In order to enhance the quality of power transmission in modular multilevel converter for high voltage direct current transmission（MMC-HVDC） under the unbalanced grid voltage

we proposed a novel MMC direct power compensation strategy in the αβ coordinate system

which did not require the separation of positive and negative sequence currents. Moreover

we theoretically analyed MMC AC side power and instantaneous power in unbalanced power system voltage. The zero-sequence current of MMC would enter the DC side and then MMC DC voltage/current would fluctuate at double-line frequency.Then

we designed a circulating-current-suppressing controller-based quasi-proportional resonant controller. Finally

we established a simulation model to verify the proposed control strategy and theoretical analysis in PSCAD. The simulation results show that MMC DC voltage is likely to fluctuate at double-line frequency when the negative sequence current is eliminated or the active power fluctuation is suppressed under the unbalanced grid voltage conditions. The direct power compensation control system can effectively suppress the negative sequence current or AC side active power of the two harmonic waves

and the circulating current control can effectively suppress the two harmonic waves of the DC side.