  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.
