A High-Frequency MMC for DC–DC Applications Using a Three-Winding Transformer With DC Flux Cancellation

Coprime Polynomial Based Dual-Circulant Modulation for Inherent Submodule Voltage Balancing in MMDC

“…For the negative stage, all of the 𝑛 SMs in upper stack are inserted, while only 𝑚 SMs (0 < 𝑚 < 𝑛) are inserted in lower stack with 𝑛 − 𝑚 SMs bypassed. For the positive stage, 𝑚 SMs in upper stack and 𝑛 SMs in lower stack are inserted [1], [16], [17]. This modulation highly satisfies the demand of voltage amplitude conversion in MMDCs, since the choice of 𝑚 can be utilized as an effective control degree of freedom for voltage regulation [16], namely, a larger 𝑚 provides a higher step-down ratio and vice versa [1], [18].…”

“…The switching patterns need to be reordered and optimized for SM capacitor ripple reduction. Noting that the SM uniformity can be obtained so long as the patterns are alternately extracted from two circulant sets in sequence, it is not necessary to choose the first pattern from the additional circulant set inserting behind the first pattern from the basic set as (17). Each pattern can be considered as the beginning of the alternation to generate different switching matrixes, and the generated patterns with evenly distributed charging and discharging cycles would be chosen and applied.…”