Cuk变换器分数阶建模与仿真分析  

Fractional Order Modeling and Simulation Analysis of of Cuk Converter

作　　者：谢玲玲[1] 宁康智 秦龙 XIE Ling-ling;NING Kang-zhi;QING Long(College of Electronic Engineering,Guangxi University,Nanning Guangxi 530000,China)

机构地区：[1]广西大学电气工程学院,广西南宁530000

出　　处：《计算机仿真》2022年第10期313-320,共8页Computer Simulation

基　　金：国家自然科学基金资助项目(61863003);广西自然科学基金资助项目(2019GXNSFAA245019)。

摘　　要：针对电感电容本质是非整数阶的事实,基于分数阶微积分理论和状态空间平均法建立了电流连续模式下Cuk变换器的四阶分数阶数学模型和分数阶状态平均模型。根据分数阶微积分定义对其进行稳态和交流小信号分析,推导了稳态工作点、电感电流的纹波、峰值和谷值的表达式以及输出电压对占空比的传递函数,分析了分数阶Cuk变换器电流连续与不连续的临界条件。研究结果表明,Cuk变换器电感电流的纹波、峰值和谷值、输出电压对占空比的传递函数、电流连续与不连续的临界条件与电感、电容的阶数有关。最后在Matlab/Simulink仿真平台上建立了Cuk变换器分数阶模型,并通过分数阶和整数阶的仿真对比,验证了分数阶建模和理论分析的正确性,为变换器的优化控制提供理论依据。A number of researchers have shown that the actual capacitor and inductor are fractional order in nature, therefore, we established the fourth-order fractional order mathematical model and the fractional order state average model of the Cuk converter in continuous conduction mode(CCM) based on the fractional order calculus theory and the state average modeling method. According to the definition of fractional order calculus, the steady-state and small-signal analysis were carried out. The expressions of the steady-state operating point, inductor current ripple, peak and valley values, and the transfer function of the output voltage to the duty ratio were derived. At the same time, the critical conditions of the continuous conduction mode to discontinuous conduction mode of the fractional order Cuk Converter were analyzed. The results indicate that the ripple, peak and valley values of the inductor current, the transfer function of the output voltage to the duty ratio, and the critical conditions of the CCM to the discontinuous conduction mode(DCM) are related to the fractional order of the inductor and the capacitor. Finally, the fractional order mathematical model and the fractional order state average model of the Cuk converter were established on the Matlab/Simulink simulation platform. The simulation results verify the correctness of the models and theoretical analysis. The proposed method provides a theoretical basis for the optimal control of the converter.

关 键 词：变换器 分数阶模型 电流连续模式 

分 类 号：TM46[电气工程—电器]