@InProceedings{GrzybowskiMacaYone:2016:FrSyPo,
author = "Grzybowski, Jos{\'e} Mario Vicensi and Macau, Elbert Einstein
Nehrer and Yoneyama, Takashi",
affiliation = "{Universidade Federal da Fronteira Sul (UFFS)} and {Instituto
Nacional de Pesquisas Espaciais (INPE)} and {Instituto
Tecnol{\'o}gico de Aeron{\'a}utica (ITA)}",
title = "Frequency synchronization in power-grid models of Kuramoto-like
oscillators",
year = "2016",
organization = "International Conference on Nonlinear Science and Complexity, 6.",
keywords = "complex networks, bifurcation analysis and applications,
synchronization in nonlinear systems.",
abstract = ": Recent studies have shown that stability and robustness in power
grids can be studied by means of conceptual models that use
oscillator models derived from the swing equation for electrical
generators and machines connected through network structures that
reproduce dynamical phenomena arising in real power-grids. A great
deal of interest resides in the comprehension of the mechanisms
leading to transitions between synchronous and incoherent states,
the latter being characterized by the emergence of undesired
situations in real power-grids, such as load shed and generation
trip. In this sense, the so-called Kuramoto-like oscillator with
bimodal distribution was studied on the basis of analytical and
numerical methods that considered network topologies corresponding
to those of real high-voltage transmission systems, from which
dynamical parameters for the persistence of synchronization in the
face of perturbations and nontrivial relations between dynamical
and topological parameters were provided. A number of other
studies also use Kuramoto-like models to study synchronization and
stability issues in power-grids. The key point here is that these
models are argued to capture the essential dynamical and
structural properties allowing the identification of fundamental
mechanisms and properties that matter for stability and robustness
purposes, which can be matched to those emerging in real
power-grids. In the context of power-grid models based on
Kuramoto-like oscillators, synchronization is defined as the
matching of the angular velocities of the oscillators, such that
synchronized oscillators evolve most likely out of phase but with
equal angular velocities over time. As such, coherence is usually
measured by means of an order parameter in the interval [0,1],
which is a function of synchronization quality and persistence
over time. In this paper, we present analytical results on the
critical coupling for synchronization in networks of Kuramoto-like
oscillators. On the basis of the maximization of the phase
deviation angle over the coupled oscillators, we seek for the
minimum coupling that can provide synchrony. The analytical
results are evaluated against an order parameter defined as the
normalized sum of absolute values of phase deviations of the
oscillators over time. The investigation of frequency
synchronization over subsets of the parameter space of the
synchronization problem for power-grid models of Kuramoto-like
oscillators is carried out, from which we conclude that the
analytical results are in good agreement with those observed in
the numerical simulations. As a final remark, we note that the
proposed approach allowed the study of synchronization in
power-grid models in a consistent and meaningful way and it may
help enhance the comprehension of power-grid dynamics in upcoming
studies.",
conference-location = "S{\~a}o Jos{\'e} dos Campos, SP",
conference-year = "16-20 May",
language = "en",
urlaccessdate = "28 abr. 2024"
}