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

Faqiang Wang; Xikui Ma

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

Faqiang Wang

Xikui Ma

Vol. 13, No. 6, pp. 1008-1015, Nov. 2013

10.6113/JPE.2013.13.6.1008

Buck converter

Equivalent averaged circuit model

Fractional calculus

Transfer functions

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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.

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Cite this article

[IEEE Style]

F. Wang and X. Ma, "Modeling and Analysis of the Fractional Order Buck Converter in DCM Operation by using Fractional Calculus and the Circuit-Averaging Technique," Journal of Power Electronics, vol. 13, no. 6, pp. 1008-1015, 2013. DOI: 10.6113/JPE.2013.13.6.1008.

[ACM Style]

Faqiang Wang and Xikui Ma. 2013. Modeling and Analysis of the Fractional Order Buck Converter in DCM Operation by using Fractional Calculus and the Circuit-Averaging Technique. Journal of Power Electronics, 13, 6, (2013), 1008-1015. DOI: 10.6113/JPE.2013.13.6.1008.