 11.5 million inhabitants in 2011 (i.e., 27.2% of the population of the CEMAC zone). It is relatively young, and a large majority live in rural areas. Although on a downtrend, population growth is 2.6% on average each year.

Fig. 1

Map of Chad

Wind characteristic of the selected locations

The wind data used were obtained from the National Office of Meteorology (ONM). These are monthly wind speed data measured for 12 sites. Geographic coordinates are shown in Table 1 .

Table 1

Geographical coordinates of stations used in the study

Zones

Station

Longitude (°E)

Latitude (°N)

Elevation (m)

Period of measurement (year)

Height of the mast (m)

Saharan zone

Faya-Largeau

19.7

17.55

233

18

10

Abeche

20.51

13.51

545

26

10

Bokoro

17.3

12.23

300

18

10

N’Djamena

15.2

12.8

294

20

10

Sahelian zone

Mongo

18.41

12.11

430

30

10

Ati

18.19

13.13

334

19

10

Mao

15.32

14.12

356

9

10

Bol

14.72

13.45

291

9

10

Am-Timan

20.17

11.2

432

28

10

Moundou

16.4

8.37

420

20

10

Sudanese zone

Pala

14.55

9.22

420

30

10

Sarh

18.23

9.9

364

20

10

Statistical analysis of wind data

To estimate the variations of the wind speed, we used the Weibull probability function which is represented by the following equation [ 26 , 27 ]:

f(v)=kc·vc(k-1)·exp-vck,(k>0,v>0,c>1), 0,v > 0,c > 1),$$\end{document}]]>
where v is the wind speed (m/s), c is the scale parameter (m/s), and k is the shape parameter (dimensionless).

Extrapolation of wind speed at different heights

Wind speed is generally measured at 10 m height, while the installation height of wind turbines is always higher than this height. Moreover, the wind speed increases with the altitude because of the existence of the atmospheric boundary layer, it is necessary to extrapolate the measured wind speed up to the hub height of the wind turbine. The most commonly used method for this purpose is the power law [ 28 ]. It is expressed by the following relation [ 29 ]:

vz2=vz10z2z10m
m=0.37-0.088lnv101-0.088lnz1010.

The Weibull parameters at the measured height are related to the parameters at the height of the wind turbine by the following expressions:

ch=c0hh0n
kh=k01-0.088lnh010/1-0.088lnh10,
where c 0 and k 0 are the scale factor and the shape parameter, respectively, at the measured height h 0 , and h is the height of the concentrator.

Estimation of electrical energy supplied by wind turbines

The performance of the wind turbines is estimated with the capacity factor ( C f ) which represents the fraction of the average power supplied by the wind turbine ( P e, moy ) compared to the nominal power of the wind turbine ( P eR ). The average power ( P e, Avg ) and the capacity factor of wind turbines are calculated using the following equations [ 30 , 31 ]:

Pe=0(v<vc)PeRvk-vckvRk-vck(vc≤v≤vR)PeR(vR≤v≤vF)0(vF<v)
Pe,ave=PeRe-vcck-e-vrckvrck-vcck-e-vfck,
and the capacity factor C f of a wind turbine is given by:
Cf=Pe,avePeR,
where V c , V r , and V f , are the zero flow wind speed, the nominal wind speed, and the shutdown speed of the wind turbine, respectively.

Annual cumulative energy production (AEP) is then estimated using equation [ 30 ]:

Eout=Pe,avg×8760.

The availability of the wind power resource for generating electricity is taken as A  = 75% and the total energy output over the WT lifetime is computed as:

EWT=8760×A×n×Pr×Cf.

Economic analysis of wind energy

According to [ 32 , 33 ], the main parameters governing the cost of producing wind energy are as follows:

These factors may vary from country to country and region to region. However, of all the parameters listed, the price of the wind turbine and other capital costs are the most important. According to [ 32 , 33 ], the specific cost of a wind turbine varies considerably from one manufacturer to another as shown in Table 2 . The choice of the ideal wind turbine is, therefore, essential to ensure economic viability, while the production of electricity is highly dependent on wind conditions. Several methods discussed in [ 34 ] have been used in the literature for calculating the cost of wind energy. The PVC method is adopted in this study, because (1) it considers the dynamic development of relevant economic factors and (2) the different cost and income variables, which are taken into account regardless of whether the money has been or will be paid or received in the past or in the future, by deducting the accumulated cost of interest (discounting) of all payment flows at a common reference time [ 34 ]. The present value of costs (PVC) is determined using relationship [ 35 ]:

PVC=1+Com×1+ir-i×1-1+i1+rn-S×1+i1+rn,
where r represents the interest rate, i the rate of inflation, t the life of the wind turbine, and S the additional costs and includes the costs of operation, maintenance, and repair.

