In low-inertia systems with a high penetration of renewable energy, the rotational kinetic energy and inertia constant are significant factors in determining frequency stability. The energy released owing to the frequency decrease during contingency represents a portion of the inertia that a synchronous machine possesses in the normal state. However, when securing inertia or planning additional resources to secure frequency stability, inertia in the normal state is analyzed as the standard rather than the amount of energy released during a fault. Therefore, in this paper, we define the actual energy emitted from a synchronous machine as Effective inertia. In order to evaluate Effective inertia in various operating conditions, we conducted a comprehensive review on approximately 24,627 cases from the years 2019, 2020, and 2021. As a result, in systems with low rotational kinetic energy, both low- and high-frequency nadirs were observed, indicating high uncertainty. However, Effective inertia presented a consistent trend regarding the energy release aligned with the minimum frequency. For instance, the rotational kinetic energy required to satisfy the frequency standard was 23 GWs, while the required Effective inertia was 858 MWs. We emphasize that securing inertia based on rotational kinetic energy includes additional imaginary energy that does not contribute to frequency, resulting in an energy requirement greater than that needed for Effective inertia. Therefore, in order to secure the frequency stability of the future system, the actual required energy amount based on Effective inertia will be presented and utilized in the inertia market and FFR (Fast Frequency Response) resource design.
The increasing interconnection of inverter-based resources (IBRs) with low short-circuit current has weakened grid strength, making phase-locked loops (PLLs) susceptible to instability due to accumulated phase-angle error under current limiting. This study defines such instability as IBR instability induced by reduced grid robustness and proposes a root-mean-square (RMS) model-based screening method. After fault clearance, the residual q-axis voltage observed by the PLL is treated as a disturbance signal and, using the PLL synchronization equations, is analyzed with a standard second-order formulation. The maximum phase angle at which synchronization fails is defined as , and the corresponding q-axis voltage is defined as . This value is then mapped to a screening metric suitable for RMS-domain assessment. The proposed methodology is applied to the IEEE 39-bus test system: the stability boundary and are obtained in Power System Simulator for Engineering (PSSE), and the results are validated through electromagnetic transient (EMT) simulations in PSCAD. The findings demonstrate that the RMS-based screening can effectively identify operating conditions that are prone to PLL instability in weak grids, providing a practical tool for planning and operation with high IBR penetration. This screening method supports power system planning for high-penetration inverter-based resources by identifying weak-grid locations that require EMT studies to ensure secure operation after grid faults.