A modular multilevel converter AC/DC small-signal admittance-based model for stability analysis of hybrid AC/DC grids

Artikel i vetenskaplig tidskrift, 2026

Modular Multilevel Converters (MMCs) have become a cornerstone technology for high-power applications such as High Voltage Direct Current transmission due to their scalability, low harmonic distortion, and high efficiency. However, their complex internal dynamics and multiple control loops introduce significant challenges in MMC modelling and stability analysis, particularly in multi-terminal hybrid AC/DC transmission grids. To address these challenges, this paper presents a novel frequency-domain MMC AC/DC small-signal admittance-based model that captures the dominant dynamic interactions between the AC and DC sides of the converter. Using dq-complex space vectors, the proposed model incorporates the MMC internal dynamics, circulating-current controller, phase-locked loop, inner current controller, and outer control loops, providing a detailed analytical representation of MMC behaviour. To address the inherently linear time-periodic (LTP) nature of MMC dynamics, the proposed formulation employs a structural reformulation in the dq-complex domain to obtain a compact linear time-invariant representation of the adopted LTP MMC model, without resorting to explicit harmonic expansions, multi-harmonic linearisation, or high-order harmonic state-space approximations. Analytical derivations of the MMC AC- and DC-side input admittances are also presented. The proposed AC/DC model enables frequency-domain stability analysis using approaches such as the Generalised Nyquist Criterion and the Positive-Mode-Damping stability criterion, while preserving the dominant AC/DC coupling structure required for converter-driven stability studies. Validation results and representative instability case studies using MATLAB/Simulink demonstrate the accuracy and robustness of the proposed model, highlighting the importance of simultaneously considering AC and DC dynamics in converter-dominated AC/DC systems.