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
figure 1

Map of Chad

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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
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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]:

$$f(v) = \left( \frac{k}{c} \right) \cdot \left( \frac{v}{c} \right)^{(k - 1)} \cdot \exp \left( { - \left( \frac{v}{c} \right)^{k} } \right),(k > 0,v > 0,c > 1),$$
(1)

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]:

$$v\left( {z_{2} } \right) = v\left( {z_{10} } \right)\left( {\frac{{z_{2} }}{{z_{10} }}} \right)^{m}$$
(2)
$$m = \frac{{\left[ {0.37 - 0.088\ln \left( {v_{10} } \right)} \right]}}{{\left[ {1 - 0.088\ln \left( {\frac{{z_{10} }}{10}} \right)} \right]}}.$$
(3)

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

$$c\left( h \right) = c_{0} \left( {\frac{h}{{h_{0} }}} \right)^{n}$$
(4)
$$k\left( h \right) = k_{0} \left[ {1 - 0.088\ln \left( {\frac{{h_{0} }}{10}} \right)} \right]/\left[ {1 - 0.088\ln \left( \frac{h}{10} \right)} \right],$$
(5)

where c0 and k0 are the scale factor and the shape parameter, respectively, at the measured height h0, 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 (Cf) which represents the fraction of the average power supplied by the wind turbine (Pe, moy) compared to the nominal power of the wind turbine (PeR). The average power (Pe, Avg) and the capacity factor of wind turbines are calculated using the following equations [30, 31]:

$$P_{{\text{e}}} = \left\{ {\begin{array}{*{20}l} 0 \hfill & {(v < v_{{\text{c}}} )} \hfill \\ {P_{{{\text{eR}}}} \frac{{v^{k} - v_{{\text{c}}}^{k} }}{{v_{{\text{R}}}^{k} - v_{{\text{c}}}^{k} }}} \hfill & {(v_{{\text{c}}} \le v \le v_{{\text{R}}} )} \hfill \\ {P_{{{\text{eR}}}} } \hfill & {(v_{{\text{R}}} \le v \le v_{{\text{F}}} )} \hfill \\ 0 \hfill & {(v_{{\text{F}}} < v)} \hfill \\ \end{array} } \right.$$
(6)
$$P_{{{\text{e}},{\text{ave}}}} = P_{{{\text{eR}}}} \left\{ {\left. {\frac{{{\text{e}}^{{ - \left( {\frac{{v_{{\text{c}}} }}{c}} \right)^{k} }} - {\text{e}}^{{ - \left( {\frac{{v_{{\text{r}}} }}{c}} \right)^{k} }} }}{{\left( {\frac{{v_{{\text{r}}} }}{c}} \right)^{k} - \left( {\frac{{v_{{\text{c}}} }}{c}} \right)^{k} }} - {\text{e}}^{{ - \left( {\frac{{v_{{\text{f}}} }}{c}} \right)^{k} }} } \right\}} \right.,$$
(7)

and the capacity factor Cf of a wind turbine is given by:

$$C_{{\text{f}}} = \frac{{P_{{{\text{e}},{\text{ave}}}} }}{{P_{{{\text{eR}}}} }},$$
(8)

where Vc, Vr, and Vf, 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]:

$$E_{{{\text{out}}}} = \, P\left( {_{{{\text{e}},{\text{avg}}}} } \right) \times 8760.$$
(9)

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:

$$E_{{{\text{WT}}}} = 8760 \times A \times n \times P_{{\text{r}}} \times C_{{\text{f}}} .$$
(10)

Economic analysis of wind energy

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

  • Investment costs (including ancillary fees for foundations, network connection, etc.);

  • Operating and maintenance costs;

  • Electricity generation/average wind speed;

  • The life of the turbine;

  • The discount rate.

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]:

$${\text{PVC}} = 1 + C_{{{\text{om}}}} \times \left[ {\frac{1 + i}{{r - i}}} \right] \times \left[ {1 - \left( {\frac{1 + i}{{1 + r}}} \right)^{n} } \right] - S \times \left( {\frac{1 + i}{{1 + r}}} \right)^{n} ,$$
(11)

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

$$r = \frac{{i_{0} - i}}{1 + i}.$$
(12)

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]:

$${\text{COE}}\left( {\$ /{\text{kWh}}} \right) = {\text{ PVC}}/{\text{E}}_{{{\text{WT}}}} .$$
(13)

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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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/m2 is recorded at Faya-Largeau and the least power density of 3163 W/m2 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
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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
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  • Bonus 300 kW/33 has the lowest capacity factor of 0.4% recorded in Bokoro and the highest capacity factor of 38.5% in Sarh.

  • Bonus 1 MW/54 has the least capacity factor of 1.05% in Bokoro and the highest capacity factor of 49.37% in Sarh.

  • 2 MW/V80 Bonus has the least capacity factor of 0.47% in Bokoro and highest capacity factor of 42.02% in Sarh.

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 Pe, m (kW/year) is the annual power produced by the turbine, Cf (%) is the capacity factor of the wind turbine, and Eout (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
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Table 18 Cost of electrical energy generated by BONUS 1 MW/54 wind turbine
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Table 19 Cost of electrical energy generated by VESTAS 2 MW/V80 wind turbine
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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:

  • The average annual speed varies from 1 m/s in Am-Timan to 4.2 m/s in N'Djamena at 10 m high. The maximum wind speed occurs in the month of March, while the least speed occurs in the months of August, September, and October.

  • The wind speed is extrapolated to 30.50 and 67 m altitude. Similarly, Weibull parameters k and c are also extrapolated to 30.50 and 67 m altitude.

  • The capacity factor values vary from one wind turbine to another: for the 300 kW/33 Bonus wind turbine, it varies from 0.4 to 38.5%. For Bonus 1 MW/54, the value varies between 1.05 and 49.37% and Vestas 2 MW/V80, it is from 0.47 to 42.02%.

  • Comparative assessment of electricity generated by the three types of wind turbines was carried out. Result of this study shows that Vestas 2 MW/V80 wind turbine with a hub height of 80 m produced the highest energy.

  • For the Sarh site, the highest capacity factor, annual power, and energy output are 42.02%, 840.42 kW/year, and 605.10 MWh/year, respectively, recorded. The least capacity factor, annual power, and energy output of 0.47%, 9.49 kW/year, and 6830 MWh, respectively are recorded in Bokoro.

  • The average least cost per kWh of electricity generated was obtained at Moundou of 143.08$/kWh/year the model Vestas 2 MW/V80, while the highest average cost of $132,343.89/kWh/year recorded in Am-Timan. Based on these values, it can be concluded that for the Am-Timan site, wind power generation, with wind turbines, is not economical.

  • 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).

  • Electrical and mechanical applications not connected to the network (water pumping, recharging of batteries) would be more suitable. On the other hand, the construction of a wind farm in the Moundou region can be considered.