An approach to inertial distribution in power grids by a modularity index

This research introduces a novel graph theory and structural analysis framework to assess inertia distribution in power grids. We define the Inertial Support Index (ISI), derived from an enhanced modularity index, to evaluate inertial robustness within identified grid communities. By integrating community detection algorithms, the grid is partitioned into cohesive clusters with strong internal connections and clear boundaries, enabling robust regional inertia distribution analysis. Our approach utilises topological data, including generator locations, transmission line admittances, and power flow, to quantify the inertial modularity of each area. The proposed methodology is validated on the New England 39-bus test system, demonstrating its accuracy and effectiveness in assessing the ISI.