Excessive capacitor fluctuations will increase the volume and cost of the modular multilevel converter(MMC)

and reduce the stability of the system. Unbalanced grid voltage not only affects power transmission and circulating current control of MMC

the negative voltage and negative current caused by unbalanced grid voltage will increase the capacitor voltage fluctuations in MMC. In order to ensure the stability of devices

the capacitor voltage fluctuations will be reduced by circulating current injection under the unbalanced grid voltage conditions. Firstly

expressions of arm voltages are derived under unbalanced conditions. Then

the reference of circulating current injection for reducing the capacitor voltage fluctuations is calculated. The effect on capacitor voltage fluctuations and DC current ripple by injecting the circulating current is analyzed

the negative 2nd harmonic circulating current reference and zero 2nd harmonic circulating current reference are chosen to achieve the control target. Based on multi-objective adjustment coefficient k and unbalance factor ε

the 3-D plot of three-phase capacitor voltage fluctuation difference value under circulating current suppression and circulating current injection are drawn. The comparison of two objectives is given. The effectiveness of the algorithm is verified by results of a MATLAB simulation and experiment platform.