  Increased share of renewable sources of energy in a power grid leads to
larger deviations in grid frequency from the nominal value resulting in more
challenging control and its modelling. In this paper we focus on the grid
frequency for the power system of Great Britain because the large share of
renewables makes it a template for other power grids in the future and because
it exhibits peculiar statistical properties, such as long-term correlations in
fluctuations, periodicity, and bi-modal distribution of the grid frequency. By
modifications of the swing equation and the underlying noise statistics, which
we justify qualitatively and quantitatively, we reproduce these peculiar
statistical properties. We apply our model to a realistic frequency response
service and show our predictions outperform a standard swing equation model.
