Critical Damping Ratio to Ensure Design Efficiency and Stability of LCL Filters

The resonance of LCL filter gives challenge to the control stability of LCL-filter-based converter systems. To suppress the filter resonance, damping methods are widely adopted. Nevertheless, the determination of damping parameters for LCL filters can be vague, insufficient or excessive, because the filter resonance is affected by multiple factors. Furthermore, due to the effect of damping resistor, the attenuation of switching-frequency current ripple may vary from the expected value, and thus, can lead to unwanted iterations to ensure proper filtering performances. The purpose of this article is to provide an efficient and accurate design method for the damping in LCL filters. A metric of "critical damping ratio" is introduced and solved for the first time. With the critical damping ratio setting at 0.28, the resonance peak on the magnitude-frequency curve of LCL filter can be precisely flattened without introducing unnecessary damping losses, and the grid-side inductor and damping resistor can be designed in an accurate and less iterative way. Moreover, a "peace-of-mind" stability performance of LCL filter can be also achieved. The simulation and experiment results are provided to verify the analysis.