Table 2

Variation in the cost of wind turbines with rated power [ 34 ]

WT size (kW)

Specific cost per kW

Average specific per kW

< 20

2200–3000

2600

20–200

1250–2300

1775

>$$\end{document}]]> 200

700–1600

1150

To estimate PVC, the following quantities and assumptions are retained [ 35 , 36 ]:

r=i0-i1+i.

In Table 2 , it is found that the cost per kW decreases with the increase in the size of the wind turbine. For the machine size above 200 kW, the average cost of a wind turbine is in the order of $ 1150/kW.

The cost of energy (COE) in kW produced is determined by the following expression [ 37 ]:

COE$/kWh=PVC/EWT.

Results and discussion

Estimation of wind resources

Average wind speed

The monthly wind speed for 12 selected sites at 10 m altitude is presented in Table 3 . It is noted that the least wind speed of 1 m/s is observed in Am-Timan in August, September, and October, while the highest of 4.2 m/s is recorded in N'Djamena in March.

Table 3

Values of the wind speed at 10 m altitude

v (m/s)

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Aver

Abeche

2.7

2.8

3.1

3

2.7

2.4

2.6

2.1

2

2.6

2.9

2.8

2.642

Am-Timan

1.5

1.6

1.4

1.5

1.7

1.5

1.3

1

1

1

1.2

1.4

1.342

Bokoro

1.7

1.9

1.9

1.7

1.7

1.7

1.6

1.3

1.2

1.2

1.5

1.6

1.583

Mongo

2.2

2.7

3.1

3.1

3.1

2.9

2.5

2.1

1.8

2.3

2.5

2.2

2.542

N’Djamena

3.6

4

4.2

3.2

3.2

3.6

3.2

2.5

2.4

2.4

3.3

3.4

3.25

Faya

4

3.8

3.7

3.3

2.9

2.7

2.3

2.2

3

3.4

3.9

3.8

3.25

Moundou

3.1

3.3

3.1

3.3

2.9

2.8

2.7

2.3

2.1

2

2.1

2.6

2.692

Pala

2.6

2.9

2.9

2.8

2.7

2.4

2.1

1.7

1.7

1.9

2

2.3

2.333

Sarh

1.9

2.2

2.4

3.2

2.3

2

1.7

1.4

1.4

1.4

1.4

1.6

1.908

Bol

2.2

2.2

2.2

2

1.9

2

2.2

1.8

1.5

1.8

2.2

2.2

2.017

Mao

2.4

2.5

2.6

2.2

2.1

2.1

2.1

1.8

1.8

2.1

2.4

2.5

2.217

Ati

1.7

1.9

2

1.8

1.8

1.8

1.8

1.4

1.4

1.5

1.7

1.8

1.717

Weibull k parameters at 10 m altitude

Table 4 presents the Weibull k parameter at 10 m altitude. From Table 4 , it can be seen that the least value of the form parameter ( k ) of the Weibull distribution of 1.062 is recorded at Am-Timan, while the highest value of 4.907 is observed at Mao in September.

Table 4

Form parameter values k at 10 m altitude

k (m/s)

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Abeche

3.051

3.513

3.187

3.547

3.051

3.083

3.118

2.789

2.786

3.292

3.76

3.59

Am-Ti

1.094

1.062

4.544

4.431

1.527

2.13

2.454

3.563

3.183

2.441

1.201

1.175

Bokoro

3.84

3.403

4.086

4.294

3.84

3.944

3.476

3.272

3.755

3.498

3.911

3.803

Mongo

3.811

3.482

3.833

3.541

3.078

3.091

2.931

2.873

2.658

3.364

3.632

3.262

N’Djamena

4.621

4.202

4.47

3.926

4.31

4.683

4.368

4.081

4.093

3.528

4.407

4.097

Faya-Larg

3.783

3.679

3.012

3.92

3.628

3.774

3.634

3.554

3.563

4.04

4.19

4.181

Moundou

3.613

3.242

3.256

2.876

3.028

3.144

3.306

2.705

3.058

2.397

3.235

3.355

Pala

3.193

3.539

3.143

3.205

3.482

3.277

3.983

3.559

3.108

3.646

2.64

2.263

Sarh

1.194

1.232

1.307

1.621

3.396

3.73

3.741

3.144

3.144

2.924

1.678

1.294

Bol

4.868

4.521

4.654

4.12

4.258

4.428

4.587

4.162

3.911

4.605

4.458

4.163

Mao

4.308

4.433

4.765

4.587

4.907

4.364

4.507

4.863

5.149

4.739

4.093

4.75

Ati

2.871

2.808

2.883

2.621

2.697

2.697

2.867

3.144

3.144

2.616

2.177

2.779

Weibull c parameters at 10 m altitude

Table 5 presents the monthly values of the scale parameter of the Weibull distribution. Thus, the least value of 1.11 m/s is recorded at Am-Timan and the highest value of 4.604 m/s is observed in N'Djamena.

