With the continuous electrification within developed countries, the task of keeping the power grid stable is becoming increasingly challenging with the demand increasingly volatile. Stochastic security-constrained unit commitment (S-SCUC) models can address the challenges posed by renewable energy variability and demand fluctuations by using probabilistic approaches to optimize the commitment and dispatch of generating units. While the goal is very defined, the approaches for modelling and simulation differ widely. In this work, we provide a brief overview of different approaches and solution techniques for the S-SCUC problem. We consider a case study using data from Baden-Württemberg, Germany, where the security constraint is a safety margin and apply Monte Carlo simulation for scenario generation. The results indicate that while the unpredictability is hard to overcome stochastic models can still lead to high accuracy and are thus helpful to grid operators. However, key statistical indicators still require improvement.