Design of the PI regulator and feedback coefficient of capacitor current for grid-connected inverter with an LCL filter in discrete-time domain

The LCL filter is widely used in grid-connected inverter due to its powerful ability of attenuating the switching-frequency harmonics. However, the frequency response of the LCL filter has a resonance peak, which would amplify the harmonics around the resonant frequency or even cause the inverter to be unstable. Active damping based on the feedback of capacitor current is an effective solution to damp the resonance oscillation. Since the one-timestep delay of the digital signal processor (DSP) can hardly be avoided, the stable margin of the inverter will be weakened. Besides, the optional range of the capacitor-current feedback coefficient will be shrunk. This paper discusses the effect of the one-timestep delay firstly, and proposes a step-by-step design method to choose the parameters of the PI-based current regulator and the capacitor-current feedback coefficient. Based on Jury stability criterion, the selectable 3D region surrounded by the parameters of PI-based regulator and capacitor-current feedback coefficient can be plotted. Further, some specific constraints such as steady-state error and phase margin etc. will decide the suitable values of PI regulator and capacitor-current feedback coefficient. A 6-kW single-phase grid-connected inverter is built to verify the proposed design method.