A Modeling and Analysis Method for Fractional-Order DC-DC Converters

This paper proposes a modeling and analysis method for fractional-order dc-dc converters operating in continuous conduction mode (CCM). As an example, a fractional-order boost converter is studied in detail. Instead of using fractional calculus, the method presented here uses a general state vector differential equation to describe the converter. By combining the principle of harmonic balance and equivalent small parameter method, an approximate analytical steady-state solution of the state variables could be obtained. Subsequently, the CCM-operating criterion of the converter is discussed based on the proposed method, and the appropriate parameters are provided to make sure that the fractional-order converter operates in CCM. In addition, a statistical analysis of harmonics is performed, from which the effects of fractional orders on harmonics can be observed. Moreover, numerical simulations are performed using the Adams-Bashforth-Moulton-typed predictor-corrector method and the Oustaloup's-filter-based approximation method. Both the dc components and ripples of the state variables obtained from these two methods are combined with those obtained by the proposed method, and they are in good agreement. Finally, the fractional-order capacitor and inductor are designed and verified by simulations, and on the basis of which experiments of the fractional-order boost converter are carried out to further verify the proposed method.