### Abstract

Synchronization between spatially distributed nodes of a power-grid is a crucial requirement for its proper operation. Using a Kuramoto-like network as a realistic physical model for the distribution of electrical power in a power-grid, we obtain coupling strengths and topological characteristics that favor the synchronous state of those technological networks. Power-grids are highly heterogeneous. They are composed of different classes of nodes and each node behaves differently. We show in this work that if a power-grid is extensive and nodes are highly connected, the coupling strength that leads to synchronization depends mainly on the eigenvalues of the Laplacian matrix, as it happens in homogeneous networks composed of equal nodes. On the other hand, if a power-grid is sparsely connected, the coupling strength that leads to synchronization is also strongly related to the correlation coefficient of the network, which means that a high number of connections between similar nodes (two power plants or two consumer centers) disfavor the synchronizability of the power-grid. We apply our results to the Brazilian power-grid system. (C) 2012 Elsevier B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 1035-1046 |

Number of pages | 12 |

Journal | Communications in Nonlinear Science & Numerical Simulation |

Volume | 18 |

Issue number | 4 |

Early online date | 12 Sep 2012 |

DOIs | |

Publication status | Published - Apr 2013 |

### Keywords

- model
- power-grid
- complex network
- synchronization
- nonidentical Kuramoto oscillators
- networks

### Cite this

**Natural synchronization in power-grids with anti-correlated units.** / Carareto, Rodrigo; Baptista, Murilo S.; Grebogi, Celso.

Research output: Contribution to journal › Article

*Communications in Nonlinear Science & Numerical Simulation*, vol. 18, no. 4, pp. 1035-1046. https://doi.org/10.1016/j.cnsns.2012.08.030

}

TY - JOUR

T1 - Natural synchronization in power-grids with anti-correlated units

AU - Carareto, Rodrigo

AU - Baptista, Murilo S.

AU - Grebogi, Celso

PY - 2013/4

Y1 - 2013/4

N2 - Synchronization between spatially distributed nodes of a power-grid is a crucial requirement for its proper operation. Using a Kuramoto-like network as a realistic physical model for the distribution of electrical power in a power-grid, we obtain coupling strengths and topological characteristics that favor the synchronous state of those technological networks. Power-grids are highly heterogeneous. They are composed of different classes of nodes and each node behaves differently. We show in this work that if a power-grid is extensive and nodes are highly connected, the coupling strength that leads to synchronization depends mainly on the eigenvalues of the Laplacian matrix, as it happens in homogeneous networks composed of equal nodes. On the other hand, if a power-grid is sparsely connected, the coupling strength that leads to synchronization is also strongly related to the correlation coefficient of the network, which means that a high number of connections between similar nodes (two power plants or two consumer centers) disfavor the synchronizability of the power-grid. We apply our results to the Brazilian power-grid system. (C) 2012 Elsevier B.V. All rights reserved.

AB - Synchronization between spatially distributed nodes of a power-grid is a crucial requirement for its proper operation. Using a Kuramoto-like network as a realistic physical model for the distribution of electrical power in a power-grid, we obtain coupling strengths and topological characteristics that favor the synchronous state of those technological networks. Power-grids are highly heterogeneous. They are composed of different classes of nodes and each node behaves differently. We show in this work that if a power-grid is extensive and nodes are highly connected, the coupling strength that leads to synchronization depends mainly on the eigenvalues of the Laplacian matrix, as it happens in homogeneous networks composed of equal nodes. On the other hand, if a power-grid is sparsely connected, the coupling strength that leads to synchronization is also strongly related to the correlation coefficient of the network, which means that a high number of connections between similar nodes (two power plants or two consumer centers) disfavor the synchronizability of the power-grid. We apply our results to the Brazilian power-grid system. (C) 2012 Elsevier B.V. All rights reserved.

KW - model

KW - power-grid

KW - complex network

KW - synchronization

KW - nonidentical Kuramoto oscillators

KW - networks

U2 - 10.1016/j.cnsns.2012.08.030

DO - 10.1016/j.cnsns.2012.08.030

M3 - Article

VL - 18

SP - 1035

EP - 1046

JO - Communications in Nonlinear Science & Numerical Simulation

JF - Communications in Nonlinear Science & Numerical Simulation

SN - 1007-5704

IS - 4

ER -