Enhancing power grid synchronization and stability through time-delayed feedback control

Taher, Halgurd; Olmi, Simona; Schöll, Eckehard

doi:10.1103/physreve.100.062306

Cited by 61 publications

(52 citation statements)

References 48 publications

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“…For a network of N oscillators with phase

where

is the damping parameter, describing the power dissipation, K is the global coupling, being related to the maximum transmitted power between nodes and

, which is the weighted adjacency matrix of the network, containing admittance elements. Very recently, this equation has been refined with the aim of application for the German HV power-grid by [ 24 ]

Generator units (

) and loads (

) are modeled with a bi-modal probability distribution with peaks at mean values of power sources and sink. The authors assume homogeneous transmission capacities, thus

.…”

Section: Models and Methodsmentioning

confidence: 99%

“…The operational limits show large dependence on voltage level, age of the infrastructure, and seasons, thus uniform handling of this parameter is also a simplification of modeling. In conclusion, returning to the equation by [ 24 ] for

and

empirical distribution values can be used instead of an uniform characterization.…”

Section: Models and Methodsmentioning

confidence: 99%

“…An illustrative example is shown to underline the importance of properly assessing

. In the paper by [ 24 ],

was used as a representation of a 400 MW power plant, which by substituting into Equation ( 6 ) will result

[s]; this will be used as

in the following example. Figure 1 shows how the moment of inertia varies for a 400 MW node, depending on the proportion of locally generated power and the share of converter-based generation units, which have no inertia.…”

Section: Models and Methodsmentioning

confidence: 99%

“…The authors of [ 23 ] introduce a method to estimate coupling strength of power grids, which is a crucial parameter of the Kuramoto-model; proper knowledge of such parameters can help in maintaining stability of the power system even in the presence of large transients. The recent work by Taher et al [ 24 ] proposes a time-delayed feedback control to the Kuramoto-model and test it on a realistic topology, with complex bimodal self-frequency distributions.…”

Section: Introductionmentioning

confidence: 99%

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Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models

Ódor

Hartmann

2020

Entropy

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Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous two-dimensional (2D) square lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D square lattice), is not sufficient for finding power-law distributed cascades. On the other hand, too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution, both for the US and Hungarian systems, remained insensitive and have kept the universal tails, being characterized by the exponent τ ≃ 1.8 . We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid.

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“…For a network of N oscillators with phase

where

is the damping parameter, describing the power dissipation, K is the global coupling, being related to the maximum transmitted power between nodes and

Generator units (

) and loads (

) are modeled with a bi-modal probability distribution with peaks at mean values of power sources and sink. The authors assume homogeneous transmission capacities, thus

.…”

Section: Models and Methodsmentioning

confidence: 99%

and

empirical distribution values can be used instead of an uniform characterization.…”

Section: Models and Methodsmentioning

confidence: 99%

“…An illustrative example is shown to underline the importance of properly assessing

. In the paper by [ 24 ],

was used as a representation of a 400 MW power plant, which by substituting into Equation ( 6 ) will result

[s]; this will be used as

Section: Models and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models

Ódor

Hartmann

2020

Entropy

View full text Add to dashboard Cite

show abstract

“…The investigation of power grid systems has been recently addressed from a nonlinear dynamics point of view, using the Kuramoto phase oscillator model with inertia [6][7][8][9][10][11][12][13][14][25][26][27] . This model represents an extended version of the standard Kuramoto model; such an extension has been developed by Tanaka et al 1,2 by including an additional term that takes into account the frequency dynamics.…”

Section: Introductionmentioning

confidence: 99%

Stability and control of power grids with diluted network topology

Tumash

Olmi

Schöll

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In the present study we consider a random network of Kuramoto oscillators with inertia in order to mimic and investigate the dynamics emerging in high-voltage power grids. The corresponding natural frequencies are assumed to be bimodally Gaussian distributed, thus modeling the distribution of both power generators and consumers: for the stable operation of power systems these two quantities must be in balance. Since synchronization has to be ensured for a perfectly working power grid, we investigate the stability of the desired synchronized state. We solve this problem numerically for a population of N rotators regardless of the level of quenched disorder present in the topology. We obtain stable and unstable solutions for different initial phase conditions, and we propose how to control unstable solutions, for sufficiently large coupling strength, such that they are stabilized for any initial phase. Finally, we examine a random Erdös-Renyi network under the impact of white Gaussian noise, which is an essential ingredient for power grids in view of increasing renewable energy sources.

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Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

Berner¹

2021

Springer Theses

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Collective phenomena in systems of interconnected dynamical units are omnipresent in nature. The swarm behavior in flocks of birds or schools of fish, the synchronous flashing of fireflies or even coherent spiking of neurons in the human brain are just a few examples of collective motion. Elucidating the mechanisms that give rise to synchronization is crucial in order to understand biological self-organization. For this sake, the theory of dynamical networks has been successfully applied over the last decades to boil down the complex dynamics from natural systems to their essentials. In addition, dynamical networks with adaptive couplings and hence non-constant network structure appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. In this thesis, we study adaptive networks and their properties which give rise to the emergence of a variety of synchronization patterns, including complete and cluster synchronization as well as solitary and chimera-like states. One of the main fields of application that is investigated in this thesis concerns neuroscience. However, the methods and approaches developed in this work are not restricted to a specific field of application.aus gekoppelten Phasenoszillatoren an und zeigen, wie das subtile Zusammenspiel zwischen Adaptivität und Netzwerkstruktur die Entstehung komplexer partieller Synchronisationsmuster hervorruft.Trotz des regen Interesses an adaptiven Netzwerken ist über das Zusammenspiel adaptiv gekoppelter Netzwerkgruppen wenig bekannt. Solche adaptiven Mehrschicht-oder Multiplex-Netzwerke kommen in neuronalen Netzwerken ganz natürlich vor. Wir schlagen ein Konzept zur Erzeugung und Stabilisierung diverser partieller Synchronisationsmuster (Phasen-Cluster) in adaptiven Netzwerken vor. Wir zeigen, dass das "Multiplexen" verschiedene stabile Phasen-Cluster-Zustände induzieren kann, selbst wenn diese in den Einschicht-Systemen nicht stabil sind oder gar nicht existieren. Weiterhin entwickeln wir eine Methode zur Analyse von Laplace-Matrizen von Multiplex-Netzwerken, die einen Einblick in die spektrale Struktur dieser Netzwerke ermöglicht und damit eine Reduktion des Stabilitätsproblems auf die von Einschicht-Netzwerken ermöglicht. Wir setzen die neue Methode ein, um analytische Ergebnisse für die Stabilität der Zustände im Mehrschicht-System zu erhalten.

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Enhancing power grid synchronization and stability through time-delayed feedback control

Cited by 61 publications

References 48 publications

Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models

Power-Law Distributions of Dynamic Cascade Failures in Power-Grid Models

Stability and control of power grids with diluted network topology

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

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