An Analytical Formulation for Mapping the Spatial Distribution of Nodal Inertia in Power Systems

Mapping the spatial distribution of nodal inertia is crucial for helping system operators identify locational frequency stability issues in the power system operation planning process. Currently, index-based methods cannot retrieve the nodal inertia values for all load buses. To do so, this paper proposes an accurate analytical formulation relying only on steady-state system parameters to determine the nodal inertia values and, thus, map the spatial distribution of system inertia. The performance and reproducibility of the proposed formulation are evaluated using three test systems: a 5-bus radial system with two synchronous generators, a multimachine IEEE 68-bus benchmark system, and a larger NPCC 140-bus test system. We validate the proposed spatial distribution of nodal inertia using time-domain simulations and numerical estimations. In addition, we compare our method against the inertia distribution indexes presented in the literature. The results indicate that our formulation adequately quantifies the nodal inertia value in system buses, with low computational cost, and providing a suitable tool for operation planning analysis.