Full metadata
Title
Critical coupling and synchronized clusters in arbitrary networks of Kuramoto oscillators
Description
The Kuramoto model is an archetypal model for studying synchronization in groups
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
Date Created
2018
Contributors
- Gilg, Brady (Author)
- Armbruster, Dieter (Thesis advisor)
- Mittelmann, Hans (Committee member)
- Scaglione, Anna (Committee member)
- Strogatz, Steven (Committee member)
- Welfert, Bruno (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
viii, 126 pages : illustrations, 1 color map
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.49277
Statement of Responsibility
by Brady Gilg
Description Source
Retrieved on July 9, 2018
Level of coding
full
Note
thesis
Partial requirement for: Ph.D., Arizona State University, 2018
bibliography
Includes bibliographical references (pages 118-121)
Field of study: Applied mathematics
System Created
- 2018-06-01 08:08:59
System Modified
- 2021-08-26 09:47:01
- 3 years 2 months ago
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