## 4 Case Study and Discussion

Table 5: Comparison of the system performance with various uncertainty modeling techniques for modeling the uncertainty of wind farming (3-month uncertainty) and with reductions of 20% and 30% in the generation of CPPs. For example, Monte Carlo methods provide extensive uncertainty coverage, which is critical for systems requiring a comprehensive exploration of potential scenarios. IGDT, on the other hand, focuses on worst-case outcomes, making it particularly effective for risk-averse strategies. Sensitivity analyses demonstrate that these differences become more pronounced under conditions of high uncertainty, emphasizing the importance of selecting the appropriate method based on specific operational objectives. Figure 12 illustrates the LOLP as a function of the percentage reduction in CPP generation without wind farm integration. The LOLP remains near zero for reductions up to 30-40%, indicating that the system can handle small reductions in CPP generation. However, beyond this threshold, the LOLP increases sharply, especially as reductions reach 50% or more. By the time CPP generation is reduced by 80-100%, the LOLP approaches 1, meaning that the likelihood of system failure or blackouts is nearly certain. This steep rise shows the system's increasing vulnerability to loss of load as conventional generation decreases without wind energy to compensate. Figure 13 depicts the LOLE as a function of CPP generation reduction, excluding wind farm integration. Like LOLP, the LOLE remains low for reductions up to 30-40%. However, beyond this point, the LOLE rises dramatically, indicating that the system becomes increasingly unable to meet load demand. When CPP generation reductions reach 70-80%, the LOLE approaches its maximum, representing thousands of expected hours of load loss per year. This shows the severe consequences of high CPP reductions on system performance. Figure 14 shows the EENS as a function of CPP generation reduction, without wind farm contributions. The EENS remains low for up to a 30-40% reduction, suggesting that the system can manage small reductions in conventional generation. However, beyond the 40% threshold, the EENS rises sharply, exhibiting exponential growth as reductions increase. By the time CPP reductions reach 70-80%, the EENS approaches extremely high levels, meaning the system cannot meet a large portion of its energy demand. This exponential rise highlights the risk of significant energy shortfalls as conventional generation continues to decline. Figure 15 illustrates system reliability as a function of CPP generation reduction, again without wind farm integration. As reductions in CPPs increase, reliability remains relatively stable only up to 30-40%. Beyond this threshold, reliability declines sharply, dropping steeply as reductions surpass 50%. By the time CPP generation reductions reach 80-100%, system reliability approaches zero, meaning the system is almost entirely unreliable. This sharp drop highlights the system's critical dependence on conventional generation to maintain stability. Figure 12: LOLP without wind farms and with the variation in the reduction in the CPPs’ generation. Figure 16 examines the impact of wind farm integration on the LOLP as CPP generation is reduced, comparing different uncertainty durations and modeling techniques. Both  
Figure 14: EENS without wind farms and with the variation in the reduction in the CPPs’ generation. Figure 13: LOLE without wind farms and with the variation in the reduction in the CPPs’ generation. Figure 15: Reliability without wind farms and with the variation in the reduction in the CPPs’ generation. sub-figures exclude the real case to focus on how models handle wind and conventional power uncertainties. Figure 16a, under a 1-month uncertainty scenario, shows the LOLP remaining low and stable for up to a 30-40% CPP generation reduction, with Monte Carlo and IGDT methods closely matching real-case performance. Beyond 40%, the LOLP rises steadily, though wind integration mitigates sharp increases.