  The wide deployment of renewable generation and the gradual decrease in the
overall system inertia make modern power grids more vulnerable to transient
instabilities and unacceptable frequency fluctuations. Time-domain
simulation-based assessment of the system robustness against uncertain and
stochastic disturbances is extremely time-consuming. In this paper, we develop
an alternative approach, which has its roots in the input-output stability
analysis for Lur'e systems. Our approach consists of a mathematically rigorous
characterization of the external disturbances that the power system is
transiently stable and the frequency constraints are not violated. The derived
certificate is efficiently constructed via convex optimization and is shown to
be non-conservative for different IEEE test cases.
