Modeling and analysis method of fractional-order buck-boost converter

In this paper, the equivalent small parameter method (ESPM) is used to establish the nonlinear mathematical model of the fractional-order buck-boost converter in continuous current mode (CCM), and the analytical expression of approximate steady-state period of converter state variable is obtained by using equivalent small parameter method and combining with harmonic balance principle. The Matlab/Simulink is used to construct the fractional-order capacitance and inductance and to build the circuit model as well as the simulation model of fractional-order buck-boost converter. Moreover, the simulation results of Oustaloup circuit model and numerical simulation model are compared with those of ESPM model to verify the validity and accuracy of the ESPM. The model is simulated by changing the orders of the capacitor and inductor to obtain the influence rule of the order of fractional element on harmonic characteristics of the state variables.