  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.
