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.

The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power transmission and distribution networks have a topological structure that is straightforward to represent and analyze as a graph. However, simple graph models neglect the comprehensive connections between components that result from Ohm's and Kirchhoff's laws. This paper describes the structure of the three North American electric power interconnections, from the perspective of both topological and electrical connectivity. We compare the simple topology of these networks with that of random [1], preferential-attachment [2] and small-world [3] networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these topological forms may be misleading as models of power systems. To study the electrical connectivity of power systems, we propose a new method for representing electrical structure using electrical distances rather than geographic connections. Comparisons of these two representations of the North American power networks reveal notable differences between the electrical and topological structure of electric power networks.Recent research in complex networks [4] has elucidated strong links between network structure and performance. Scale-free networks, which are characterized by strongly heterogeneous (power-law) node connectivity (degree), are uniquely robust to random failures but vulnerable to directed attacks [2,5]. Graphs with exponential degree distributions, such as the random graph [1] and small-world networks [3] are more equally vulnerable to random failures and directed attacks. Scale-free networks also tend to lose synchronization when attacked at hub nodes [6], which is not the case for random graphs. And, for controllable networks, scale-free networks can be synchronized by controlling a small number of highly connected nodes [7], or even a single node [8]. On the other hand, ref. [9] shows that many classes of networks fail to synchronize, arguing that degree distribution alone is not sufficient to characterize the performance of a network. References [10,11] describe how network structure influences consensus (a form of synchronization), and how different ways of representing a system a graph may affect the conclusions that one draws about performance.Others [12,13] show that it is possible to maintain synchronization in evolving network topologies.Given that network structure can dramatically influence performance, and given the size, complexity and importance of electric power systems, it is not surprising that power grids are the subject of substantial study from a complex networks perspective [14]. The fact that data from many countries show a power-law in power system blackout sizes [15], leads naturally to the conjecture that this mi...

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