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The impedance-based stability analysis of single-phase voltage source converters (VSCs) emphasizes the precise impedance modeling. Considering the complexity of dq-frame impedance modeling and measurement, this paper proposes a mirror-frequency impedance modeling and measurement approach of single-phase VSCs in the stationary frame based on harmonic linearization. First, the mirror frequency definition is put forward and the dynamics of the second-order generalized phase-locked loop considering the mirror-frequency effects is validated by simulations. Next, the impedance model considering the mirror-frequency effects and dc-link voltage control loops is compared with the conventional one-dimension impedance model and a mirror-frequency impedance measurement method is presented, which are verified by experiments on the hardware-in-the-loop platform. The results indicate that the mirror-frequency impedance model considering the dc-link voltage control is more accurate and better captures the cross-coupling dynamics of VSCs. Finally, the different bandwidths of dc-link voltage control loops and different capacitances are designed to study the impacts of dc-link voltage control loops and ripples on impedance. The experiments and impedance-based analysis illustrate that the wider bandwidth of dc-link voltage control loops or the less capacitance with high dc-link voltage ripple will expand the frequency range of negative impedance in the low frequency.
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Zhang et al. (2018) studied this question.
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