## 4 Proposed Hybrid Model of NLMPC and Data-Driven Approach
### Implementation
Furthermore, in this study, the reference temperature for the turbines is set to 360 degrees Celsius to prevent thermal stress. Figure 3 demonstrates that only the proposed method successfully maintains the turbine temperature at the reference point of 120 degrees Celsius, ensuring optimal performance and stability during disturbances. Therefore, it can be concluded that the proposed approach demonstrates superior performance in controlling the output mechanical power of the generators, achieving the lowest generation cost and minimal temperature deviation from the reference temperature. Additionally, as shown in Figures 5 and 6, the voltage and frequency deviations for all three generators remain within the acceptable standard range of less than 5%, further validating the effectiveness of the proposed method in maintaining system stability and efficiency. As demonstrated in Figures 2-5, the proposed method (PM) not only achieves the fastest response in restoring power system stability but also excels in minimizing generation

Figure 2: Schematic diagram of the IEEE 9-Bus case study [41]. costs, outperforming other advanced techniques. Figures 5 and 6, in particular, highlight PM's exceptional ability to regulate bus voltage, maintaining minimal voltage deviation throughout system operations, thereby ensuring enhanced stability and reliability. Furthermore, Figure 7 provides a detailed representation of generator output during the described scenario, offering insights into the dynamic performance of the system under the PM method. The data in Figures 4 and 7 further elucidate the impact of line outages on the optimal generation point and turbine temperature, with a specific focus on how the PM method compares to alternative approaches. These figures clearly show that PM is highly efficient in real-time identification of new stable generation points and in the precise control of turbine temperature, consistently achieving the target set point of 120 degrees Celsius. This analysis underscores the precision, responsiveness, and effectiveness of the PM method in determining the optimal secure operating point, even amidst both planned and unplanned disturbances. The results confirm PM's superiority in maintaining system stability and operational efficiency, solidifying its role as a leading approach in advanced power system management. Table 2 provides a comparison of PM's performance with prior state-of-the-art studies in a range of contingency scenarios, emphasizing voltage deviation,

Figure 4: Turbine temperature comparison across various control methods. Figure 3: Total generation cost across various control methods. frequency deviation, and overall generating cost. The data demonstrate PM's remarkable capacity to quickly and precisely determine the system's safe and ideal generation point in the wake of disruptions. In every studied situation, PM consistently achieves the lowest total generating cost, as the table makes evident. To further bolster its supremacy over other methods, PM excels in both speed and precision when it comes to decreasing voltage deviations and damping system oscillations. Figure 5: Generator output voltage in the system under the proposed controller for the specified fault scenario. Figure 6: Output frequency of generators in the system with the proposed controller during the specified fault scenario. The proposed hybrid NLMPC approach, integrating data-driven methods, demonstrates superior performance across multiple metrics when compared to other advanced control strategies, as evidenced by the results presented in Figures 3-7 and Table 2. The analysis below provides a comprehensive quantitative comparison of generation costs, turbine temperature regulation, voltage deviation, and frequency deviation under various scenarios. The symbols \(\checkmark\) and \(\checkmark\) indicate whether a reference has examined a specific parameter. A \(\checkmark\) signifies that the parameter has been analyzed, whereas \(\checkmark\) indicates that it has not been considered.