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## 1 Structural Vulnerability of Power Grids to Disasters:

### Citations

3316 |
Collective dynamics of “small-world” networks
- Watts, Strogatz
- 1998
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Citation Context ...ower grid topologies pertaining to the Western US grid and the grid under the Union for Coordination of Transmission of Electricity (UCTE) in Europe. The Western US grid has 4941 nodes and 6594 edges =-=[31]-=- while the power grid of the UCTE has 1254 buses and 1811 lines [32]. Failure propagation simulation and determined bounds for these networks are shown in Figs. 7 and 8. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ... |

1009 | Error and attack tolerance of complex networks
- Albert, Jeong, et al.
- 2000
(Show Context)
Citation Context ... terminating. The final state will often include greater number of failures than the initial state and efforts are made to study the effect of the grid structure in influencing the spread. References =-=[10]-=-, [30] study the effect of removing nodes from power grid graphs based on their centrality and degree measures and its effect on network connectivity. The authors of [11] analyze the propagation of st... |

893 | Matrix Perturbation Theory
- Stewart, Sun
- 1990
(Show Context)
Citation Context ...his area. Let normalized eigenvector u1 correspond to the largest eigenvalue βA of adjacency matrix AG . By definition u1 satisfies max ‖x‖2=1 xTAGx = u T 1AGu1 = βA (17) The Perron-Frobenius theorem =-=[34]-=- states that eigenvector u1 is a positive vector. Using this fact with Eq. (17), it is clear that removing edges from graph G (or deleting 1s from AG) always leads to a reduction in the magnitude of i... |

750 |
An analysis of approximations for maximizing submodular set functions-i
- Nemhauser, Wolsey, et al.
- 1978
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Citation Context ...m 1. The trace of A2rG , where AG is the adjacency matrix of grid graph G is a supermodular function of the constituent edges in the graph. A real-valued function f defined over set S is supermodular =-=[35]-=- if f(A⋃C) ≥ f(B⋃C) for B ⊂ A and A,B,C are subsets of S. In other words, the returns due to addition of C are not diminishing. Proof: Note that the ith diagonal element in A2rG is equal to the number... |

155 |
Catastrophic cascade of failures in interdependent networks,
- Buldyrev, Parshani, et al.
- 2010
(Show Context)
Citation Context ...ze the propagation of structural failures in complex random networks based on similar neighborhood propagation rules. This approach has been extended to study interdependent networks failures as well =-=[12]-=- where nodes of two different networks depend on one another for survivability. Similarly, references [14], [15] have analyzed node and edge percolation based techniques to understand failure propagat... |

121 |
Cascade-based attacks on complex networks
- Motter, Lai
- 2002
(Show Context)
Citation Context ...nating. The final state will often include greater number of failures than the initial state and efforts are made to study the effect of the grid structure in influencing the spread. References [10], =-=[30]-=- study the effect of removing nodes from power grid graphs based on their centrality and degree measures and its effect on network connectivity. The authors of [11] analyze the propagation of structur... |

116 | Zero duality gap in optimal power flow problem.
- Lavaei, Low
- 2012
(Show Context)
Citation Context ... capacity of transmission lines and the graphical properties (whether tree-like or loopy) affect the locational marginal electricity prices as well as the convergence of Optimal power flow algorithms =-=[2]-=-. Insufficient line capacities and network structure can lead to highly fluctuation prices and even negative prices [3]. From an reliability perspective, the grid structure influences the extent of da... |

86 | Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization
- Dobson, Carreras, et al.
- 2007
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Citation Context ...edistributing of the power flows for optimal dispatch. This can lead to some transmission lines running above their prescribed capacities and subsequently tripping due to overheating. Subsequently in =-=[7]-=-, the authors incorporate recovery mechanism for the tripped transmission lines into the failure model and show that the size of blackout has a power-law distribution as seen in reality. Reference [8]... |

38 | Epidemic spreading in complex networks with degree correlations. Statistical Mechanics of Complex Networks
- Boguna, Pastor-Satorras, et al.
- 2003
(Show Context)
Citation Context ... be found in [26]. It is worth mentioning that parallel analytical techniques are also used in studying social, biological and cyber-networks for information dissemination and spread of viruses [20], =-=[21]-=-. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable [16]. Existing work [22], [23], [24] has demonst... |

