## 4 Proposed Hybrid Model of NLMPC and Data-Driven Approach
### Implementation
The findings from this study could pave the way for more resilient and adaptive control solutions, ensuring that power systems can maintain optimal performance even under the most challenging conditions. In this study, similar to the previous case study, various scenarios involving sudden and deliberate contingencies have been analyzed, as detailed in Table 3. Table 3 provides a comprehensive comparative analysis of the performance of the PM against previous state-of-the-art (SOTA) research, focusing on key metrics such as total generation cost, total frequency deviation, and voltage deviation under different scenarios, including those involving line outage or generator outage. The data presented in this table clearly illustrate PM's significant superiority over previous methods in swiftly and accurately identifying the secure and optimal generation configuration for the system following disturbances. This superiority is particularly evident in the precision and speed with which PM responds to these disruptions. Moreover, the table highlights that PM consistently achieves the lowest total generation cost across all scenarios, making it the most cost-effective solution. Additionally, PM demonstrates exceptional capability in mitigating system oscillations, delivering the highest speed and accuracy among the methods evaluated. This positions PM as the most proficient and reliable approach in maintaining system stability and efficiency in the face of various operational challenges. Table 3 compares the PM with previous SOTA control methods under various contingency scenarios in the IEEE 11-bus system. Key performance metrics include turbine temperature, voltage deviation, maximum frequency deviation, and total generation costs. The following analysis evaluates the effectiveness of each method based on these metrics. Figure 8: Schematic of the IEEE standard model of the 11-Bus [PERSON]’s two-area system [39]. #### 5.2.1 Turbine Temperature Regulation

The ability to maintain turbine temperature near the reference value of 360 \({}^{\circ}\)C is a critical factor for ensuring system stability and preventing thermal stress:

* **PM**: Across all scenarios, PM consistently maintains turbine temperatures close to the reference value, with deviations as low as 1-2 \({}^{\circ}\)C (e.g., 361.2 \({}^{\circ}\)C during a line interruption between Bus 7 and 8). * **SOTA Methods**: Other methods show significantly larger deviations, with temperature ranging from 421.37 \({}^{\circ}\)C to 751.37 \({}^{\circ}\)C under similar scenarios. For instance, a line interruption between Bus 8 and 9 results in a temperature of 362.92 \({}^{\circ}\)C for PM, while SOTA methods yield temperatures of 521.44 \({}^{\circ}\)C to 751.37 \({}^{\circ}\)C.
* **Analysis**: The PM demonstrates superior temperature regulation, reducing the risk of thermal stress by maintaining turbine performance within safe operational limits. #### 5.2.2 Voltage Deviation

Voltage stability is essential for maintaining reliable system operations:
* **PM**: Voltage deviations for PM remain minimal, ranging from 0.1031 pu to 0.1371 pu across all scenarios. For example, during a line interruption between Buses 5 and 6, the PM achieves a voltage deviation of 0.1371 pu compared to 0.4118 pu and 0.511 pu for SOTA methods. * **SOTA Methods**: Competing methods exhibit significantly higher deviations, with values exceeding 0.2 pu and reaching as high as 0.511 pu in some cases. * **Analysis**: The PM maintains voltage deviations well within acceptable limits, enhancing power quality and reducing the likelihood of voltage instability or cascading failures. #### 5.2.3 Maximum Frequency Deviation

Frequency stability is a critical indicator of a system's resilience to disturbances:

* **PM**: The PM achieves the lowest frequency deviations, ranging from 1.81% to 3.7%. For example, during a line interruption between Bus 7 and 8, the PM records a deviation of 3.7%, compared to 7.1% and 5.21% for SOTA methods.