Compared to the traditional modular multilevel converter (MMC) and alternative arm converter (AAC), the hybrid multilevel converter (HMC) exhibits superiority in terms of cost and volume. In the HMC, the pulse width of the direction switch (DS) is conventionally utilized to maintain capacitor voltage balancing (CVB). However, this method has certain limitations, including a restricted range of modulation indices and the inability to support pure reactive power operation. To address these drawbacks, a new CVB method based on the phase angle of the DS is proposed in this paper. Compared to the traditional method, the proposed method enables the HMC to achieve a full range of modulation index and four-quadrant operation. Additionally, it demonstrates improved performance in terms of SM capacitance and capacitor voltage ripple, especially under severe grid voltage sags and low power factors. A comparative analysis is conducted between two CVB methods, focusing on the SM number, switch number, and SM capacitance. Furthermore, a unified control strategy considering asymmetrical and symmetrical grid voltage sags is proposed for these two CVB methods. Finally, the effectiveness and superiority of the proposed CVB methods are verified by simulation and experimental testing.