Abstract
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.
Highlights
T HE frequency-domain modeling and analysis is an efficient approach for dynamic studies of electric power systems [1]
The frequency coupling indicates the dynamic coupling between different frequency components caused by the time-periodic operating trajectory, and the phase dependence implies the dependence of the frequency-coupling dynamics
It is found that the phase dependence is related to the initial phase of the steady-state voltage and always comes with the frequency-coupling terms, which has a critical impact on the frequency-domain validation of the off-diagonal elements of the ac admittance matrix and the elements of the ac–dc voltage-transfer matrix of the voltage-source converter (VSC)
Summary
T HE frequency-domain modeling and analysis is an efficient approach for dynamic studies of electric power systems [1]. To further explore the modeling and validation solutions for the αβ-frame complex-valued model of VSCs, this article proposes first a general αβ-frame, three-port small-signal circuit model for the converter power stage, based on complex vectors and linearizations directly around the time-periodic trajectories. The three-port equivalent circuit model reveals the frequency-coupling and phase-dependent characteristics of the ac–dc power conversion, and provides an explicit mathematical basis for modeling the closed-loop control dynamics for VSCs. Based on the rigorous derivation, the physical insight behind the αβ-frame complex-valued model is clarified, i.e., the phase dependence is merely related to the initial phase of the input voltage, which appears together with the frequency-coupling terms. The effectiveness of the frequency scan approach and the theoretical findings are validated by nonlinear time-domain simulations and experimental tests
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