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Conventional generators in power grids are steadily substituted with newrenewable sources of electric power. The latter are connected to the grid viainverters and as such have little, if any rotational inertia. The resultingreduction of total inertia raises important issues of power grid stability,especially over short-time scales. We have constructed a model of thesynchronous grid of continental Europe with which we numerically investigatefrequency deviations as well as rates of change of frequency (RoCoF) followingabrupt power losses. The magnitude of RoCoF's and frequency deviations stronglydepend on the fault location, and we find the largest effects for faultslocated on the slowest mode - the Fiedler mode - of the network Laplacianmatrix. This mode essentially vanishes over Belgium, Eastern France, WesternGermany, northern Italy and Switzerland. Buses inside these regions are onlyweakly affected by faults occuring outside. Conversely, faults inside theseregions have only a local effect and disturb only weakly outside buses.Following this observation, we reduce rotational inertia through threedifferent procedures by either (i) reducing inertia on the Fiedler mode, (ii)reducing inertia homogeneously and (iii) reducing inertia outside the Fiedlermode. We find that procedure (iii) has little effect on disturbancepropagation, while procedure (i) leads to the strongest increase of RoCoF andfrequency deviations. These results for our model of the European transmissiongrid are corroborated by numerical investigations on the ERCOT transmissiongrid.

Disturbance propagation, inertia location and slow modes in large-scale high voltage power grids