Complete position synchronization in the power grid system

Sun Ho Choi, Intae Ryoo, Bum Il Hong

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We present a sufficient condition for synchronization of power grid model when the moment of inertia is zero. Unlike the Kuramoto model, the power grid model contains nonlinear terms of the first- and second-order derivatives. We assume that the natural frequencies are all the same and larger than coupling strength K>0. These conditions allow us to use a Lyapunov functional and a priori estimate method. From the Lyapunov functional, we can obtain the exponential decay result for the phase difference maxi,ji(t)−θj(t)|, where θi is the ith phase angle such that the ensemble approaches complete position synchronization.

Original languageEnglish
Pages (from-to)19-25
Number of pages7
JournalApplied Mathematics Letters
Volume84
DOIs
Publication statusPublished - Oct 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Ltd

Keywords

  • A priori estimate
  • Kuramoto model
  • Lyapunov functional
  • Position synchronization
  • Power grid model

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