An Analytical Approach for Obtaining Steady-State Periodic Solutions of Fractional-Order quasi-Z-Source Rectifier

This paper contributes to establish the mathematical model of fractional-order single-phase quasi-Z-source PWM rectifier (FO-qZSR). Instead of using fractional calculus, a general state vector differential equation is introduced here to describe FO-qZSR. By combining equivalent small parameter method (ESPM) with harmonic balance principle, the steady-state analytical appropriate periodic solution of FO-qZSR is obtained. Both the dc components and ripples of state variables are related to fractional order of inductors and capacitors. Finally, the proposed theoretical analysis is confirmed by establishing the mathematical and circuit model using FOTF toolbox in Matlab/Simulink platform.