A co-generation plant consisting of a solid oxide fuel cell, a supercritical carbon dioxide Brayton cycle, an organic Rankine cycle, and a domestic heat recovery was modeled based on the zero-dimensional approach. The minimization of Gibbs free energy and Lagrange method of undetermined multipliers were applied to find the unknown moles in the reactions. The effects of the current density, the fuel utilization ratio, and the anode recycle ratio were investigated on the plant performance. Net power, heated water and fuel flow rates, energy and exergy efficiencies, and CO2 emission were considered as outputs of the co-generation plant. The contributions of the parameters were determined using analysis of variance results and half-normal plot of the standardized effects. The regression models of the outputs were achieved with high credibility. The findings indicated that the current density had the highest contribution to plant performance. The multi-objective optimization showed that the current density of 7787.879 A/m2 and the anode recycle ratio of 0.424 is the optimum condition. In this state, the electrical exergy efficiency, the heated water flow rate, and the CO2 co-generation emission were 43.01%, 2769 gr/s, and 213.6 kg/(MW.h), respectively.
