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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.

Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing the describing function to compute harmonic amplitude and frequency remains incomplete. This is because a) it can not cover the cases where hard limits are not triggered, and b) it can not provide a complete trajectory for authentic linear analysis to confirm the presence of SO. Hence, two analytical methods are proposed by returning to the essential principle of harmonic balance. a) A dedicated approach is proposed to solve steady-state harmonics via Newton–Raphson iteration with carefully chosen initial values. The method encompasses all potential hard limit triggered cases. b) By employing extended multiharmonic linearization theory and considering loop impedance, an authentic linear analysis of SO is conducted. The analysis indicates that the initial negative damping modes transform into multiple positive damping modes as SO develops. Simulation validations are performed on a two-level voltage source converter using both PSCAD and RT-LAB. Additionally, valuable insights into the work are addressed considering the modularity and scalability of the proposed methods.