  In the present study we consider a random network of Kuramoto oscillators
with inertia in order to mimic and investigate the dynamics emerging in
high-voltage power grids. The corresponding natural frequencies are assumed to
be bimodally Gaussian distributed, thus modeling the distribution of both power
generators and consumers: for the stable operation of power systems these two
quantities must be in balance. Since synchronization has to be ensured for a
perfectly working power grid, we investigate the stability of the desired
synchronized state. We solve this problem numerically for a population of N
rotators regardless of the level of quenched disorder present in the topology.
  We obtain stable and unstable solutions for different initial phase
conditions, and we propose how to control unstable solutions, for sufficiently
large coupling strength, such that they are stabilized for any initial phase.
Finally, we examine a random Erd\"os-Renyi network under the impact of white
Gaussian noise, which is an essential ingredient for power grids in view of
increasing renewable energy sources.
