For the three selected villages, solar irradiation data was sourced from the NASA Surface Meteorology and Solar Energy database, covering a 22-year period from July 1983 to June 2005 [26] . The data shows that solar radiation is available nearly throughout the year, as shown in Figure 4 , with an annual average of 4.75 kWh/m²/day. The lowest solar radiation occurs in January and December, while the highest levels are observed in April and June.

Based on the area of the photovoltaic modules (Apv) and the solar radiation (Ir) the photovoltaic output power (Ppv) can be determined as the following equation [27] [28] :

$P_{pv}=A_{pv}\ast {\eta }_{pv}\ast I_r$ (1)

With: η_pv: overall efficiency of the module, it is given by:

${\eta }_{pv}={\eta }_r\ast {\eta }_{pc}\ast \left[1-{\beta }_t\left(T_c-T_{NOCT}\right)\right]$ (2)

η_r: reference efficiency of the photovoltaic module. It depends on the technology used. η_pc is the degradation factor. Here, η_pc will be equal to 0.9. β_t is the coefficient of the influence of the temperature of the photovoltaic. T_c is the cell temperature (°C). TNOCT is the optimal operating Cell Temperature.

The diesel generator (DG) is crucial for maintaining the stability of the hybrid system. However, its efficiency decreases significantly as the load demand reduces. Consequently, fuel consumption becomes a major factor, making the operating cost a significant consideration. The fuel consumption of the generator Q as a function of its electrical power is given as follows [29] [30] :

$Q=F_0\ast P+F_1\ast P_{gen}$ (3)

where P is the generated power, P_gen [kW] is the rated power, F₀ (L/hr) and F₁ (Lhr/kWrate) are coefficients of the fuel consumption parameters. These coefficients can be obtained from the technical sheet of the selected diesel generator model when it operates at 50% and 100% of its nominal load.

To store the excess energy product by intermittent RE and to control the charge process, the battery capacity is determined as following equation [30] :

$C_{bat}=\frac{E_L\ast AD}{{\eta }_{inv}\ast {\eta }_{bat}\ast DOD}$ (4)

Where EL is the load demanded, AD is autonomy days, η_nv is converter efficiency, η_bat is battery efficiency and DOD is depth of discharge (80%).

The levelized cost of electricity (LCOE) is a key indicator for determining the price at which electricity must be sold to break even over the project’s lifetime. It accounts for all costs associated with electricity production, including investment, operation, maintenance, and fuel costs. The LCOE is calculated using the following equation [31] :

$LCOE=\frac{{{\displaystyle \sum }}_{t=1}^N\left(\frac{I_t+M_t+F_t}{{\left(1+r\right)}^t}\right)}{{{\displaystyle \sum }}_{t=1}^N\left(\frac{E_t}{{\left(1+r\right)}^t}\right)}$ (5)

Where:

N = Project lifetime.

I_t = Investment costs in year t [US$].

M_t = Maintenance costs in year t [US$].

F_t = Fuel costs in year t [US$].

E_t = Annual Energy delivered by the system in year t [kWh].

r = discount or rate of return [%].

In order to estimate the necessary financing, the total Net Present Cost (NPC) of a system is determined by equation (6). The NPC is the present values of all components that include essentially the capital costs and O&M over the lifetime of project [32] .

$NPC=\underset{t=1}{\overset{N}{{\displaystyle \sum }}}\left(\frac{C_t}{{\left(1+r\right)}^t}\right)$ (6)

Where: $C_t=R_t-M_t-F_t-I_t$ the net cash-flow for period (t), i.e. revenue Rt minus expanses.

A discount rate (of 10% is recommended for projects of this type in sub-Saharan Africa [33] .

The Renewable energy fraction (REF) is the proportion of total energy generated by renewable energy sources in system and is determined as follows:

$REF=\left(1-\frac{\Sigma P_{DG}}{\Sigma P_{RE}}\right)\ast 100$ (7)

Where PDG is the diesel generator output power and PRE is the power from renewable energy sources.

The Load Factor (LF) is determined as ratio of the average load power to the peak load, as given in equation (8):

$LF=\left(\frac{L_{average}}{L_{peak}}\right)$ (8)

Where L_average and L_peak are average load demand and peak load demand, respectively.

