Graph Theory-Based Topological and Nodal Analysis for Identifying Critical Points to Enhance Resilience in Electrical Distribution Systems

The resilience of power grids has become increasingly critical due to the growing frequency of extreme climatic events. This study integrates graph-theoretical metrics, physics-adapted metrics based on Kirchhoff's laws, spectral analysis for global resilience evaluation, and power flow simulations. The analysis identifies key nodes with high centrality as critical to maintaining grid stability and evaluates their importance by simulating targeted faults. Results demonstrate that spectral analysis, through evaluating eigenvalues, reflects the network's vulnerability when critical nodes are disrupted. These findings emphasize the effectiveness of combining these methods to assess resilience comprehensively, identify critical points in the network, and determine where to prioritize structural improvements.