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 
                 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 
  conference-location = "S{\~a}o Jos{\'e} dos Campos, SP",
      conference-year = "16-20 May",
             language = "en",
        urlaccessdate = "25 jan. 2021"