## 8 Simulation Results
### Scenario 3  
In Scenario 3, PV plants produce 80% of the total generation of the grid, operating at their full capacity (4912.64 MW), while synchronous generators supply only 20% (1245.9 MW, see Table 1). This scenario simulates extreme renewable integration, where the POD-P controller faces constraints due to the PV plants operating at their maximum capacity. The first simulation, with the FFT detection function disabled, highlights the system's response under minimal synchronous generation conditions. The damping ratio of the electromechanical mode in this scenario is 1.12%, indicating lower system stability as the share of renewable increases. Figure 10a presents the frequency of the grid terminals. This response shows the smallest initial peak among the scenarios. This behavior, as previously noted in Scenario 2, is due to the reduced synchronous inertia, which lessens the system's ability to resist frequency changes after a disturbance. Moreover, the reduced damping ratio leads to the most prolonged oscillatory behavior of any scenario. Figure 10b focuses on the frequency at the PV plant terminals and the generator speeds. When the FFT function is enabled, the POD-P controller damps inter-area oscillations by modulating the active power setpoint in the PPC. With the POD-P controller activated, the damping ratio improves to 9.16%, highlighting the controller's capability to enhance system stability even under high-renewable-penetration conditions. Figure 11a illustrates the significant reduction in frequency oscillations across all grid terminals, while Figure 11b confirms system stabilization at the PV terminals and synchronous generator speeds. A limitation arises during the simulation, as highlighted in Figure 12: the PPC cannot further increase its active power setpoint because the PV plants are already operating at their maximum capacity (100%). This operational constraint leads to a slight but significant frequency drop (Figure 11a), which can critically affect system stability under conditions of high levels of renewable energy penetration. In systems dominated by inverter-based renewable generation, the absence of synchronous inertia further amplifies this vulnerability, increasing the grid's susceptibility to frequency deviations. If not properly managed, this issue can escalate into a frequency event, where reduced terminal frequencies threaten the grid's ability to operate within safe limits. Figure 10: Scenario 3. System response without the POD-P controller activated following the terminal short-circuit event (t = 5 s) and the line short-circuit event (t = 80 s): (**a**) frequency at all grid terminals [p.u. ]; (**b**) frequency at PV terminals [p.u.] and speed of synchronous generators [p.u.]. To mitigate this limitation, simulations were repeated with the anti-windup filter of the PID controller activated. This filter effectively prevents excessive frequency deviations by constraining the controller's output, ensuring it does not drive the system beyond its physical limits. The advantages of this strategy are clearly demonstrated in Figures 13 and 14, where the initial frequency drop observed without the filter is successfully corrected. With the anti-windup filter activated, oscillations are rapidly damped and the system promptly returns to a steady state. This confirms the critical role of the filter in enhancing the robustness and reliability of the POD-P controller under saturation conditions. To further quantify the performance of the POD-P controllers across these scenarios, Table 2 summarizes the electromechanical mode damping ratios for each scenario, with and without the POD-P controller activated. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Damping Ratio [\%]** & **Scenario 1** & **Scenario 2** & **Scenario 3** \\ \hline POD-P deactivated & 3.19 & 1.76 & 1.12 \\ POD-P activated & 11.86 & 10.61 & 9.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Damping ratio of each scenario, with and without the POD-P controller activated. Figure 11: Scenario 3.