Table 5

Parameter values c at 10 m altitude

c (m/s)

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sept

Oct

Nov

Dec

Abeche

3.021

3.111

3.461

3.332

3.021

2.684

2.906

2.358

2.246

2.898

3.21

3.107

Am-Timan

1.551

1.638

1.533

1.645

1.887

1.693

1.466

1.11

1.117

1.128

1.276

1.48

Bokoro

1.88

2.115

2.093

1.868

1.88

1.877

1.779

1.45

1.328

1.334

1.657

1.77

Faya-Larg

4.426

4.212

4.142

3.645

3.217

2.988

2.551

2.443

3.331

3.749

4.291

4.181

Mongo

2.434

3.001

3.428

3.443

3.467

3.243

2.802

2.356

2.025

2.561

2.773

2.454

N'Djamena

3.938

4.4

4.604

3.534

3.515

3.935

3.512

2.755

2.644

2.666

3.62

3.746

Moundou

3.439

3.682

3.458

3.702

3.246

3.128

3.009

2.586

2.349

2.256

2.343

2.896

Pala

2.903

3.221

3.24

3.126

3.001

2.676

2.317

1.888

1.9

2.107

2.25

2.596

Sarh

2.017

2.353

2.601

3.573

2.56

2.215

1.882

1.564

1.564

1.569

1.567

1.731

Bol

2.4

2.41

2.406

2.203

2.089

2.193

2.408

1.981

1.657

1.97

2.412

2.421

Mao

2.636

2.742

2.839

2.408

2.289

2.305

2.301

1.963

1.957

2.294

2.644

2.731

Ati

1.907

2.133

2.243

2.026

2.024

2.024

2.019

1.564

1.564

1.688

1.919

2.022

Extrapolation of data at different altitudes

Wind data from the ONM were used to determine monthly variations of statistical parameters at 10 m in height. These quantities are then extrapolated to 30, 50 and 70 m in height.

Extrapolation of wind speed to 30.50, and 67 m altitude

The average wind speed at 30 m altitude is presented in Table 6 . From Table 6 , it can be seen that the minimum speed of 1.502 m/s is recorded at Am-Timan in the months of August, September, and October, while the maximum speed of 5.490 m/s is recorded in the month of March in N'Djamena.

Table 6

Mean wind speed at 30 m altitude

Month

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

3.683

2.166

2.425

5.253

3.061

4.173

4.776

3.56

2.681

3.061

3.311

2.425

Feb

3.806

2.296

2.681

5.015

3.683

4.415

5.253

3.929

3.061

3.061

3.436

2.681

Mar

4.173

2.035

2.681

4.896

4.173

4.173

5.49

3.929

3.311

3.061

3.56

2.808

Apr

4.051

2.166

2.425

4.415

4.173

4.415

4.294

3.806

4.294

2.808

3.061

2.554

May

3.683

2.425

2.425

3.929

4.173

3.929

4.294

3.683

3.186

2.681

2.935

2.554

Jun

3.311

2.166

2.425

3.683

3.929

3.806

4.776

3.311

2.808

2.808

2.935

2.554

Jul

3.56

1.903

2.296

3.186

3.436

3.683

4.294

2.935

2.425

3.061

2.935

2.554

Aug

2.935

1.502

1.903

3.061

2.935

3.186

3.436

2.425

2.035

2.554

2.554

2.035

Sept

2.808

1.502

1.77

4.051

2.554

2.935

3.311

2.425

2.035

2.166

2.554

2.035

Oct

3.56

1.502

1.77

4.536

3.186

2.808

3.311

2.681

2.035

2.554

2.935

2.166

Nov

3.929

1.77

2.166

5.134

3.436

2.935

4.415

2.808

2.035

3.061

3.311

2.425

Dec

3.806

2.035

2.296

5.015

3.061

3.56

4.536

3.186

2.296

3.061

3.436

2.554

Aver

3.609

1.955

2.272

4.348

3.483

3.668

4.349

3.223

2.6835

2.828

3.08

2.445

Extrapolation of the wind speed to 50 m altitude

Table 7 presents the average wind speed at altitude of 50 m. From Table 7 , it can be seen that the minimum average wind speed of 1.814 m/s is recorded in Am-Timan in August, September, and October, while the maximum speed of 6.217 m/s is recorded in N'Djamena in March.

