Power grids are large-scale engineered systems that are indispensable to modern society, yet they remain inherently vulnerable to disturbances. Ongoing transitions in the energy sector—particularly the increasing penetration of renewable sources and inverter-based technologies—introduce new challenges, including reduced system inertia and faster propagation of fluctuations. As many emerging technologies rely on Direct Current (DC) components, understanding their impact on grid stability has become increasingly important.

Recent studies have shown that even without explicitly considering HVDC mechanisms, large interregional power flows can destabilize transmission grids, potentially leading to segmentation and system-wide failures [1]. This is further underscored by the 2025 Iberian blackout, where failures in HVDC interconnections between France and Spain were identified as contributing factors and elements that were first overloaded [2].

In our work, we aim to investigate the effect of including HVDC lines in a power grid system and extend the simple second-order Kuramoto Model to include a term that mimics inverter-based frequency control strategies. Here, in the new term, using different linear and non-linear activation functions, we can study their effects during the synchronisation process. Our dynamical simulations show that improvements in the phase synchronization stabilization, as well as in the cascade sizes, occur when we impose a threshold mechanism on our system. Though this comes at the expense of large relaxation times, meaning that node-level frequency and phase fluctuations will be damped out much slower.

In this work, we investigate the role of HVDC lines in power grid stability using an extended second-order Kuramoto model. We introduce an additional term describing HVDC connections that captures inverter-based frequency control strategies, allowing for both linear and nonlinear activation functions that will ultimately set the power flow across the line. This framework enables a systematic study of how such simple control mechanisms and otherwise constant power flow influence synchronization dynamics.

To accurately capture large-scale network behavior, we perform extensive simulations on GPU-accelerated architectures (where applicable), allowing us to study the full AC network and directly compare it with DC-augmented configurations. Our results show that introducing threshold-based control mechanisms can significantly enhance phase synchronization stability and reduce cascade sizes. However, these benefits come at the cost of increased relaxation times, leading to slower damping of node-level frequency and phase fluctuations [3].

References
[1] María Martínez-Barbeito, Damià Gomila, Pere Colet, Julian Fritzsch, and Philippe Jacquod. “Transmission grid stability with large interregional power flows”. In: Phys. Rev. Res. 7 (1 2025), p. 013137. DOI: 10.1103/PhysRevResearch.7.013137. URL:https://link.aps.org/doi/10.1103/PhysRevResearch.7.013137.
[2] ENTSOE. 28 April 2025 Blackout. 2026. URL: https://www.entsoe.eu/publications/blackout/28-april-2025-iberian-blackout/.
[3] Kristóf Benedek and Géza Ódor. The effect of HVDC lines in power-grids via Kuramoto modelling. 2025. arXiv: 2512.24122 [physics.soc-ph]. URL: https://arxiv.org/abs/2512.24122.

Across HVDC lines, operators usually transmit a constant amount of power between dispatches, whereas through regular AC connections, we typically tie this amount to the phase angle differences.