Control Loop Stability Criterion and Interaction Law Analysis for Grid-connected Inverter in Weak Grid

The study of stability criterion and interaction analysis for grid-connected inverter under weak grid is of great value. Different from traditional impedance stability criterion, this paper proposes control loop stability criterion for grid-connected inverter from the perspective of controller bandwidth overlap. Firstly, the system d-q overall small-signal model G0 considering phase-locked loop (PLL) of grid-connected inverter under weak grid is given and split into three multiplied independent parts: grid impedance, phase-locked loop and current controller. Then using the equivalent loop ratio expression obtained by combining PLL and grid impedance together and then divided by the current controller, the control loop stability criterion is proposed. The proposed stability criterion can not only maintain the independence of each single loop, but also can analyze the overall system stability. So, further analysis of the interaction law among the three parts under this control loop stability criterion is carried out by deducing the expression of the bandwidth ratio n of the PLL and current controller. And it is found that under the weak grid, the interaction between the links will be generated when the bandwidth ratio is greater than the threshold of n. This phenomenon can be represented by the overlapping area of amplitude-frequency curves in the bode diagram for G0. And the weaker the grid or the closer the bandwidth of PLL is to current controller, the larger the overlapping area of amplitude-frequency curves, and the more likely it is to lead the closed-loop gain to infinity. Furthermore, when the bandwidth of the current controller is fixed, the threshold of n varies in the regions of less than 1 as well as more than 1 with the change of the grid strength. Therefore, the system can remain stable no matter what the bandwidth ratio of the phase-locked loop to the current controller is greater or less than 1. Accuracy of the proposed control loop stability criterion and interaction analysis is verified through simulation and experimental results.