The LLCL-filter-based grid-tied inverter performs better than the LCL-type grid-tied inverter due to its outstanding switching-frequency current harmonic elimination capability, but the positive resonance peak must be suppressed by passive or active damping methods. This paper proposes a class of fractional-order LLCL (FOLLCL) filters, which provides rich features by adjusting the orders of three inductors and one capacitor of the filter. Detailed analyses are performed to reveal the frequency characteristics of the FOLLCL filter; the orders must be selected reasonably to damp the positive resonance peak while reserving the negative resonance peak to attenuate the switching-frequency harmonics. Furthermore, the control system of the grid-tied inverter based on the FOLLCL filter is studied. When the positive resonance is suppressed by the intrinsic damping effect of the FOLLCL filter, the passive or active damper can be avoided; the grid current single close-loop is adequate to control the grid-tied inverter. For low-frequency applications, proportional-resonant (PR) controller is more suitable for the FOLLCL-type grid-tied inverter compared with the proportional-integral (PI) and fractional-order PI controllers due to its overall performance. Simulation results are consistent with theoretical expectations.

The integer-order LCL (IOLCL) filter has excellent high-frequency harmonic attenuation capability but suffers from resonance, which causes system instability in grid-connected inverter applications. This paper studied a class of resonance-free fractional-order LCL (FOLCL) filters and control problems of single-phase FOLCL-type grid-connected inverters (FOGCI). The Caputo fractional calculus operator was used to describe the fractional-order inductor and capacitor. Compared with the conventional IOLCL filter, by reasonably selecting the orders of the inductor and capacitor, the resonance peak of the FOLCL filter could be effectively avoided. In this way, the FOGCI could operate stably without passive or active dampers, which simplified the design of control system. Furthermore, compared with a single-phase integer-order grid-connected inverter (IOGCI) controlled by an integer-order PI (IOPI) controller, the FOGCI, combined with a fractional-order PI (FOPI) controller, could achieve greater gain and phase margins, which improved the system performance. The correctness of the theoretical analyses was validated through both simulation and hardware-in-the-loop experiments.