State of charge(SoC) balancing is the key to achieve dynamic energy balancing among multiple modules in cascaded H-bridge battery energy storage systems(BESS), but traditional SoC balancing techniques could exacerbate DC-side transient voltage surges. This paper proposes a compound control strategy integrating SoC balancing and voltage surge suppression. Firstly, a mathematical model of battery energy SoC and output power is established, and a power balancing coefficient is constructed to integrate SoC balancing objective into charge and discharge control. An adaptive power balancing coefficient control method is proposed, which achieves SoC balancing while satisfying the rated power output of the system. Furthermore, addressing the issue of excessive DC-side voltage fluctuations caused by sudden changes in grid-side power, a closed-loop transfer function model of the DC/DC converter is established, revealing the mechanism by which key parameters affect transient respons. And voltage surge suppression is achieved through a method based on capacitor voltage feedforward. Finally, simulations and hardware-in-loop experiments verify the superior performance of the proposed control strategy.