Under unbalanced grid, three cluster voltages are typically controlled balanced and unchanged for the star-connected cascaded H-bridge static synchronous compensator (CHB STATCOM), however, to deal with the unbalanced grid voltages, the modulation voltages become unbalanced, which would result in fewer steps of the staircase voltages and unbalanced double-line-frequency ripples across the cluster voltages. Thus, the harmonic performance of the currents is deteriorated. In addition, the negative sequence currents are always injected for active power redistribution, which degrades the power quality. To improve the current performance under the unbalanced grid, three cluster voltages are regulated to different values and three-phase modulation voltages can maintain balance. Based on this concept, three cluster voltages can be derived by decomposing the positive- and negative-sequence components from the converter voltages to meet the balance of three-phase currents. To ensure the cluster voltages stable, the zero-sequence voltage is further extracted to analyze the active power distribution. It is interesting to find that the total active power in each phase induced by both the negative and zero-sequence voltages is equal to zero, which reveals the CHB STATCOM has the natural zero-active-power feature. To keep three unequal cluster voltages within a certain boundary, the relationship between the unbalanced grid voltages and the cluster voltages is established, based on which the algorithm of limiting the cluster voltages is proposed. The theoretical analysis and the proposed control scheme are verified by the simulation and experimental results.