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http://dx.doi.org/10.6113/JPE.2013.13.6.1008

Modeling and Analysis of the Fractional Order Buck Converter in DCM Operation by using Fractional Calculus and the Circuit-Averaging Technique  

Wang, Faqiang (State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University)
Ma, Xikui (State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University)
Publication Information
Journal of Power Electronics / v.13, no.6, 2013 , pp. 1008-1015 More about this Journal
Abstract
By using fractional calculus and the circuit-averaging technique, the modeling and analysis of a Buck converter with fractional order inductor and fractional order capacitor in discontinuous conduction mode (DCM) operations is investigated in this study. The equivalent averaged circuit model of the fractional order Buck converter in DCM operations is established. DC analysis is conducted by using the derived DC equivalent circuit model. The transfer functions from the input voltage to the output voltage, the duty cycle to the output voltage, the input impedance, and the output impedance of the fractional order Buck converter in DCM operations are derived from the corresponding AC-equivalent circuit model. Results show that the DC equilibrium point, voltage ratio, and all derived transfer functions of the fractional order Buck converter in DCM operations are affected by the inductor order and/or capacitor order. The fractional order inductor and fractional order capacitor are designed, and PSIM simulations are performed to confirm the correctness of the derivations and theoretical analysis.
Keywords
Buck converter; Equivalent averaged circuit model; Fractional calculus; Transfer functions;
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