An Analytical Method for Nodal Inertia Estimation of Power Systems

The significance of system inertia, especially its non-uniform spatial distribution, is becoming paramount in the power system. The scope of inertia estimation has traditionally been the estimation of overall or total system inertia. However, as frequency dynamics become increasingly localized with the increasing penetration level of inverter-based resources (IBRs), the need for higher spatial resolution (geographically localized estimation) and faster temporal resolution (online or continuous estimation) in inertia estimation becomes paramount. This paper proposes an analytical method to estimate the spatial inertia distribution down to the transmission bus level, i.e., nodal inertia. Depending on data availability, the proposed method is flexible and can be used in two ways: ① to estimate nodal inertia under any given operating condition (or snapshot), or ② to continuously estimate nodal inertia under both ambient and transient conditions using available measurements from local phasor measurement units (PMUs). The novelty of the proposed method lies in its analytical formulation, which does not require rate of change of frequency (ROCOF) measurements or rate of change of power injections, making it immune to the noise associated with the estimation of these derived quantities. Additionally, the proposed method does not require defining near-zero ROCOF thresholds, which is a system-specific and nontrivial problem. The proposed method is mode-agnostic, which makes it more general than the dominant mode-based linearized methods. The applicability of the proposed method is demonstrated through simulation studies performed on the IEEE 39-bus and IEEE 68-bus test systems with varying penetration levels of IBRs. The robustness of the proposed method is numerically assessed against modeling and measurement uncertainties.