28 | topological models provide good information about electricity infrastructure vulnerability,” Chaos, vol. 20, 033122, 2010. Junjian Qi (S’12–M’13) received the B.E. and Ph.D. degree both in Electrical Engineering from Shandong University in 2008 and Tsingh
- Hines, Cotilla-Sanchez, et al.
- 1984
(Show Context)
Citation Context ...n dissemination and spread of viruses [20], [21]. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable =-=[16]-=-. Existing work [22], [23], [24] has demonstrated that the structure of real power grids as well as their finite sizes create significant deviations in observed graph parameters from those predicted i... |

25 | Approximate model of european interconnected system as a benchmark system to study effects of cross-border trades. - Bialek - 2005 |

24 | The n-k problem in power grids: New models, formulations, and numerical experiments,”
- Bienstock, Verma
- 2010
(Show Context)
Citation Context ...[7], the authors incorporate recovery mechanism for the tripped transmission lines into the failure model and show that the size of blackout has a power-law distribution as seen in reality. Reference =-=[8]-=- analyzes the problem of finding the optimal k lines in the grid that can be used for interdiction in the grid to create failures. Power Flow based analysis has been done to analyze geographically cor... |

19 |
Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks”.
- Wang, Scaglione, et al.
- 2010
(Show Context)
Citation Context ...spread of viruses [20], [21]. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable [16]. Existing work =-=[22]-=-, [23], [24] has demonstrated that the structure of real power grids as well as their finite sizes create significant deviations in observed graph parameters from those predicted in random graphs. Thi... |

14 | Power grid vulnerability to geographically correlated failures - analysis and control implications
- Bernstein, Bienstock, et al.
- 2012
(Show Context)
Citation Context ...m of finding the optimal k lines in the grid that can be used for interdiction in the grid to create failures. Power Flow based analysis has been done to analyze geographically correlated failures in =-=[9]-=-. Similarly, an interdiction based analysis on grid resilience considering short term impacts is discussed in [25]. However, these models include solving a Optimal Power Flow (OPF) or similar optimiza... |

12 |
The impact of wind generation on the electricity spot-market price level and variance: The texas experience.
- Woo, Horowitz, et al.
- 2011
(Show Context)
Citation Context ...l electricity prices as well as the convergence of Optimal power flow algorithms [2]. Insufficient line capacities and network structure can lead to highly fluctuation prices and even negative prices =-=[3]-=-. From an reliability perspective, the grid structure influences the extent of damage following an natural or man-made disaster. In particular, it affects the propagation of failures after an initial ... |

12 |
Resilience to degree-dependent and cascading node failures in random geometric networks
- Kong, Yeh
- 2010
(Show Context)
Citation Context ...tion rules. This approach has been extended to study interdependent networks failures as well [12] where nodes of two different networks depend on one another for survivability. Similarly, references =-=[14]-=-, [15] have analyzed node and edge percolation based techniques to understand failure propagation in random graphs generated by stochastic geometry. An interaction graph based model is presented in [1... |

11 |
Effective vaccination strategies for realistic social networks.
- Miller, Hyman
- 2007
(Show Context)
Citation Context ...rs can be found in [26]. It is worth mentioning that parallel analytical techniques are also used in studying social, biological and cyber-networks for information dissemination and spread of viruses =-=[20]-=-, [21]. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable [16]. Existing work [22], [23], [24] has d... |

10 |
Time to Replace the Saffir-Simpson Hurricane
- Kantha
(Show Context)
Citation Context ...s and loss of service. Over the years, natural disasters like earthquakes, floods, hurricanes have caused extensive power outages due to damage of grid equipment and loss of network connectivity [4], =-=[5]-=-. Such disasters also affect co-located interdependent transportation and communication infrastructure as well. Thus there is a greater need to quantify the effect of the grid structure on failure pro... |

9 | Random graph dynamics”, Cambridge University Press, 2006. 9[18 - Durrett - 2011 |

7 | Cascading link failure in the power grid: A percolation-based analysis
- Xiao, Yeh
(Show Context)
Citation Context ...ules. This approach has been extended to study interdependent networks failures as well [12] where nodes of two different networks depend on one another for survivability. Similarly, references [14], =-=[15]-=- have analyzed node and edge percolation based techniques to understand failure propagation in random graphs generated by stochastic geometry. An interaction graph based model is presented in [19] whe... |

6 |
Telecommunications Power Plant Damage Assessment for Hurricane Katrina Site Survey and Follow-Up Result
- Kwasinski, Weaver, et al.
(Show Context)
Citation Context ...slands and loss of service. Over the years, natural disasters like earthquakes, floods, hurricanes have caused extensive power outages due to damage of grid equipment and loss of network connectivity =-=[4]-=-, [5]. Such disasters also affect co-located interdependent transportation and communication infrastructure as well. Thus there is a greater need to quantify the effect of the grid structure on failur... |

