Fractional-order LC filter modeling, implementation, and analysis for distributed power generation system

This paper proposes a comprehensive mathematical modeling and analysis considering fractional-order LC filters (FOLCF) in the utility grid-connected mode (UGCM) and the standalone mode (SM) of operation for the distributed power generation system. The fractional-order behavior of LC filter elements helps to more properly depict a practical inductor or capacitor than the integer-order LC filters (IOLCF) in the distributed power generation system. The fractional-order model of UGCM and SM is obtained in the synchronously rotating reference frame using coordinate transformation. A detailed stability and time domain analysis is performed on the developed FO UGCM and SM mathematical models. The stability of fractional-order LC filters increases for orders (p,q)$$ \left(p,q\right) $$ less than 1, based on the performance evaluation of the FO and IO mathematical models for UGCM and SM with the corresponding designed controller gains. The FOLCFs are approximated using the constant phase element method, which gives a compact and exact approximation of the fractional-order inductor and capacitor elements. The implementation of FOLCF with UGCM and SM operations verifies the effectiveness of the proposed model in real-time simulation. The results show the FOLCF model provides better dynamic tracking and disturbance rejection response than the IOLCF model. Hence, the FOLCF model imparts immunity against local load disturbances to regulate the point of common coupling voltage and frequency in standalone mode. Furthermore, a significant improvement in % total harmonic distortion is also observed in grid current and load voltage.