Stability Assessment of Modular Multilevel Converters Based on Linear Time-Periodic Theory: Time-Domain vs. Frequency-Domain

The periodic characteristic of modular multilevel converter (MMC), which originates from the multi-harmonic couplings among internal dynamics, results in challenges to develop the linear time-invariant (LTI) model of MMC. The linearization of MMC is inherently around time-periodic equilibrium trajectory. In this paper, two different methods to assess small-signal stability of MMC are compared. Both are based on the linear time-periodic (LTP) systems theory, but one is in the time domain (TD) and the other is in the frequency domain (FD). The LTP model of MMC is derived from the linearized arm averaged model. Then, an LTI model for the LTP system is constructed in the FD through the harmonic state-space method. Small-signal stability analysis based on Floquet theory and generalized Nyquist criterion, that accompany TD and FD, are introduced and compared. It is demonstrated that models developed in both domains can effectively capture the small-signal behavior of MMC. Third and higher-order harmonic components of the states have significant effect on the impedance-based stability analysis of MMC around mid-frequency range. Analytical results are validated by electromagnetic transient simulations based on the MMC aggregated model.