Comprehensive Derivation of Small-Signal Model for Virtual-Admittance Based Grid-Forming Modular Multilevel Converters

Paper in proceeding, 2025

This paper aims to develop an accurate small-signal model of a Grid-Forming Modular Multilevel Converter (GFM-MMC) using a virtual-admittance-based control strategy to establish a general foundation for stability analysis and control design. Yet, the presence of fundamental and second-order harmonics, along with the DC component in the GFM-MMC, complicates the small-signal model derivation. This paper presents a comprehensive framework for modeling and deriving the small-signal model of a GFM-MMC, incorporating fundamental, secondorder, and DC components. To achieve this, a time-invariant representation of the converter dynamics is developed using dqframes synchronized with both the fundamental and second-order harmonic components. The analytically derived input admittance model is then validated through simulation results.