The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly. Here, we analyse an open database of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open database and analyses constitute a step towards more shared, collaborative energy research.

The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, affecting power-grid operation and power-grid frequency. Problems raised by this ongoing transition are increasingly addressed by transdisciplinary research approaches, ranging from purely mathematical modelling to applied case studies. These approaches require a stochastic description of consumer behaviour, fluctuations by renewables, market rules, and how they influence the stability of the power-grid frequency. Here, we introduce an easy-to-use, data-driven, stochastic model for the power-grid frequency and demonstrate how it reproduces key characteristics of the observed statistics of the Continental European and British power grids. Using data analysis tools and a Fokker–Planck approach, we estimate parameters of our deterministic and stochastic model. We offer executable code and guidelines on how to use the model on any power grid for various mathematical or engineering applications.

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 analyze 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. Furthermore, 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 analyze in how far dynamically modeled frequency properties match the ones of real trajectories.

A general problem for evaluating Markovian stochastic processes is the retrieval of the moments or the Kramers-Moyal coefficients M from data or time-series. The Kramers-Moyal coefficients are derived from an Taylor expansion of the master equation that describes the probability evolution of a Markovian stochastic process. Given a set of stochastic data, ergodic or quasi-stationary, the extensive literature of stochastic processes awards a set of measures, such as the Kramers-Moyal coefficients or its moments, which link stochastic processes to a probabilistic description of the process or of the family of processes (Risken, 1996). Most commonly known is the Fokker-Planck equation or truncated forward Kolmogorov equation, partial differential equations, obtained from the Taylor expansion of the master equation.

The large variability of renewable power sources is a central challenge in the transition to a sustainable energy system. Electricity markets are central for the coordination of electric power generation. These markets rely evermore on short-term trading to facilitate the balancing of power generation and demand and to enable systems integration of small producers. Electricity prices in these spot markets show pronounced fluctuations, featuring extreme peaks as well as occasional negative prices. In this article, we analyze electricity price time series from the European Power Exchange market, in particular the hourly day-ahead, hourly intraday, and 15-min intraday market prices. We quantify the fluctuations, correlations, and extreme events and reveal different time scales in the dynamics of the market. The short-term fluctuations show remarkably different characteristics for time scales below and above 12 h. Fluctuations are strongly correlated and persistent below 12 h, which contributes to extreme price events and a strong multifractal behavior. On longer time scales, they get anticorrelated and price time series revert to their mean, witnessed by a stark decrease of the Hurst coefficient after 12 h. The long-term behavior is strongly influenced by the evolution of a large-scale weather pattern with a typical time scale of four days. We elucidate this dependence in detail using a classification into circulation weather types. The separation in time scales enables a superstatistical treatment, which confirms the characteristic time scale of four days, and motivates the use of $q$-Gaussian distributions as the best fit to the empiric distribution of electricity prices.