With the increasing integration of inverter-based resources, the contribution of synchronous generators to power grids has decreased, resulting in a reduction in system inertia. Currently, acquiring the reserve power to mitigate the volatility associated with renewable-energy sources are difficult. Hence, evaluating the frequency stability of power systems and formulating operational and planning strategies based on these evaluations are becoming increasingly important. In this paper, we propose the definition and formalization of the frequency nadir index (FNI) by identifying the linear characteristics of inertia, frequency regulating reserve space (FRRS), and governor free (G/F) reserve in relation to frequency nadir, particularly under assumed contingencies such as generator dropout and sudden load fluctuation. Furthermore, we present an effective methodology for evaluating frequency stability using the FNI equation by extracting inertia, FRRS, and G/F reserve information from the power-system data. This approach is straightforward and efficiently computes the frequency nadir based on the size of the generator failure using readily available power-system data within a short timeframe.

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.