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

Power systems often include a specific set of lines that are crucial for the regular operations of the grid. Identifying the reasons behind the criticality of these lines is an important challenge in power system studies. When a line fails, the line outage distribution factor (LODF) quantifies the changes in power flow on the remaining lines. This paper proposes a network analysis from a local structural perspective to investigate the impact of local structural patterns in the underlying graph of power systems on the LODF of individual lines. In particular, we focus on graphlet analysis to determine the local structural properties of each line. This research analyzes potential connections between specific graphlets and the most critical lines based on their LODF. In this regard, we investigate N-1 and N-2 contingency analysis for various test cases and identifies the lines that have the greatest impact on the LODFs of other lines. We then determine which subgraphs contain the most significant lines. Our findings reveal that the most critical lines often belong to subgraphs with a less meshed but more radial structure. These findings are further validated through various test cases. Particularly, it is observed that networks with a higher percentage of ring or meshed subgraphs on their most important line (based on LODF) experience a lower LODF when that critical line is subject to an outage. Additionally, we investigate how the LODF of the most critical line varies among different test cases and examine the subgraph characteristics of those critical lines.