With the increasing integration of grid-connected inverter-based resources (IBRs) and the declining generation from fossil-fuel-based synchronous generators, the instability of grid voltage and frequency has become a growing concern. To address this issue, E-STATCOMs, which combine energy storage (ES) with static synchronous compensator (STATCOM), are gaining attention as a solution for enhancing grid stability. Conventional multilevel converter-based E-STATCOM topologies can be categorized into two types: those that distribute the ES within the multilevel converter and those that centralize it in the DC-link. Of the two, centralized ES installation is more advantageous in terms of management and maintenance. However, the inherent structure of single-star multilevel topology poses challenges for centralized ES installation. As a result, double-star multilevel topology is commonly implemented, which leads to an enlarged footprint and increased cost. To overcome these limitations, this paper proposes an E-STATCOM topology that employs a zigzag transformer to decouple the ES from the single-star multilevel converter. Furthermore, this paper presents a control strategy to ensure the stable and reliable operation of the proposed E-STATCOM topology. The feasibility and effectiveness of the proposed topology and control strategy are validated through simulation and experimental results.