Stability analysis of digitally controlled LCL-type grid-connected inverter considering the delay effect

Owing to LCL-filter resonance, a single loop may not be adequate to stabilise the digitally controlled LCL-type grid-connected inverter, thus the capacitor-current-feedback active damping is usually introduced. However, the computation and pulse-width modulation delays of the digitally controlled system significantly affect system stability and damping performance. Moreover, the delay varies when the duty-ratio update instant and sampling instant are changed. In this study, the Nyquist diagram is used to investigate the system stability taking into consideration the delay effect in the continuous domain. Then, the general conclusions and formulas can be drawn: if the LCL-filter resonance is above the critical frequency, the Nyquist diagram of single loop may not encircle the critical point, and therefore stabilise the system; and if it is below, a damping strategy is required. However, given the delay effect, the active damping loop may be unstable, and two unstable open-loop poles will be generated in the grid current loop under certain conditions. Then its Nyquist diagram should encircle the critical point to ensure the system is stable. Furthermore, the restriction of the cross-over frequency discussed. Experimental results based on a 5 kW prototype have been provided to verify the theoretical analysis.