Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to solve these problems, but are subject to several limitations. One of the limitations is the ability to model a heterogeneous system in a consistent manner using the standard graph-theoretic formulation. In this paper, we propose a network-of-networks approach for modeling power transmission networks in order to explicitly incorporate heterogeneity in the model. This model distinguishes between different components of the network that operate at different voltage ratings, and also captures the intra and inter-network connectivity patterns. By building the graph in this fashion we present a novel, and fundamentally different, perspective of power transmission networks. Consequently, this novel approach will have a significant impact on the graph-theoretic modeling of power grids that we believe will lead to a better understanding of transmission networks.
Pagani and Aiello, in @cite_6 , present a survey of the most relevant work using complex network analysis to study the power grid. In this survey they remark that most of the networks studied were High Voltage from either North America, Europe, or China. They remark that most of the surveyed work show that degree distribution is exponential. The geography of the country seems to be important as the results differ somewhat between countries with differing geographies. One point of agreement between all studies is that the power grid is resilient to random failures but extremely vulnerable to attacks targeting nodes with high degree or high betweenness scores.
@cite_6
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The statistical tools of Complex Network Analysis are of useful to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention for its societ al relevance is that of electricity distribution. In this paper, we present a survey of the most relevant scientific studies investigating the properties of different Power Grids infrastructures using Complex Network Analysis techniques and methodologies. We categorize and explore the most relevant literature works considering general topological properties, physical properties, and differences between the various graph-related indicators and reliability aspects. We also trace the evolution in such field of the approach of study during the years to see the improvement achieved in the analysis.