Augmented synchronization of power systems

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 redefines the nominal motion as augmented synchronization rather than a certain equilibrium. Single-machine examples and the IEEE 9- bus system verify our results and illustrate promising implications.