Data-Driven Model of the Power-Grid Frequency Dynamics

Abstract

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. We offer executable code and guidelines on how to use the model on any power grid for various mathematical or engineering applications.

Stochastic properties of the frequency dynamics in real and synthetic power grids

“…Hence the generation curve is step-like, while the demand varies continuously. From step to step, the power balance rapidly switches from positive to negative or vice versa, leading to large deviations of the grid frequency, which become visible in the autocorrelation function, see also [14]. In addition, daily routine, scheduled events, etc., contribute to an increased correlation every hour and 24 hours, see black arrows in fig.…”

“…Notable exceptions are high-frequency disturbances, which are typically localised [43,44], or inter-area oscillations, where energy is oscillating from one part of the grid to another one. The synthetic model of the frequency dynamics is discussed in detail in [14]. It is given as a linear stochastic differential equation:…”

“…Before we compare results of the synthetic model with the real data, we need to determine suitable parameters. Details are given in [14] on how to estimate the parameters from a given frequency trajectory. In short, the noise amplitude is estimated based on the stochastic fluctuations around the observed frequency trajectory, while the power imbalance ∆P ext is directly read from the rise or sag of the frequency at the scheduled time points of dispatch, which are proportional to the missing or exceeding amount of power.…”

“…(Notice that in our case we include the real power generation from Germany for December 2017, thus circumvent extracting the power generation ∆P ext from the data). Primary control c 1 is recovered by studying the process' affinity to revert its trajectory to the dispatched power and secondary control c 2 is estimated from the frequency recovery rate to the nominal value after a scheduled action [14].…”

“…A more sophisticated analysis of the power-grid frequency dynamics is paramount, as all power generators and consumers have to ensure the stability of the grid in the presence of many effects simultaneously impinging on it. In such analyses it is both relevant to study existing power grids [13] as well as to evaluate any forecasts and models of the frequency dynamics expected in future grids [14].…”