This paper proposes a novel branch voltage-balancing control strategy for a hexagonal converter (Hexverter). First, the state-space model based on the double-dq transformation is analyzed in-depth along with the necessary basic mathematical derivation, and the active/reactive power control model in the dq reference frame for the Hexverter is proposed. Second, a zero-sequence double-loop network consisting of a Y-loop and a Hex-loop circulating current was established. This study proposes a method to suppress the Y-loop circulating current by connecting a capacitor at the neutral point. We then establish a novel branch voltage-balancing control strategy based on the transfer power model. The essence of the proposed control strategy is to control the charging and discharging states of each submodule via the zero-sequence voltages and the Hex-loop circulating current to regulate the power transfer between adjacent submodules and branches, thereby effectively ensuring the dynamic balance of the DC voltages of the submodules. The branch voltage-balancing control model and power control model proposed in this paper are based on zero-sequence and positive-sequence networks, respectively. The relative independence of the positive-and zero-sequence networks leads to decoupling of the branch voltage-balancing control model and the power control model; thus, the respective control objectives can be achieved by adjusting the respective control variables independently. It has a stronger adaptability to diverse power grid operating parameters. Finally, the validity and correctness of the mathematical model and control strategy proposed in this study are verified using MATLAB/Simulink.INDEX TERMS Hexverter, double-dq transformation, the zero-sequence double-loop network, the transfer power model, the voltage balancing control, circulating current suppression.