5 | An interaction model for simulation and mitigation of cascading failures
- Qi, Sun, et al.
(Show Context)
Citation Context ...4], [15] have analyzed node and edge percolation based techniques to understand failure propagation in random graphs generated by stochastic geometry. An interaction graph based model is presented in =-=[19]-=- where power flow based cascading information is used to generate an interaction graph for the network to study the inter-nodal dependencies on cascades. A good review of works pertaining to grid resi... |

4 |
The power grid as a complex network: a survey”, Physica A: Statistical Mechanics and its Applications
- Pagani, Aiello
- 2013
(Show Context)
Citation Context ...nt deviations in observed graph parameters from those predicted in random graphs. This is because popular random network models like Erdos-Renyi, Barabasi-Albert, small world and configuration models =-=[13]-=- do not accurately capture the specific nature of the spatio-temporal evolution of power grids. Further, sharp breakdown thresholds emerge in analysis of topological failure models on random graphs th... |

2 |
An initial model fo complex dynamics in electric power system blackouts
- Dobson, Carreras, et al.
- 2001
(Show Context)
Citation Context ...ter and to incorporate the insights gained into transmission planning techniques to improve grid resilience. There is existing work that studies the impact of structure on grid reliability. Reference =-=[6]-=- describes a widely accepted and realistic DC model for the propagation of equipment (nodes and links) failures in cascading outages in the power grid. Deepjyoti Deka and Sriram Vishwanath are with th... |

2 |
Cascade-based Attack Vulnerability on
- Wang, Rong
(Show Context)
Citation Context ...encing the spread. References [10], [30] study the effect of removing nodes from power grid graphs based on their centrality and degree measures and its effect on network connectivity. The authors of =-=[11]-=- analyze the propagation of structural failures in complex random networks based on similar neighborhood propagation rules. This approach has been extended to study interdependent networks failures as... |

1 | Generative Growth Model for Power Grids
- Deka, Vishwanath
- 2013
(Show Context)
Citation Context ... of viruses [20], [21]. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable [16]. Existing work [22], =-=[23]-=-, [24] has demonstrated that the structure of real power grids as well as their finite sizes create significant deviations in observed graph parameters from those predicted in random graphs. This is b... |

1 |
Analytical Models for Power Networks: The case of the Western US and ERCOT grids”, arxiv preprint, 2015. Available at: http://arxiv.org/abs/1204.0165
- Deka, Vishwanath
(Show Context)
Citation Context ...ruses [20], [21]. However, the accuracy of percolation based techniques and 2further of the use of random graphs in modeling power grid cascading failures is debatable [16]. Existing work [22], [23], =-=[24]-=- has demonstrated that the structure of real power grids as well as their finite sizes create significant deviations in observed graph parameters from those predicted in random graphs. This is because... |

1 |
Interdiction Analysis of Electric Grids combining cascading outage and medium-term impacts
- Wang, Baldick
- 2014
(Show Context)
Citation Context ...wer Flow based analysis has been done to analyze geographically correlated failures in [9]. Similarly, an interdiction based analysis on grid resilience considering short term impacts is discussed in =-=[25]-=-. However, these models include solving a Optimal Power Flow (OPF) or similar optimization problem to study the propagation of failures. Such an approach is harder to analyze. In particular, it seldom... |

1 |
Research on Resilience of Power Systems Under Natural DisastersA
- Wang, Chen, et al.
- 2015
(Show Context)
Citation Context ...n is used to generate an interaction graph for the network to study the inter-nodal dependencies on cascades. A good review of works pertaining to grid resilience to natural disasters can be found in =-=[26]-=-. It is worth mentioning that parallel analytical techniques are also used in studying social, biological and cyber-networks for information dissemination and spread of viruses [20], [21]. However, th... |

1 |
Empirically validated availability model of information and communication technologies facilities under hurricane conditions
- Krishnamurthy, Kwasinski
- 2014
(Show Context)
Citation Context ...ane Center and used to 3Fig. 1. IEEE 14-bus test system [27] Fig. 2. Initial Node Failure (j) and Secondary Node Failure (i) predict the scale of damage and help in planning for evacuation strategies =-=[28]-=-. As we are concerned with connectivity in the network, we consider secondary failures in surviving nodes that get separated from the rest of the network due to initial failures in all of their neighb... |