Voltage Balancing Control Strategy for Hybrid MMC Based on BADS-Optimized Second Harmonic Injection

Under overmodulation conditions, the capacitor voltages of half-bridge and full-bridge submodules in hybrid modular multilevel converters (MMCs) may become unbalanced. This imbalance not only gives rise to overvoltage stress on submodule capacitors, jeopardizing equipment safety, but also degrades power quality and may even trigger operational instability. To address this issue, this paper proposes a minimum second harmonic circulating current injection method based on Bayesian Adaptive Direct Search (BADS) within the overall framework of model predictive control for MMCs. The method efficiently solves complex objective functions by alternately performing local Bayesian optimization and global grid search. Optimal second harmonic injection values under different modulation indices are obtained through offline computation and curve fitting. This approach achieves dynamic capacitor voltage balancing across a wide modulation range while minimizing operational losses caused by harmonic currents.