In this work, the trigeneration system, consisting of a proton-conducting solid oxide fuel cell (SOFC–H+) and a single-stage LiBr absorption chiller, was proposed. The SOFC–H+ and single-stage LiBr absorption chiller models were developed through Aspen Plus V10. From the sensitivity analysis, the results show that increases in temperature and fuel utilization can improve the performance of the SOFC–H+. Conversely, the air to fuel (A/F) molar ratio and pressure negatively affect the electrical efficiency and overall system efficiency. In the case of the absorption chiller, the coefficient of performance was increased and made stable according to a constant value when the generator temperature was increased from 90 to 100 °C. When the optimization was performed, it was found that the SOFC–H+ should be operated at 700 °C and 10 bar with fuel utilization of 0.8 and A/F molar ratio of 2 to achieve a maximum overall efficiency of 93.34%. For the energy and exergy analysis, a combined heat and power SOFC–H+ was found to have the highest energy and exergy efficiencies, followed by the trigeneration process. This indicates that the integration of the SOFC–H+ and LiBr absorption chiller is possible to efficiently produce electricity, heating and cooling.
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