Access to electricity in many remote rural areas of the world is wanting and often relies on decentralized concepts that are environmentally detrimental, costly, and unreliable. The purpose of this study was to examine an approach to meet this need that is based on an external biomass-fueled cogeneration system incorporating combined cycles for maximizing efficiency while ensuring robust operation. Specifically, the first and second laws of thermodynamics were analyzed in a system composed of a Brayton-Stirling cycle and a water boiler to compare efficiency, heat and electricity generation under three different power layouts of cogeneration for applications in the range of 100–200 kW electrical power output. The results show that overall efficiency is maximized at 85% with a hybrid power layout for cases where the turbine inlet temperature is 1273 K, the pressure ratio is 0.4, the regenerator effectiveness is 0.95, and the dead volume of the Stirling engine is 0.3. These findings provide a basis for implementing cogeneration systems to improve the reliability and robustness of power systems for rural electrification.