Resiliência de redes de Kuramoto: uma aplicação a sistemas elétricos de potência - Ercílio Inácio Moreira (2019)
Dynamic networks have been the subject of great interest in the scientific community. This is justified by the countless number of physical systems that can be represented by these models. Most related studies focus on the stability and resilience of such systems. The stability of a dynamical system is an important problem in nonlinear science, especially when considering interconnected systems. In this work, a resilience analysis was performed using Kuramoto models, motivated by their ability to represent power grids. The investigations follows along two lines. First, two examples were studied: a test system and a large scale model of the Brazilian power grid. The goal was to determine the effect of the choice of representation (Effective Network, Structure-Preserving or Synchronous Motor) on the resilience measure of these systems. By using a concept called basin stability, which quantifies non-local stability and gives the likelihood that a perturbed system returns to the stable state, it was found that the approaches are not fully equivalent with respect to generator classification. In previous studies, basin stability was used but limited to homogeneous power grids. Then, in the second investigation, a similar approach was adopted, extending it to heterogeneous power grids. From a sample of randomly generated power grid topologies, we studied how the basin stability of an electric power system is affected by two main factors: (i) the heterogeneity of the power grid; and (ii) the tripping time, which defines the time for a protection device to isolate the perturbed generator from the rest of the network. The numerical simulations showed that while for a completely homogeneous network, the shorter the tripping time, the better the basin stability, for a heterogeneous one, the best choice of tripping time may not be the shortest. Contrariwise, in a highly heterogeneous network, the best choice may be to not isolate the perturbed generator from the network at all. Finally, this methodology was also applied to the analysis of a model of the Brazilian electric power grid.