Effect of phase-locked loop on small-signal perturbation modelling and stability analysis for three-phase LCL-type inverter connected to weak grid

For three-phase LCL-type inverter connected to weak grid, the bandwidth and dynamics of phase-locked loop (PLL) directly affect small-signal perturbation modelling, which causes the control dq frame of PLL being no longer aligned with the system dq frame of weak grid. Thus, considering the effect of PLL, a small-signal perturbation admittance model is firstly built. Secondly, by the rotating matrix, variables in the system dq frame are transformed into the control dq frame. Then, the interaction between two dq frames is established based on an admittance model in consideration of the PLL, and the inverter output admittance is obtained. Finally, the effect of PLL, grid impedance and LCL-type filter parameters on system stability are analysed. As a conclusion, with an increase in PLL bandwidth and grid impedance, the system stability gradually is decreased, even resulting in the system instability. In addition, the larger the active damping coefficient is, the better the system stability is. While, the increase of filter capacitance and grid-side inductance leads to the decrease of system stability. The conclusions have certain guiding significance and reference value for the design and safe operation of three-phase LCL-type grid-connected inverter. The simulation and experiment verify the validity of theoretical analysis.