A Network-of-Networks Model for Electrical Infrastructure Networks

Abstract

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.

A generative graph model for electrical infrastructure networks

“…We associate a graph with a power grid in the same manner as described in [19]. Namely, power grid graphs are undirected graphs in which each vertex additionally has a "type" according to its voltage level.…”

“…Of course, actual power-flows may be directional, vary in magnitude, etc, but such properties depend on the particular dynamics and operational state of the grid. As introduced in [19], a power grid graph with multiple voltage levels can be decomposed as the union of same-voltage subgraphs and transformer edges. More precisely, the subgraph induced by voltage level X ∈ X consists of all vertices of voltage X and all edges between them.…”

“…The weight of a vertex i ∈ H is the number of vertices in C i in G and the weight of a edge {i, j} is the number of transformer edges between C i and C j in G. In the language of graph theory, interconnection graphs are weighted, attributed quotient graphs (under the equivalence relation of belonging to the same connected component within a same-voltage subgraph) with attributes given by voltage levels, and additional vertex and edge weightings based on multiplicities. With the exception of the edge and vertex weights, an identical construct was considered in [19].…”

“…In regard to this issue, Halappanavar et al [19] argue that the inherently heterogeneous nature of the real-world power grid necessitates graph models which, at a minimum, account for different node and edge types. Accordingly, they argue it may be inappropriate to apply graph algorithms or metrics to the entire power grid graph in a way that treats vertices or edges within a network as homogenous in type.…”

“…Our model aims to match, according to user-specified input, meaningful structural properties encountered in real power grid graph data. The paper is organized as follows: in Section 2, we describe the graph theoretic basics underlying the model, which largely mirrors that which is presented in [19]. Then, in Section 3, we investigate characteristics of real-world power grid graphs.…”