The method of exergy analysis is presented for a solid oxide fuel cell (SOFC) power plant involving external steam reforming and fed by methane and ethanol. The parameters for optimal operation of the integrated SOFC plant are specified after minimizing the existing energy and exergy losses. A comparison of methane and ethanol as appropriate fuels for a SOFC-based power plant is provided in terms of efficiency of exergy assuming the minimum allowable (for carbon-free operation) reforming factors for both cases. Then, a parametric analysis provides guidelines for practical design. The analysis employs parameters such as the extension of the steam reforming reaction and the hydrogen utilization in the SOFC and proves that the appropriate adjustment of the plant performance can be achieved by simply interrelating them in order to control the energy losses to environment and the participation of combustion processes in the power cycle. Energy losses from the SOFC stack are found also of negative impact to plant efficiency and are minimized through an appropriate thermal management between the mixtures incoming and outgoing the stack, attaining the adiabatic regime of SOFC operation. It is concluded that the exergy calculations pinpoint the losses accurately and that the exergy analysis gives a better insight of the system’s process.