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

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

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

Phys. Rev. Research 2, 013339 – Published 19 March 2020

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 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.

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Received 1 October 2019
Accepted 19 December 2019

DOI:https://doi.org/10.1103/PhysRevResearch.2.013339

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Collective dynamics Dynamics of networks

Nonlinear Dynamics

Authors & Affiliations

Mehrnaz Anvari ^1,2,*, Leonardo Rydin Gorjão ^3,4,†, Marc Timme^5,6,‡, Dirk Witthaut ^3,4,§, Benjamin Schäfer ^7,5,6,∥, and Holger Kantz¹

¹Max Planck Institute for the Physics of Complex Systems (MPIPKS), 01187 Dresden, Germany
²Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, P.O. Box 60 12 03, D-14412 Potsdam, Germany
³Forschungszentrum Jülich, Institute for Energy and Climate Research - Systems Analysis and Technology Evaluation (IEK-STE), 52428 Jülich, Germany
⁴Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
⁵Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, Technical University of Dresden, 01062 Dresden, Germany
⁶Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
⁷School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom

^*anvari@pik-potsdam.de
^†l.rydin.gorjao@fz-juelich.de
^‡marc.timme@tu-dresden.de
^§d.witthaut@fz-juelich.de
^∥b.schaefer@qmul.ac.uk

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Vol. 2, Iss. 1 — March - May 2020

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