Based on analysis of the dynamic process of the arm capacitors during start-up and DC fault of a MMC, an improved equivalent electro-magnetic simulation model of MMC is proposed in this paper, and according to the dynamic characteristics of the total capacitor voltage of an arm, an averaged value model of MMC for its operating condition simulaton is proposed. Then detailed switching, equivalent and averaged value electro-magnetic models of a 21-level MMC are built on PSCAD/EMTDC. By taking simulations during start-up, current step, AC fault and DC fault, the proposd equivalent model and average value model are proved to be suitable to replace the detailed simulation model of MMC in the converter-level study and power system level study with significantly increased simulation speed.