The hydro condition that can be used as an electricity-generating resource is one that has a particular flow and head capacity, as the electricity generated by micro-hydro is also highly dependent on the height of the waterfall and the water flow.

A visit to the site of the Ecole Supérieure des Sciences Agronomiques (ESSA) enabled us to measure the geographical coordinates of the future hydroelectric power station and the flow rate of the Mandraka river.

Depending on the river flow, small hydropower is often a profitable source of renewable energy.

Figure 1 shows the principle of a micro-hydropower plant.

It should be noted that the machine room houses several items of equipment, including the hydraulic turbine, the electric generator, the alternator, the electrical cabinet and the transformer, among others.

The geographical coordinates of the components of the hydroelectric micropower station to be installed are summarized in the following Table 1 .

From this table, we can calculate the head of the micropower station and determine the main components of the layout.

For this purpose, the opening height H of the water intake is defined by (1).

$H=r+y$ (1)

where r is the freeboard and y is the height of water in the section.

Water velocity in a section of the feeder channel [11] - [13] is given by Chezy’s formula (2):

$V=C\sqrt{R_h\times I}$ (2)

where C is the proportionality coefficient, Rh is the hydraulic radius and I is the longitudinal slope of the channel.

The loading chamber is given by the following equation:

$S_{chamber}=\frac{V_{cbas}\times S_{duct}}{V_{chamber}}$ (3)

Here $S_{chamber}$ is the cross-sectional area of the charging chamber, $S_{duct}$ is the cross-sectional area of the penstock, $V_{chamber}$ is the velocity at the inlet to the loading chamber et $V_{cbas}$ is the velocity at the outlet from the loading chamber.

The internal diameter of the penstock is deduced from the Hazen-William formula [14] :

$Q_{\max }=0.2785\times {\left(\frac{\Delta H}{L}\right)}^{0.54}\times C_1\times D_{in}^{2.63}$ (4)

$D_{in}={\left(\frac{Q_{\max }}{0.2785\times {\left(\frac{\Delta H}{L}\right)}^{0.54}\times C_1}\right)}^{\frac{1}{2.63}}$ (5)

where $Q_{\max }$ is the maximum flow carried by the section, L the length of the section, $\Delta H$the difference in altitude between the two ends of the section and $C_1$ the coefficient of friction of the material used.

The pressure drop equation is as follows:

$Pd=J\times L$ (6)

where $Pd$ is the pressure drop, $J$ is the pressure drop per metre, $L$ is the length of penstock

The theoretical power available from hydropower can be calculated from the flow rate, water density, net head and local acceleration due to gravity [15] - [17] :

$P={\eta }_{TG}\times \rho \times g\times Q\times H$ (7)

where ${\eta }_{TG}$ is the efficiency of the turbine and generator, $Q$ is the flow rate in m³/s, $H_n$ is the Net height in m.

The specific speed of the turbine is given by (8):

$n_s=\frac{0.2626\times N\times P^{1/2}}{H_n^{5/4}}$ (8)

where P is the effective power (kW) of the wind turbine and N is its rotation speed (rpm).

Depending on the values of $n_s$, the type of turbine best suited to the configuration will be selected.

Figure 2 shows the evolution of average monthly irradiation in the village of Mandraka.

This figure provides information on the least sunny month of the year, in particular June, with solar irradiation of 3.26 kWh/m²/day. This value will be used to size the photovoltaic generator.

The peak power of the PV system is described by Equation (9):

$P_c=\frac{C_j}{K\times E_i}$ (9)

where $C_j$ is the daily energy consumption, $E_i$ the sunshine of the place and K a coefficient varying between 0.5 and 0.7.

The numbers of modules in series and in parallel are given respectively by (10) and (11):

$N_s=\frac{U}{U_{\mathrm{mod}}}$ (10)

$N_p=\frac{P_c}{N_s\times P_{\mathrm{mod}}}$ (11)

where U is the requested voltage and $P_{\mathrm{mod}}$ the unit power of the module.

