High voltage direct current(HVDC)transmission based on modular multilevel converter(MMC)is widely used in large-scale renewable energy delivery.However,the lagged inertia of MMC controllers may under-mine the small-signal stability.Firstly,the mechanical inertia of synchronous generators is analyzed,and a second-order unified expression of inertia applicable to MMC controller is proposed.Secondly,based on the dynamic and in-ertial delay of MMC closed-loop controller,a small-signal stability criterion for MMC controller connected to weak power grid is presented.Finally,through simulation analysis of a double-side MMC grid-connected system,the cor-rectness of the proposed stability criterion is validated.