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.
To track the sinusoidal current under stationary frame and suppress the effects of low-order grid harmonics, the multi-resonant quasi-proportional plus resonant (PR) controller has been extensively used for digitally controlled LCL-type pulse-width modulation (PWM) converters with capacitor-current-feedback active damping. However, designing the controller is difficult because of its high order and large number of parameters. Moreover, the computation and PWM delays of the digitally controlled system significantly affect damping performance. In this study, the delay effect is analyzed by using the Nyquist diagrams and the system stability constraint condition can be obtained based on the Nyquist stability criterion. Moreover, impact analysis of the control parameters on the current loop performance, that is, steady-state error and stability margin, identifies that different control parameters play different decisive roles in current loop performance. Based on the analysis, a simplified controller design method based on the system specifications is proposed. Following the method, two design examples are given, and the experimental results verify the practicability and feasibility of the proposed design method.
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