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| Abstract: |
| According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies. |
| Key words: Buck converter fractional order continuous conduction mode(CCM) modeling dynamic analysis bifurcation |
| DOI：10.11916/j.issn.1005-9113.17107 |
| Clc Number:TN710 |
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| Descriptions in Chinese: |
| 电流电感连续模式下分数阶Buck变换器的建模与动力学分析 丁大为，李宗智，王年 （安徽大学 电子信息工程学院，合肥 230601） 创新点说明：1）本文基于分数阶理论以及实际电容和实际电感在本质上是分数阶的事实，建立电感电流连续模式下Buck变换器的分数阶数学和分数阶状态平均模型，并进行理论分析，给出Buck变换器运行于电感电流连续模式下的参数条件。 2）建立运行于电感电流连续模式下Buck变换器的分数阶数值仿真模型和电路模型，并进行数值和电路仿真分析，以验证分数阶建模与理论分析的正确性，研究发现分数阶数对变换器各个参数（如电感电流，输出电压，纹波等）都有较大影响。 3）建立电流控制型Buck变换器模型，并对其动力学行为进行分析，研究发现分数阶数会影响变换器的分岔点，对其动力学行为有较大影响。 综上所述，由于实际电感和实际电容在本质上是分数阶的事实，若仍然采用整数阶模型描述电感电流连续模式下的Buck 变换器将会得出错误的结论。因此，应建立能真实反映电感电流连续模式下Buck变换器动力学行为的分数阶模型。 关键词：Buck变换器，分数阶，电流电感连续模式（CCM），建模，动力学分析，分岔点 |
