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

Marc Timme,Benjamin Schäfer,Dirk Witthaut,Mehrnaz Anvari,Leonardo Rydin Gorjão,Holger Kantz

doi:10.1103/physrevresearch.2.013339

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.

Highlights

A stable electric power supply is essential for the functioning of our society [1]
For the rest of this section, we focus our analysis on the frequency measurements from Baden-Württemberg as an example, and where we aim to refer to general statistic features, we refer to the Central European power grid (CE) grid
We have presented an analysis of the statistics of power-grid frequency dynamics, with an emphasis on nonstandard behavior

Summary

INTRODUCTION

A stable electric power supply is essential for the functioning of our society [1]. The ongoing energy transition towards renewable generation fundamentally changes the conditions for the operation of the power system [2]. 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]. We aim for a dynamical model of the power-grid frequency including the role of trading and regulator action in the power grid Such a model may help especially to plan future grids with a high share of renewable energies. We demonstrate how our model reproduces key aspects of the stochastic and deterministic behavior of real trajectories

POWER-GRID FREQUENCY OVERVIEW

STOCHASTIC PROPERTIES

STOCHASTIC MODEL

QUANTITATIVE COMPARISON BETWEEN MODEL AND DATA

DISCUSSION