The structure of electrical networks: a graph theory based analysis

Atkins, Karla; Chen, Jiangzhuo; Kumar, V. S. Anil; Marathe, Achla

doi:10.1504/ijcis.2009.024874

Cited by 23 publications

(18 citation statements)

References 17 publications

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“…This phenomenon, along with other vulnerabilities of the power grid, was studied from a few different viewpoints. First, several papers studied common topological properties of power grid networks and probabilistic failure propagation models, so that one can evaluate the behavior of a generic grid as a self-organized critical system using, for example, percolation theory (see [5], [12], [23], [25], [26], [30], [35], [39], [41] and references therein). These works are closely related to a long line of research in the power community which uses monte carlo techniques to analyze system reliability (e.g., [10])…”

Section: Related Workmentioning

confidence: 99%

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Power grid vulnerability to geographically correlated failures — Analysis and control implications

Bernstein

Bienstock

Hay

et al. 2014

IEEE INFOCOM 2014 - IEEE Conference on Computer Communications

148

156

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We consider power line outages in the transmission system of the power grid, and specifically those caused by a natural disaster or a large scale physical attack. In the transmission system, an outage of a line may lead to overload on other lines, thereby eventually leading to their outage. While such cascading failures have been studied before, our focus is on cascading failures that follow an outage of several lines in the same geographical area. We provide an analytical model of such failures, investigate the model's properties, and show that it differs from other models used to analyze cascades in the power grid (e.g., epidemic/percolation-based models). We then show how to identify the most vulnerable locations in the grid and perform extensive numerical experiments with real grid data to investigate the various effects of geographically correlated outages and the resulting cascades. These results allow us to gain insights into the relationships between various parameters and performance metrics, such as the size of the original event, the final number of connected components, and the fraction of demand (load) satisfied after the cascade. In particular, we focus on the timing and nature of optimal control actions used to reduce the impact of a cascade, in real time. We also compare results obtained by our model to the results of a real cascade that occurred during a major blackout in the San Diego area on Sept. 2011. The analysis and results presented in this paper will have implications both on the design of new power grids and on identifying the locations for shielding, strengthening, and monitoring efforts in grid upgrades.

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Section: Related Workmentioning

confidence: 99%

“…In these experiments, the actual Western Interconnect map was used, which includes the relevant parts of Northern Baja California in Mexico 5. Recently, some of the media publications mentioned the fact that this was not the only fault in that area.…”

mentioning

confidence: 99%

Power grid vulnerability to geographically correlated failures — Analysis and control implications

Bernstein

Bienstock

Hay

et al. 2014

IEEE INFOCOM 2014 - IEEE Conference on Computer Communications

148

156

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“…In contrast with these works, we focus on failures within a specific geographical region (e.g., [2], [3], [15]), implying that the failed components do not necessarily share the same physical resource. To the best of our knowledge, geographically correlated failures have been rarely considered [6], [7], [16]- [18] and in most cases, the assumption is that the failures of the components are deterministic.…”

Section: Related Workmentioning

confidence: 99%

Network vulnerability to single, multiple, and probabilistic physical attacks

Agarwal

Efrat

Ganjugunte

et al. 2010

2010 - Milcom 2010 Military Communications Conference

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Abstract-Telecommunications networks heavily rely on the physical infrastructure and, are therefore, vulnerable to natural disasters, such as earthquakes or floods, as well as to physical attacks, such as an Electromagnetic Pulse (EMP) attack. Largescale disasters are likely to destroy network equipment and to severely affect interdependent systems such as the power-grid. In turn, long-term outage of the power-grid might cause additional failures to the telecommunication network.In this paper, we model an attack as a disk around its epicenter, and provide efficient algorithms to find vulnerable points within the network, under various metrics. In addition, we consider the case in which multiple disasters happen simultaneously and provide an approximation algorithm to find the points which cause the most significant destruction. Finally, since a network element does not always fail, even when it is close to the attack's epicenter, we consider a simple probabilistic model in which the probability of a network element failure is given. Under this model, we tackle the cases of single and multiple attacks and develop algorithms that identify potential points where an attack is likely to cause a significant damage.Index Terms-Network survivability, geographic networks, network design, Electromagnetic Pulse (EMP), computational geometry.

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“…Here again, optimisation criteria consists usually in minimizing the cost of activated components and/or the minimization of the size of the sequence of modifications between two consecutive configurations. In such planning schedules, vulnerability of configurations can be taken into account by considering various graph theory metrics [1]. Note that in this context, balanced planning schedules can also be provided by configuring the network in balanced subnetworks [21,9,12] or by considering balanced configurations in terms of power of loads [20].…”

Section: Introductionmentioning

confidence: 99%

Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

Barth

Mautor

Moissac³

et al. 2021

Theoretical Computer Science

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We consider power distribution networks containing source nodes producing electricity and nodes representing electricity consumers. These sources and these consumers are interconnected by a switched network. Configuring this network consists in deciding which switches are activated and the orientation of the links between these switches, so as to obtain a directed acyclic graph (DAG) from the producer nodes to the consumer nodes. This DAG is valid if the electric flow it induces satisfies the demand of each consumer without exceeding the production capacity of each source and the flow capacity of each switch. We show that the problem of deciding if such a valid DAG exists is NP-complete. In the case where such a valid DAG exists, we study the problem of determining a valid DAG that balances the ratio between the amount of electricity produced and the maximum production capacity for each source. We show that this minimization problem is also NP-complete in the general case but that it becomes polynomial in the case of ring network topologies.

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The structure of electrical networks: a graph theory based analysis

Cited by 23 publications

References 17 publications

Power grid vulnerability to geographically correlated failures — Analysis and control implications

Power grid vulnerability to geographically correlated failures — Analysis and control implications

Network vulnerability to single, multiple, and probabilistic physical attacks

Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

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The structure of electrical networks: a graph theory based analysis

Cited by 23 publications

References 17 publications

Power grid vulnerability to geographically correlated failures &#x2014; Analysis and control implications

Power grid vulnerability to geographically correlated failures &#x2014; Analysis and control implications

Network vulnerability to single, multiple, and probabilistic physical attacks

Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

Contact Info

Product

Resources

About

Power grid vulnerability to geographically correlated failures — Analysis and control implications

Power grid vulnerability to geographically correlated failures — Analysis and control implications