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

Abstract

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 analyse 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. Further, 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 analyse in how far dynamically modelled frequency properties match the ones of real trajectories.

Data-Driven Model of the Power-Grid Frequency Dynamics

“…We specifically highlighted how the model approximates probability distributions and autocorrelation functions of realistic grids. A more detailed analysis of the mathematical properties of both real trajectories and the model is presented in [31].…”

“…The model presented here can easily be extended in multiple directions: We could apply more advanced stochastic measures to compare the synthetic trajectory with the real trajectory, as partially done in [31]. Simultaneously, the frequency dynamics considered here could be extended by voltage amplitude dynamics.…”

“…The power-grid frequency is not following a simple Gaussian process but displays heavy tails and regular correlation peaks, see Fig. 2 and [22,30,31] for more detailed analysis. To get a better understanding of the different factors impacting the grid frequency, we give an overview of these: First, we review the innate and humanly devised control systems, continue with the market and power dispatch design and close the section with a stochastic description of the noise acting on the power grid.…”

“…In fact, we only observe the cumulative effect of the noise in how it influences the power-grid frequency, regardless whether it originates from local disturbances or systemwide variations. Aggregating all sources of noise allows it to be handled as a stochastic process, see also [31] for more details.…”

A multiplex, multi-timescale model approach for economic and frequency control in power grids

“…Still, it indicates that it is interesting to further study the interactions of the layers in the future. In fact, the interaction between higher-layer energy management and the frequency dynamics of the power grid is an effect that is observed in real power grids, where trading intervals are very visible in the statistics of power grid frequency signals 54,55 . We expect that the type of model we have set up here is highly useful to study and reproduce some of these results without having to go to highly specific market models.…”