Strongly coupled overdamped pendulums

Luca, R. De

doi:10.1590/s1806-11172008000400004

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…The assumption that each generator is strongly overdamped is captured by the smallness of the perturbation parameter = M max /D min . This choice of the perturbation parameter and the subsequent singular perturbation analysis (in Section IV) is similar to the analysis of Josephson arrays [26], coupled overdamped mechanical pendula [47], flocking models [48], and also classic transient stability analysis [4,Theorem 5.2], [36]. In the linear case, this analysis resembles the well-known overdamped harmonic oscillator, which features one slow and one fast eigenvalue.…”

Section: Discussion Of the Perturbation Assumptionmentioning

confidence: 92%

Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

Dörfler

Bullo

2010

Proceedings of the 2010 American Control Conference

166

258

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Motivated by recent interest for multi-agent systems and smart power 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. Here, non-uniform Kuramoto oscillators are characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. Extending methods from transient stability, 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 standard Kuramoto model. 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 system parameters and initial conditions.

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Section: Discussion Of the Perturbation Assumptionmentioning

confidence: 92%

Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

Dörfler

Bullo

2010

Proceedings of the 2010 American Control Conference

166

258

View full text Add to dashboard Cite

show abstract

“…The assumption that each generator is strongly overdamped is captured by the smallness of the perturbation parameter = (M max )/(πf 0 D min ). This choice of the perturbation parameter and the subsequent singular perturbation analysis is similar to the analysis of Josephson arrays [16], coupled overdamped mechanical pendula [32], and also classic transient stability analysis [3, Theorem 5.2], [27].…”

Section: Discussion Of the Perturbation Assumptionmentioning

confidence: 99%

Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

Dörfler¹,

Bullo²

2012

SIAM J. Control Optim.

567

403

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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.

show abstract

Strongly coupled overdamped pendulums

Cited by 2 publications

References 3 publications

Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators

Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

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