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Abstract

Frequency measurements indicate the state of a power grid. In fact, deviations from the nominal frequency determine whether the grid is stable or in a critical situation. We aim to understand the fluctuations of the frequency on multiple time scales with a recently proposed method based on detrended fluctuation analysis. It enables us to infer characteristic time scales and generate stochastic models. We capture and quantify known features of the fluctuations like periodicity due to the trading market, response to variations by control systems, and stability of the long time average. We discuss similarities and differences between the British grid and the continental European grid. The power grid (main) frequency, as an observable variable, is not only easily measurable but also contains significant information about the state (and therefore stability) of the considered grid. The information in the frequency variations can include the functionality of control systems, the effect of regular dispatches due to the trading market and moreover the effect of fluctuations in renewable energies (REs) and demands on the grid. Therefore, disentangling the interplay of control systems, dispatch and fluctuations from REs and demands provides deeper insight into the dynamics of the frequency and, consequently, enables us to model or forecast it. Detrended fluctuation analysis (DFA) is a well-known method for scaling analysis. Recently, it has been shown that one can also recognize typical characteristic time scales in datasets via the DFA fluctuation function. Employing this new approach, we recognize characteristics time scales of the frequency and attempt to recognize the role of the trading market, control systems, REs, as well as consumers in the short- and long-time fluctuations from seconds to weeks. Finally, we model the frequency variations by a superposition of autoregressive models of order two AR(2), a daily cycle, and an additional regulatory component for long periods of time