The number of panels required is given by the following equation:

$N=N_s\times N_p$ (12)

The capacity of the accumulator battery is defined by the following relationship:

$C_b=\frac{N_j\times C_j}{R_{bat}\times U_{bat}\times DM}$ (13)

where $N_j$ is the number of days of autonomy, DM is the depth of discharge (%) and $R_{bat}$ is the battery efficiency (between 75% and 90%). For the purposes of this study, the number of days of autonomy considered is 2 days.

Knowing C_b, we can determine the number of batteries in series and in parallel.

The economic hypotheses for this study are:

It’s important to note that the profitability of the project will depend on the selling price of the kilowatt-hour (kWh) of electricity. The production cost per kWh of electricity generated by the plant is given by the overall discounted cost formula (14):

$C_{kWh}={\left(\frac{{{\displaystyle \sum }}_1^{n}I+{{\displaystyle \sum }}_1^n{D}_a}{{{\displaystyle \sum }}_1^n{E}_a}\right)}_{discounted}$ (14)

where n is the year number (equal to the project deadline), I the investment, D_a annual spending (equal to 5% of investment) and E_a the average annual power production.

$C_{kWh}$ calcul gives:

$C_{kWh}\approx 1040\text{Ar}/\text{kWh}$

Note that the Internal Rate of Return (IRR) and the Profitability Index (PI) of the project depend only on the ability of users to pay electricity.

The Net Present Value of a project is difference between net flow of cash and investment. The project is profitable if NPV is greater than or equal to zero. It is given by the following equation [17] :

$\text{NPV}=-I+\underset{i=1}{\overset{n}{{\displaystyle \sum }}}\frac{C{F}_i-C_i}{{\left(1+a\right)}^i}$ (15)

where $C{F}_i$: Represent the cash-flows from year 1 to year n, $C_i$: The operating cost from year 1 to year n, a: The discount rate and I: The initial investment.

Surveys of the various categories of electricity users at the Saha Maintsoanala station have enabled us to estimate the site’s electrical requirements. The figures below show the hourly variations in demand for the different categories of Mandraka users.

Peak consumption is reached between 5 pm and 9 pm and corresponds to a total power of 26.22 kW ( Figure 3 ). The overall power generation system will therefore need to produce a total power equal to 26.22 kW to meet the electricity demand of the village of Mandraka.

Table 2 shows the sizing results for the micro-hydropower plant.

As the calculated specific speed is between 60 m/s and 420 m/s, we’ll be choosing a Banki-Michell type turbine.

It should be noted that the power produced by the micro-hydropower plant (24.64 kW) does not meet user demand (26.22 kW), so a solar photovoltaic system is essential. These photovoltaic generators will power the Ecole Primaire Publique (EPP), the administrative department, the workroom and the street lighting equipment in the village of Mandraka.

Table 3 shows the energy requirements for photovoltaic energy.

Total daily consumption EjEj, calculated for the four subscriber categories (administrative office, workroom, public elementary school (EPP) and public lighting), amounts to 10,515 Wh/d, or 3838 kWh/year, with a power of 1760 W.

The sizing based on this calculated power is appropriate, as the difference between the total power obtained (26.22 kW) and that of the hydraulic power plant (24.64 kW) is 1.76 kW, or 1760 watts. This slight oversizing is also recommended to ensure reliable consumption for users.

Having carried out the sizing calculations for the photovoltaic system, the results obtained are as follows.

Table 4 shows the results for the size of PV system components needed to produce the additional power required to meet consumer demand.

This table shows the results for the technical characteristics of each energy consumer group. It also specifies the number of solar panels required for each consumer group.

The realization of the project to supply the village with electricity through the renewable energy system requires an investment of 227,626,018 Ariary (Ar) or 63229.5 Euros. The operating cost amounts to 29,152,668 Ar or 8098 Euros. Note that the current Euro is equal to 3600 Ar. Table 5 gives the system’s investment budget estimate.

We’d like to point out that the profitability of hydroelectric power plant infrastructures is spread over a period of more than 15 to 20 years, depending on the scale of the infrastructure to be installed. So, for this case, it is essential that we study two different cases, i.e., the case where the NPV is positive and the case where the NPV is Negative.