Table 7

Mean wind speed at 50 m altitude

Mois

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

4.255

2.569

2.86

5.962

3.569

4.791

5.447

4.119

3.147

3.569

3.846

2.86

Feb

4.39

2.715

3.147

5.705

4.255

5.055

5.962

4.524

3.569

3.569

3.983

3.147

Mar

4.791

2.421

3.147

5.576

4.791

4.791

6.217

4.524

3.846

3.569

4.119

3.289

Apr

4.658

2.569

2.86

5.055

4.791

5.055

4.923

4.39

4.923

3.289

3.569

3.004

May

4.255

2.86

2.86

4.524

4.791

4.524

4.923

4.255

3.708

3.147

3.429

3.004

Jun

3.846

2.569

2.86

4.255

4.524

4.39

5.447

3.846

3.289

3.289

3.429

3.004

Jul

4.119

2.272

2.715

3.708

3.983

4.255

4.923

3.429

2.86

3.569

3.429

3.004

Aug

3.429

1.814

2.272

3.569

3.429

3.708

3.983

2.86

2.421

3.004

3.004

2.421

Sept

3.289

1.814

2.121

4.658

3.004

3.429

3.846

2.86

2.421

2.569

3.004

2.421

Oct

4.119

1.814

2.121

5.186

3.708

3.289

3.846

3.147

2.421

3.004

3.429

2.569

Nov

4.524

2.121

2.569

5.834

3.983

3.429

5.055

3.289

2.421

3.569

3.846

2.86

Dec

4.39

2.421

2.715

5.705

3.569

4.119

5.186

3.708

2.715

3.569

3.983

3.004

Aver

4.172

2.33

2.687

4.978

4.033

4.236

4.98

3.746

3.145

3.31

3.589

2.882

Table 8 shows the extrapolation of the wind speed to 67 m altitude. Minimum speed of 2.021 m/s is recorded in the months of August, September, and October in Am-Timan. The maximum speed of 6.677 m/s is recorded in the month of March in N'Djamena. It can be deduced that the wind speed increases with altitude.

Table 8

Mean wind speed at 67 m altitude

Mois

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

4.622

2.833

3.144

6.411

3.897

5.185

5.873

4.479

3.449

3.897

4.19

3.144

Feb

4.764

2.99

3.449

6.143

4.622

5.462

6.411

4.905

3.897

3.897

4.335

3.449

Mar

5.185

2.675

3.449

6.008

5.185

5.185

6.677

4.905

4.19

3.897

4.479

3.6

Apr

5.046

2.833

3.144

5.462

5.185

5.462

5.324

4.764

5.324

3.6

3.897

3.298

May

4.622

3.144

3.144

4.905

5.185

4.905

5.324

4.622

4.044

3.449

3.749

3.298

Jun

4.19

2.833

3.144

4.622

4.905

4.764

5.873

4.19

3.6

3.6

3.749

3.298

Jul

4.479

2.515

2.99

4.044

4.335

4.622

5.324

3.749

3.144

3.897

3.749

3.298

Aug

3.749

2.021

2.515

3.897

3.749

4.044

4.335

3.144

2.675

3.298

3.298

2.675

Sept

3.6

2.021

2.353

5.046

3.298

3.749

4.19

3.144

2.675

2.833

3.298

2.675

Oct

4.479

2.021

2.353

5.6

4.044

3.6

4.19

3.449

2.675

3.298

3.749

2.833

Nov

4.905

2.353

2.833

6.277

4.335

3.749

5.462

3.6

2.675

3.897

4.19

3.144

Dec

4.764

2.675

2.99

6.143

3.897

4.479

5.6

4.044

2.99

3.897

4.335

3.298

Aver

4.534

2.576

2.959

5.38

4.386

4.601

5.382

4.083

3.445

3.622

3.918

3.167

Extrapolation of the Weibull k and c parameters

Table 9 presents the extrapolation of the shape parameter at 30 m altitude. From Table 9 , it can be seen that the least l value of 1.072 is recorded in February in Am-Timan, while the highest value of 5.199 is recorded in Mao in the month of September.

