This paper explores the potential of a combined solid oxide fuel cell and gas turbine technology for medium- to large-scale power generation, emphasizing its applicability and sustainability, particularly with biomass feedstock. An innovative heat integration process is developed for a modified solid oxide fuel cell and gas turbine power plant, incorporating a steam power cycle, compressed air energy storage, a Kalina cycle, and a domestic hot water production subsystem. The system utilizes biomass through a downdraft gasifier, enabling a comprehensive evaluation of thermodynamic, economic, and environmental performance during both charging and discharging phases. A detailed parametric sensitivity analysis is performed to investigate two operational modes. Subsequently, five multi-objective optimization scenarios are formulated and optimized using the cuckoo search algorithm and two decision-making approaches. The results indicate that the optimization scenario focusing on exergetic round-trip efficiency and the unit cost of products during the discharging phase achieves superior thermodynamic and environmental performance. Specifically, the system exhibits energetic and exergetic round-trip efficiencies of 59.20 % and 51.06 %, respectively, with a levelized total emission of 0.64 kg/MWh. Furthermore, when considering the objectives of exergetic round-trip efficiency and net present value, the optimal economic performance is achieved with a payback period of 1.54 years and a net present value of $7.44 million.