A Fast Estimation of the Intrinsic Low-Frequency Oscillation Modes of Modular Multilevel Converter Based on AC Impedance Modeling

Complex power electronic topologies, such as modular multilevel converter (MMC), frequently experience broadband oscillation. To reveal the theoretical mechanism, this article models MMC based on linear-time-periodic-variable (LTPV) approach and obtains analytical expression of its ac-side admittance explicitly, formulated as a six-degree polynomial fraction. Three intrinsic oscillation modes of MMC topology are then estimated, and Foster-type circuit corresponding to the impedance is synthesized, revealing the root cause of multiple oscillation modes. It is found that due to the existence of arm capacitors, MMC impedance presents multiple LC oscillations. Increasing the capacitance can mitigate the oscillation, making the output impedance close to the filter inductor of two-level converter. The derivation and analysis are extended to single-loop grid-forming control, current control, and multiple-loop control. Correctness of the impedance model and oscillation frequency estimation is verified through impedance measurement and hardware-in-the-loop test.