Impedance-Based AC/DC Terminal Modeling and Analysis of the MMC-BTB System

Impedance-based small-signal stability analysis is widely applied in practical engineering with modular multilevel converters (MMCs). However, the deficiencies of existing impedance models (IMs) and the idealized extension for the single MMC influence the analyses in multiterminal systems. In this article, these gaps are filled by focusing on an MMC-based back-to-back system. To obtain the steady-state harmonics of the system, a numerical method is initially proposed based on Newton–Raphson iteration in the frequency domain. Then, by substituting the shared terminal dynamics with active or passive devices, theoretical AC/DC IMs based on typical control loops with pure time delays are directly established via multiharmonic linearization. Further aided by the derived IMs, two neglected aspects in the current literature are investigated, including the influence of power transformers on low-frequency impedance characteristics and the rationality of using simplified IMs for high-frequency resonance studies. The stability of interlinking systems needs to be comprehensively analyzed at both AC and DC terminals. The analyses help to position the instability source, obtain the stability margin, and guide the supplementary control strategy. All IMs and analyses are verified via frequency scans and simulations in PSCAD.