The load-following capabilities of power plants became increasingly important in recent years as a means of ensuring a reliable operation of future power systems. In this work, we propose a generic approach, based on reachability analysis, to rigorously verify the safety of critical components that often pose limitations on the flexibility of conventional power plants to perform fast load changes. The proposed reachability algorithm makes it possible to compute the bounds of all possible trajectories for a range of operating conditions while simultaneously meeting the practical requirements of a real power plant. As an example, we consider the verification of the water level inside a drum unit. In contrast to previous work, our results are based on measurement data of a realistic configuration of a boiler system located within a 450 MW combined cycle plant in Germany. We use an abstract model which considers the modelling errors to ensure that all dynamic behaviors of the process are replicated by the abstraction. Through the implementation of our abstract model, we formally guarantee that the water level inside the drum always remains within safe limits for load changes equivalent to 40 MW which, as a result, exploits the power plant's adaptability and load-following capabilities.