Augmented Synchronization of Power Systems

TL;DR

This paper introduces the concept of augmented synchronization as a practical, equilibrium-independent approach to power system stability, bridging the gap between theoretical models and real-world observations.

Contribution

It formulates conditions under which augmented synchronization guarantees convergence to system stability without prior equilibrium knowledge.

Findings

Augmented synchronization implies convergence to the equilibrium set.

Conditions for initial states achieving augmented synchronization are derived.

Results verified on single-machine and IEEE 9-bus system examples.

Abstract

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.