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.
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.