A boldsymbol d-boldsymbol q frame impedance model of modular multilevel converter (MMC), which is suitable for high-frequency resonance (HFR) analysis under the condition that the number of submodules in MMC reaches hundreds level, is presented in this work. A 10th-order dynamic phasor model for the MMC is linearized and combined with a control subsystem model. A modular modeling approach based on transfer matrix is applied to the overall linearized model to derive the impedance model. The validity and accuracy of the model are verified using a 501-level MMC aggregated model in SIMULINK. Results show that the impedance model has satisfactory accuracy in the frequency ranging from 1 to 3000 Hz. Then, the impedance model is used to analyze an HFR accident in a realistic MMC project. Therefore, a high time delay in controller is proved can provide negative resistance in high frequency and cause instability.
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Zhu et al. (2020) studied this question.
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