Do topological models provide good information about electricity infrastructure vulnerability?

Abstract

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss, and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern U.S. power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack-vectors that appear to cause the most damage depend on the measure chosen. While the topological metrics and the power grid model show some similar trends, the vulnerability metrics for individual simulations show only a mild correlation. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading.

Suppressing cascades of load in interdependent networks

“…To capture different amounts of demand, numbers of redundancies, ages of infrastructure, susceptibility to sagging power lines (16,17), and other factors that affect the rate at which cascades of load shedding and failures begin in each network, we introduce a load disparity parameter r as follows. Each node in c is r times more likely than a node in d to receive a new grain of sand.…”

“…We expect that this work will stimulate calculations of critical points in interconnectivity among networks subjected to other dynamics, such as linearized power flow equations in electrical grids (16,17) and other domain-specific models. As critical infrastructures such as power grids, transportation, communication, banks, and markets become increasingly interdependent, resolving the risks of large cascades and the incentives that shape them becomes ever more important.…”

“…Researchers have begun to model cascades of load and failure within individual power grids using probabilistic models (15), linearized electric power dynamics (16,17), and game theory (18).…”

Sometimes There Is No ''Most-Vital'' Arc: Assessing and Improving the Operational Resilience of Systems

“…In this context, vital arcs are those that contribute most to these graph theoretic measures, such as the average path length between every pair of nodes or the size of the largest connected component (e.g., Albert et al 2000;Holme et al 2002). A drawback of this is that when applied to real systems (e.g., Albert et al 2004;Schneider et al 2011), these simple measures of connectivity often fail to capture the most salient features of network function (e.g., Doyle et al 2005, Hines et al 2010, making them of limited value to operators of real network-centric infrastructure systems (Alderson 2008, Alderson andDoyle 2010).…”

Visualizing the Electrical Structure of Power Systems

“…This is plausibly a consequence of some structural power-law distribution in electrical networks, however trying to infer the vulnerability of a power system from basic topological measures remains quite dubious [32]. Purely topologic models of a power system offer only limited insight into how a system will behave, as they neglect the physical flow equations that govern power propagation through the network.…”