Network desynchronization by non-Gaussian fluctuations

Hindes, Jason; Jacquod, Philippe; Schwartz, Ira B.

doi:10.1103/physreve.100.052314

Cited by 19 publications

(64 citation statements)

References 60 publications

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“…Our analytical results are corroborated by numerical simulations on realistic power grids. Compared to earlier works on noise propagation in complex synchronous networks of oscillators and power grids [9,[13][14][15][16][17][19][20][21][22][23][24][25], our manuscript (i) goes beyond the white-noise limit, and includes in particular regimes of long noise correlation time that are particularly relevant for high-voltage power networks, (ii) is based on analytical calculations, and (iii) considers the case of multiple sources of power feed-in noise. Our approach relies on a single restrictive assumption, that the non-Gaussianities can be modelled by the first few cumulants of their distribution.…”

Section: Introductionmentioning

confidence: 99%

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Tyloo¹,

Hindes²,

Jacquod³

2022

Preprint

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Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Therefore, substituting new renewables for traditional generation induces stronger and more frequent disturbances and modifies the way disturbances propagate across AC electric power grids. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local grid-frequency data. Large frequency deviations may induce grid instabilities, leading in worstcase scenarios to cascading failures and large-scale blackouts. In this manuscript, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. We show that for a single source of fluctuations, non-Gaussianities in the form of finite skewness and positive kurtosis of the noise distribution propagate over the entire network when the noise correlation time is larger than the network's intrinsic time scales, but that they vanish over short distances if the noise fluctuates rapidly. We furthermore show that a Berry-Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our results show that the persistence of non-Gaussian fluctuations of feed-in power have a global impact on power-grid dynamics when they fluctuate over time scales larger than the intrinsic time scales of the system, which, we argue, is the relevant regime in real power grids. Our predictions are corroborated by numerical simulations on realistic models of power grids.

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Section: Introductionmentioning

confidence: 99%

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Tyloo¹,

Hindes²,

Jacquod³

2022

Preprint

Self Cite

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“…Analysis and modelling of the power grid frequency and its statistics and complex dynamics have become * b.schaefer@qmul.ac.uk increasingly popular in the interdisciplinary community, attracting also much attention from mathematicians and physicists. Studies have investigated for example different dynamical models [13][14][15], compared centralised vs. decentralised topologies [16][17][18], investigated the effect of fluctuations on the grid's stability [19,20], or how fluctuations propagate [21,22]. Further research proposed real-time pricing schemes [23], optimised the placement of (virtual) inertia [24,25], or investigated cascading failures in power grids [26][27][28][29].…”

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confidence: 99%

Open data base analysis of scaling and spatio-temporal properties of power grid frequencies

Gorjão

Jumar

Maaß

et al. 2020

Preprint

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Abstract The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly. Here, we analyse an open data base of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open data base and analyses may constitute a step towards more shared, collaborative energy research.

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“…What we can easily extract from a power-grid is, for example, the frequency f i = dθ i /dt (or angular velocity) at a particular location. This is given, in good approximation, by a Langevin equation [46]…”

Section: Background and Methods Of Analysis A Power-grid Frequency Dy...mentioning

confidence: 99%

Spatio-temporal complexity of power-grid frequency fluctuations

Gorjão,

Schäfer,

Witthaut

et al. 2021

Preprint

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Power-grid systems constitute one of the most complex man-made spatially extended structures. These operate with strict operational bounds to ensure synchrony across the grid. This is particularly relevant for power-grid frequency, which operates strictly at 50 Hz (60 Hz). Nevertheless, small fluctuations around the mean frequency are present at very short time scales < 2 seconds and can exhibit highly complex spatio-temporal behaviour. Here we apply superstatistical data analysis techniques to measured frequency fluctuations in the Nordic Grid. We study the increment statistics and extract the relevant time scales and superstatistical distribution functions from the data. We show that different synchronous recordings of power-grid frequency have very distinct stochastic fluctuations with different types of superstatistics at different spatial locations, and with transitions from one superstatistics to another when the time lag of the increment statistics is changed.

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Network desynchronization by non-Gaussian fluctuations

Cited by 19 publications

References 60 publications

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Open data base analysis of scaling and spatio-temporal properties of power grid frequencies

Spatio-temporal complexity of power-grid frequency fluctuations

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