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.
Many researchers have explored the use of random graphs to model power grid @cite_11 @cite_13 @cite_2 @cite_6 @cite_7 @cite_10 , but in each case the resulting random graph does not fully model the structure of interest. In most cases, authors attempt to match graph characteristics from power grid networks, such as degree distribution, average path length, and clustering coefficient, in their random models.
@cite_7 @cite_10 @cite_6 @cite_2 @cite_13 @cite_11
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An electrical power grid is a critical infrastructure. Its reliable, robust, and efficient operation inevitably depends on underlying telecommunication networks. In order to design an efficient communication scheme and examine the efficiency of any networked control architecture, we need to characterize statistically its information source, namely the power grid itself. In this paper we studied both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. We made several interesting discoveries: the power grids are sparsely connected and the average nodal degree is very stable regardless of network size; the nodal degrees distribution has exponential tails, which can be approximated with a shifted Geometric distribution; the algebraic connectivity scales as a power function of network size with the power index lying between that of one-dimensional and two-dimensional lattice; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a Double Pareto LogNormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random power grids featuring the same topology and electrical characteristics we found from the real data. 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. Numerous recent papers have found important relationships between network structure and risks within networks. These results indicate that network structure can dramatically affect the relative effectiveness of risk identification and mitigation methods. With this in mind this paper provides a comparative analysis of the topological and electrical structure of the IEEE 300 bus and the Eastern United States power grids. Specifically we compare the topology of these grids 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 abstract models do not provide substantial utility for modeling power grids. To better represent the topological properties of power grids we introduce a new graph generating algorithm, the minimum distance graph, that produces networks with properties that more nearly match those of known power grids. While these topological comparisons are useful, they do not account for the physical laws that govern flows in electricity networks. To elucidate the electrical structure of power grids, we propose a new method for representing electrical structure as a weighted graph. This analogous representation is based on electrical distance rather than topological connections. A comparison of these two representations of the test power grids reveals dramatic differences between the electrical and topological structure of electrical power systems. In this article, we model electric power delivery networks as graphs, and conduct studies of two power transmission grids, i.e., the Nordic and the western states (U.S.) transmission grid. We calculate values of topological (structural) characteristics of the networks and compare their error and attack tolerance (structural vulnerability), i.e., their performance when vertices are removed, with two frequently used theoretical reference networks (the Erdos-Renyi random graph and the Barabasi-Albert scale-free network). Further, we perform a structural vulnerability analysis of a fictitious electric power network with simple structure. In this analysis, different strategies to decrease the vulnerability of the system are evaluated. Finally, we present a discussion on the practical applicability of graph modeling. 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, preferential-attachment, and small-world 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 structures of electric power networks.