Multi-frequency Impedance Modeling and Stability Analysis of the Three-phase LCL-type Grid-connected Inverter Considering Sideband Effect

The three-phase LCL-type grid-connected inverters are widely used in power grid, but the frequency coupling issues could lead to instability problems such as high-frequency oscillation of the three-phase LCL-type grid-connected system, which is hard to analyze using traditional impedance model. So in this paper, considering the characteristic of high-frequency coupling caused by the sideband effect of the sinusoidal pulse width modulation (SPWM) modulator, a complex transfer function of the SPWM modulator is first derived, which can clearly reflect the dynamic coupling between disturbance frequency components and sideband frequency components. Then, a comprehensive multi-frequency impedance model of the three-phase LCL-type grid-connected inverter under the dq-frame is established. Based on the proposed model and the generalized Nyquist criterion, the high-frequency oscillation phenomenon of the grid-connected system under the weak grid is analyzed, and the frequencies of the resulting oscillation components are predicted. To verify the accuracy of the proposed model and the validity of the theoretical analysis, the corresponding simulations under different conditions are carried out.