  The operation of power systems is affected by diverse technical, economic and
social factors. Social behaviour determines load patterns, electricity markets
regulate the generation and weather-dependent renewables introduce power
fluctuations. Thus, power system dynamics must be regarded as a non-autonomous
system whose parameters vary strongly with time. However, the external driving
factors are usually only available on coarse scales and the actual dependencies
of the dynamic system parameters are generally unknown. Here, we propose a
physics-inspired machine learning model that bridges the gap between
large-scale drivers and short-term dynamics of the power system. Integrating
stochastic differential equations and artificial neural networks, we construct
a probabilistic model of the power grid frequency dynamics in Continental
Europe. Its probabilistic prediction outperforms the daily average profile,
which is an important benchmark. Using the integrated model, we identify and
explain the parameters of the dynamical system from the data, which reveals
their strong time-dependence and their relation to external drivers such as
wind power feed-in and fast generation ramps. Finally, we generate synthetic
time series from the model, which successfully reproduce central
characteristics of the grid frequency such as their heavy-tailed distribution.
All in all, our work emphasises the importance of modelling power system
dynamics as a stochastic non-autonomous system with both intrinsic dynamics and
external drivers.