Table 9

Extrapolation of the parameter k to 30 m

Mois

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

3.081

1.105

3.878

3.82

3.848

3.648

4.666

3.224

1.206

4.916

4.35

2.899

Feb

3.547

1.072

3.436

3.715

3.516

3.274

4.243

3.574

1.244

4.565

4.476

2.835

Mar

3.218

4.588

4.126

3.041

3.871

3.288

4.514

3.174

1.32

4.7

4.812

2.911

Apr

3.582

4.474

4.336

3.958

3.576

2.904

3.964

3.236

1.637

4.16

4.632

2.647

May

3.081

1.542

3.878

3.664

3.108

3.058

4.352

3.516

3.429

4.3

4.955

2.723

Jun

3.113

2.151

3.983

3.811

3.121

3.175

4.729

3.309

3.767

4.471

4.407

2.723

Jul

3.149

2.478

3.51

3.67

2.96

3.338

4.411

4.022

3.778

4.632

4.551

2.895

Aug

2.816

3.598

3.304

3.589

2.901

2.731

4.121

3.594

3.175

4.203

4.911

3.175

Sept

2.813

3.214

3.792

3.598

2.684

3.088

4.133

3.138

3.175

3.949

5.199

3.175

Oct

3.324

2.465

3.532

4.08

3.397

2.42

3.563

3.682

2.953

4.65

4.785

2.642

Nov

3.797

1.213

3.949

4.231

3.668

3.267

4.45

2.666

1.694

4.502

4.133

2.198

Dec

3.625

1.187

3.84

4.222

3.294

3.388

4.137

2.285

1.307

4.204

4.796

2.806

Aver

3.262

2.424

3.797

3.783

3.329

3.132

4.274

3.285

2.39

4.438

4.667

2.802

Table 10 presents values of k at altitude of 50 m. From Table 10 , it can be seen that at 50 m altitude the minimum k value of 1.077 is recorded at Am-Timan in February and the maximum value of 5.223 at Mao is recorded in September.

Table 10

Extrapolation of the parameter k to 50 m

Mois

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

3.095

1.11

3.895

3.837

3.866

3.665

4.688

3.239

1.211

4.938

4.37

2.912

Feb

3.564

1.077

3.452

3.732

3.532

3.289

4.262

3.59

1.25

4.586

4.497

2.848

Mar

3.233

4.609

4.145

3.055

3.888

3.303

4.534

3.188

1.326

4.721

4.834

2.925

Apr

3.598

4.495

4.356

3.976

3.592

2.917

3.983

3.251

1.644

4.179

4.653

2.659

May

3.095

1.549

3.895

3.68

3.122

3.072

4.372

3.532

3.445

4.319

4.978

2.736

Jun

3.127

2.161

4.001

3.828

3.136

3.189

4.75

3.324

3.784

4.492

4.427

2.736

Jul

3.163

2.489

3.526

3.686

2.973

3.354

4.431

4.04

3.795

4.653

4.572

2.908

Aug

2.829

3.614

3.319

3.605

2.914

2.744

4.14

3.61

3.189

4.222

4.933

3.189

Sept

2.826

3.229

3.809

3.614

2.696

3.102

4.152

3.153

3.189

3.967

5.223

3.189

Oct

3.339

2.476

3.548

4.098

3.412

2.432

3.579

3.698

2.966

4.671

4.807

2.654

Nov

3.814

1.218

3.967

4.25

3.684

3.282

4.47

2.678

1.702

4.522

4.152

2.208

Dec

3.642

1.192

3.858

4.241

3.309

3.403

4.156

2.296

1.313

4.223

4.818

2.819

Aver

3.277

2.435

3.814

3.8

3.344

3.146

4.293

3.3

2.401

4.458

4.689

2.815

Table 11 presents extrapolated values of parameter k at 67 m altitude. The least value of 1.08 is observed in Am-Timan in February, while the highest value of 5.237 is recorded in Mao in September.

Table 11

Extrapolation of the parameter k to 67 m

Months

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

3.103

1.113

3.905

3.848

3.876

3.675

4.7

3.247

1.214

4.951

4.381

2.92

Fév

3.573

1.08

3.461

3.742

3.541

3.297

4.274

3.599

1.253

4.598

4.509

2.856

Mar

3.241

4.621

4.156

3.063

3.898

3.312

4.546

3.197

1.329

4.733

4.846

2.932

Apr

3.608

4.507

4.367

3.987

3.601

2.925

3.993

3.26

1.649

4.19

4.665

2.666

May

3.103

1.553

3.905

3.69

3.131

3.08

4.384

3.541

3.454

4.331

4.991

2.743

Jun

3.136

2.166

4.011

3.838

3.144

3.198

4.763

3.333

3.794

4.504

4.438

2.743

Jul

3.171

2.496

3.535

3.696

2.981

3.362

4.442

4.051

3.805

4.665

4.584

2.916

Aug

2.837

3.624

3.328

3.615

2.922

2.751

4.151

3.62

3.198

4.233

4.946

3.198

Sept

2.834

3.237

3.819

3.624

2.703

3.11

4.163

3.161

3.198

3.978

5.237

3.198

Oct

3.348

2.483

3.558

4.109

3.421

2.438

3.588

3.708

2.974

4.684

4.82

2.661

Nov

3.824

1.222

3.978

4.261

3.694

3.29

4.482

2.685

1.707

4.534

4.163

2.214

Dec

3.651

1.195

3.868

4.252

3.318

3.412

4.167

2.302

1.316

4.234

4.831

2.826

Aver

3.286

2.441

3.824

3.81

3.353

3.154

4.304

3.309

2.407

4.47

4.701

2.823

Table 12 presents extrapolated values of the scale parameter c at 30 m altitude. From Table 12 , it can be seen that the minimum value of 1.65 m/s is recorded in the month of August in Am-Timan, while the maximum value of 5.964 m/s is recorded in N'Djamena in the month of March.

