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This paper proposes a unified impedance model of grid-connected voltage-source converters for analyzing dynamic influences of the phase-locked loop (PLL) and current control. The mathematical relations between the impedance models in the different domains are first explicitly revealed by means of complex transfer functions and complex space vectors. A stationary (αβ-) frame impedance model is then proposed, which not only predicts the stability impact of the PLL, but also reveals its frequency coupling effect. Furthermore, the impedance shaping effects of the PLL on the current control in the rotating (dq-) frame and the stationary ( αβ-) frame are structurally comapred. The frequency-domain case studies on a three-phase grid-connected converter are next presented, and subsequently validated in time-domain simulations and experimental tests. The close correlations between the measured results and theoretical analysis confirm the effectiveness of the stationary-frame impedance model.
Wang et al. (2017) studied this question.