A techno-economic study of a hybrid PV/Battery/Grid-connected system for energy supply is carried out in this paper to respond to the problem of electrical load shedding. An optimal design of the system is realized thanks to a double-objective optimization based on a proposed operational strategy of the system and on Firefly Algorithm (FA). The system is designed for household energy supply in three different towns of the northern part of Cameroon. For different LPSP (Loss of Power Supply Probability), the double objective simulation determines the optimal configurations of the system with their related cost. The optimal and reliable PV/Battery subsystem configuration corresponding to LPSP of 0% obtained for one household is composed for the towns of Maroua and Garoua by 8 PV modules and a battery capacity of 11.304 kWh with 1-day autonomy. For the town of Ngaoundéré, it is composed by 10 PV modules and battery capacity of 11.304 kWh with 1-day autonomy. The related investment costs corresponding to these optimal configurations are USD 6225.6 for Maroua and Garoua and USD 7136.6 for Ngaoundéré. The great proportion of the monthly energy demand consumed by the load is provided by the PV/Battery system. The monthly PV/Battery energy represents 60.385% to 72.546% of the load consumed in Maroua, 58.371% to 71.855% of the load consumed in Garoua, and 61.233% to 74.160% of the load consumed in Ngaoundéré. The annual main grid energy consumed for one household is 1299.524 kWh in Maroua, 1352.818 kWh in Garoua, and 1260.876 kWh in Ngaoundéré. Moreover, the annual PV/Battery energy consumed for one household is 1580.730 kWh in Maroua, 1527.815 kWh in Garoua, and 1619.530 kWh in Ngaoundéré. Thus, the PV/Battery system, by reducing the grid energy consumption, acts as the principal source of energy of the whole system. The time the PV/Battery/Grid-connected system needs to be economically more advantageous than the electric grid without blackouts is 17 years for Maroua and 18 years for both Garoua and Ngaoundéré. It is demonstrated in this paper that the hybrid PV/Battery/Grid-connected system is an effective solution for electrical load shedding in sub-Saharan zones. This system is very useful for grid energy consumption reduction. For a long-term investment, the PV/Battery/Grid-connected system is more economically advantageous than the main grid alone.