On synchronization in power-grids modelled as networks of second-order Kuramoto oscillators.

This work concerns analytical results on the role of coupling strength in the phenomenon of onset of complete frequency locking in power-grids modelled as a network of second-order Kuramoto oscillators. Those results allow estimation of the coupling strength for the onset of complete frequency locking and to assess the features of network and oscillators that favor synchronization. The analytical results are evaluated using an order parameter defined as the normalized sum of absolute values of phase deviations of the oscillators over time. The investigation of the frequency synchronization within the subsets of the parameter space involved in the synchronization problem is also carried out. It is shown that the analytical results are in good agreement with those observed in the numerical simulations. In order to illustrate the methodology, a case study is presented, involving the Brazilian high-voltage transmission system under a load peak condition to study the effect of load on the syncronizability of the grid. The results show that both the load and the centralized generation might have concurred to the 2014 blackout.