The Economic Distance Limit (EDL) corresponding to the distance from grid where the NPC of the extending grid equal to the NPC of the stand-alone system. The EDL can be calculated on HOMER using follows equation [32] :

$D_{grid}=\frac{\left(C_{NPC}\ast CRF\left(i,R_{proj}\right)\right)-C_{power}\ast L_{tot}}{C_{cap}\ast CRF\left(i,R_{proj}\right)+C_{om}}$ (9)

Where: CNPC is the Total Net Present Cost, CRF is the Capital Recovery Factor, i is the Interest rate (%), Rpro is the Project life time in years, Cpower is the Cost of power from the grid in ($/kWh), L_tot is the Total primary and deferrable load in (kWh/year). C_cap is the Capital cost of grid extension in ($/km), Com is the O&M cost of grid extension in ($/year/km).

In order to analyze and design the proposed hybrid system, HOMER (Hybrid Optimization Model for Electric Renewable) simulation tool have been used. HOMER software is one of the major global standards in the field of microgrid optimization in all sectors, from electrification of decentralized villages to large structures connected to the network. It integrates powerful tools for simulating and optimizing technical-economic analyses [34] [35] . The HOMER algorithm selected the best system configurations based on the lowest NPC (Net Present Cost). Figure 5 illustrates the block diagram and principle operating of the Homer software. Also, the costs and simulation parameters of hybrid system for this study electrification are summarized in Table 1 . The Diesel generator is already on site in this case study, the economic calculation will therefore be free of its capital cost. This being in any case low compared to its operating cost, this will have little influence on the results due to actual price of the fuel in Mauritania (1.3 $/L) [36] .

The simulation results for the hybrid PV/Diesel Generator/Battery systems across the three villages—Voulaniya, Wali, and Nouawmghar—reveal key insights into their respective energy needs, costs, and system performance. According to the National Statistics Agence (ANSADE) in 2023, the total population of the Voulaniya amounts to 3339 inhabitants, the Wali about 8406 inhabitants, and 690 inhabitants in Nouamghar (ANSADE. 2024). The load profile for each community was obtained from the consumption data of the diesel generator installed on-site, as illustrated in Figure 6 . These load consumption are used to assess the performance of proposed PV/diesel/battery system.

Table 2 presents the Daily Energy Demanded and Load Factor for each measures load profiles. It can observe that Voulaniya has a relatively lower peak load and daily energy demand compared to Wali and Nouawmghar, resulting in a higher load factor. This indicates a more stable and predictable energy consumption pattern. For Wali exhibits the highest peak load and daily energy demand, with a lower load factor. This suggests significant variability and higher energy needs. Nouawmghar has moderate peak load and energy demand, with the lowest load factor, indicating more variability in energy usage.

Figure 7 . shows the HOMER Schematic of the proposed system. The obtained optimal components resultants for each case are shown in Table 3 . Voulaniya has the smallest PV generator size and battery capacity but maintains a reasonable renewable energy fraction. It also has the highest excess electricity percentage, indicating potential overproduction. Wali features the largest PV generator and battery capacity, with a higher renewable energy fraction but also a lower excess electricity percentage. This indicates a more balanced integration of renewables and demand. Nouawmghar has the smallest PV generator relative to its load but achieves the highest renewable energy fraction. Its excess electricity percentage is the lowest, suggesting optimal use of generated renewable energy.

It can be noted from Table 4 that Voulaniya has the highest levelized cost of electricity and total net present cost, making it the most cost-effective option among the three villages. Its operating cost is moderate, with a relatively high fuel consumption and CO₂ emissions. Wali has the highest total net present cost but the lowest levelized cost of electricity. It also has the highest operating costs and CO₂ emissions, reflecting its higher diesel usage. For Nouawmghar shows a balance between cost and performance. While its levelized cost of electricity is higher, its total net present cost is similar to Voulaniya, and it has the lowest operating cost and CO₂ emissions.

Table 5 represents the Breakeven Grid Extension Distance Economic. It can be noted that: Voulaniya has the shortest breakeven grid extension distance, indicating that extending the grid to this village is less economically favorable compared to installing a hybrid system due to its distance to the existing grid. Wali has the longest distance, making grid extension more viable in a distance less than 40 km. Nouawmghar falls in between, with a moderately favorable distance for grid extension relative to its hybrid system costs.

This study evaluates the optimal hybrid energy solutions for rural electrification in Mauritania, focusing on a combination of diesel generators, solar photovoltaic (PV) panels, and batteries. By employing HOMER software for techno-economic analysis, the research provides a comprehensive assessment of system performance across three diverse villages—Voulaniya, Wali, and Nouawmghar.

(1) System Configurations and Economic Viability:

(2) Economic Distance Limit (EDL):

(3) System Design Considerations: