A new molten carbonate fuel cell hybrid power generation system using two-stage sodium thermo-electrochemical converter/two-stage thermoelectric generator: Performance analysis and multi-objective grasshopper optimization

To enhance the poor power density of the molten carbonate fuel cell, a novel combination of two-stage sodium thermo-electrochemical converter and a two-stage thermoelectric generator is introduced to recover the heat waste of the molten carbonate fuel cell for further power generation. The performance criteria of the hybrid system in terms of power outputs, efficiencies, exergy destruction, and cost rate are mathematically derived and analyzed using energy, exergy, and exergoeconomic methods. Finally, the grasshopper multi-objective optimizer and decision-making procedures are applied to find the maximum power density and exergy efficiency for the hybrid system with the minimum power density cost rate. It is found that the preferable optimum operation of the system provides the highest power density of 2652.1 W/m2 with 53.96% and 57.58% energetic and exergetic efficiencies which are 42.28% and 38.89% larger than the individual molten carbonate fuel cell, respectively. Moreover, the minimum power density cost rate is calculated by 1.13 $/h m2, indicating a 26.14% improvement compared to the design condition and a 0.51 $/h m2 increase relative to the sole molten carbonate fuel cell. The results suggest that the present system is a favorable alternative to other hybrid systems. •A combination of TNa-TEC/TTEG is employed to boost the low performance of an MCFC.•Thermodynamic and economic criteria are mathematically formulated for the system.•The influence of main design parameters is evaluated on the system's performance.•The capability of the TNa-TEC/TTEG relative to other solid-state generators is revealed.•MOGOA and decision-making are applied to find the optimal performance of the system.