###### Abstract
The LOLP is the probability that a power system will experience a shortage in generation capacity relative to demand, potentially leading to involuntary load shedding. It measures the likelihood of an energy deficit over a specified period. The LOLP refers to a probability of outages, where the loss of load expectation (LOLE) describes an expected value. The LOLE represents the expectation that available generation capacity will be inadequate to supply customers' demand at a given period. Renewable power plants and energy islands play a paramount role in electricity generation due to the transition to green and sustainable energies. The uncertain and intermittent nature of these systems makes the power system reliability assessment more complicated. Monte Carlo simulation, Bayesian Networks, and State Enumeration methods are widely used techniques for modeling uncertainty in power systems, particularly as the integration of RESs adds significant variability. Monte Carlo simulation generates numerous random scenarios based on uncertain variables, such as load demand and renewable generation, enabling system operators to evaluate probabilistic outcomes and assess risks like generation shortfalls or equipment failures. Bayesian Networks provide a probabilistic graphical approach that models the dependencies between system components and allows operators to update risk assessments dynamically as new information becomes available, making them especially useful for real-time decision-making. State Enumeration, on the other hand, systematically evaluates all possible system states under uncertainty, often in a reduced or aggregated form, to identify the worst-case scenarios or critical system vulnerabilities. These methods help ensure robust decision-making in the face of uncertainties in both power generation and system demand, enabling more reliable and resilient grid operations. Risk modeling in safety science is evolving to address complex challenges like hybrid threats, emphasizing private sector roles in resilience and the importance of geopolitical awareness [2]. The precautionary principle, often criticized, is reframed as a valuable tool for managing significant uncertainties when integrated with scientific decision-making [3]. Additionally, systems thinking, such as the iceberg model, supports a shift from reactive to proactive safety strategies, promoting sustainable risk management [4]. These approaches collectively advance the field toward holistic and anticipatory frameworks. This paper aims to provide a comprehensive evaluation of uncertainty and risk modeling techniques in power systems, focusing on their applications and implications in renewable energy integration. To complement this theoretical review, we include a detailed case study that demonstrates the practical distinctions between various methods. The inclusion of the case study serves the following purposes:  
* While most review articles provide theoretical insights, this case study enhances understanding by showing how these methods perform in real-world scenarios. By applying the techniques to a power system integrating wind farms, we assess their impact on key reliability indices such as loss of load expectation (LOLE), loss of load probability (LOLP), and expected energy not supplied (EENS). * The case study enables a direct, systematic comparison of modeling techniques, such as Monte Carlo simulation, Markov Chain Monte Carlo (MCMC), RO, and IGDT. This practical analysis helps highlight the suitability of different approaches for varying uncertainty durations and levels. * Presenting practical examples alongside theoretical discussions fosters greater reader engagement, offering a clearer perspective on the applicability of these techniques in real-world challenges. The main contribution of this paper is evaluating the impact of multiple uncertainty modeling techniques on system reliability and comparing them with a real case in different scenarios of wind farm integration.