General Scope

Frequency stability in modern power systems is increasingly compromised by the replacement of synchronous generators with distributed energy resources, which typically do not contribute to system inertia. This issue becomes particularly critical following large disturbances such as system splits. This work investigates the local rate of change of frequency (RoCoF) after system splits and its dependency on parameters such as inertia distribution and network topology.

Main Results

The investigation is based on a test system representing a large interconnected transmission network, while remaining sufficiently simple to isolate the effects of model parameter variations on the maximum RoCoF. The analyzed parameters include total system inertia (mechanical and virtual) and its spatial distribution. A strong influence is observed from both the magnitude and distribution of inertia, the averaging time window of the RoCoF signal, and the power exchange across the split interface. Notably, the spatial distribution of inertia has an impact comparable to that of the total system inertia. Even a reduction of the RoCoF averaging window (typically 500 ms) by 100 ms significantly increases the observed maximum RoCoF. The relationship between RoCoF and power exchange is found to be approximately linear. In contrast, voltage setpoints, generator loading, average line length, and delays between breaker operations have a comparatively minor impact.

The maximum RoCoF typically occurs at buses electrically close to the system split. However, no simple correlation with electrical distance is observed, and high RoCoF values can also occur at remote locations depending on the dominant oscillatory modes of the system.

Methods

Local RoCoF is analyzed using numerical simulations in the RMS domain. Generic models are employed for synchronous machines, automatic voltage regulators, governors, distributed generators, and loads. RoCoF is computed either directly from discrete frequency differences between simulation time steps or using a Savitzky–Golay filter to improve noise suppression.

Relevance

Frequency stability following system splits is one of the most critical challenges in interconnected, low-inertia power systems. The resulting frequency excursions and RoCoF can trigger widespread disconnection of generation and load, potentially leading to large-scale blackouts. Previous research has not sufficiently addressed the spatial variability of RoCoF in parameter sensitivity analyses, which can result in unrealistic assessments of generator robustness and protection schemes. This gap has contributed to real-world system failures, such as the 2025 blackout of the Iberian Peninsula.

Major Conclusions

The spatial distribution of inertia is as influential on the maximum RoCoF as the total system inertia itself. Additional key factors include the averaging time window used for RoCoF estimation and the power exchange across the split interface. Parameters such as line length and generator loading have a comparatively smaller effect. The findings contribute to improved requirements for the robustness of distributed energy resources, the design of protection schemes for large disturbances, and operational planning.