Enhancing the resilience of critical infrastructures: Statistical analysis of power grid spectral clustering and post-contingency vulnerability metrics

Controlled islanding can enhance power grid resilience and help mitigate the effect of emerging failure by splitting the grid into islands that can be rapidly and independently recovered and managed. In practice, controlled islanding is challenging and requires vulnerability assessment and uncertainty quantification. In this work, we investigate robustness drops due to N - k line failures and a controlled partitioning strategy for mitigating their consequences. A spectral clustering algorithm is employed to decompose the adjacency matrix of the damaged network and identify optimal network partitions. The adjacency matrix summarizes the power system topology, and different dynamic and static electrical factors such as line impedance and flows are employed to weigh the importance of the grid's cables. Differently from other works, we propose a statistical correlation analysis between vulnerability metrics and goodness of cluster scores. We investigate expected trends in the scores for randomized contingencies of increasing orders and examine their variability for random outages of a given size. We observed that the spectral radius and natural connectivity vary less on randomized failure events of a given size and are more sensitive to the selection of the adjacency matrix weights. Vulnerability scores based on the algebraic connectivity have a higher coefficient of variation for a given damage size and are less dependent on the specific dynamic and static electrical weighting factors. We show a few consistent patterns in the correlations between the scores for the vulnerability of the grid and the optimal clusters. The strength and sign of the correlation coefficients depend on the different electrical factors weighting the transmission lines and the grid-specific topology.