## 4 Case Study
### Case Study Comparison  
Two case studies have been created using the partial datasets from 2019 and 2024. The goal of these case studies is to verify the effectiveness of the proposed RL method against a common baseline, specifically looking at the annual energy harvested \(E_{turbine}\) and annual \(LC\). In this case, a static k-omega-squared controller acts as the baseline, with the feedback gain \(k\) optimally tuned such that the HKT continuously tracks the optimal \(\lambda\) throughout Region 2. Figure 10 shows the environmental conditions for the 2019 and 2024 case study years, respectively. Similar to the training environments, the profiles of \(T_{amb}\) and \(u_{0}\) are quite similar between the two case study years. However, the LMP data in 2019 are significantly higher than in 2024. Figure 11 shows the applied values of \(k\) for 2019 and 2024, respectively. A key takeaway from this figure is that, in relation to Figure 10, as \(T_{amb}\) increases and peak values of \(u_{0}\) decrease toward the midpoint of the mission profile, the applied values of \(k\) also begin to decrease in both years. This phenomenon is somewhat intuitive as \(T_{amb}\) acts as a lower bound for \(T_{j}\) in reference to the thermal network in Figure 4. Therefore, as \(T_{amb}\) increases, the cost associated with the operation of the power electronics estimated using (24) also increases, and torque should be reduced to minimize these costs. Also, during instances of high environmental temperatures, rapid increases in the applied values of \(k\) can be found around local peaks in LMP data. This phenomenon is much more apparent in the 2024 case study, most notably between 1.75 \(\times\) 10\({}^{7}\) and 2.25 \(\times\) 10\({}^{7}\) s. This shows that, despite the increased negative reward that accompanies the high environmental temperatures, the  
Figure 9: Normalized reward profiles for each training year in the training set. The reward signals for each year are normalized by the initial reward received under the highly exploratory policy in the first training epoch. reward associated with maximizing energy outweighs the negative rewards associated with device aging. The most significant results that can be drawn from the plots in Figure 11 are the differences in the applied values of \(k\) between 2019 and 2024. Referring to Figure 10, the LMP data in 2019 are significantly higher than in 2024. This difference is highlighted by the \(k\) profiles between the two years. In 2019, the high cost of energy leads the RL agent to apply values of \(k\) much closer to \(k_{opt}\) to maximize energy generation at the expense of damaging the power electronic devices. In 2024, the low cost of energy drives the RL agent to favor the preservation of the power electronics by applying values of \(k\) that are significantly lower than \(k_{opt}\), except in times where the cost of energy spikes. Therefore, significant reductions in energy generation can be expected in the 2024 case study. The thermal profiles of \(T_{j}\) for the baseline and RL-based control for both case study years are shown in Figure 12. The general relationship between the two cases is that both the thermal cycle amplitudes \(\Delta T_{j}\) and mean junction temperatures are significantly lower under the RL-based control method compared to the baseline. The results in Figure 13 show that, under the proposed control scheme, the number of thermal cycles with amplitude  
Figure 11: Profiles of feedback gain values \(k\) applied by the baseline and RL-based controllers for (**a**) 2019 and (**b**) 2024. Figure 10: Plots of ambient temperature \(T_{amb}\), LMP data, and flow velocity \(u_{0}\) for the (**a**) 2019 and (**b**) 2024 case studies, respectively. greater than 20 \({}^{\circ}\)C has been greatly reduced, but the number of low-amplitude thermal cycles less than 5 \({}^{\circ}\)C has increased.