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Summary form only given: This article presents three dynamic linear state space models of Modular Multilevel Converter (MMC) which are suitable for small-signal dynamic studies and controller design. The three models differ by the number of states (two, six and ten) and therefore are suitable for different applications based on the required accuracy. The 2nd and 6th order models ignore dynamics of the second harmonics and circulating current suppression control. The main challenges of dynamic analytical modelling of MMC are the non-linear multiplication terms in equations for modulating oscillating signals. The multiplication non-linear terms is therefore considered directly in the rotating DQ frame. This requires simultaneous modeling in zero sequence, fundamental frequency DQ and double fundamental frequency DQ2 frames. The proposed linear analytical models are implemented in state-space in MATLAB. The validity and accuracy of the models are verified against detailed 401 level MMC model in PSCAD/EMTDC in both: time and frequency domains. The results show very good accuracy for the 10th order model and decreasing accuracy for the lower order models.
Jamshidifar et al. (Fri,) studied this question.