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D-Q Frame Impedance Modeling of Modular Multilevel Converter Based on Dynamic Phasors

Ad-q frame impedance model of modular multilevel converter (MMC) is presented in this paper. The basis of the modeling method is dynamic phasors and transfer matrix. The 10th-order dynamic phasor model for the MMC is linerized. Then, a 14th-order transfer matrix in the rotating d-q frame can be derived, by combining the 10th-order linearized electrical model and the controller model. The proposed analytical impedance model obtained from the transfer matrix is implemented in MATLAB. The validity and accuracy of the model are verified against a 81-level MMC aggregate model in MATLAB/SIMULINK in frequency domain. The results show that the impedance model has good accuracy at 1–3000 Hz, thus this model can be used in the stability and resonance analysis of MMC in a wide frequency range. The influence of phase-locked loop (PLL) and arm equivalent capacitance on the MMC dynamic is also studied using the proposed impedance model. The results show that high PLL bandwidth and small arm equivalent capacitance can lead to instability. Furthermore, the simulation results verify the suitability of the proposed model.