  Conventional generators in power grids are steadily substituted with new
renewable sources of electric power. The latter are connected to the grid via
inverters and as such have little, if any rotational inertia. The resulting
reduction of total inertia raises important issues of power grid stability,
especially over short-time scales. We have constructed a model of the
synchronous grid of continental Europe with which we numerically investigate
frequency deviations as well as rates of change of frequency (RoCoF) following
abrupt power losses. The magnitude of RoCoF's and frequency deviations strongly
depend on the fault location, and we find the largest effects for faults
located on the slowest mode - the Fiedler mode - of the network Laplacian
matrix. This mode essentially vanishes over Belgium, Eastern France, Western
Germany, northern Italy and Switzerland. Buses inside these regions are only
weakly affected by faults occuring outside. Conversely, faults inside these
regions have only a local effect and disturb only weakly outside buses.
Following this observation, we reduce rotational inertia through three
different procedures by either (i) reducing inertia on the Fiedler mode, (ii)
reducing inertia homogeneously and (iii) reducing inertia outside the Fiedler
mode. We find that procedure (iii) has little effect on disturbance
propagation, while procedure (i) leads to the strongest increase of RoCoF and
frequency deviations. These results for our model of the European transmission
grid are corroborated by numerical investigations on the ERCOT transmission
grid.
