Real-Time Simulation of Hybrid Modular Multilevel Converters Using Shifted Phasor Models

The real-time simulation of modular multilevel converter (MMC) is essential to the evaluation and validation of its control and protection systems. Moreover, the dynamics at both sub-module level and system level are expected from the real-time simulations of MMCs. To achieve this objective, this paper proposes the shifted phasor modeling (SPM) of the MMC by representing each sub-module with a Thevenin equivalent circuit that is derived using shifted phasors with improved accuracy. The efficiency of the SPM is guaranteed by modeling each arm as a switch-dependent Thevenin equivalent circuit. The computational burden remains almost unchanged even when the number of sub-modules increases considerably. The proposed model is materialized using field programmable gate array. And, thus the real-time simulation of MMC-based DC grids can be realized to capture the dynamics at the system level as well as the sub-module level. The effectiveness of this paper has been validated in terms of both accuracy and efficiency on a two-terminal MMC-based low-voltage direct current system.