The cascaded H-bridge static var generator (SVG) has been employed to provide reactive power and regulate grid voltages for many years because of its good modularity, easy scalability, and improved harmonic performance. A novel cluster-balancing power control method combining negative-sequence currents and zero-sequence voltage is proposed to redistribute the unbalanced active powers and eliminate the power oscillation under asymmetrical conditions. Simultaneously, the dynamic performance of the SVG power balance control can be improved under asymmetrical conditions with the zero-sequence voltage expression derived in this paper. On the basis of the proposed method, the fault ride through capability of star-connected SVG under asymmetrical conditions is compared among active power oscillation elimination (APOE), reactive power oscillation elimination (RPOE), and balanced positive sequence current (BPSC) injection references calculation strategies from the perspective of the zero-sequence voltage, maximum phase voltage, and maximum phase current. The method provides the theoretical reference for power control under asymmetric conditions and the analysis results show that under asymmetrical conditions, the current of BPSC is minimal and symmetrical, while the RPOE has the least voltage and no zero- sequence voltage needs to be injected. Finally, the results of simulation and experiment have been given to verify the theoretical studies.