Topological Graph Metrics for Detecting Grid Anomalies and Improving Algorithms

Power grids are naturally represented as graphs, with buses as nodes and power lines as edges. Graph theory provides many ways to measure power grid graphs, allowing researchers to characterize system structure and optimize algorithms. We apply several topological graph metrics to 33 publicly-available power grids. Results show that a straightforward, computationally inexpensive set of checks can quickly identify structural anomalies, especially when a broad set of test networks is available to establish norms. Another application of graph metrics is the characterization of computational behavior. We conclude by illustrating one compelling example: the close connection between clique analysis and semidefinite programming solver performance. These two applications demonstrate the power of purely topological graph metrics when utilized in the right settings.

I. Introduction

The buses and transmission lines of a power grid translate naturally to the nodes and edges of a graph. This connection has been recognized for many years, and numerous graph structural properties have been studied with various power systems applications [1], [2]. Graph-theoretical methods have been used to identify system vulnerabilities [3]–[5], detect structural anomalies [6], generate and validate synthetic grids [7]–[10], create meaningful visualizations [11], [12], and perform partitioning [13], [14]. The graph analysis methods employed may be divided into two categories: weighted, where electrical information is embedded in the graph, and unweighted, where only topology is considered. Though there is a fundamental difference between a power system's topology and its electrical structure [4], [8], [15], unweighted graph analysis is ideal for quickly detecting unusual connectivity patterns. The topological algorithms used in this paper are computationally inexpensive, and interpretation of numerical results is straightforward. Consequently, it is feasible to scan large power grids to check for structural anomalies.