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Stability of a Distributed Generation Network Using the Kuramoto Models
[chapter]
2009
Lecture Notes in Computer Science
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to study this problem we analyze the phase stability of a small size distributed generation grid (the network), by means of a modified Kuramoto Model. • In our model, contrarily to the standard Kuramoto ...
In the near future, a major source of concern for the continuity of service of the Power System will be the Distributed Generation (DG). ...
to study this problem we analyze the phase stability of a small size distributed generation grid (the network), by means of a modified Kuramoto Model. • In our model, contrarily to the standard Kuramoto ...
doi:10.1007/978-3-642-03552-4_2
fatcat:psjhhgfhzvcqhmv5nvewnsgsvy
Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators
2010
Proceedings of the 2010 American Control Conference
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phase differences suffice for the synchronization of non-uniform Kuramoto oscillators as well as the transient stability of the power network model. ...
by P has a globally reachable node. the synchronization and transient stability problem for a network-reduction model of a power system. • Provide the conditions depending on network parameters and initial ...
doi:10.1109/acc.2010.5530690
fatcat:mjrjeplyw5babogjlz3jqyouui
Approximate solution for frequency synchronization in a finite-size Kuramoto model
2015
Physical Review E
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Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behavior, such as frequency synchronization (FS) as a paradigm, in real-world networks ...
Furthermore, we present a criterion to determine the stability of the FS solution. ...
In general, the finite-size Kuramoto model reaches FS if the coupling strength is larger than a critical value, K C [21] . ...
doi:10.1103/physreve.92.062808
pmid:26764745
fatcat:h2446p4tszhmthsianybtnlzo4
Interarea Oscillations Chimera in Power Systems
[article]
2019
arXiv
pre-print
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This model facilitates better understanding of the complex dynamics of a power network. ...
A standard four generator power system with all-to-all connectivity is considered and results obtained from the proposed model are verified. ...
Acknowledgements The authors would like to thank Prof. S. D. Varwandkar for his valued discussions and feedbacks towards the outcome of this work. ...
arXiv:1911.10338v1
fatcat:nouk46wgzvbw5aapmh3qc254py
Approximate solution for frequency synchronisation in a finite-size Kuramoto model
[article]
2015
arXiv
pre-print
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Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks ...
Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, without imposing any restriction on the distribution of the natural ...
Figure 3 3 shows the effectiveness of our condition to gauge the stability for the FS solution of the finite-size Kuramoto model, considering different Ω distributions and different number of oscillators ...
arXiv:1509.04244v1
fatcat:ynfsei25ofcirmerdujj2nl4r4
Hysteretic transition of coarse-grained power grid model on small-world network
[article]
2015
arXiv
pre-print
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We study synchronous phenomena of a coarse-grained power grid model, the swing equation, on small-world networks. ...
On the other hand, a trigger of instantaneous power failure, which is described by the hysteretic transition, might disappear on an appropriate small-world network. ...
Acknowledgments This research has been received financial supports from the project of Japan Science and Technology agency, JST-CREST. J. Phys. Soc. Jpn.
FULL PAPERS ...
arXiv:1501.06959v1
fatcat:4scyyfwb6jdlbaedor3o5wog5a
Power-law distributions of dynamic cascade failures in power-grid models
[article]
2020
arXiv
pre-print
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Here we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. ...
We have focused on the exploration of network heterogeneity effects, starting from homogeneous 2D lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid ...
Acknowledgments: We thank Benjamin Schäfer, Jeffrey Kelling and Benjamin Carreras for the useful comments.
Conflicts of Interest: The authors declare no conflict of interest. ...
arXiv:2005.03458v3
fatcat:sp37f5zmfraefhp32mgciuszqy
Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators
2012
SIAM Journal of Control and Optimization
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Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. ...
By combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying ...
Indeed, the similarity between the Kuramoto model and the power network models used in transient stability analysis is striking. ...
doi:10.1137/110851584
fatcat:zcdz7d6mxrdhbhneoig2opsbzm
Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form
[article]
2017
arXiv
pre-print
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A frequently used qualitative approach relies on simplified nonlinear network models like the Kuramoto model. ...
We present a new energy-based formulation of the Kuramoto model as port-Hamiltonian system of differential-algebraic equations. ...
At the lowest levels of such a model hierarchy simplified nonlinear network models like the Kuramoto model are placed which are often used for a qualitative analysis of the network behavior [10, 16] . ...
arXiv:1712.03160v1
fatcat:qpyin5k4sjfurmretrjct32tqi
The Kuramoto model in complex networks
2016
Physics reports
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We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. ...
Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. ...
at the tricritical point of a
standard Kuramoto model using the Chapman-Enskog method [311]. ...
doi:10.1016/j.physrep.2015.10.008
fatcat:dgrjabfngrb7viafuinublmjci
Epidemic Self-synchronization in Complex Networks
[chapter]
2009
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
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The algorithm requires a periodic coupling of nodes to a single random one-hop-neighbor. The strength of the nodes' couplings is given as a function of the degrees of both coupling partners. ...
From simulations on networks under the effect of churn, we draw the conclusion that special coupling functions can be used to enhance synchronization resilience in power-law Peer-to-Peer topologies. ...
First of all, their decentralized character prohibits the usage of models that involve an all-to-all coupling as e.g. used in the original Kuramoto model. ...
doi:10.1007/978-3-642-02469-6_56
fatcat:744f6wqelbazpevvdsuzaclp6m
Dynamical consequences of lesions in cortical networks
2008
Human Brain Mapping
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In the second model, node dynamics are governed by a more realistic neural mass model, and we assess long-run inter-regional interactions using a measure of directed information flow. ...
To investigate how network embedding influences a region's functional role, and the consequences of its being damaged, we implement two models of oscillatory cortical interactions, both of which inherit ...
ACKNOWLEDGMENTS OS and CH were supported by the J.S. McDonnell Foundation. ...
doi:10.1002/hbm.20579
pmid:18438885
fatcat:wqn7x5ya3ffl7kdzry6zudp4pq
Stability and control of power grids with diluted network topology
2019
Chaos
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The corresponding natural frequencies are assumed to be bimodally Gaussian distributed, thus modeling the distribution of both power generators and consumers, which must be in balance. ...
We consider sparse random networks of Kuramoto phase oscillators with inertia in order to mimic and investigate the dynamics emerging in high-voltage power grids. ...
Such a power separation implies using a bimodal distribution of the power (corresponding to the dimensionless natural frequencies in the dimensionless Kuramoto model) within the network. ...
doi:10.1063/1.5111686
pmid:31893638
fatcat:2ezyg7sfcbbgvb33t3zrp6y6qy
Synchronization Strategies for Multi-agent Networked Control Systems
[article]
2021
arXiv
pre-print
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In this thesis, a diverse set of applications from power flow point of view are taken into consideration and modelled/analyzed using synchronization as the central theme. ...
The concepts of synchronization and network control systems have been used extensively in the near past to map, analyze and solve defined set of objectives. ...
Kuramoto-type models have been widely used to study the dynamics of a power system network through swing equations [105] . ...
arXiv:2107.01605v1
fatcat:wndaxvuzovb2jcpjtqv2otznuq
A universal order parameter for synchrony in networks of limit cycle oscillators
2017
Chaos
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We rigorously proof that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. ...
Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. ...
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
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