Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators
Florian Dörfler,Francesco Bullo +1 more
TLDR
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.Abstract:
Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with nontrivial 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 nonuniform Kuramoto model. Here, nonuniform Kuramoto oscillators are characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to necessary and sufficient tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive ...read more
Citations
More filters
Journal ArticleDOI
Synchronization in complex networks of phase oscillators: A survey
Florian Dörfler,Francesco Bullo +1 more
TL;DR: This survey reviews the vast literature on the theory and the applications of complex oscillator networks, focusing on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology.
Journal ArticleDOI
Synchronization in complex oscillator networks and smart grids
TL;DR: This work presents a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network of a strongly coupled and sufficiently homogeneous network.
Journal ArticleDOI
Kron Reduction of Graphs With Applications to Electrical Networks
Florian Dörfler,Francesco Bullo +1 more
TL;DR: This paper provides a comprehensive and detailed graph-theoretic analysis of Kron reduction encompassing topological, algebraic, spectral, resistive, and sensitivity analyses and leads to novel insights both on the mathematical and the physical side.
Journal ArticleDOI
The Kuramoto model in complex networks
Francisco A. Rodrigues,Thomas K. Dm. Peron,Thomas K. Dm. Peron,Peng Ji,Peng Ji,Jürgen Kurths +5 more
TL;DR: In this article, B. Sonnenschein, E.R. dos Santos, P.J. Schultz, C.A. Ha, M.K. Choi and C.P.
Journal ArticleDOI
Spontaneous synchrony in power-grid networks
TL;DR: In this article, a condition for the stability of the synchronous state enables identification of network parameters that enhance spontaneous synchronization, highlighting the possibility of smart grids that operate optimally in real-world systems.
References
More filters
Book
Power System Stability and Control
TL;DR: In this article, the authors present a model for the power system stability problem in modern power systems based on Synchronous Machine Theory and Modelling, and a model representation of the synchronous machine representation in stability studies.
Journal ArticleDOI
Consensus and Cooperation in Networked Multi-Agent Systems
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Book
Parallel and Distributed Computation: Numerical Methods
TL;DR: This work discusses parallel and distributed architectures, complexity measures, and communication and synchronization issues, and it presents both Jacobi and Gauss-Seidel iterations, which serve as algorithms of reference for many of the computational approaches addressed later.
Book
Matrix Analysis and Applied Linear Algebra
TL;DR: The author presents Perron-Frobenius theory of nonnegative matrices Index, a theory of matrices that combines linear equations, vector spaces, and matrix algebra with insights into eigenvalues and Eigenvectors.