Building blocks of the basin stability of power grids

Kim, Heetae; Lee, Sang Hoon; Holme, Petter

doi:10.1103/physreve.93.062318

Cited by 30 publications

(37 citation statements)

References 22 publications

(50 reference statements)

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“…Basin stability and derived concepts have been successfully applied recently [39], e.g. for power grids [19,31,40,41], chimera states [29], explosive synchronisation [48] delayed dynamics [25] and resilience measures [34].…”

Section: Introductionmentioning

confidence: 99%

Potentials and limits to basin stability estimation

Schultz¹,

Menck²,

Heitzig³

et al. 2017

New J. Phys.

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Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. Their application requires numerical estimation via Monte Carlo sampling and integration of differential equations. Here, we analyse the applicability of basin stability to systems with basin geometries that are challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.

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Section: Introductionmentioning

confidence: 99%

Potentials and limits to basin stability estimation

Schultz¹,

Menck²,

Heitzig³

et al. 2017

New J. Phys.

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“…However, it is not always true. The counterintuitive phenomena of suddenly decreased B have been witnessed from seemingly quite stable cases with B ; 1 even when K is increased [21]. This phenomenon, therefore, leaves characteristic peaks of B as a function of K, and implies that the power grid may suddenly become unstable unexpectedly, even with larger values of coupling strength.…”

Section: Synchronization Stability Of Power Gridsmentioning

confidence: 99%

“…The main question is whether the power-grid system retains synchronization after being perturbed or falls into desynchronization. The volume of the basin of attraction to synchronization in the phase space of perturbation is interpreted as the probability of synchronization recovery, so-called 'basin stability', which has been widely used to quantify the synchronization stability of power grids [16,17,20,21,[24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

“…The infinite busbar model represents a power grid that includes an oscillatory power-grid node and a connected system as an environment, where the basin stability of power-grid nodes increases monotonically as the coupling strength increases (see section 3.1 for details) [17]. However, [21] revealed in small systems that the transition of basin stability shows various patterns including sudden drooping of the basin stability for the increased value of coupling strength. Although the basin stability is still useful even when the transition features anomalous patterns, and it is reliable even in the presence of fractal basin boundaries according to [26], the potential inconsistency should be clarified by uncovering the underlying mechanism in order to guarantee secure electricity supply.…”

Section: Introductionmentioning

confidence: 99%

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Multistability and variations in basin of attraction in power-grid systems

et al. 2018

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Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the unsynchronized states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

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“…In order to study the performance of various approaches, we make use of probabilistic methods [16][17][18][19][20][21][22][23][24] , that is, we define a scenario ensemble and evaluate the expected performance of the system with respect to the ensemble average by sampling over the ensemble. This approach allows us to study the properties of the system for the whole ensemble, rather than in individual case studies.…”

Section: Introductionmentioning

confidence: 99%

A multiplex, multi-timescale model approach for economic and frequency control in power grids

Strenge

Schultz

Kurths

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Power systems are subject to fundamental changes due to the increasing infeed of decentralised renewable energy sources and storage. The decentralised nature of the new actors in the system requires new concepts for structuring the power grid, and achieving a wide range of control tasks ranging from seconds to days. Here we introduce a multiplex dynamical network model covering all control timescales. Crucially, we combine a decentralised, self-organised lowlevel control and a smart grid layer of devices that can aggregate information from remote sources. The safety-critical task of frequency control is performed by the former, the economic objective of demand matching dispatch by the latter. Having both aspects present in the same model allows us to study the interaction between the layers. Remarkably, we find that adding communication in the form of aggregation does not improve the performance in the cases considered. Instead, the self-organised state of the system already contains the information required to learn the demand structure in the entire grid. The model introduced here is highly flexible, and can accommodate a wide range of scenarios relevant to future power grids. We expect that it is especially useful in the context of low-energy microgrids with distributed generation.Highly decentralised power grids, possibly in the context of prosumer systems, require new concepts for their stable operation. We expect that both self-organised systems as well as intelligent devices with communication capability that can aggregate information from remote sources will play a central role. Here we introduce a multiplex network model that combines both aspects, and use it in a basic scenario and uncover surprising interactions between the layers.

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Building blocks of the basin stability of power grids

Cited by 30 publications

References 22 publications

Potentials and limits to basin stability estimation

Potentials and limits to basin stability estimation

Multistability and variations in basin of attraction in power-grid systems

A multiplex, multi-timescale model approach for economic and frequency control in power grids

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