  We study the synchronization and stability of power grids within the Kuramoto
phase oscillator model with inertia with a bimodal frequency distribution
representing the generators and the loads. We identify critical nodes through
solitary frequency deviations and Lyapunov vectors corresponding to unstable
Lyapunov exponents. To cure dangerous deviations from synchronization we
propose time-delayed feedback control, which is an efficient control concept in
nonlinear dynamic systems. Different control strategies are tested and compared
with respect to the minimum number of controlled nodes required to achieve
synchronization and Lyapunov stability. As a proof of principle, this
fast-acting control method is demonstrated using a model of the German power
transmission grid.
