Small-Signal Dynamic DQ Model of Modular Multilevel Converter for System Studies

Aliakbar Jamshidifar* (Corresponding Author), Dragan Jovcic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

179 Citations (Scopus)
134 Downloads (Pure)


This paper presents three dynamic linear state-spacemodels of the modular multilevel converter (MMC) which aresuitable for small-signal dynamic studies and controller design.The three models differ by the number of states (two, six, andten) and, therefore, are suitable for different applications basedon the required accuracy. The 2nd- and 6th-order models ignoredynamics of the second harmonics and circulating currentsuppression control (CCSC). The main challenges of dynamicanalytical modelling of MMC are the nonlinear multiplicationterms in ABC frame equations for modulating oscillating signals.The multiplication nonlinear terms are therefore considereddirectly in the rotating DQ frame. This requires simultaneousmodeling in zero sequence, fundamental frequency DQ anddouble fundamental frequency DQ2 frames. The proposed linearanalytical models are implemented in state space in MATLAB.The validity and accuracy of the models are verified against adetailed 401-level MMC model in PSCAD/EMTDC in both timeand frequency domains. The results show very good accuracy forthe 10th-order model and decreasing accuracy for the lower ordermodels. The influence of phase-locked loop and CCSC gains onthe MMC dynamic is also studied using the proposed 10th model,and the results verify the suitability of the model for this purpose.
Original languageEnglish
Pages (from-to)191 - 199
Number of pages9
JournalIEEE Transactions on Power Delivery
Issue number1
Early online date28 Sept 2015
Publication statusPublished - 1 Feb 2016

Bibliographical note

This work was funded by the European Research Council under the Ideas program in FP7 under Grant 259328, 2010. Paper no. TPWRD-00046-2015.


  • Converters
  • HVDC transmission
  • power system control
  • power system dynamics
  • power system modeling


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