Stationary-Frame Complex-Valued Frequency-Domain Modeling of Three-Phase Power Converters

The stationary-frame complex-valued frequency-domain modeling has been applied to characterize the frequency-coupling dynamics of three-phase converters. Yet, those models are generally derived through mathematical transformations of the linearized time-invariant models in the rotating dq -frame. A step-by-step modeling method with clear physical insight in the stationary frame is still missing. This article attempts to fill in the void by introducing a general stationary ( $\alpha \beta$ )-frame, three-port equivalent circuit model for the converter power stage, based on the direct linearization around time-periodic trajectories. The model not only reveals the frequency-coupling effect of the ac–dc dynamic interaction but also provides an explicit theoretical basis for incorporating the control dynamics. Moreover, the dependence of the frequency-coupling terms on the initial phase of the input voltage is pointed out. Considering the phase-dependent feature, a frequency scan method that can accurately measure the $\alpha \beta $ -frame converter model is proposed. The measured frequency responses in both the nonlinear time-domain simulations and experimental tests validate the effectiveness of the frequency scan method and the theoretical analysis.