The aim of this paper is to investigate the ability of cascaded H-bridge STATic COMpensator in star and delta configuration to exchange negative-sequence current with the connecting grid. Zero-sequence voltage for the star and zero-sequence current for the delta configuration are utilized to guarantee dc-capacitor voltage balancing. A general solution for the required zero-sequence voltage/current for any kind of unbalanced condition is provided. The obtained solutions show that a singularity for both configurations exists under specific conditions, leading to infinite zero-sequence requirement. In case of star configuration, this singularity occurs when the amplitude of the positive- and negative-sequence components of the current output of the converter are equal. Analogously, the singularity for the delta configuration occurs when the amplitude of the positive- and negative-sequence components of the voltage at the converter terminals are equal. This singularity impacts the ratings of the system and imposes a limitation in the utilization of the compensator for unbalance compensation purposes, both in industrial and utility applications. Experimental results are presented to validate the theoretical analysis.