Delocalization of disturbances and the stability of ac electricity grids

Kettemann, Stefan

doi:10.1103/physreve.94.062311

Cited by 49 publications

(77 citation statements)

References 18 publications

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“…We can now formally divide left-hand side (20) and right-hand side (22) by h 2 and take the limit  h 0 to obtain the final continuum limit of the Poisson equation,…”

Section: Rs Rs Rs Rs Rsmentioning

confidence: 99%

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Non-local impact of link failures in linear flow networks

et al. 2019

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The failure of a single link can degrade the operation of a supply network up to the point of complete collapse. Yet, the interplay between network topology and locality of the response to such damage is poorly understood. Here, we study how topology affects the redistribution of flow after the failure of a single link in linear flow networks with a special focus on power grids. In particular, we analyze the decay of flow changes with distance after a link failure and map it to the field of an electrical dipole for lattice-like networks. The corresponding inverse-square law is shown to hold for all regular tilings. For sparse networks, a long-range response is found instead. In the case of more realistic topologies, we introduce a rerouting distance, which captures the decay of flow changes better than the traditional geodesic distance. Finally, we are able to derive rigorous bounds on the strength of the decay for arbitrary topologies that we verify through extensive numerical simulations. Our results show that it is possible to forecast flow rerouting after link failures to a large extent based on purely topological measures and that these effects generally decay with distance from the failing link. They might be used to predict links prone to failure in supply networks such as power grids and thus help to construct grids providing a more robust and reliable power supply.

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“…We can now formally divide left-hand side (20) and right-hand side (22) by h 2 and take the limit  h 0 to obtain the final continuum limit of the Poisson equation,…”

Section: Rs Rs Rs Rs Rsmentioning

confidence: 99%

“…However, this is not necessarily the case during power outages (see, e.g. [15]), raising the question of how networks flows are rerouted after failures [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Non-local impact of link failures in linear flow networks

et al. 2019

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“…Two further variants "Hom±IN" (with and without internal nodes) are obtained by homogenising the transmission line properties as well as the generated and consumed powers. Corresponding homogeneous power grid structures have been investigated in various previous studies [7,12,13,14,30,31], typically for the case of loss-free transmission lines. For the homogenisation, we here also consider a loss-free situation, i.e.…”

Section: Parameters For Extended and Simplified Variants Of The Ieee mentioning

confidence: 99%

Power grid stability under perturbation of single nodes: Effects of heterogeneity and internal nodes

Wolff

Lind

Maass

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Non-linear equations describing the time evolution of frequencies and voltages in power grids exhibit fixed points of stable grid operation. The dynamical behaviour after perturbations around these fixed points can be used to characterise the stability of the grid. We investigate both probabilities of return to a fixed point and times needed for this return after perturbation of single nodes. Our analysis is based on an IEEE test grid and the second-order swing equations for voltage phase angles θ j at nodes j in the synchronous machine model. The perturbations cover all possible changes ∆θ of voltage angles and a wide range of frequency deviations in a range ∆f = ±1 Hz around the common frequency ω = 2πf =θ j in a synchronous fixed point state. Extensive numerical calculations are carried out to determine, for all node pairs (j, k), the return times t jk (∆θ, ∆ω) of node k after a perturbation of node j. We find that for strong perturbations of some nodes, the grid does not return to its synchronous state. If returning to the fixed point, the times needed for the return are strongly different for different disturbed nodes and can reach values up to 20 seconds and more. When homogenising transmission line and node properties, the grid always returns to a synchronous state for the considered perturbations, and the longest return times have a value of about 4 seconds for all nodes. The neglect of reactances between points of power generation (internal nodes) and injection (terminal nodes) leads to an underestimation of return probabilities.

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“…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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Delocalization of disturbances and the stability of ac electricity grids

Cited by 49 publications

References 18 publications

Non-local impact of link failures in linear flow networks

Non-local impact of link failures in linear flow networks

Power grid stability under perturbation of single nodes: Effects of heterogeneity and internal nodes

The footprint of atmospheric turbulence in power grid frequency measurements

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