In a power system, when a fault occurs, a Static Synchronous Compensator (STATCOM) is often required to inject negative-sequence current to compensate for unbalanced conditions. In high-voltage applications, single-star multilevel converters are commonly used in STATCOM systems to efficiently interface with high-voltage levels. However, during unbalanced condition compensation, these circuits experience cluster energy imbalance, which must be addressed through the balancing control. The conventional cluster energy balancing method utilizes zero-sequence voltage to redistribute active power for system balance. Under severe unbalance, a large negative-sequence current must be injected to compensate grid or load asymmetry. In conventional single-star multilevel converters, the zero-sequence component of the cluster output voltage is then actively regulated to eliminate the resulting cluster-energy imbalance; however, the required increase in this component can drive the converter into over-modulation. This limitation reduces the effectiveness of negative-sequence current injection, making it difficult to effectively compensate for unbalanced loads and grid conditions. To overcome this limitation, this paper proposes a modified power converter structure that retains the single-star multilevel converter topology while incorporating a zigzag transformer, along with a new cluster energy balancing control method. The proposed approach significantly enhances the range and capability of negative-sequence current compensation. The effectiveness of the proposed control strategy and converter design is validated through mathematical analysis, simulations, and experimental results.