Stability of a Distributed Generation Network Using the Kuramoto Models

Fioriti, Vincenzo; Ruzzante, Silvia; Castorini, Elisa; Marchei, Elena; Rosato, Vittorio

doi:10.1007/978-3-642-03552-4_2

Cited by 15 publications

(13 citation statements)

References 7 publications

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“…Notice that, with the exception of the inertial terms M iθi and the possibly non-unit coefficients D i , the power network dynamics (8)-(10) are a perfect electrical analog of the coupled oscillator model (1) with ω i ∈ {−P l,i , P m,i , P d,i }. Thus, it is not surprising that scientists from different disciplines recently advocated coupled oscillator approaches to analyze synchronization in power networks (Tanaka et al, 1997;Subbarao et al, 2001;Hill and Chen, 2006;Filatrella et al, 2008;Buzna et al, 2009;Fioriti et al, 2009;Simpson-Porco et al, 2013;Dörfler and Bullo, 2012b;Rohden et al, 2012;Dörfler et al, 2013;Mangesius et al, 2012;Motter et al, 2013;Ainsworth and Grijalva, 2013). The theoretical tools presented in this article establish how frequency synchronization in power networks depend on the nodal parameters (P l,i , P m,i , P d,i ) as well as the interconnecting electrical network with weights a ij .…”

Section: Electric Power Network With Synchronous Generators and Dc/amentioning

confidence: 87%

Synchronization in complex networks of phase oscillators: A survey

2014

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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Section: Electric Power Network With Synchronous Generators and Dc/amentioning

confidence: 87%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…Indeed, the similarity between the Kuramoto model and the power network models used in transient stability analysis is striking. Even though power networks have often been referred to as coupled-oscillators systems, the similarity to a second-order Kuramoto-type model has been mentioned only recently in the power systems community in simulation studies for simplified models [25], [26], [27]. In the coupled-oscillators literature, second-order Kuramoto models have often been analyzed [20], but we know of only one article mentioning power networks [28].…”

Section: Introductionmentioning

confidence: 99%

“…Via a singular perturbation analysis, we show that the transient stability analysis for the classic swing equations with overdamped generators reduces, on a long time-scale, to the problem of synchronizing non-uniform Kuramoto oscillators with multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. This reduction to a non-uniform Kuramoto model is arguably the missing link connecting transient stability analysis and networked control, a link that was hinted at in [10], [12], [25], [26], [27], [28].…”

Section: Introductionmentioning

confidence: 99%

Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

Dörfler¹,

Bullo²

2012

SIAM J. Control Optim.

603

412

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Motivated by recent interest for multi-agent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto model characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. By extending methods from synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the classic Kuramoto model. 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 network parameters and initial conditions.

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“…(i) We set normally-distributed {ω i } for each node. It is because that previous studies on real networks such as power grids and brain networks have assumed that the natural frequencies of belonging oscillators are symmetrically fluctuating around the averaged frequency [4,22,29].…”

Section: B Estimation Of the Mean Synchronization Costmentioning

confidence: 99%

“…(i) First, we define the synchronization cost, S ij , due to phase difference between frequencysynchronized phase oscillators i and j in the Kuramoto model. We adopt the Kuramoto model because the model has been used as approximation of various systems including power grids [2, 21,22] and large-scale brain networks [23,24].…”

Section: Introductionmentioning

confidence: 99%

Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators

Watanabe

2013

Physica A: Statistical Mechanics and its Applications

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Functions of some networks, such as power grids and large-scale brain networks, rely on not only frequency synchronization, but also phase synchronization. Nevertheless, even after the oscillators reach to frequency-synchronized status, phase difference among oscillators often shows non-zero constant values. Such phase difference potentially results in inefficient transfer of power or information among oscillators, and avoid proper and efficient functioning of the network. In the present study, we newly define synchronization cost by the phase difference among the frequency-synchronized oscillators, and investigate the optimal network structure with the minimum synchronization cost through rewiringbased optimization. By using the Kuramoto model, we demonstrate that the cost is minimized in a network topology with rich-club organization, which comprises the densely-connected center nodes and peripheral nodes connecting with the center module. We also show that the network topology is characterized by its bimodal degree distribution, which is quantified by Wolfson's polarization index.Furthermore, we provide analytical interpretation on why the rich-club network topology is related to the small amount of synchronization cost. * takawatanabe-tky@umin.ac.jp

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Stability of a Distributed Generation Network Using the Kuramoto Models

Cited by 15 publications

References 7 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

Rich-club network topology to minimize synchronization cost due to phase difference among frequency-synchronized oscillators

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