  This paper introduces a novel concept of local synchronization of power
systems devices based on the difference between the complex frequency of the
voltage and current injected at terminals. Formal definitions are provided to
account for bounded and asymptotic local synchronization. The definitions are
suitable for modern power systems as they remove classical assumptions limiting
the application of the concept of synchronization to synchronous machines and
omitting voltage dynamics. The paper also provides a systematic analytical
description of the synchronization mechanisms of common power system devices.
Finally, a variety of examples is included to illustrate the theoretical value
and practical application of the proposed definitions to power systems modeling
and stability analysis.
