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As the next generation of advanced adiabatic compressed air energy storage systems is being developed, designing a novel integrated system is essential for its successful adaptation in the various grid load demands. This study proposes a novel design framework for a hybrid energy system comprising a CAES system, gas turbine, and high-temperature solid oxide fuel cells, aiming for power generation and energy storage solutions. The overall model of the hybrid power generation system was constructed in Aspen PlusTM, and the mass balance, energy balance, and thermodynamic properties of the thermal system were simulated and analyzed. The results demonstrate that the hybrid system utilizes the functional complementarity of CAES and solid oxide fuel cells (SOFCs), resulting in the cascade utilization of energy, a flexible operation mode, and increased efficiency. The overall round-trip efficiency of the system is 63%, and the overall exergy efficiency is 67%, with a design net power output of 12.5 MW. Additionally, thermodynamic analysis shows that it is advisable to operate the system under lower ambient temperatures of 25 °C, higher compressor and turbine isentropic efficiencies of 0.9, a higher fuel utilization of 0.62, and optimal SOFC/MGT split air flow rates of 1.1 kg/s. The results of this article provide guidance for designing innovative hybrid systems and system optimization.