  The frequency constitutes a key state variable of electrical power grids.
However, as the frequency is subject to several sources of fluctuations,
ranging from renewable volatility to demand fluctuations and dispatch, it is
strongly dynamic. Yet, the statistical and stochastic properties of the
frequency fluctuation dynamics are far from fully understood. Here, we analyse
properties of power grid frequency trajectories recorded from different
synchronous regions. We highlight the non-Gaussian and still approximately
Markovian nature of the frequency statistics. Further, we find that the
frequency displays significant fluctuations exactly at the time intervals of
regulation and trading, confirming the need of having a regulatory and market
design that respects the technical and dynamical constraints in future highly
renewable power grids. Finally, employing a recently proposed synthetic model
for the frequency dynamics, we combine our statistical and stochastic analysis
and analyse in how far dynamically modelled frequency properties match the ones
of real trajectories.
