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.