Synchronization in Complex Oscillator Networks and Smart Grids
arXiv:1208.0045 · doi:10.1073/pnas.1212134110
Abstract
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among them. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here we present a novel, concise, and closed-form condition for synchronization of the fully nonlinear, non-equilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters, or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters, they are statistically correct for almost all networks, and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks such as electric power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex networks scenarios and in smart grid applications.
References in corpus (5)
Cited by in corpus (245)
- The Kuramoto model in complex networks
- Synchronization and Power Sharing for Droop-Controlled Inverters in Islanded Microgrids
- Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
- Chimera States in Mechanical Oscillator Networks
- On the existence and linear approximation of the power flow solution in power distribution networks
- Breaking the Hierarchy: Distributed Control & Economic Optimality in Microgrids
- Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
- Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
- Comparative analysis of existing models for power-grid synchronization
- Lyapunov Functions Family Approach to Transient Stability Assessment
- Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
- Predicting commuter flows in spatial networks using a radiation model based on temporal ranges
- Collective phenomena emerging from the interactions between dynamical processes in multiplex networks
- Data-Driven Control of Complex Networks
- Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
- Chimera states: Effects of different coupling topologies
- Optimal synchronization of complex networks
- Models for the modern power grid
- Impact of network topology on synchrony of oscillatory power grids
- Taming Instabilities in Power Grid Networks by Decentralized Control
- Control of coupled oscillator networks with application to microgrid technologies
- Critical links and nonlocal rerouting in complex supply networks
- Basin stability for chimera states
- Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems
- Implicit energy regularization of neural ordinary-differential-equation control
- The Key Player Problem in Complex Oscillator Networks and Electric Power Grids: Resistance Centralities Identify Local Vulnerabilities
- Enhancing power grid synchronization and stability through time delayed feedback control
- Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices
- Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
- Survivability of Deterministic Dynamical Systems
- A Framework for Robust Assessment of Power Grid Stability and Resiliency
- What adaptive neuronal networks teach us about power grids
- Reconfigurable optical implementation of quantum complex networks
- Cycle flows and multistabilty in oscillatory networks: an overview
- Flocking in complex environments -- attention trade-offs in collective information processing
- Synchronization and Stability for Quantum Kuramoto
- Modeling and Recognition of Smart Grid Faults by a Combined Approach of Dissimilarity Learning and One-Class Classification
- Network susceptibilities: theory and applications
- Escape Routes, Weak Links, and Desynchronization in Fluctuation-driven Networks
- Nonlocal failures in complex supply networks by single link additions
- Linear Stability and the Braess Paradox in Coupled Oscillators Networks and Electric Power Grids
- Non-Euclidean Contraction Theory for Robust Nonlinear Stability
- Functional observability and target state estimation in large-scale networks
- Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise
- The Size of the Sync Basin Revisited
- Cascading Failures as Continuous Phase-Space Transitions
- A universal order parameter for synchrony in networks of limit cycle oscillators
- Delay Regulated Explosive Synchronization in Multiplex Networks
- Multistability of Phase-Locking and Topological Winding Numbers in Locally Coupled Kuramoto Models on Single-Loop Networks
- Deciphering the imprint of topology on nonlinear dynamical network stability
- Low-dimensional behavior of Kuramoto model with inertia in complex networks
- A Theory of Solvability for Lossless Power Flow Equations -- Part I: Fixed-Point Power Flow
- Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
- Three-dimensional chimera patterns in networks of spiking neuron oscillators
- Cascading failures in spatially-embedded random networks
- Optimizing Synchronization Stability of the Kuramoto Model in Complex Networks and Power Grids
- Synchronization transitions in globally coupled rotors in presence of noise and inertia: Exact results
- Control of Synchronization in two-layer power grids
- Synchronization of phase oscillators on complex hypergraphs
- Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control
- Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together
- Emergence of scale-free blackout sizes in power grids
- Effect of assortative mixing in the second-order Kuramoto model
- A Theory of Solvability for Lossless Power Flow Equations -- Part II: Conditions for Radial Networks
- Building blocks of the basin stability of power grids
- Multistability of Phase-Locking in Equal-Frequency Kuramoto Models on Planar Graphs
- Improving power grid transient stability by plug-in electric vehicles
- Curing Braess' Paradox by Secondary Control in Power Grids
- Functional Control of Oscillator Networks
- Rotor-angle versus voltage instability in the third-order model for synchronous generators
- Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators
- Lossy DC Power Flow
- Network experiment demonstrates converse symmetry breaking
- Toward Dynamic Stability Assessment of Power Grid Topologies using Graph Neural Networks
- Synchrony-optimized networks of Kuramoto oscillators with inertia
- Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
- SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
- Multistability and Variations in Basin of Attraction in Power-grid Systems
- Optimal synchronization of directed complex networks
- Noise-Induced Desynchronization and Stochastic Escape from Equilibrium in Complex Networks
- The Kuramoto model on oriented and signed graphs
- Reinforcement Learning for Distributed Transient Frequency Control with Stability and Safety Guarantees
- Asynchronous Networks and Event Driven Dynamics
- Aging transition in systems of oscillators with global distributed-delay coupling
- Reconstructing Network Dynamics of Coupled Discrete Chaotic Units from Data
- Extended finite-size scaling of synchronized coupled oscillators
- Dynamics of Reaction-Diffusion Oscillators in Star Networks
- Synchronization centrality and explosive synchronization in complex networks
- Stochastic thermodynamics in many-particle systems
- Self-consistent Method and Steady States of Second-order Oscillators
- Accelerated Distributed Dual Averaging over Evolving Networks of Growing Connectivity
- A Matrix Valued Kuramoto Model
- Network desynchronization by non-Gaussian fluctuations
- Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs
- Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs
- Secant and Popov-like Conditions in Power Network Stability
- Synchronization in repulsively coupled oscillators
- Topologically Protected Loop Flows in High Voltage AC Power Grids
- Directed Flow of Information in Chimera States
- Prevalence and scalable control of localized networks
- Synchronization of Kuramoto Oscillators in Dense Networks
- Multistability and anomalies in oscillator models of lossy power grids
- Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators
- Quantum-like states on complex synchronized networks
- Mediated Remote Synchronization of Kuramoto-Sakaguchi Oscillators: the Number of Mediators Matters
- Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression
- Global topological control for synchronized dynamics on networks
- Observer-Based Distributed Leader-Follower Tracking Control: A New Perspective and Results
- Dynamical equivalence between Kuramoto models with first- and higher-order coupling
- Rare slips in fluctuating synchronized oscillator networks
- Emerging chimera states under non-identical counter-rotating oscillators
- Enhancing network synchronization by phase modulation
- Multistability in lossy power grids and oscillator networks
- Multi-Agent Algorithms for Collective Behavior: A structural and application-focused atlas
- Revealing dynamics, communities and criticality from data
- Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators
- Stability of rotatory solitary states in Kuramoto networks with inertia
- Multifaceted dynamics of Janus oscillator networks
- On structural and dynamical factors determining the integrated basin instability of power-grid nodes
- When is sync globally stable in sparse networks of identical Kuramoto oscillators?
- Finite Size Scaling in the Kuramoto Model
- Active hydrodynamics of synchronization and ordering in moving oscillators
- Delayed feedback control of synchronization in weakly coupled oscillator networks
- Superconductor--Insulator Transition in a non-Fermi Liquid
- Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form
- Curing critical links in oscillator networks as power grid models
- Collective frequency variation in network synchronization and reverse PageRank
- Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
- Stability of Remote Synchronization in Star Networks of Kuramoto Oscillators
- Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays
- Erosion of synchronization: Coupling heterogeneity and network structure
- Non-linear network dynamics with consensus-dissensus bifurcation
- Periodic orbits in the Ott-Antonsen manifold
- Comparing the Locking Threshold for Rings and Chains of Oscillators
- Analysis of risk propagation using the world trade network
- On controlling networks of limit-cycle oscillators
- Stationary patterns in star networks of bistable units: Theory and application to chemical reactions
- Stochastic thermodynamics of inertial-like Stuart-Landau dimer
- Optimizing Pinning Control of Complex Dynamical Networks Based on Spectral Properties of Grounded Laplacian Matrices
- Unified Virtual Oscillator Control for Grid-Forming and Grid-Following Converters
- Synchronization conditions in the Kuramoto model and their relationship to seminorms
- Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses and voltage dynamics
- Structural Emergency Control Paradigm
- Leader-Follower Synchronization of a Network of Boundary-Controlled Parabolic Equations With In-Domain Coupling
- Periodic Coupling inhibits Second-order Consensus on Networks
- Solvability of Power Flow Equations Through Existence and Uniqueness of Complex Fixed Point
- Analysis of the Dynamics and Topology Dependencies of Small Perturbations in Electric Transmission Grids
- Critical parameters of the synchronisation's stability for coupled maps in regular graphs
- Decreased resilience in power grids under dynamically induced vulnerabilities
- Delay master stability of inertial oscillator networks
- Geometric unfolding of synchronization dynamics on networks
- Accelerating Optimal Experimental Design for Robust Synchronization of Uncertain Kuramoto Oscillator Model Using Machine Learning
- Dynamics of fully coupled rotators with unimodal and bimodal frequency distribution
- Inverse Stability Problem and Applications to Renewables Integration
- Partial Phase Cohesiveness in Networks of Kuramoto Oscillator Networks
- Fluctuation Response Patterns of Network Dynamics -- an Introduction
- Synchronization of Identical Boundary-Actuated Semilinear Infinite-Dimensional Systems
- Reinforcement Learning Optimizes Power Dispatch in Decentralized Power Grid
- Dual communities in spatial networks
- System Size Identification from Sinusoidal Probing in Diffusive Complex Networks
- How do higher-order interactions shape the energy landscape?
