Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative

In previous studies, researchers used the fractional definition of Caputo to study fractional-order power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation. The fractional definition is crucial for the application of fractional-order theory into electric engineering, which directly influences the accuracy of model and operational characteristics of power converter. This paper analyzes fractional-order Buck converter according to the fractional definition of Riemann-Liouville. Firstly, the converter model operating in continuous conduction mode (CCM) is established under Riemann-Liouville fractional definition, and it shows that voltage gain and inductor current are relative with the order, but they are independent of order in the model of Caputo fractional definition. Secondly, the different steady-state characteristics of CCM Buck converter are researched under the models of Caputo and Riemann-Liouville derivative. Finally, the feasible simulations and experiments verify that the model derived by Riemann-Liouville fractional definition is more accurate and suitable for analyzing Buck converter.

[1]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[2]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[3]  Slobodan Cuk,et al.  A general unified approach to modelling switching-converter power stages , 1976, 1970 IEEE Power Electronics Specialists Conference.

[4]  A. Jonscher.  Dielectric relaxation in solids , 1983 .

[5]  S. Westerlund.  Dead matter has memory , 1991 .

[6]  S. Westerlund,et al.  Capacitor theory , 1994 .

[7]  I. Podlubny.  Fractional differential equations , 1998 .

[8]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[9]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[10]  Karabi Biswas,et al.  Rational approximation of fractional operator — A comparative study , 2010, 2010 International Conference on Power, Control and Embedded Systems.

[11]  Fan Yang,et al.  A note on the definition of fractional derivatives applied in rheology , 2011 .

[12]  Ahmed S. Elwakil,et al.  High-quality factor asymmetric-slope band-pass filters: A fractional-order capacitor approach , 2012, IET Circuits Devices Syst..

[13]  Liu Chong-Xin,et al.  Modeling and dynamics analysis of the fractional-order Buck—Boost converter in continuous conduction mode , 2012 .

[14]  Xikui Ma,et al.  Modeling and Analysis of the Fractional Order Buck Converter in DCM Operation by using Fractional Calculus and the Circuit-Averaging Technique , 2013 .

[15]  Faqiang Wang,et al.  Fractional order Buck–Boost converter in CCM: modelling, analysis and simulations , 2014 .

[16]  Jiri Petrzela,et al.  A note on fractional-order two-terminal devices in filtering applications , 2014, 2014 24th International Conference Radioelektronika.

[17]  Debasmita Mondal,et al.  Experimental studies on realization of fractional inductors and fractional‐order bandpass filters , 2015, Int. J. Circuit Theory Appl..

[18]  Ningning Yang,et al.  Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus , 2016 .

[19]  Bo Zhang,et al.  A Modeling and Analysis Method for Fractional-Order DC–DC Converters , 2017, IEEE Transactions on Power Electronics.

[20]  A. Moshar Movahhed,et al.  Fractional Modeling and Analysis of Buck Converter in CCM Mode Peration , 2017 .

[21]  Ahmad Taher Azar,et al.  Modeling and analysis of fractional order DC-DC converter. , 2017, ISA transactions.

[22]  Maneesha Gupta,et al.  Design and implementation of DDCC-based fractional-order oscillator , 2018, International Journal of Electronics.

[23]  Durbadal Mandal,et al.  Accurate integer-order rational approximation of fractional-order low-pass Butterworth filter using a metaheuristic optimisation approach , 2018, IET Signal Process..

[24]  Siddhartha Sen,et al.  Optimal Design for Realizing a Grounded Fractional Order Inductor Using GIC , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Bo Zhang,et al.  High-Power Fractional-Order Capacitor With 1 < α < 2 Based on Power Converter , 2018, IEEE Trans. Ind. Electron..

[26]  Chengmin Hou,et al.  New concepts of fractional Hahn’s q,ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$q,\omega $\end{document}-derivativ , 2018, Advances in Difference Equations.

[27]  Zirui Jia,et al.  Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode , 2018, Int. J. Bifurc. Chaos.

[28]  Dazhi Zhao,et al.  Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds , 2019, Appl. Math. Comput..