In-depth data on the network structure and hourly activity of the Central Chilean power grid

Kim, Heetae; Olave-Rojas, David; Álvarez-Miranda, Eduardo; Son, Seung‐Woo

doi:10.1038/sdata.2018.209

Cited by 25 publications

(17 citation statements)

References 24 publications

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“…In a spatial network, the location of nodes and edges in space can heavily inform both the structure of the network and the behavior of dynamical processes on it. Indeed, obtaining a meaningful understanding of power grids [3][4][5], granular systems [6], rabbit warrens [7], and many other systems is impossible without considering the physical relationships between nodes in a network. For example, when studying traffic patterns on a transportation network, it is important to include information both about the physical distances between points and about the locations and directions of paths between heavily trafficked areas [8].…”

Section: Introductionmentioning

confidence: 99%

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Feng

Porter

2020

Phys. Rev. Research

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Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks-including both synthetic and natural ones-using topological methods that we developed recently for analyzing spatial systems. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs that were spun by spiders under the influence of various psychotropic substances.

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Section: Introductionmentioning

confidence: 99%

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Feng

Porter

2020

Phys. Rev. Research

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“…Since the values of ς k are different for different k, we are unable to compute a closed form solution for (25). However, a root-finding algorithm can be used to calculate the peak time and the maximum absolute flow through the line.…”

Section: The Swing Equation and Its Modal Decompositionmentioning

confidence: 99%

“…For large enough γ we expect the peak time to be the root of (25) closest to the origin. Then a good choice of the initial guess for the root-finding algorithm can be obtained by Taylor expanding (25) up to third order about the origin and setting the third order expansion equal to zero. This leads to the following initial guess,…”

Section: The Swing Equation and Its Modal Decompositionmentioning

confidence: 99%

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Modal Decomposition of the Linear Swing Equation in Networks with Symmetries

Bhatta,

Hayat,

Sorrentino

2021

Preprint

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Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to explain how network symmetries affect the swing equation transient and steady state dynamics. We introduce a modal decomposition that allows us to study transient effects, such as the presence of overshoots in the system response. This modal decomposition provides insight into the peak flows within the network lines and allows a rigorous characterization of the effects of symmetries in the network topology on the dynamics. Our work applies to both cases of homogeneous and heterogeneous parameters. Further, the model is used to show how small perturbations propagate in networks with symmetries. Finally, we present an application of our approach to a large power grid network that displays symmetries.

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“…The weighted networks are: Central Chilean Power Grid (GRID): Nodes represent power plants, substations, taps, and junctions in the Chilean power grid. Edges represent transmission lines, with distances in kilometers [9]. The capacity of each line in kilovolts is also provided.…”

Section: Datasetsmentioning

confidence: 99%

PATHATTACK: Attacking Shortest Paths in Complex Networks

Miller¹,

Shafi²,

Ruml³

et al. 2021

Preprint

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Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide Web. An adversary with the capability to perturb the graph might make the shortest path between two nodes route traffic through advantageous portions of the graph (e.g., a toll road he owns). In this paper, we introduce the Force Path Cut problem, in which there is a specific route the adversary wants to promote by removing a minimum number of edges in the graph. We show that Force Path Cut is NP-complete, but also that it can be recast as an instance of the Weighted Set Cover problem, enabling the use of approximation algorithms. The size of the universe for the set cover problem is potentially factorial in the number of nodes. To overcome this hurdle, we propose the PATHATTACK algorithm, which via constraint generation considers only a small subset of paths-at most 5% of the number of edges in 99% of our experiments. Across a diverse set of synthetic and real networks, the linear programming formulation of Weighted Set Cover yields the optimal solution in over 98% of cases. We also demonstrate a time/cost tradeoff using two approximation algorithms and greedy baseline methods. This work provides a foundation for addressing similar problems and expands the area of adversarial graph mining beyond recent work on node classification and embedding.

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In-depth data on the network structure and hourly activity of the Central Chilean power grid

Cited by 25 publications

References 24 publications

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence

Modal Decomposition of the Linear Swing Equation in Networks with Symmetries

PATHATTACK: Attacking Shortest Paths in Complex Networks

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