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,j|θi(t)−θj(t)|, where θi is the ith phase angle such that the ensemble approaches complete position synchronization.
Original language | English |
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Pages (from-to) | 19-25 |
Number of pages | 7 |
Journal | Applied Mathematics Letters |
Volume | 84 |
DOIs | |
Publication status | Published - Oct 2018 |
Bibliographical note
Publisher Copyright:© 2018 Elsevier Ltd
Keywords
- A priori estimate
- Kuramoto model
- Lyapunov functional
- Position synchronization
- Power grid model