- Stabilizing Stuart-Landau oscillators via time-varying networks
- A Phase Model with Large Time Delayed Coupling
- Strong coupling yields abrupt synchronization transitions in coupled oscillators
- Modeling and optimizing a distributed power network : A complex system approach of the prosumer management in the smart grid
- Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies
- Synchronized states of power grids and oscillator networks by convex optimization
- Toward Distributed Stability Analytics for Power Systems with Heterogeneous Bus Dynamics
- How modular structure determines operational resilience of power grids
- Lyapunov Approach to Consensus Problems
- Influence of cumulative damage on synchronization of Kuramoto oscillators on networks
- Optimal location of reinforced inertia to stabilize power grids
- Hysteresis, Phase Transitions and Dangerous Transients in Electrical Power Distribution Systems
- Basin sizes depend on stable eigenvalues in the Kuramoto model
- Transient Stability Analysis of Power Grids with Admissible and Maximal Robust Positively Invariant Sets
- Analytical solution to swing equations in power grids
- Large and small fluctuations in oscillator networks from heterogeneous and correlated noise
- Data-driven Selection of Coarse-Grained Models of Coupled Oscillators
- Analytic solution to swing equations in power grids with ZIP Load Models
- Stability of entrainment of a continuum of coupled oscillators
- Power Network Uniqueness and Synchronization Stability from a Higher-order Structure Perspective
- Locating fast-varying line disturbances with the frequency mismatch
- Broadcasting solutions on networked systems of phase oscillators
- Reconstructing Network Structures from Partial Measurements
- On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization
- Global Practical Node and Edge Synchronization in Kuramoto Networks: A Submodular Optimization Framework
- Phase and amplitude synchronisation in power-grid frequency fluctuations in the Nordic Grid
- On the region of attraction of phase-locked states for swing equations on connected graphs with inhomogeneous dampings
- Switching Synchronization in One-Dimensional Memristive Networks
- Topological phase locking in stochastic oscillators
- Explainable Machine Learning Control -- robust control and stability analysis
- Synchronization failure caused by interplay between noise and network heterogeneity
- A Double-Layered Framework for Distributed Coordination in Solving Linear Equations
- Grass-roots optimization of coupled oscillator networks
- A Suboptimality Approach to Distributed H2 Control by Dynamic Output Feedback
- Distributed Transient Frequency Control for Power Networks with Stability and Performance Guarantees
- Control of dynamical systems with neural networks
- Counting equilibria of the Kuramoto model using birationally invariant intersection index
- Reentrant transition in coupled noisy oscillators
- Optimal flock formation induced by agent heterogeneity
- Lyapunov-Regularized Reinforcement Learning for Power System Transient Stability
- Towards Distributed Stability Analytics of Dynamic Power Systems: A Phasor-Circuit Theory Perspective
- Scalable distributed and decentralized controller synthesis for interconnected linear discrete-time systems
- Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique
- Nonlinear Modal Decoupling of Multi-Oscillator Systems with Applications to Power Systems
- Resilience of the slow component in timescale separated synchronized oscillators
- Notes on Resonant and Synchronized States in Complex Networks
- Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information
- On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach
- Predicting the Oscillatory Regimes of Global Synchrony Induced by Secondary Clusters
- Controlling Complex Systems
- Global network control from local information
- Order parameter allows classification of planar graphs based on balanced fixed points in the Kuramoto model
- Grand Challenges in Resilience: Autonomous System Resilience through Design and Runtime Measures
- Distributed Neighbor Selection in Multi-agent Networks
- Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression
- Synchronization of Heterogeneous Kuramoto Oscillators with Arbitrary Topology
- Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach
- Modelling power grids as pseudo adaptive networks
- On the Critical Coupling of the Finite Kuramoto Model on Dense Networks
- Explosive Synchronization in Multilayer Dynamically Dissimilar Networks
- Unstable delayed feedback control to change sign of coupling strength for weakly coupled limit cycle oscillators
- Compositional Transient Stability Analysis of Multi-Machine Power Networks
- High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators
- Disorder-promoted stability
- Mean-field approach for frequency synchronization in complex networks of two oscillator types
- Equivalent Conditions for the Synchronization of Identical Linear Systems over Arbitrary Interconnections
- A Suboptimality Approach to Distributed Optimal Control
- Power Network Regulation Benchmark for Switched-Mode Optimal Control
- Sign Stability via Root Locus Analysis
- Optimal Graph Laplacian
- Greedy optimization for growing spatially embedded oscillatory networks
- The effect of HVDC lines in power-grids via Kuramoto modelling
- Stochastic Uncertainty Propagation in Power System Dynamics using Measure-valued Proximal Recursions
- Basins with tentacles
- A Graph Decomposition motivated by the Geometry of Randomized Rounding
- Subcritical Bifurcations in the Kuramoto Model with Positive Coupling
- Computing Economic-Optimal and Stable Equilibria for Droop-Controlled Microgrids
- Oscillatory states, standing waves, and additional synchronized clusters in networks of second-order oscillators: uncovering the role of inertia
- Optimal frequency regulation in nonlinear power networks including turbine-governor dynamics
- A Dynamical Approach to Efficient Eigenvalue Estimation in General Multiagent Networks
- Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators
- Double-layered distributed transient frequency control with regional coordination for power networks
- Towards Electronics-based Emergency Control in Power Grids with High Renewable Penetration
- Spectral Gradient Iterative Edge Attack for Synchronization Suppression in Complex Networks