MMC impedance modeling and system stability research based on harmonic state space theory

Modular Multilevel Converter (MMC), renowned for its high modularity and flexible voltage levels, has been widely adopted in AC/DC system interconnections and renewable energy transmission. However, the wideband oscillations caused by the interaction between MMC and AC/DC systems remain a critical issue to be addressed. This paper first introduces mathematical modeling methods for MMC, highlighting that traditional average-value models lack sufficient accuracy. To address this limitation, a dynamic phasor model based on Harmonic State Space (HSS) theory is proposed, which more accurately captures the harmonic coupling characteristics of MMC. Utilizing harmonic linearization principles, a small-signal impedance model of MMC is established, and its accuracy is validated using a frequency scanning method. Furthermore, the impacts of the current control loop, phase-locked loop (PLL), and circulating current suppression controller on the AC-side impedance characteristics are analyzed. System stability is verified through RTDS (Real-Time Digital Simulator) simulations. The results demonstrate that parameter variations in the PLL and circulating current suppression controller significantly affect system stability, particularly in high-frequency ranges. This study provides a theoretical foundation for stability analysis and control parameter optimization in MMC-based systems.