Table 12

Extrapolation of parameter c at 30 m altitude

Months

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

4.076

2.232

2.656

5.756

3.354

4.583

5.179

3.932

2.83

3.311

3.604

2.69

Feb

4.186

2.345

2.954

5.504

4.052

4.874

5.725

4.319

3.253

3.324

3.735

2.977

Mar

4.609

2.209

2.926

5.421

4.569

4.605

5.964

4.342

3.561

3.319

3.854

3.115

Apr

4.454

2.354

2.64

4.83

4.587

4.898

4.697

4.204

4.744

3.065

3.321

2.841

May

4.076

2.665

2.656

4.315

4.616

4.35

4.674

4.052

3.51

2.921

3.173

2.839

Jun

3.663

2.416

2.652

4.036

4.346

4.207

5.176

3.653

3.08

3.052

3.193

2.839

Jul

3.936

2.121

2.527

3.499

3.808

4.062

4.67

3.208

2.658

3.321

3.188

2.833

Aug

3.259

1.65

2.1

3.365

3.256

3.542

3.751

2.666

2.249

2.784

2.761

2.249

Sept

3.119

1.659

1.94

4.452

2.84

3.248

3.614

2.681

2.249

2.37

2.754

2.249

Oct

3.926

1.674

1.948

4.954

3.511

3.131

3.641

2.944

2.256

2.77

3.179

2.41

Nov

4.306

1.871

2.37

5.597

3.773

3.24

4.8

3.124

2.253

3.326

3.614

2.706

Dec

4.181

2.14

2.515

5.467

3.378

3.924

4.951

3.555

2.465

3.337

3.721

2.836

Aver

3.983

2.111

2.49

4.766

3.841

4.055

4.737

3.557

2.926

3.075

3.341

2.715

Table 13 presents extrapolated values of parameter c at 50 m altitude. From Table 13 , it can be seen that the minimum value of parameter c is 1.984 m/s in the month of August in Am-Timan, while the maximum value of 6.727 m/s is recorded in N'Djamena in the month of March.

Table 13

Extrapolation of parameter c to 50 m

Months

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

4.686

2.644

3.119

6.503

3.892

5.237

5.883

4.528

3.313

3.846

4.168

3.157

Feb

4.805

2.771

3.45

6.233

4.659

5.553

6.471

4.951

3.781

3.86

4.312

3.476

Mar

5.266

2.618

3.42

6.144

5.223

5.262

6.727

4.976

4.121

3.854

4.442

3.629

Apr

5.097

2.781

3.101

5.505

5.242

5.579

5.361

4.825

5.412

3.573

3.857

3.325

May

4.686

3.129

3.119

4.945

5.273

4.984

5.336

4.659

4.065

3.414

3.693

3.323

Jun

4.233

2.85

3.114

4.642

4.98

4.828

5.879

4.222

3.59

3.559

3.715

3.323

Jul

4.532

2.519

2.974

4.053

4.393

4.67

5.332

3.731

3.121

3.857

3.709

3.315

Aug

3.788

1.984

2.495

3.905

3.785

4.1

4.329

3.13

2.663

3.262

3.236

2.663

Sept

3.633

1.995

2.314

5.095

3.324

3.776

4.179

3.147

2.663

2.798

3.228

2.663

Oct

4.521

2.012

2.323

5.64

4.066

3.647

4.209

3.439

2.67

3.246

3.7

2.843

Nov

4.936

2.236

2.798

6.333

4.353

3.767

5.473

3.639

2.667

3.862

4.179

3.174

Dec

4.8

2.54

2.961

6.193

3.92

4.519

5.636

4.114

2.905

3.875

4.297

3.32

Aver

4.582

2.506

2.932

5.432

4.426

4.66

5.401

4.113

3.414

3.584

3.878

3.184

The extrapolated values of parameter c extrapolated at 67 m altitude are presented in Table 14 . From Table 14 , the minimum value of 2.205 m/s is recorded in Am-Timan in August, while the maximum value of 7.208 m/s is recorded in N'Djamena in March. It is found that the value of c increases with altitude, and hence, it can be concluded that the site assessed is windy.

