Correlation analysis of different vulnerability metrics on power grids

• We analyze the correlation between different power grid vulnerability metrics.
• Source–demand considered metrics quantify larger power grid vulnerability.
• Two source–demand considered vulnerability metrics are highly correlated.
• The clustering coefficient based vulnerability metric is weakly correlated with others.
• Blackout size has a mild correlation with source–demand considered metrics.

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)(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 VV 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 VPSVPS, which is equivalent to the important load shed metric in power engineering, has mild correlation with source–demand considered topology-based metrics VSDEVSDE and VCLVCL, but weak correlation with other topology-based metrics VEVE, VLCSVLCS and VCCVCC, 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.