  Power system transient stability has been translated into a Lyapunov
stability problem of the post-disturbance equilibrium for decades. Despite
substantial results, conventional theories suffer from the stringent
requirement of knowing the post-disturbance equilibrium a priori. In contrast,
the wisdom from practice, which certificates stability by only the observation
of converging frequencies and voltages, seems to provide an
equilibrium-independent approach. Here, we formulate the empirical wisdom by
the concept of augmented synchronization and aim to bridge such a
theory-practice gap. First, we derive conditions under which the convergence to
augmented synchronization implies the convergence to the equilibrium set,
laying the first theoretical foundation for the empirical wisdom. Then, we
reveal from what initial values the power system can achieve augmented
synchronization. Our results open the possibility of an equilibrium-independent
power system stability analytic that re-defines the nominal motion as augmented
synchronization rather than certain equilibrium. Single-machine examples and
the IEEE 9-bus system well verify our results and illustrate promising
implications.
