In this paper, several modeling methods for the continuous current mode (CCM) fractional-order Cuk converter are investigated. First, the state space averaging method is used to establish the model. Based on this model, the expressions of inductors’ current and capacitor voltage as well as the transfer functions are derived. Then, the equivalent small parameter method (ESPM) is employed to model the converter. Based on the Oustaloup filter principle, the approximate models of fractional-order capacitor and inductors are constructed, which consist of integer-order components, to build the circuit model (CM) of the converter. In addition, the numerical model (NM) of the converter is established. Simulation results are provided to compare the modeling methods, which show that the ESPM has some advantages over the other methods. Finally, the hardware-in-the-loop experiment is conducted to verify the effectiveness of the circuit model.

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