Small-Signal Stability Analysis of Inertia-Based Grid-Forming MMC Interfaced with a Grid of Varying Short-Circuit Ratio

Modular Multilevel Converters (MMCs) play a crucial role in high-voltage direct current (HVDC) transmission systems, particularly for integrating offshore wind power. Grid-forming (GFM) control has been proposed for MMC to enhance stability when connected to low-inertia grids; however, systems with high short-circuit ratios (SCRs) are susceptible to sub-synchronous oscillations (SSOs). This paper develops a detailed small-signal model of GFM-controlled MMCs that accurately captures dynamic interactions among controllers, circulating currents, and submodule capacitor voltage dynamics. Stability analysis reveals that conventional tuning methods fail to decouple inner current control and voltage control loops, leading to instability. To address this, a novel control tuning algorithm for cascaded voltage and current controllers is proposed, ensuring robust operation across varying SCRs. The effectiveness of the proposed method is validated through eigenvalue analysis and time-domain simulations, demonstrating its ability to dampen oscillations and enhance stability in grids with low and high SCRs.