Fractional Order Modeling and Dynamical Analysis of Peak-Current-Mode Controlled Synchronous Switching Z-Source Converter

Based on the facts that the inductor and the capacitor are fractional in nature, the fractional calculus is adopted to establish the fractional mathematical model of the peak current mode controlled synchronous switching Z-source converter. According to the state average modeling method, the fractional state averaged model of the synchronous switching Z-source converter is built and the theoretical analysis is carried out. Then, using the forecast correction numerical calculation method, the discrete mathematical model of synchronous switching Z-source converter is established. The bifurcation diagrams are obtained with the reference current as the bifurcation parameter, to study the dynamical behaviors. And the complex dynamical behaviors, such as period-double bifurcation, subharmonic oscillation, chaos, and multiple periodic windows, are revealed. Based on the Oustaloup filter algorithm, the fractional mathematical model of the synchronous switching Z-source converter is built in MATLAB/Simulink. Under different values of reference current, time-domain simulation waveforms and phase portraits of the converter are obtained. It is shown that the time-domain simulation results verify the validation of the fractional model and the dynamical analysis.