Theoretical Analysis of a Fractional-Order LLCL Filter for Grid-Tied Inverters

Abstract

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.