## 4 Case Study and Discussion
In Figure 16b, under a 3-month uncertainty, a similar trend is observed, but differences between models become more pronounced over time. IGDT and Monte Carlo continue to perform best, with the LOLP increasing more rapidly after a 40% reduction. Compared to Figure 13 (without wind farms), wind farms significantly lower LOLP even as CPP generation decreases, highlighting wind's role in reducing load loss risks. Figure 17 explores the impact of wind farms on the LOLE under both 1-month and 3-month uncertainty scenarios. In Figure 17a, wind farms help maintain a low LOE even as CPP generation decreases, with Monte Carlo and IGDT closely matching real-case performance. In Figure 17b, under a 3-month uncertainty, the LOLE rises more rapidly beyond a 40% CPP reduction. Again, Monte Carlo and IGDT deliver reliable predictions over extended periods. Compared to Figure 13 (without wind farms), Figure 17 shows that wind farms significantly reduce the LOLE, particularly in longer uncertainty scenarios, proving their importance in enhancing reliability under reduced CPP generation. Figure 18 assesses the EENS with wind farm integration. In Figure 18a, under 1-month uncertainty, the EENS stays stable up to a 30-40% CPP reduction but increases sharply beyond 50%. Monte Carlo and IGDT closely align with real-case results. In Figure 18b, under 3-month uncertainty, the EENS rises steeply after a 40% reduction, with Monte Carlo performing best over the longer horizon. Figure 18 compared to Figure 14 (without wind farms) shows that wind farms mitigate the EENS, though their effectiveness lessens with longer uncertainty periods. Figure 19 evaluates the overall system reliability with wind farm integration. In Figure 19a, under 1-month uncertainty, reliability remains high up to a 40% CPP reduction, with wind stabilizing the system. In Figure 19b, under 3-month uncertainty, reliability drops more after a 40% reduction, as wind's impact lessens. Monte Carlo remains the most reliable for extended uncertainties. Figure 16: LOLP with wind farms and the variation in the reduction in the CPPs’ generation. (**a**) One-month uncertainty (excluding real case). (**b**) Three-month uncertainty (excluding real case). Compared to Figure 15 (without wind farms), wind farms significantly boost reliability, especially in short-term scenarios, though their effect diminishes over longer periods. The results underscore the pivotal role of integrating wind farms in enhancing the reliability of power systems, particularly when conventional power generation faces significant reductions. The Monte Carlo simulation coupled with K-Means proved to be the most effective in closely aligning with real-case scenarios and managing uncertainties across both short and longer durations. These findings highlight the necessity of adopting advanced modeling techniques to accurately predict and manage the dynamics of power systems with high renewable penetration. The successful application of these models demonstrates their potential in guiding energy policy and system design to ensure stability and reliability in the evolving energy landscape. Figure 17: LOLE with wind farms and the variation in the reduction in the CPPs’ generation. (**a**) One-month uncertainty (excluding real case). (**b**) Three-month uncertainty (excluding real case). Figure 18: EENS with wind farms and the variation in the reduction in the CPPs’ generation. (**a**) One-month uncertainty (excluding real case). (**b**) Three-month uncertainty (excluding real case).