Solid oxide fuel cell (SOFC) technology offers a clean and efficient way to generate electricity from natural gas. Since various integration options with thermal cycles have been proposed to achieve even higher electrical efficiencies, it is interesting to see how these compare. In addition, the influence of the SOFC operating parameters on thermal cycles is not yet adequately addressed. In this study, a stand-alone SOFC system is thermodynamically analysed and compared to configurations combined with a gas turbine or steam turbine, as well as a novel SOFC-reciprocating engine combined cycle system. The results are mapped in contour plots for the entire SOFC operating envelope, revealing the influence of fuel utilisation, cell voltage, average stack temperature and gas turbine pressure ratio on different combined cycles. An exergy analysis is included to quantify notable losses in the systems and identify potential further improvements. The pressurised SOFC-gas turbine combined cycle achieves the highest electrical efficiencies for stack operation at moderate cell voltages and high temperatures, while the steam turbine combined cycle is more efficient at high cell voltages and low stack temperatures. The SOFC-reciprocating engine combined cycle shows similar behaviour to the steam turbine combined cycle, but achieves slightly lower efficiencies.