This title appears in the Scientific Report :
2017
Please use the identifier:
http://hdl.handle.net/2128/16007 in citations.
Please use the identifier: http://dx.doi.org/10.1063/1.4994177 in citations.
Cycle flows and multistability in oscillatory networks
Cycle flows and multistability in oscillatory networks
We study multistability in phase locked states in networks of phase oscillators under both Kuramoto dynamics and swing equation dynamics - a popular model for studying coarse-scale dynamics of an electrical AC power grid. We first establish the existence of geometrically frustrated states in such sy...
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Personal Name(s): | Manik, Debsankha (Corresponding author) |
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Timme, Marc / Witthaut, Dirk | |
Contributing Institute: |
Systemforschung und Technologische Entwicklung; IEK-STE |
Published in: | Chaos, 27 (2017) 8, S. 083123 - |
Imprint: |
Woodbury, NY
American Institute of Physics
2017
|
DOI: |
10.1063/1.4994177 |
PubMed ID: |
28863499 |
Document Type: |
Journal Article |
Research Program: |
Kollektive Nichtlineare Dynamik Komplexer Stromnetze Helmholtz Young Investigators Group "Efficiency, Emergence and Economics of future supply networks" Assessment of Energy Systems – Addressing Issues of Energy Efficiency and Energy Security |
Link: |
Get full text OpenAccess OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.1063/1.4994177 in citations.
We study multistability in phase locked states in networks of phase oscillators under both Kuramoto dynamics and swing equation dynamics - a popular model for studying coarse-scale dynamics of an electrical AC power grid. We first establish the existence of geometrically frustrated states in such systems - where although a steady state flow pattern exists, no fixed point exists in the dynamical variables of phases due to geometrical constraints. We then describe the stable fixed points of the system with phase differences along each edge not exceeding pi/2 in terms of cycle flows - constant flows along each simple cycle - as opposed to phase angles or flows. The cycle flow formalism allows us to compute tight upper and lower bounds to the number of fixed points in ring networks. We show that long elementary cycles, strong edge weights, and spatially homogeneous distribution of natural frequencies (for the Kuramoto model) or power injections (for the oscillator model for power grids) cause such networks to have more fixed points. We generalize some of these bounds to arbitrary planar topologies and derive scaling relations in the limit of large capacity and large cycle lengths, which we show to be quite accurate by numerical computation. Finally, we present an algorithm to compute all phase locked states - both stable and unstable - for planar networks. |