Submodule capacitor voltage balancing control of hybrid MMC under over-modulation based on dynamic arm reference voltage allocation

The hybrid modular multilevel converter (MMC) may experience an inter-group capacitor voltage imbalance between full-bridge submodule (FBSM) and half-bridge submodule (HBSM) groups during over-modulation operation. To address this issue, this paper first analyzes the group-level energy variation within an arm under over-modulation and reveals the mechanism of capacitor voltage imbalance between the FBSM and HBSM groups. Subsequently, an energy-based capacitor voltage balancing control is proposed, which regulates the allocation coefficient of the arm reference voltage between HBSMs and FBSMs and expands the available energy-regulation margin of HBSMs to enhance the energy balancing capability. This method achieves energy balance between the FBSM and HBSM groups without introducing significant adverse effects on the operation of the hybrid MMC. In addition, a cross-iteration algorithm is developed to determine the steady-state operating point, based on which the operating region under energy-balance constraints is further analyzed. The results show that the proposed control effectively extends the stable operating region. Finally, the effectiveness of the proposed control is validated through simulations and experiments.