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...

The modeling of cascading failure in power systems is difficult because of the many different mechanisms involved; no single model captures all of these mechanisms. Understanding the relative importance of these different mechanisms is an important step in choosing which mechanisms need to be modeled for particular types of cascading failure analysis. This work presents a dynamic simulation model of both power networks and protection systems, which can simulate a wider variety of cascading outage mechanisms, relative to existing quasi-steady state (QSS) models. The model allows one to test the impact of different load models and protections on cascading outage sizes. This paper describes each module of the developed dynamic model and demonstrates how different mechanisms interact. In order to test the model we simulated a batch of randomly selected $N-2$ contingencies for several different static load configurations, and found that the distribution of blackout sizes and event lengths from the proposed dynamic simulator correlates well with historical trends. The results also show that load models have significant impacts on the cascading risks. This dynamic model was also compared against a QSS model based on the dc power flow approximations; we find that the two models largely agree, but produce substantially different results for later stages of cascading.Comment: 8 pages, 9 figures, 5 tables, submitted to IEEE transaction

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Cascading failure in electric power systems is a complicated problem for which a variety of models, software tools, and analytical tools have been proposed but are difficult to verify. Benchmarking and validation are necessary to understand how closely a particular modeling method corresponds to reality, what engineering conclusions may be drawn from a particular tool, and what improvements need to be made to the tool in order to reach valid conclusions. The community needs to develop the test cases tailored to cascading that are central to practical benchmarking and validation. In this paper, the IEEE PES working group on cascading failure reviews and synthesizes how benchmarking and validation can be done for cascading failure analysis, summarizes and reviews the cascading test cases that are available to the international community, and makes recommendations for improving the state of the art.