Impedance Model of dq Current-Controlled Single-Phase Inverters in αβ-Frame With Capturing the Frequency-Coupling Effect

The stability of the single-phase grid-connected inverter with dq current control is usually analyzed based on the widely established dq-frame impedance model. However, the voltage perturbation is aligned with the $\alpha-$axis, which leads to the inconvenience of the dq-impedance model verification. Moreover, the guidance of the dq-impedance model in the harmonic resonance identification is unintuitive since the frequency-coupling effect contributes to the complex frequency translation between different control frame. To facilitate the impedance measurement and the enhancement of the physical insight, this paper builds the $\alpha\beta-$frame impedance matrix of single-phase inverter-grid system with the dq current control. The $\alpha-$axis impedance is further elaborated with capturing the frequency-coupling effect, which can be employed to evaluate the stability and the harmonic resonance of the single-phase inverter-grid system. Finally, the impedance characteristic is frequency swept by the MATLAB/Simulink, which verifies the correctness of the proposed impedance model and its application in the harmonic stability analysis.