Phase Model with Feedback Control for Power Grids

A phase model with feedback control is studied as a dynamical model of power grids. As an example, we study a model network corresponding to the power grid in the Kyushu region. The standard frequency is maintained by the mutual synchronization and the feedback control. Electric failures are induced by an overload. We propose a local feedback method in which the strength of feedback control is proportional to the magnitude of generators. We find that the electric failures do not occur until the utilization ratio is close to 1 under this feedback control. We also find that the temporal response for the time-varying input power is suppressed under this feedback control. We explain the mechanisms using the corresponding global feedback method.