Abstract: For the control and protection design of modular multi-level converter（MMC） based DC grids, it is necessary to fully consider the high frequency electro-magnetic dynamics of the system level and the device level. Traditionally, the MMC accelerated model cannot extend the simulation time-step to more than 50 microseconds due to the limitations of numerical stability. Additionally, these models cannot produce the desired wide frequency band phasors simultaneously. To resolve these issues, an efficient model of MMC based DC grids was proposed based on the rotational transform. As a result, this model can extend the time-step to more than 100 microseconds. It can improve the simulation efficiency significantly while satisfy the accuracy expectations. Especially, it can produce instantaneous and wide frequency band phasor waveforms. This method was further applied to a large-scale MMC based AC/DC grid in China integrating four-terminal VSC converters. The simulation results have verified the advantages of this model in simulation accuracy and simulation efficiency.