Frequency Coupling Admittance Modeling of Quasi-PR Controlled Inverter and Its Stability Comparative Analysis Under the Weak Grid

This paper intends to comparatively study the stabilities of grid-connected inverters with three closely related controllers: quasi-proportional resonance (quasi-PR), proportional integral (PI), and proportional resonance (PR) under the weak grid. Firstly, considering the influence of frequency coupling characteristic, a frequency coupling admittance model of quasi-PR controlled inverter is established. Then, the admittance characteristics of the quasi-PR, PI and PR controlled inverters are compared. Admittance characteristics of the PI and PR controlled inverters are similar while the quasi-PR controlled inverter is quite different: the amplitude of the quasi-PR controlled inverter is larger than that of the PI controlled inverter and the phase difference between the two inverters is obvious in the mid-high frequency areas, which are mainly caused by the resonance bandwidth of the quasi-PR controller. Furthermore, the stabilities of the quasi-PR, PI and PR controlled inverters are analyzed. The stabilities of the PI and PR controlled inverters are similar but the quasi-PR controlled inverter is more sensitive to weak grid and high inverter output power. To achieve the same system stability, the voltage outer-loop bandwidth of the quasi-PR controlled inverter should be designed narrower than that of the PI and PR controlled inverters. Finally, experiments verify the correctness of the analyses.