Analyzing Power Grid Structure with Triangle Centrality Metrics

Studies to solve the transmission expansion problem (TEP) for a power system can benefit from employing complex network or graph theory metrics to speed up analysis and lead to more realistic methodologies. Currently, very little research has been conducted on solving TEP problems by understanding the electric grid as a spatially embedded complex network, and no work has been done before to explore the relation between the graph theory metric triangle centrality and power grid structure. Triangle centrality is the focus of this paper because it can provide insights into grid structure, and because it can be computed very quickly. This paper outlines a method to rapidly compute the triangle centrality for the graph of a power system, and also describes the methodology to test for a correlation between triangle centrality and power grid structure to determine triangle centrality's potential for assisting in solutions to the TEP. The structural metrics used in this paper are transmission line overloading, minimum bus voltage, islanded load, islanded generation, and number of contingency violations. Different sized synthetic power grid cases are used to test the relationship between triangle centrality and grid metrics.