## 3 Calculation Results and Discussion
### Hybrid System Off-Design Performance Evaluation under Variable Operation Parameters
#### 3.3.3 Effect of Variable AS-Ratio on Hybrid System Performance
Figure 12: AS-reformer variation and performance variation in SOFC and GT. Figure 12A illustrates the key performance parameters of the SOFC, including electric power, fuel utilization, and electric efficiency. The SOFC working temperature is also included to assess how this variation in AS-reformers influences it. Six different AS-reformer fractions (1 to 6) selected in Table 6 range from 0.001 to 0.4 and yield diverse outcomes, revealing a notable reduction in electric efficiency and fuel utilization in the SOFC. Between AS-reformer 1 and 2, the SOFC FU is 100%, and this is undesirable. It is also noted that there is a rapid decrease in the electric efficiency of the SOFC from AS-reformer 2 to 3. This shows that the electric efficiency is very sensitive to variations in AS-reformer values. From 0.0025 to 0.0550, the electric efficiency of the stack drops from 80% to 4%. Within the same AS-reformer change, the SOFC FU changes from 100% to 8%. The design point fraction of 0.00475 yields an electric efficiency of 45.89% and an SOFC FU of 75.15%, which yields an SOFC output power of 102.5 kW. Therefore, AS-reformer fractions greatly influence the SOFC electric power generation capabilities, prompting system designers to pay attention in its selection and control, especially in dynamic applications. As the AS-reformer fraction increases, Figure 13 demonstrates a parallel rise in CPOx-generated fuel, causing a decrease in SOFC fuel utilization (Figure 12A), approaching 0% at higher AS-reformer fractions. This leads to reduced voltage, inefficient electrochemical reactions, and a drop in stack power from the targeted 100 to 35 kW (Figure 12A). Excessive fuel flow rates in fuel cells result in poor fuel utilization, incomplete oxidation, and heightened overpotential, diminishing overall energy conversion efficiency. Potential consequences include temperature instabilities and risks such as system overloading, leading to increased component wear. Variable AS-reformer fractions induce similar temperature variations in both the SOFC and CPOx reactor, as shown in Figures 12A and 13. Considering the hybrid system's propulsion role, essential performance parameters include thrust generation, TSFC, and overall efficiency (derived from the GT's propulsive  
Figure 13: AS-reformer variation and performance variation with CPOx. and thermal efficiencies). Figure 12B demonstrates the unique influence of each AS-ratio on hybrid system performance, with thrust and overall efficiency trending upward. Notably, TSFC decreases from 310 to 235 mg/s/N, indicating improved efficiency as more thrust is generated for the same fuel input. However, this improvement in GT performance comes at the expense of electric power generation, underscoring the significance of optimizing the AS-ratio to strike a balance between propulsive and electric power requirements in the hybrid system. AS-Cathode Variation and Its Effect on Hybrid System Performance  
The design point cathode fraction constitutes 0.84532 of the total HPC outlet air fraction for electrochemical reactions and cooling in the SOFC stack. Throughout this analysis, the O/C ratio is maintained at a constant value of 0.85, the current density is held at 5000 Am\({}^{-2}\), the HX-\(\xi\) is constant at 23%, the HPC outlet air temperature is compressed and kept constant at 850.22 K, the GT FAR is sustained at 0.02715, and the total engine inlet air flow remains constant. The sole varied parameter is the AS-ratio, and perturbations in the AS-cathode are detailed in Table 7, where each unique AS-cathode fraction value is assigned, and the remaining fractions are determined using Equation (55) to ensure proportional variations consistent with the design point AS-ratio. The resulting hybrid performance variations are graphically illustrated in Figures 14 and 15. Figure 14: AS-cathode variation and performance variation in SOFC and GT. Perturbations in AS-cathode significantly impact SOFC electric power generation.