Table 14

Extrapolation of parameter c to 67 m

Months

Abec

Am-T

Bok

Fay

Mon

Mou

N’Dja

Pala

Sarh

Bol

Mao

Ati

Jan

5.075

2.913

3.419

6.975

4.239

5.653

6.328

4.909

3.625

4.19

4.53

3.46

Feb

5.201

3.049

3.771

6.693

5.047

5.984

6.941

5.353

4.122

4.205

4.682

3.798

Mar

5.683

2.885

3.739

6.6

5.638

5.679

7.208

5.379

4.48

4.199

4.819

3.961

Apr

5.506

3.059

3.401

5.934

5.659

6.011

5.783

5.221

5.836

3.902

4.202

3.639

May

5.075

3.43

3.419

5.348

5.691

5.388

5.757

5.047

4.421

3.733

4.028

3.636

Jun

4.599

3.134

3.415

5.029

5.384

5.224

6.324

4.588

3.919

3.887

4.052

3.636

Jul

4.914

2.78

3.266

4.408

4.767

5.058

5.753

4.069

3.422

4.202

4.046

3.628

Aug

4.129

2.205

2.754

4.252

4.126

4.459

4.7

3.431

2.933

3.571

3.544

2.933

Sept

3.965

2.216

2.56

5.505

3.637

4.116

4.542

3.449

2.933

3.078

3.535

2.933

Oct

4.902

2.235

2.57

6.074

4.423

3.98

4.573

3.76

2.941

3.555

4.035

3.126

Nov

5.338

2.476

3.078

6.797

4.726

4.107

5.9

3.971

2.938

4.208

4.542

3.478

Dec

5.195

2.802

3.252

6.652

4.268

4.9

6.07

4.473

3.192

4.221

4.666

3.633

Aver

4.965

2.765

3.22

5.856

4.8

5.047

5.823

4.471

3.73

3.912

4.223

3.488

Comparison of the wind energy potential at the three climatic zones assessed

From the comparison of wind characteristics in the three selected climatic zones at 10 m altitude, it can be deduced that:

The minimum wind speed of 1.342 m/s is recorded at Am-Timan, while the maximum speed of 3.25 m/s is recorded at N'Djamena and Faya-Largeau.

As for the power density, the highest power density of 28,609 W/m 2 is recorded at Faya-Largeau and the least power density of 3163 W/m 2 is recorded at Bokoro.

Estimation of electric power generation by wind turbines

Three wind turbines were selected for the estimation of wind power generation: Bonus 300 kW/33, Bonus 1 MW/54, and Vestas 2 MW/V80. Their rated power (Pr) is 300, 1000, and 2000 kW, respectively.

Table 15 shows the characteristic properties of selected wind turbines (Bonus 300 kW/33, Bonus 1 MW/54 and Vestas 2 MW/80).

Table 15

Characteristics of selected wind turbines

Characteristics

Bonus 300 kW/33

AN Bonus 1 MW/54

Vestas 2 MW/80

Rated power Pr (kW)

300

1000

2000

Hub height h (m)

30

50

67

Rotor diameter (m)

33.4

54.2

80

Rated wind speed Vr (m/s)

14

15

16

Cut-in wind speed Vc (m/s)

3

3

4

Cut-off wind speed Vf (m/s)

25

25

25

For the three wind turbines, the one whose power is high is Vestas 2 MW/V80 including Faya-Largeau (327.18 kW) and Bokoro (9.49 kW). The wind turbine with the lowest power is Bonus 300 kW/33, Faya-Largeau (61.53 kW), and Bokoro (1.19 kW).

Annual energy generated by the three turbines for the 12 selected locations in Chad

Table 16 shows the annual energy generated by wind turbines selected for this study. It can be seen from Table 16 that:

Table 16

Calculated annual energy estimate for selected wind turbines for selected sites

Sites

BONUS 300 kW/33

BONUS 1 MW/54

VESTAS 2 MW/V80

Pe,m

Cf (%)

Eout

Pe,m

Cf (%)

Eout

Pe,m

Cf (%)

Eout

Abeche

7.52

2.51

5418

197.43

19.74

142,148

327.18

16.36

235,569

Am-Timan

50.18

16.73

36,132

240.28

24.03

173,003

382.92

19.15

275,703

Bokoro

1.19

0.4

855

10.49

1.05

7554

9.49

0.47

6830

Mongo

36.02

12.01

25,935

172.26

17.23

124,026

283.76

14.19

204,304

N'Djamena

34.18

11.39

24,609

152.89

15.29

110,080

283.31

14.17

203,984

Faya-Larg

61.53

20.51

44,301

266.06

26.61

191,564

488.34

24.42

351,603

Moundou

56.07

18.69

40,373

257.30

25.73

185,257

435.46

21.77

313,533

Pala

31.78

10.59

22,879

154.81

15.48

111,464

247.86

12.39

178,457

Sarh

115.50

38.5

83,159

493.72

49.37

355,477

840.42

42.02

605,101

Bol

1.99

0.66

1435

13.79

1.38

9925

16.84

0.84

12,124

Mao

3.42

1.14

2461

20.03

2.00

14,423

29.39

1.47

21,162

Ati

12.45

4.15

8964

77.93

7.79

56,109

96.59

4.83

69,548

In addition, Vestas 2 MW/V80 wind turbine produces highest energy output of 601.10 MWh/year and capacity factor of 42.02% in Sarh. According to [ 1 ], the value of this factor is generally affected by the intermittent nature of the wind, the availability of the machine and the efficiency of the turbine. Capacity factor usually varies from 20 to 70% in practice.

