Frequency-domain modeling is an effective technique in the dynamic analysis of power electronic converters-based power systems. In this paper, a unified single-input single-output (SISO) loop gain modeling for the three-phase grid-tied VSCs under both symmetric and asymmetric ac grids is presented, which facilitates the physical measurement and stability analysis. Based on the linear-time-periodic (LTP) modeling technique, the harmonic admittance model of the three-phase grid-tied VSC is developed in the stationary (αβ)-frame. Instead of the transfer function matrix, the frequency-coupling effects are modeled by the transfer function vector, which simplifies the modeling process. According to the idea of mathematical induction, a two-by-two recursive admittance matrix (RAM) model that can accurately capture the coupling dynamics introduced by the power grid is derived. The RAM has an analytical form and is easy to include harmonic coupling components of arbitrary order. Furthermore, the RAM is converted to its equivalent SISO models following the concept of loop gain. The system stability is thus assessed by the SISO stability criteria (e.g., Nyquist stability criterion). In addition, the loop gain allows the traditional SISO perturbation and measurement scheme to be used for detecting the stability margin information. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above.

This paper proposes a recursive single-input single-output (SISO) impedance modeling framework for single-phase voltage source rectifiers, which can greatly simplify both the modeling procedure and the resulting impedance model. During the modeling process, frequency-coupling effects are modeled by the reduced-order transfer function vector rather than the transfer function matrix, so the modeling complexity is reduced. Moreover, the recursive SISO impedance model has an analytical form. And the recursive SISO impedance model can characterize the frequency-coupling dynamics of arbitrary order with a low computation burden. Experiments validate the accuracy of the recursive SISO impedance modeling.

Time-periodicity and non-linearity pose a challenge to the precise input impedance modeling of single-phase power converters. In this study, a precise input impedance model with measurability of the single-phase voltage source rectifier (VSR), which considers the frequency-coupling effect (FCE), is established. Meanwhile, it is revealed that the rectifier input impedance is dependent of the grid impedance. In the proposed modeling approach, only Laplace transform and frequencyshifting operation are required, which avoids the complicated convolution calculation in the frequency domain. In addition, the influence of grid impedance on the input impedance is studied. Simulations are conducted to verify the effectiveness of the proposed method.