Network susceptibilities: Theory and applications

Manik, Debsankha; Rohden, Martin; Ronellenfitsch, Henrik; Zhang, Xiaozhu; Hallerberg, Sarah; Witthaut, Dirk; Timme, Marc

doi:10.1103/physreve.95.012319

Cited by 55 publications

(50 citation statements)

References 45 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider linear supply network models, where the flow between two adjacent nodes is proportional to the difference of the nodal potential, pressure or voltage phase angle. Linear models are applied to hydraulic networks [31], vascular networks of plants and animals [28,[32][33][34][35], economic inputoutput networks [36] as well as electric power grids [37][38][39][40][41][42]. The linearity allows to obtain several rigorous bounds for flow rerouting in general network topologies and to solve special cases fully analytically.…”

Section: Introductionmentioning

confidence: 99%

Non-local impact of link failures in linear flow networks

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Non-local impact of link failures in linear flow networks

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also we have given a new description of the time dependent dynamics derived in an analytic manner directly from the system matrix describing the generator and grid (see (27)-(30) ). Moreover the effects of low grid inertia are now shown explicitly in the equations via a grid to generator inertia ratio (see (10) and (22)). We have also provided analytic equations describing the dynamics of the grid and generator frequencies (see (14), (15), and (29)).…”

Section: Discussionmentioning

confidence: 99%

“…Here we shall compare two physically acceptable two-body coupled oscillator models, namely, a Kuramoto-like [10]- [12] and a cage model [13], [14]. Both yield insights into the general phase behavior of a generator connected to a power grid with finite inertia such as prevails in Ireland.…”

mentioning

confidence: 99%

Comparison of Coupled Nonlinear Oscillator Models for the Transient Response of Power Generating Stations Connected to Low Inertia Systems

Zarifakis

Byrne

Coffey

et al. 2020

IEEE Trans. Power Syst.

View full text Add to dashboard Cite

Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation stations. Whereas the Kuramoto model is good for describing high inertia grid systems, the cage one allows both high and low inertia grids to be modelled. This is illustrated by comparing both the synchronization time and relaxation towards synchronization of each model by treating their equations of motion in a common framework rooted in the dynamics of many coupled phase oscillators. A solution of these equations via matrix continued fractions is implemented rendering the characteristic relaxation times of a grid-generator system over a wide range of inertia and damping. Following an abrupt change in the dynamical system, the power output and both generator and grid frequencies all exhibit damped oscillations now depending on the (finite) grid inertia. In practical applications, it appears that for a small inertia system the cage model is preferable.Index Terms-Power system stability, Power system transients, Power system protection, Rate of change of frequency or ROCOF, Renewable energy sources, Synchronous generators.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Network susceptibilities: Theory and applications

Cited by 55 publications

References 45 publications

Non-local impact of link failures in linear flow networks

Non-local impact of link failures in linear flow networks

Comparison of Coupled Nonlinear Oscillator Models for the Transient Response of Power Generating Stations Connected to Low Inertia Systems

Monte Carlo basin bifurcation analysis

Contact Info

Product

Resources

About