State-space model and PQ operating zone analysis of hybrid MMC

Xiaojun Lu, Wang Xiang, Weixing Lin, Jinyu Wen

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11 Citations (Scopus)
42 Downloads (Pure)


A steady-state time-invariant (SSTI) state-space model is proposed in this paper for the hybrid modular multilevel converter (hybrid MMC). To analyze the internal dynamics of the hybrid MMC, the phasor modelling method is employed with considering three different frequency components in modulation signals. Originating from the state-space model, the steady-state model is obtained for analytically illustrating operating characteristics of the hybrid MMC. A ‘scan and check’ method is proposed to determine the feasible PQ operating zone of the hybrid MMC with considering multiple operating constraints, especially the requirement for successful voltage balancing of half-bridge sub-modules (HBSMs). The accuracy of the state-space model is verified by comparing the time-domain response with the equivalent electromagnetic model of a hybrid MMC in PSCAD/EMTDC. Feasible operating zones of the tested system under different DC terminal voltages are calculated. The effects of different operating constraints on limiting the PQ operating zone are analyzed. The impact of converter parameters such as the sub-module ratio, the arm reactance and the sub-module capacitance on the operating zone is presented in detail.

Original languageEnglish
Pages (from-to)99-108
Number of pages10
JournalElectric Power Systems Research
Early online date16 May 2018
Publication statusPublished - 30 Sept 2018


  • analytical model
  • HVDC transmission
  • hybrid modular multilevel converter
  • small-signal analysis
  • steady-state analysis


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