Over the past years, the linearized modeling techniques for power converters have been continuously developed to capture the small-signal dynamics beyond half the switching frequency. This paper reviews and compares the small-signal modeling approaches based on a buck converter with voltage-mode control. The study includes the small-signal averaged modeling approach, the describing function method, and the harmonic statespace modeling approach, in order to be able to better select the correct method when modeling and analyzing a power electronic circuit as well as a power-electronic-based power system. The model comparison points out that the describing-function-based models do improve the modeling accuracy beyond the halfswitching frequency of the converter, yet they fail to predict the frequency-coupling interactions (e.g., beat frequency oscillations) among multiple converters, and instead, harmonic state-space models in the multiple-input multiple-output form are required.

This article proposes a multifrequency admittance model for voltage-source converters with three-phase unbalanced grid voltages. The model is derived with multiple complex vectors and harmonic transfer functions, which is merely dependent on its own input voltage trajectory, and can accurately capture the frequency-coupling dynamics. The dynamic effects of both the basic synchronous-reference-frame phase-locked loop (PLL) and its alternative with a notch filter of the negative-sequence voltage component are compared. It is revealed that the notchfiltered PLL significantly weakens the frequency-coupling effects, which leads to a reduced order of the admittance model. The developed model is validated by a frequency scan, and the frequency-coupling effects impacted by different PLLs and voltage unbalance factors are verified by the experimental tests. Finally, a case study on stability analysis in unbalanced grids proves the significance of the model.

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