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Power systems often include a specific set of lines that are crucial for theregular operations of the grid. Identifying the reasons behind the criticalityof these lines is an important challenge in power system studies. When a linefails, the line outage distribution factor (LODF) quantifies the changes inpower flow on the remaining lines. This paper proposes a network analysis froma local structural perspective to investigate the impact of local structuralpatterns in the underlying graph of power systems on the LODF of individuallines. In particular, we focus on graphlet analysis to determine the localstructural properties of each line. This research analyzes potentialconnections between specific graphlets and the most critical lines based ontheir LODF. In this regard, we investigate N-1 and N-2 contingency analysis forvarious test cases and identifies the lines that have the greatest impact onthe LODFs of other lines. We then determine which subgraphs contain the mostsignificant lines. Our findings reveal that the most critical lines oftenbelong to subgraphs with a less meshed but more radial structure. Thesefindings are further validated through various test cases. Particularly, it isobserved that networks with a higher percentage of ring or meshed subgraphs ontheir most important line (based on LODF) experience a lower LODF when thatcritical line is subject to an outage. Additionally, we investigate how theLODF of the most critical line varies among different test cases and examinethe subgraph characteristics of those critical lines.

Impact of Higher-Order Structures in Power Grids' Graph on Line Outage Distribution Factor