Case 1: If the NPV is positive, i.e., the project is interesting, we need to calculate the corresponding price per kWh.

Thus, if the NPV is positive, the price per kWh is greater than Ar 1040.

Second case: Negative NPV, i.e., the project is no longer worthwhile.

Thus, if NPV Negative, the price per kWh is less than Ar 1040.

So, if the selling price per kWh of electricity is greater than Ar 1040, the project is profitable.

Table 6 shows the influence of the kWh selling price on the payback period.

For the current project:

$\text{NPV}=157036279\text{Ar}$

Since the NPV is positive, the project is profitable.

Table 6 shows that, if the price per kilowatt-hour (kWh) is 1040 Ar, the period required to amortize the investment is 4 years, 11 months and 27 days. However, when the price reaches 2500 Ar, this period is reduced to 3 years, 7 months and 27 days.

We conducted a survey to estimate the household monthly expenditure of substitutable energy by electricity. To achieve this, we have taken into account the needs of existing households in the village and estimate the current expenditure in energy that they are used to making per month according to their financial means, for the operation of their equipment and for enlightenment. These expenses relate to the use of cells, batteries, candles, lighting gas and kerosene. To this end, households have been subdivided into three categories, according to their standard of living: low-income, middle- income and well-off households. The results of these surveys show that most households in the village of Mandraka, already spend a part of their monthly income to meet their basic energy needs ( Figure 4 ).

Figure 4 shows that low-income, middle-income and well-off households spend respectively 18,700, 26,000 and 32,300 Ar per month for their energy supply.

Another survey was conducted to assess the monthly substitutable energy expenditure of other categories of energy consumers in Mandraka village ( Figure 5 ).

It emerges from this work that users of restaurants, grocery stores, lodges and public service spend respectively 38,400, 16,500, 56,740 and 40,400 Ar per month for their energy supply.

We conducted a socio-economic survey among the population of the village of Mandraka, in order to make a comparative study of expenditure on electric energy and substitutable energies by the use of cells, batteries, candles, lighting gas, kerosene. These surveys take into account the needs of the inhabitants in order to estimate the energy expenditure they usually make per month, to operate their equipment and for lighting, before and after supplying the village with electricity through the renewable energy system. For this purpose, consumers have been classified by type of activity. The results are shown in Figure 6 and Figure 7 .

Figure 6 and Figure 7 show that, in general, supplying the village with electricity through the renewable energy system greatly reduces the monthly energy expenditure of consumers.

Figure 6 and Figure 7 show that, overall, supplying the village with electricity from the renewable energy system greatly reduces consumers’ monthly energy costs.

The installation of the micro-hydro plant and the solar photovoltaic system is also a significant asset for the local population, as the electricity generated by these resources will obviously be an engine for economic development, enabling them to combat the area’s isolation, the lack of information and communication, and the reduction or elimination of poverty through the practice of income-generating activities.

The investment required to bring this project to fruition amounts to Ar 227,626,018 or 63229.5 euros, with a cost of Ar 29,152,668 or 8098 euros, and the payback period (DRCI) and/or financial profitability of such an infrastructure with a high initial investment range from 15 to 20 years or even more.

Access to electricity will mark a decisive turning point in the region’s development, promoting the integration of New Information and Communication Technologies (NICT). The creation of cybercenters will improve access to information, erasing the image of a “landlocked area”. Literacy will increase, and the computerization of administration will eliminate bureaucratic delays, accelerating local development.

Leisure facilities (auditoriums, video games, karaoke, nightclubs) will energize social life and combat idleness, also attracting tourists. Electricity will encourage greater affluence, thanks in particular to the region’s rich natural resources. ESSA’s student hostel will also be able to welcome tourists, boosting local revenues. The restaurant, which currently serves around 550 customers a month, will see its clientele triple, prompting the construction of new gargotes and chalets to meet growing demand.

Small shops and local businesses will thrive, improving the standard of living for local residents. Finally, a year-round RN2 will facilitate inter-municipal trade in agricultural produce and charcoal, strengthening the regional economy.