Escape routes, weak links, and desynchronization in fluctuation-driven networks

Schäfer, Benjamin; Matthiae, Moritz; Zhang, Xiaozhu; Rohden, Martin; Timme, Marc; Witthaut, Dirk

doi:10.1103/physreve.95.060203

Cited by 51 publications

(57 citation statements)

References 39 publications

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“…Hence, to operate energy systems with arXiv:1909.09110v1 [nlin.AO] 19 Sep 2019 a high share of renewable energies, a solid understanding of the impact of fluctuating feed-in on the grid's frequency is necessary. Previous studies described the stochastic behaviour of the grid frequency using stochastic optimisation [20], a simulated robustness analysis [21], Fokker-Planck approaches [22,23], or tracing the impact of wind feed-in on the grid frequency [24,25]. However, the mathematical properties of the underlying stochastic process have not been studied comprehensively.…”

Section: Introductionmentioning

confidence: 99%

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

Anvari

Gorjão

Timme

et al. 2020

Phys. Rev. Research

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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.

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Section: Introductionmentioning

confidence: 99%

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

Anvari

Gorjão

Timme

et al. 2020

Phys. Rev. Research

Self Cite

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“…This will lead to faster frequency dynamics with larger amplitudes [34]. If grid design and control strategies are not properly adapted, such frequency fluctuations may become highly critical for the grid stability [19]. Thus, an explicit expression for increment probabilities is desirable to correctly quantify this risks.…”

Section: In Practice Z(t) Is Obtained From the Hilbert Transform H[umentioning

confidence: 99%

“…Such models have been used to analyze aspects of synchronization [16] and the interplay of stability and topology [17], as well as relaxation after singular [18] and stochastic [19,20] perturbations. The impact of intermittent feed-in on power grids has been addressed in [20,21]: Numerical results indicate that intermittency propagates in a power grid and affects the frequency increment distributions of nodes distant to the feed-in.…”

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confidence: 99%

The footprint of atmospheric turbulence in power grid frequency measurements

Haehne

Schottler

Waechter

et al. 2018

EPL

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-Fluctuating wind energy makes a stable grid operation challenging. Due to the direct contact with atmospheric turbulence, intermittent short-term variations in the wind speed are converted to power fluctuations that cause transient imbalances in the grid. We investigate the impact of wind energy feed-in on short-term fluctuations in the frequency of the public power grid, which we have measured in our local distribution grid. By conditioning on wind power production data, provided by the ENTSO-E transparency platform, we demonstrate that wind energy feedin has a measurable effect on frequency increment statistics for short time scales (< 1 s) that are below the activation time of frequency control. Our results are in accordance with previous numerical studies of self-organized synchronization in power grids under intermittent perturbation and give rise to new challenges for a stable operation of future power grids fed by a high share of renewable generation. editor's choice

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“…At K=10 the system typically synchronizes completely with ω i =0. While a large number of works have studied the stability of this synchronous state as a function of the local network topology [24,[26][27][28][29][30][31][32][33][34][35][36], comparatively little is known about the intermediate regime.…”

Section: Kuramoto Networkmentioning

confidence: 99%

Monte Carlo basin bifurcation analysis

2020

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Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds-Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart-Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language.world applications: the Dodds-Watts model of social and biological contagion, a network of second order Kuramoto oscillators, used e.g. to model power grids and a network of Stuart-Landau oscillators, of importance for many chemical and biological systems, will follow in section 3. Lastly, these results and the performance and applicability of the presented method will be discussed in section 4.

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Escape routes, weak links, and desynchronization in fluctuation-driven networks

Cited by 51 publications

References 39 publications

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

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

The footprint of atmospheric turbulence in power grid frequency measurements

Monte Carlo basin bifurcation analysis

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