A Complete HSS-Based Impedance Model of MMC Considering Grid Impedance Coupling

Harmonic state space (HSS) is seen as an effective impedance modeling method to precisely characterize the internal harmonic features of the modular multilevel converter (MMC). However, the existing MMC impedance models assume the ideal grid, ignoring the grid impedance, and they also do not incorporate the widely used dual-loop control and phase-locked loop (PLL). In this article, a complete MMC impedance model based on HSS is proposed to reveal the grid impedance coupling effect of MMC. The model analysis results demonstrate that the MMC impedance is coupled with the grid impedance due to the internal harmonics. This coupling causes MMC to be affected by the grid impedance and may cause instability. On the other hand, the proposed model not only consists of the ac current and the circulating current control, but also incorporates dc voltage outer loop and PLL with a clear physical meaning. Based on the proposed model, this article illustrates the factors that will enhance the coupling, which shows that the proposed model has to be used to improve the accuracy of the analysis. Finally, effectiveness of the proposed model is verified by simulation and experimental results.