In hot-humid cities, conventional trigeneration can be reduced to combined cooling and power system. Solid oxide fuel cell is a high-temperature prime mover with high electrical efficiency, its efficiency may be further boosted up with bottoming cycle like gas turbine, Stirling engine and organic Rankine cycle. Besides using waste heat recovered from the prime mover to energize absorption chiller, the surplus electricity can be used to drive the conventional compression chiller as supplement. However, there is little knowledge about the effectiveness of such combined cooling and power system under different operating conditions. System models with various bottoming cycles are therefore developed, and their part-load performances are investigated. The effects of fuel inlet temperature and current density of fuel cell stack; compression ratio of gas turbine; Stirling engine type; working fluid of organic Rankine cycle; and fuel cell stack part-load ratio are explored. It is found that the combined cooling and power system with bottoming cycles of gas turbine and Stirling engine have higher boost of electrical efficiency. Gas turbine bottoming cycle is recommended when building energy demands are relatively constant, while Stirling engine bottoming cycle is suggested for variable energy demands.