Impedance Modeling and Stability Analysis of the Cascaded Three-phase Symmetric Systems Using Complex Transfer Functions

Impedance-based stability analysis method has been widely adopted for addressing the small-signal stability issues of power electronics-based systems. For the three-phase ac systems, the impedance models (IMs) are generally obtained in the rotating dq-frame and represented by the 2 × 2 transfer matrices, with which the system stability can be predicted through the Generalized Nyquist Criterion (GNC). However, the computational process of GNC as well as the derivation of the impedance matrices aggravates the complexity of stability analysis. This paper presents a simpler impedance modeling process for the three-phase symmetric systems. The IMs can be directly established by the complex transfer functions (CTFs) in the dq-frame, while keeping the equivalent relationship with the original impedance matrices. Consequently, the original multiple-input multiple-output (MIMO) system is simplified to a single-input single-output (SISO) system without losing any accuracy. Further, it is also proved that the Nyquist criterion originally used for dc systems can replace the GNC to predict stability of the cascaded three-phase symmetric system, which thus avoids the massive matrix calculations and leads to the remarkable simplification of the stability analysis. Case study of a three-phase grid-connected voltage source inverter system consisting of the frequency-domain analyses and experimental tests is presented. The obtained results confirm the correctness of the theoretical analyses.