Towards realistic statistical models of the grid frequency

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, bi-modality,and heavy tails in the 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 realistic frequency response services and show our predictions outperform a standard swing equation model.