  The aggressive integration of distributed renewable sources is changing the
dynamics of the electric power grid in an unexpected manner. As a result,
maintaining conventional performance specifications, such as transient
stability, may not be sufficient to ensure its reliable operation in stressed
conditions. In this paper, we introduce a novel criteria in transient stability
with consideration of operational constraints over frequency deviation and
angular separation. In addition, we provide a robustness measure of the region
of attraction, which can quantify the ability of the post-fault system to
remain synchronized even under disturbances. To assess this new stability
specification, we adopt the notion of Input-to-State Stability (ISS) to the
context of power systems and introduce a new class of convex Lyapunov
functions, which will result in tractable convex-optimization-based stability
certificates. As a result, we are able to quantify the level of disturbance a
power system can withstand while maintaining its safe operation. We illustrate
the introduced stability specification and certificate on the IEEE 9 bus
system.
