Correlation analysis of different vulnerability metrics on power grids

Many scholars have used different metrics to quantify power grid vulnerability in the literature, but how correlated these metrics are is an interesting topic. This paper defines vulnerability as the performance drop of a power grid under a disruptive event, and selects six frequently used performance metrics, including efficiency (E), source–demand considered efficiency (SDE), largest component size (LCS), connectivity level (CL), clustering coefficient (CC), and power supply (PS), to respectively quantify power grid vulnerability V under different node or edge failure probabilities fp and then analyzes the correlation of these six vulnerability metrics. Taking the IEEE 300 power grid as an example, the results show that the flow-based metric VPS, which is equivalent to the important load shed metric in power engineering, has mild correlation with source–demand considered topology-based metrics VSDE and VCL, but weak correlation with other topology-based metrics VE, VLCS and VCC, which do not differentiate source–demand nodes. Similar results are also found in other types of failures, other system operation parameters and other power grids. Hence, one should be careful to use topology-based metrics to quantify the real vulnerability of power grids.