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Stability of a Distributed Generation Network Using the Kuramoto Models [chapter]

Vincenzo Fioriti, Silvia Ruzzante, Elisa Castorini, Elena Marchei, Vittorio Rosato
2009 Lecture Notes in Computer Science  
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

F Dorfler, F Bullo
2010 Proceedings of the 2010 American Control Conference  
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

Chengwei Wang, Nicolás Rubido, Celso Grebogi, Murilo S. Baptista
2015 Physical Review E  
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]

Pratik K. Bajaria, Sushama R. Wagh, Navdeep M. Singh
2019 arXiv   pre-print
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]

Chengwei Wang, Nicolas Rubido, Celso Grebogi, Murilo S. Baptista
2015 arXiv   pre-print
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]

Eiichi Sasaki, Masayuki Ohzeki, Yoshito Ohta
2015 arXiv   pre-print
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]

Géza Ódor, Bálint Hartmann
2020 arXiv   pre-print
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

Florian Dörfler, Francesco Bullo
2012 SIAM Journal of Control and Optimization  
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]

Volker Mehrmann, Riccardo Morandin, Simona Olmi, Eckehard Schöll
2017 arXiv   pre-print
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

Francisco A. Rodrigues, Thomas K. DM. Peron, Peng Ji, Jürgen Kurths
2016 Physics reports  
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]

Ingo Scholtes, Jean Botev, Markus Esch, Peter Sturm
2009 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
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

Christopher J. Honey, Olaf Sporns
2008 Human Brain Mapping  
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

Liudmila Tumash, Simona Olmi, Eckehard Schöll
2019 Chaos  
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]

Pratik K. Bajaria
2021 arXiv   pre-print
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

Malte Schröder, Marc Timme, Dirk Witthaut
2017 Chaos  
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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