Block Diagonal Dominance-based Model Reduction Method Applied to MMC Asymmetric Stability Analysis

Frequency-domain model reduction is a crucial concern in applying the prevailing impedance method for the stability analysis of complex systems, e.g., the modular multilevel converter (MMC). Recently, it has been shown that under symmetric conditions, a 2×2 matrix-based impedance model characterizing the two coupled frequencies of MMC are sufficient for its stability analysis. However, when the asymmetry occurs, principally, a much higher number of frequency couplings will appear in the MMC and thereby leads to a significant rise in the model dimension. Enlighted by this issue, there is an urgent need of finding a suitable frequency-domain method that can serve as a general criterion for model reduction. To this end, this paper proposes a block diagonal dominance (BDD)-based model reduction method and applied it to the asymmetric MMC. Basically, the BDD can decompose an N-dimensional task to N one-dimensional tasks, via which a significant reduction in model dimension can be realized. It is shown that by properly shifting the impedance model from one domain to another (e.g., α-β domain to $d-q$ domain), the BDD property can be achieved for most asymmetric scenarios. Finally, various case studies considering different asymmetry degrees are conducted to validate the effectiveness of the proposed method.