Capacitor Voltage Balance Control of Hybrid Modular Multilevel Converters With Second- Order Circulating Current Injection

The capacitor voltage imbalance between the full-bridge sub-modules (FBSMs) and half-bridge submodules (HBSMs) may occur in the hybrid modular multilevel converters under the overmodulation operation. In this paper, the sub-module output voltage model under overmodulation is established first to explore the mechanism of capacitor voltage imbalance. With the established sub-module output voltage model, the complementary second-order voltage component in FBSMs and HBSMs is disclosed, which makes the second-order circulating current a novel control freedom to balance the capacitor voltages. With proper design of the magnitude and the phase angle of the injected second-order circulating current, the energy between the FBSMs and HBSMs is transferred and the capacitor voltage imbalance under overmodulation is eliminated. Moreover, the relationship between the sub-module capacitor voltage ripples and injected circulating current is also investigated to optimize the capacitor voltage ripple. Finally, the simulation and experiment results show that the proposed second-order circulating current injection method can not only balance the capacitor voltage but also reduce the voltage ripples of capacitors and current stress of semiconductor devices.