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Learning from two-level voltage source converters, the existing impedance-based stability analyses of modular multilevel converters (MMCs) primarily focus on system modes with finite closed-loop transfer functions, which consider perturbations of the current flowing into the public AC/DC terminal as the input. However, this approach may be insufficient for MMCs due to their actively controlled circulating circuit, resulting from the distributed modulation of each arm and the circulating current control (CCC). To address this limitation, two cases that are not covered by the AC/DC terminal stability analysis are initially presented to support the conjecture. Subsequently, an inner loop impedance for the circulating circuit is established, which considers the dynamics of public terminals and divides the injected voltage perturbation by the corresponding current perturbation at the same frequency. To avoid the need for a right-half plane pole check when applying the Nyquist criterion, a logarithmic derivative-based criterion is proposed to directly identify the system modes. By utilizing the inner loop impedance, it becomes possible to achieve CCC parameter tuning with stability constraints and conduct an internal stability analysis of MMC-based systems. This work provides a strong foundation for the integration of power-electronicized power systems from the perspective of classical control theories.

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 solving 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., Comment: Accepted by IEEE TPEL

Multiple types of Nyquist-like impedance-based criteria are utilized for the small-signal stability analysis of converter-based AC systems. It is usually considered that the determinant-based criterion can determine the overall stability of a system while the eigenvalue-based criterion can give more insights into the mechanism of the instability. This paper specifies such understandings starting with the zero-pole calculation of impedance matrices obtained by state-spaces with the Smith-McMillan form, then clarifying the absolute reliability of determinant-based criterion with the common assumption for impedance-based analysis that each subsystem can stably operate before the interconnection. However, ambiguities do exist for the eigenvalue-based criterion when an anticlockwise encirclement around the origin is observed in the Nyquist plot. To this end, a logarithmic derivative-based criterion to directly identify the system modes using the frequency responses of loop impedances is proposed, which owns a solid theoretical basis of the Schur complement of transfer function matrices. The theoretical analysis is validated using a PSCAD simulation of a grid-connected two-level voltage source converter., Comment: Accepted by CSEE JPES

Nyquist criterion-based impedance ratio criteria (IRCs) have been widely applied for inspecting the risk of small-signal instability among converter-based AC power systems. Aided by a comparative study on voltage source converter, including the single-input single-output (SISO) and multiple input multiple output (MIMO) analyses in both the dq and the sequence domain, two aspects are emphasized in this paper: 1) the sufficiency of SISO analysis when the mapping function (MF) is observable to potentially unstable modes, and 2) the inconvenience of IRCs with an unintended right-half plane pole emergence of MF due to the source-load partition. The strictness of analyses is proved by a systematical deduction of explicit analytical impedance models using the state space. Moreover, a novel criterion that relies on the logarithmic derivative of MFs is proposed, which can identify the system modes directly, serve as an alternative to IRCs, and be extended to other transfer function-based stability analyses., Comment: techinical issue

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. Such gaps are filled by focusing on an MMC-based back-to-back system in this paper. To obtain the steady-state trajectory of the system, a numerical method is first 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 that consider typical control loops with the pure time delay, are directly established based on the multiharmonic linearization. Further aided by the derived IMs, two neglected aspects in the current literature, i.e., the influence of power transformers on low-frequency impedance characteristics and the rationality of using simplified IMs for high-frequency resonance studies, are investigated. It is confirmed that the stability of interlinking systems should be comprehensively analyzed at both AC and DC terminals. This helps position the instability source, obtain the stability margin, and guide the supplementary control strategy. All IMs and analyses are verified by frequency scans and simulations in PSCAD.