基于R-L分数阶定义的PCCM Boost变换器建模与分析  

Modeling and Analysis of PCCM Boost Converter Based on Definition of R-L Fractional-order

作　　者：王仁明[1] 李啸[1] 张赟宁 WANG Renming;LI Xiao;ZHANG Yunning(College of Electrical Engineering and New Energy,China Three Gorges University,Yichang 443002,China)

机构地区：[1]三峡大学电气工程与新能源学院,宜昌443002

出　　处：《电源学报》2024年第2期19-26,共8页Journal of Power Supply

基　　金：国家自然科学基金资助项目(61603212)。

摘　　要：研究了基于R-L分数阶定义的电感电流伪连续PCCM(pseudo-continuous conduction mode)Boost变换器模型,并由此导出了变换器的状态平均模型,然后推导出升压比,直流静态工作点,电感电流波纹以及输出电压波纹的表达式。结果表明,与基于Caputo分数阶定义下的变换器模型相应表达式比较,R-L分数阶定义下的直流静态工作点和升压比不仅与占空比相关,而且还与电感和电容的阶数有关,输出电压波纹的表达式不仅与分数阶电感的阶数α有关,与分数阶电容的阶数β也相关。电感和电容的阶数对状态变量的直流分量和分数阶PCCM Boost的稳态特性有很大影响。最后,在MATLAB/SIMULINK中搭建了R-L分数阶PCCM Boost变换器数学模型和电路模型,仿真结果显示R-L分数阶PCCM Boost变换器模型的分析结果比其他PCCM Boost模型的分析结果更加稳定,误差更小。In this paper,a Boost converter model in the pseudo-continuous conduction mode(PCCM)of inductive cur-rent based on the definition of R-L fractional-order is studied.On this basis,the state-space averaging model of the con-verter is derived.Then,the expressions for the step-up ratio,DC static operating point,inductive current ripple,and out-put voltage ripple are derived.Results show that compared with the corresponding expressions derived on the basis of the definition of Caputo fractional-order,the derived expressions for DC static operating point and step-up ratio under the definition of R-L fractional-order are related to both the duty cycle and the orders of the capacitor and inductor.The ex-pression for output voltage ripple is not only related to the orderαof fractional-order inductor,but also related to the or-derβof fractional-order capacitor.Therefore,the orders of inductor and capacitor obviously affect the DC component of state variables and the stable-state characteristics of factional-order PCCM Boost converter.Finally,a mathematical mod-el and a circuit model of the R-L fractional-order PCCM Boost converter are built in MATLAB/SIMULINK,and simula-tion results show that the analysis result of the R-L fractional-order PCCM Boost converter model is more stable than that of the other PCCM Boost model,and the corresponding error is smaller.

关 键 词：BOOST变换器 分数阶模型 电感电流伪连续模式 状态空间平均法 

分 类 号：TM46[电气工程—电器]