Sequence Impedance Modeling and Characteristic Analysis of Full Fractional-Order Grid-Forming Inverters

Conventional integer-order parameter designs of grid-forming inverters provide limited degrees of freedom for impedance adjustment, motivating the exploration of additional approaches for flexible impedance reshaping across different frequency ranges. This paper establishes a full fractional-order grid-forming inverter (FFO-GFMI) by incorporating fractional-order inductor-capacitor (LC) filters, corresponding decoupling control, and fractional-order multi-loop controllers into a conventional grid-forming inverter. Based on the harmonic linearization method, positive- and negative-sequence impedance models of the FFO-GFMI are developed to characterize its broadband impedance characteristics. The developed models are validated through impedance scanning, and the effects of fractional-order parameters on broadband impedance characteristics are systematically investigated. The results reveal that fractional-order LC filters mainly regulate medium- and high-frequency resonance characteristics, while fractional-order control loops provide effective low- and medium-frequency impedance reshaping. Furthermore, load-step simulations demonstrate that the selected fractional-order configuration improves dynamic performance, reducing the active power settling time from 0.3121 s to 0.1974 s and the active power overshoot from 19.75% to 4.51%.