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Transient Stability Analysis of Power Grids with Admissible and Maximal Robust Positively Invariant Sets

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbances and obtain the sets for each component separately. From this we deduce transient stability properties for the entire system. We demonstrate the results of our approach through an example of one machine connected to one load and a multi-machine system.