Unified SISO Loop Gain Modeling, Measurement, and Stability Analysis of Three-Phase Voltage Source Converters

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.