## 1 Introduction
[26], the aircraft SOFC/GT system is thoroughly examined using Numerical Propulsion System Simulation (NPSS) software. This study includes a detailed aerodynamic analysis of the GT, SOFC, and reformer, providing realistic representations and highlighting aerodynamic losses. The research evaluates the fuel consumption variation for each system configuration, resulting in a reduction in fuel consumption by 4-8%. Similarly, [PERSON] et al. [27] contributed to the field by performing hybrid system optimization. This study identified local optimum fuel cell operating states through the analysis of operating voltage and percentage fuel oxidation. The authors concluded that the performance benefits of the SOFC/GT can be optimized by using careful external aerodynamic design. The application of the SOFC/GT hybrid system for primary propulsion in aircraft has been supported by these studies, demonstrating the proof of concept. Extensive research has been conducted on various aspects, including modeling practices, configuration designs, performance evaluation with fuel variations, and performance optimization at the design point within the context of hybrid systems. However, certain areas have not received adequate attention, specifically the identification of critical operational parameters, methods for parameter selection, and evaluation of their impact on system performance. The lack of clear explanations from previous authors regarding the selection and justification of specific critical parameters has created ambiguity in the design of SOFC/GT systems for aircraft applications. This research aims to fill this gap by identifying the key operational parameters essential for achieving optimal performance, providing guidance on parameter selection, and examining their influence on overall system performance. This study focuses on three critical parameters associated with each component of the hybrid system: the oxygen-to-carbon ratio (O/C ratio) of the reformer, the fuel utilization of the SOFC, and the high-pressure compressor (HPC) outlet air split ratio (AS-ratio) to the reformer, SOFC, and GT. These parameters play a crucial role in delivering sufficient electric power and thrust. The research begins by establishing the optimal design point performance under specific conditions and then systematically analyzes the impact of varying each parameter within a predetermined range. The assessment of parameter variations provides valuable insights into the sensitivity and robustness of the system, highlighting areas that require attention during design and performance optimization. Given the interconnected nature of the components, understanding the influence of these variable operational parameters on individual components and the overall hybrid system is crucial. The primary objective is to ensure consistent fulfillment of the aircraft's fluctuating electric power demands by the SOFC while effectively meeting propulsive requirements with the gas turbine under varying working conditions. Additionally, it is essential to ensure that the CPOx system meets the reformed fuel demand under these variable conditions. This research represents a significant innovation by identifying critical operational parameters essential for achieving optimal performance in the SOFC/GT hybrid system. By providing insights into parameter selection methods and demonstrating the potential system response when parameters are not carefully chosen, this study contributes valuable knowledge for developing effective strategies to adapt to variable flight conditions. The findings strengthen the existing research foundation and significantly advance the understanding and implementation of the SOFC/GT hybrid system in aircraft propulsion.