In the face of a significant power crisis, Bangladesh is turning towards renewable energy solutions, a move supported by the government’s initiatives. This article presents the findings of a study conducted in a residential area of Pabna, Bangladesh, using HOMER (Hybrid Optimization of Multiple Energy Resources) Pro software version 3.14.2. The study investigates the feasibility and efficiency of a grid-connected hybrid power system, combining photovoltaics (PV), a biomass generator, and wind energy. The simulation produced six competing solutions, each featuring a distinct combination of energy sources. Among the configurations analyzed, the grid-connected PV–biomass generator system emerged as the most cost-effective, exhibiting the lowest COE at USD 0.0232, a total net present cost (NPC) of USD 321,798.00, and an annual operating cost of USD 6060.59. The system presents a simple payback period of 9.25 years, highlighting its economic viability. Moreover, this hybrid model significantly reduces CO2 emissions to 78,721 kg/year, compared to the 257,093 kg/year emissions from a solely grid-connected system, highlighting its environmental benefits. Sensitivity analyses further reveal that the system’s performance is highly dependent on solar irradiance, indicating that slight variations in solar input can significantly impact the system’s output. This study underscores the potential of integrating multiple renewable energy sources to address the power crisis in Bangladesh, offering a sustainable and economically viable solution while also mitigating environmental impacts.