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