Vulnerability-oriented power system renormalization for critical skeleton network analysis

Fast risk screening in large-scale transmission networks requires compact equivalent models that reduce network complexity while preserving reliability-relevant structures. Existing power system reduction and equivalencing methods mainly focus on electrical equivalence, regional power-flow characteristics, or planning-oriented representations, whereas vulnerable skeleton branches are rarely considered as explicit preservation targets during network coarse graining. This paper proposes a vulnerability-oriented power system renormalization method for critical skeleton network analysis. A composite diffusion metric integrating electrical coupling strength, branch power-flow stress, and post-contingency power-flow redistribution is developed to guide vulnerability-oriented spectral partitioning and skeleton retention. Combined with Ward equivalencing, the proposed framework constructs a renormalized equivalent power network (REPN) that preserves inter-area tie branches, skeleton buses, and intra-area vulnerable structures. An OPN-to-REPN coverage-mapping framework is further established to evaluate cross-scale consistency of electrical responses and vulnerable skeleton branch identification. Tests on six public systems ranging from 118 to 3375 buses demonstrate bus and branch compression ratios of 29.50–56.12% and 20.41–45.73%, respectively. At ρ = 10%, the hit rate and average precision for vulnerable skeleton branch consistency range from 94.74% to 100% and from 93.11% to 100%, respectively. Full-grid N-1 contingency validation on the IEEE 118-bus system further shows that the compressed representation retains substantial post-contingency risk information beyond the explicitly retained skeleton space, achieving an F1-score of 0.8424 and a severity correlation coefficient of 0.8497. The proposed framework provides a reliability-oriented reduced representation for vulnerability screening in large-scale transmission networks.