Fig. 4: Resilience and vulnerability patterns.

a Resilience pattern. The kernel density estimation of the largest failure (the greatest drop in customers served) in each resilient case (where the grid survives without a complete blackout) among the 1000 realizations. The darker color (blue) represents areas where the largest failures occur in the majority of resilient cases. b Vulnerability pattern. Similar to (a) but for vulnerable cases (where the grid experiences a catastrophic system-wide blackout) among the 1000 realizations. c Identified critical transmission lines in the transmission network. The critical index for a transmission line is defined as the proportion of instances where its failures directly contribute to catastrophic blackouts (a 100% complete outage occurs as soon as the line fails) across all realizations. Only those lines with a critical index higher than 5% are highlighted (blue), while the remaining lines are colored in gray. The names of substations associated with these critical lines are labeled. The transmission network with highlighted critical lines of (c) is overlaid on a basedmap from Esri⁵⁷. d Resilience and vulnerability patterns of the top four critical transmission lines. The resilience pattern boxplots (blue) show the distributions of line failure times in instances where the system ultimately remains functional despite the failure of the corresponding lines. The vulnerability pattern boxplots (red) show similar distributions in instances where a catastrophic blackout occurs following the failure of the specific lines. Tiny gray dots represent individual data points. The horizontal black line within each box indicates the median, box edges show the interquartile (50%) range, and whiskers extend to the 5th and 95th percentiles.