Analytical Framework for Assessing Effective Regional Inertia

TL;DR

This paper introduces a topology-aware framework to assess effective regional inertia by partitioning the power network into coherent regions using an extended slow coherency approach that includes load buses. It derives a closed-form nodal inertia expression and defines an effective regional inertia $H_{\text{eff}}^{\mathcal{R}}$ alongside a minimum-inertia criterion for new devices, enabling informed placement of inertial resources. Case studies on IEEE 39-bus and 68-bus systems demonstrate that adding inertia does not universally improve regional inertia due to spatial distribution and network topology, highlighting the importance of region-aware metrics for inverter-based resources. The framework advances regional frequency analysis by preserving local dynamics and linking inertia distribution, topology, and coherent-region structure to inertia adequacy and device allocation decisions.

Abstract

This paper proposes a novel formulation of effective regional inertia that explicitly accounts for both system topology and the spatial distribution of inertia. Unlike traditional approaches that model a region as an aggregated machine with an equivalent inertia, the proposed metric provides a topology-aware representation. The methodology builds on an analytical framework that extends classical slow coherency theory to address network partitioning and regional frequency stability. Based on these partitions, we develop a systematic procedure to evaluate the effective inertia of each region, enabling a more accurate interpretation of local inertial contributions, including those from virtual inertia provided by inverter-based resources (IBRs). Case studies on the IEEE 39-bus and 68-bus systems demonstrate that the integration of inertial devices does not uniformly improve system frequency response, underscoring the importance of the proposed metric for effective regional inertia assessment.

Figures (15)

• Figure 1: WSCC 9-bus system with a new inertial device connected at bus 8.
• Figure 2: (a) Equivalent system seen from bus 9, and (b) the nodal inertia at bus 8 as a function of the device inertia constant $H_\mathrm{device}$.
• Figure 3: Nodal inertia distribution across all buses as a function of $H_\mathrm{device}$.
• Figure 4: Frequency response at bus 8 under a 1 p.u. load step for different inertia scenarios connected at the same bus.
• Figure 5: Power system region with the location of a new device highlighted.