The increasing feed-in of renewable energy and the legal requirement to use existing power grids to its maximal capacity, make it increasingly difficult to maintain a stable power supply. Today, analysis of power grids in industry and academia is mainly done by simulation to investigate single use cases. However, initial states, parameters, and disturbances are typically not exactly known, resulting in an infinite number of future scenarios.
Set-based methods are developed to ensure stability of smart grids under all operating conditions. A special focus is on transient stability, the effects of variable energy production, and the detection of situations which result in voltage collapse. In order to scale the developed methods to industrially relevant problems, compositional methods are investigated, which can verify the overall stability by analyzing smaller sub-systems.