Fractional order Buck–Boost converter in CCM: modelling, analysis and simulations

In this paper, the modelling, analysis and the power electronics simulator (PSIM) simulations of the fractional order Buck–Boost converter operating in continuous conduction mode (CCM) operation are investigated. Based on the three-terminal switch device method, the average circuit model of the fractional order Buck–Boost converter is established, and the corresponding DC equivalent circuit model and AC small signal equivalent circuit model are presented. And then, the equilibrium point and the transfer functions are derived. It is found that the equilibrium point is not influenced by the inductor’s or the capacitor’s order, but both these orders are included in the derived transfer functions. Finally, the comparisons between the theoretical analysis and the PSIM simulations are given for confirmation.