scholarly journals Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Ningning Yang ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Boost Converter ◽  
Practical Significance ◽  
Order Model ◽  
Fractional Order Model ◽  
Conduction Mode ◽  
Continuous Conduction Mode

In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM). Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.

Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode

2018 ◽  
Vol 28 (05) ◽  
pp. 1850061 ◽  
Author(s):  
Zirui Jia ◽  
Chongxin Liu
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Fractional Order ◽  
Transfer Functions ◽  
Circuit Simulation ◽  
Boost Converter ◽  
Averaged Model ◽  
Conduction Mode ◽  
State Average ◽  
Continuous Conduction Mode

By using fractional-order calculus theory and considering the condition that capacitor and inductor are naturally fractional, we construct the fractional mathematical model of the magnetic coupled boost converter with tapped-inductor in the operation of continuous conduction mode (CCM). The fractional state average model of the magnetic coupled boost converter in CCM operation is built by exploiting state average modeling method. In these models, the effects of coupling factor, which is viewed as one generally, are directly pointed out. The DC component, the AC component, the transfer functions and the requirements of the magnetic coupled boost converter in CCM operation are obtained and investigated on the basis of the state averaged model as well as its fractional mathematical model. Using the modified Oustaloup’s method for filter approximation algorithm, the derived models are simulated and compared using Matlab/Simulink. In order to further verify the fractional model, circuit simulation is implemented. Furthermore, the differences between the fractional-order mathematical models and the corresponding integer-order mathematical models are researched. Results of the model and circuit simulations validate the effectiveness of theoretical analysis.

Modeling and performance analysis of the fractional order quadratic Boost converter in discontinuous conduction mode-discontinuous conduction mode

2016 ◽  
Vol 30 (06) ◽  
pp. 1650014 ◽  
Author(s):  
Cheng Tan ◽  
Zhi-Shan Liang
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Boost Converter ◽  
Equivalent Model ◽  
Type I ◽  
Type Ii ◽  
Order Model ◽  
Discontinuous Conduction Mode ◽  
And Performance ◽  
Conduction Mode

In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM–DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM–DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.

scholarly journals Modeling and Analysis of the Fractional-Order Flyback Converter in Continuous Conduction Mode by Caputo Fractional Calculus

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1544
Author(s):  
Chen Yang ◽  
Fan Xie ◽  
Yanfeng Chen ◽  
Wenxun Xiao ◽  
Bo Zhang
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Transfer Functions ◽  
Circuit Simulation ◽  
Mutual Inductance ◽  
Power Electronic ◽  
Power Electronic Converters ◽  
Flyback Converter ◽  
Conduction Mode ◽  
Continuous Conduction Mode

In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-order mutual inductance. This paper introduces a fractional-order flyback converter with a fractional-order mutual inductance and a fractional-order capacitor. The equivalent circuit model of the fractional-order mutual inductance is derived. Then, the state-space average model of the fractional-order flyback converter in continuous conduction mode (CCM) are established. Moreover, direct current (DC) analysis and alternating current (AC) analysis are performed under the Caputo fractional definition. Theoretical analysis shows that the orders have an important influence on the ripple, the CCM operating condition and transfer functions. Finally, the results of circuit simulation and numerical calculation are compared to verify the correctness of the theoretical analysis and the validity of the model. The simulation results show that the fractional-order flyback converter exhibits smaller overshoot, shorter setting time and higher design freedom compared with the integer-order flyback converter.

Fractional Order Modeling and Analysis of Buck-Boost Converter

2015 ◽  
Vol 789-790 ◽  
pp. 842-848
Author(s):  
Li Feng Yi ◽  
Kai Ru Zhang ◽  
Jun Liu
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Fractional Calculus ◽  
Simulation Model ◽  
Fractional Order ◽  
Theoretical Foundation ◽  
Boost Converter ◽  
Modeling And Analysis ◽  
Simulation Results ◽  
Conduction Mode

Considered the theoretical foundation of fractional order, the fractional mathematical model of the Buck-Boost converter in continuous conduction mode operation is built and analyzed in theory. Based on the improved Oustaloup fractional calculus for filter algorithm, the simulation model is framed by using the Matlab/Simulink software. And the simulation results are compared with that of integer order. It proves the correctness of the fractional order mathematical model and the theoretical analysis.

scholarly journals Chaos in the Shimizu-Morioka Model With Fractional Order

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhangzhi Wei ◽  
Xin Zhang
Keyword(s):  
Fractional Calculus ◽  
Phase Diagrams ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Order Model ◽  
Dynamical Behaviors ◽  
Fractional Order Model

The investigation of dynamical behaviors for fractional-order chaotic systems is a new trend recently. This article is numerically concerned with the Shimizu-Morioka model with a fractional order. We find that chaos exists in the fractional-order model with order less than three by utilizing the fractional calculus techniques, and some phase diagrams are also constructed.

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