Optimized Controller Design for <inline-formula> <tex-math notation="TeX">$LCL$</tex-math></inline-formula>-Type Grid-Connected Inverter to Achieve High Robustness Against Grid-Impedance Variation

Abstract

Capacitor-current-feedback active damping is an effective method to suppress the LCL-filter resonance in grid-connected inverters. However, due to the variation of grid impedance, the LCL-filter resonance frequency will vary in a wide range, which challenges the design of the capacitor-current-feedback coefficient. Moreover, if the resonance frequency is equal to one-sixth of the sampling frequency (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /6), the digitally controlled LCL-type grid-connected inverter can be hardly stable no matter how much the capacitor-current-feedback coefficient is. In this paper, the optimal design of the capacitor-current-feedback coefficient is presented to deal with the wide-range variation of grid impedance. First, the gain margin requirements for system stability are derived under various resonance frequencies. By evaluating the effect of grid impedance on gain margins, an optimal capacitor-current-feedback coefficient is obtained. With this feedback coefficient, stable operations will be retained for all resonance frequencies except (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /6). Second, in order to improve system stability for a resonance frequency of (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> /6), a phase-lag compensation for the loop gain is proposed. Finally, a 6-kW prototype is tested to verify the proposed design procedure.