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Synchronization of a Kuramoto-like model for power grids with frustration

Xiaoxue Zhao, ,School of Mathematics, Harbin Institute of Technology, Harbin 150001, China, Zhuchun Li, ,School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China
2020 Networks and Heterogeneous Media  
We discuss the complete synchronization for a Kuramoto-like model for power grids with frustration.  ...  For nonidentical oscillators with frustration, we present a framework leading to complete frequency synchronization where the initial phase configurations are located inside the half of a circle.  ...  We would like to thank the anonymous referee for his/her comments which helped us to improve this paper.  ... 
doi:10.3934/nhm.2020030 fatcat:uutwj7f6lfegpifreu52tvcmcq

Heterogeneity effects in power grid network models

Géza Ódor, Bálint Hartmann
2018 Physical review. E  
We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power grid networks, generated from real data.  ...  The temporal behavior of de-synchronization avalanches after a sudden quench to low K values, has been followed and duration distributions with power-law tails have been detected.  ...  Most of the numerical work was done on NIIF supercomputers of Hungary. Additional information The authors declare no competing financial interests. 9/12  ... 
doi:10.1103/physreve.98.022305 fatcat:ec2ra3gjjjblvauyplvagmmjlu

Synchronization dynamics on the EU and US power grids [article]

Géza Ódor, Shengfeng Deng, Bálint Hartmann, Jeffrey Kelling
2022 arXiv   pre-print
Near K_c the exponents of the PL-s for the US power grid vary with T as 1.4 ≤τ≤ 2.1, in agreement with the empirical blackout statistics, while on the EU power grid we find somewhat steeper PL-s characterized  ...  Dynamical simulation of the cascade failures on the EU and USA high-voltage power grids has been done via solving the second-order Kuramoto equation.  ...  Acknowledgments We thank Róbert Juhász and Lilla Barancsuk for the useful comments. Support from the advantaged ELKH  ... 
arXiv:2205.13472v1 fatcat:qi34hs4p6bafni6pwvfip4xw34

Perfect synchronization in networks of phase-frustrated oscillators [article]

Prosenjit Kundu, Chittaranjan Hens, Baruch Barzel, Pinaki Pal
2018 arXiv   pre-print
Demonstrating our results on first and second order phase-frustrated Kuramoto dynamics, we implement them on both model and real power grid networks, showing how to achieve synchronization in a phase frustrated  ...  Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators  ...  Sakaguchi-Kuramoto model of phase frustrated oscillators [3, [16] [17] [18] ; setting α → 0 we arrive at the classic Kuramoto dynamics [2] .  ... 
arXiv:1801.05660v2 fatcat:shxigpdsu5amrouy3ogbekenfi

Model Reduction for the Kuramoto-Sakaguchi Model: The Importance of Non-entrained Rogue Oscillators [article]

Wenqi Yue, Lachlan D. Smith, Georg A. Gottwald
2020 arXiv   pre-print
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators.  ...  Here we extend a model reduction method based on collective coordinates to capture the collective dynamics of finite size Kuramoto-Sakaguchi models.  ...  neurons [5] to chemical oscillators [6, 7] and power grid systems [8] .  ... 
arXiv:2004.06344v2 fatcat:7ik75i6lsfbxzfnxsk6fqq3vm4

Enhancing power grid synchronization and stability through time delayed feedback control [article]

Halgurd Taher, Simona Olmi, Eckehard Schöll
2019 arXiv   pre-print
We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal frequency distribution representing the generators and the loads.  ...  As a proof of principle, this fast-acting control method is demonstrated using a model of the German power transmission grid.  ...  To this purpose we have studied the Kuramoto model with inertia in the presence of a bimodal distribution of generator and load power, which leads to a fully frequency synchronized, stable network for  ... 
arXiv:1901.05201v1 fatcat:j65cjbfaqfathb5cdjo6nlprpi

Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators [article]

Darka Labavic, Hildegard Meyer-Ortmanns
2017 arXiv   pre-print
Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution  ...  We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies.  ...  INTRODUCTION As model for classical oscillators we consider the Kuramoto model, a paradigm for synchronization phenomena with applications to natural and artificial systems [1] .  ... 
arXiv:1705.04079v1 fatcat:6hc2n77yafgevmg55sf3ahq764

Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators

DARKA LABAVIC, HILDEGARD MEYER-ORTMANNS
2017 Indian Academy of Sciences – Conference Series  
Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution  ...  We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies.  ...  Acknowledgements We would like to thank the organizers of the PNLD-2016 conference for a stimulating meeting from July 24-29 in Berlin.  ... 
doi:10.29195/iascs.01.01.0019 fatcat:pbwytktb3rewjcyqdxj6petsvm

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs [article]

Géza Ódor, Jeffrey Kelling
2019 arXiv   pre-print
At this crossover point we observe power-law–tailed synchronization durations, with τ_t ≃ 1.2(1), away from experimental values for the brain.  ...  The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization,  ...  Bussmann and the Center for Information Services and High Performance Computing (ZIH) at TU Dresden via the GPU Center of Excellence Dresden. We thank S. Gemming for support.  ... 
arXiv:1903.00385v3 fatcat:jcbkponeavcyfli5c2bb6xnq2e

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

Géza Ódor, Jeffrey Kelling
2019 Scientific Reports  
At this crossover point we observe power-law-tailed synchronization durations, with τt ≃ 1.2(1), away from experimental values for the brain.  ...  The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization,  ...  Bussmann and the Center for Information Services and High Performance Computing (ZIH) at TU Dresden via the GPU Center of Excellence Dresden. We thank S. Gemming for support.  ... 
doi:10.1038/s41598-019-54769-9 pmid:31873076 pmcid:PMC6928153 fatcat:lfcks4vqw5eqljpemoo2vtvlru

The effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph [article]

Géza Ódor, Jeffrey Kelling, Gustavo Deco
2020 arXiv   pre-print
We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph.  ...  We also compare the connectome results with those, obtained on a regular cube with N=10^6 nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated  ...  Juhász and A. Ponce for the useful comments and Wesley Cota for generating and providing us modules of KKI-18 as well as precursor of Fig. 1 .  ... 
arXiv:1912.06018v3 fatcat:pncngryytzf6defa6xcrmzbsv4

A universal order parameter for synchrony in networks of limit cycle oscillators

Malte Schröder, Marc Timme, Dirk Witthaut
2017 Chaos  
The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids.  ...  We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network  ...  ACKNOWLEDGMENTS We gratefully acknowledge support from the G€ ottingen Graduate School for Neurosciences and Molecular Biosciences (  ... 
doi:10.1063/1.4995963 pmid:28764398 fatcat:tfrtcrqd7bcl3kfl2ehabufptu

Enhancing synchronization by optimal correlated noise [article]

Sherwood Martineau, Tim Saffold, Timothy Chang, Henrik Ronellenfitsch
2022 arXiv   pre-print
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and  ...  Specifically, using analytical arguments we show that in the case of a two-oscillator model, there exists a sharp transition from a regime where the optimal synchrony-enhancing noise is perfectly anti-correlated  ...  Each matrix entry corresponds to one oscillator in the grid with neighbors as shown. (c) Optimal covariance matrix of a frustrated 7 × 7 periodic square grid of oscillators.  ... 
arXiv:2107.08509v2 fatcat:c5kwiyiyf5hovkwi3lndv3ub74

Synchronization in network geometries with finite spectral dimension

Ana P. Millán, Joaquín J. Torres, Ginestra Bianconi
2019 Physical review. E  
Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model.  ...  We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater  ...  100010434, with code LCF/BQ/ES15/10360004).  ... 
doi:10.1103/physreve.99.022307 fatcat:2ntqjjcjujezxlla45gkgqf3ai

Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model

Gemma Rosell-Tarragó, Albert Díaz-Guilera
2021 Physical review. E  
Despite considering a linear approximation of the model, we show that the obtained tuned parameters for the case of full synchronization enhance frequency synchronization in the nonlinear model as well  ...  In this paper, we draw on an extension of the Kuramoto model, called the Kuramoto-Sakaguchi model, which adds a phase lag parameter to each node.  ...  A previous work proposes a methodology to enhance frequency synchronization for the nonlinear Kuramoto-Sakaguchi model (extension of the Kuramoto model with a node phase lag parameter) [21] .  ... 
doi:10.1103/physreve.103.012216 pmid:33601612 fatcat:j7w6vxztuffudge5muxf4vld3e
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