Where P e, m (kW/year) is the annual power produced by the turbine, C f (%) is the capacity factor of the wind turbine, and E out (MWh/year) is the annual production of accumulated energy.

Cost of electrical energy generated by the wind energy

Costs per kilowatt-hour (kWh) of electrical energy generated by the three wind turbines at 12 selected sites. This calculation was performed for the maximum and minimum values of thes specific cost of wind turbines (Tables  17 , 18 , 19 ).

Table 17

Cost of electrical energy generated by Bonus 300 kW/33 wind turbine

Locations

Pout

Per

Cf (%)

EWT

CUSS

CXAF

Abeche

7.52

300

2.51

82,391.09

960.59

5801.97

Am-Timan

50.18

300

16.73

549,504.95

215,527.37

1,301,785.29

Bokoro

1.19

300

0.4

13,002.03

73,249.9

442,429.41

Faya

61.53

300

20.51

673,753.5

193.91

1171.2

Mongo

36.02

300

12.01

394,426.67

281.27

1698.88

Moundou

56.07

300

18.69

614,002.64

168.23

1016.13

N’Djamena

34.18

300

11.39

374,250.2

281.79

1702.02

Pala

31.78

300

10.59

347,950.49

742.03

4481.88

Sarh

115.5

300

38.5

1,264,705.29

2083.28

12,583.03

Bol

1.99

300

0.66

21,818.97

6044.97

36,511.62

Mao

3.42

300

1.14

37,432.58

7313.61

44,174.2

Ati

12.45

300

4.15

136,324.22

1635.68

9879.49

Table 18

Cost of electrical energy generated by BONUS 1 MW/54 wind turbine

Locations

Pout

Per

Cf (%)

EWT

CUSS

CXAF

Abeche

197.43

1000

19.74

2,161,858.5

118.22

714.05

Am-Timan

240.28

1000

24.03

2,631,109.8

27,527.15

166,264

Bokoro

10.49

1000

1.05

114,876.45

6226.88

37,610.3

Faya

266.06

1000

26.61

2,913,378.9

130.13

785.98

Mongo

172.26

1000

17.23

1,886,247

174.7

1055.2

Moundou

257.3

1000

25.73

2,817,435

110.45

667.15

N’Djamena

152.89

1000

15.29

1,674,101.7

191.6

1157.24

Pala

154.81

1000

15.48

1,695,191.4

349.21

2109.21

Sarh

493.72

1000

49.37

5,406,234

649.77

3924.59

Bol

13.78

1000

1.38

150,934.8

2081.97

12,575.1

Mao

20.03

1000

2.00

219,361.35

2510.57

15,163.8

Ati

77.93

1000

7.79

853,333.5

539.67

3259.62

Table 19

Cost of electrical energy generated by VESTAS 2 MW/V80 wind turbine

Locations

Pout

Per

Cf (%)

EWT

CUSS

CXAF

Abeche

327.18

2000

16.36

3,582,621

147.39

890.25

Am-Timan

382.92

2000

19.15

4,192,996

132,343.89

799,357.1

Bokoro

9.49

2000

0.47

103,916

56,876.63

343,534.87

Faya

488.34

2000

24.42

5,347,279

159.67

964.4

Mongo

283.75

2000

14.19

3,107,150

234.9

1418.8

Moundou

435.46

2000

21.77

4,768,309

143.08

864.21

N’Djaména

283.31

2000

14.17

3,102,266

224.59

1356.5

Pala

247.86

2000

12.39

2,714,045

619.44

3741.39

Sarh

840.42

2000

42.02

9,202,555

1733.31

10,469.17

Bol

16.84

2000

0.84

1,84,420

4935.24

29,808.88

Mao

29.39

2000

1.47

3,21,821

5896.99

35,617.82

Ati

96.59

2000

4.83

1,057,661

1369.09

8269.3

The results obtained are shown in Table 17 which shows that the lowest value of the cost of wind power varies from $143.08/kWh/year to $132,343.89/kWh/year. This value was obtained for the Vestas 2 MW/V80 wind turbine.

Conclusion

In this study, comprehensive estimation of the electrical energy generated and cost per kilowatt-hour of electrical energy generated by three different types of wind turbines at selected locations in Chad are carried out. The results obtained showed that:

Acknowledgements

We make a point of thanking the persons in charge of the National Meteorology for Chad, as the personnel who deal with the collection and the processing weather data on these sites, to have placed at our disposal the data which were used in our work.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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