基于分数阶R-L定义的分数阶CCM Boost变换器建模及仿真分析

Modeling and simulation analysis of fractional-order CCM Boost converter based on fractional-order R-L definition

为了建立更加符合实际运行情况的DC-DC变换器模型,该文基于电感和电容本质上是分数阶的事实,采用分数阶微积分理论和状态空间平均法,建立了电感电流连续模式(Continuous conduction mode,CCM)下Boost变换器的分数阶数学模型及分数阶状态空间平均模型。根据分数阶Riemann-Liouville(R-L)定义对分数阶CCM Boost变换器进行了理论分析,推导了R-L定义下的直流静态工作点、升压比、电感电流纹波以及输出电压纹波的表达式,与Caputo定义下的表达式相比,R-L定义下直流静态工作点和升压比的表达式不仅与导通时间占空比相关还与分数阶电容和电感的阶数相关,输出电压纹波的表达式也存在较大差异。最后在MATLAB/SIMULINK中建立了分数阶CCM Boost变换器的仿真模型,仿真结果表明,采用R-L定义对分数阶CCM Boost变换器进行理论分析更加符合该变换器的实际工作情况。仿真结果验证了理论分析的正确性,所提方法可以推广到其他分数阶DC-DC变换器中。

In order to build a DC-DC converter model more in line with actual operating conditions,and based on the fact that inductance and capacitance are essentially fractional-order,using fractional-order calculus theory and state space averaging,a fractional-order mathematical model and a fractional-order state-space average model of the Boost converter in continuous conduction mode(CCM)are established.According to the fractional-order Riemann-Liouville(R-L)definition,a theoretical analysis of the fractional-order CCM Boost converter is performed.The expressions of DC static operating point,boost ratio,inductor current ripple and output voltage ripple under the definition of R-L are derived.Compared with the expressions defined by the fractional-order Caputo definition,the expressions of the DC static operating point and the boost ratio under the definition of R-L are not only related to the on-time duty cycle,but also to the order of the fractional-order capacitor and inductor.There are also large differences in the expression of output voltage ripple.Finally,a simulation model of a fractional-order CCM Boost converter is established in Matlab/Simulink.The simulation results show that the theoretical analysis of the fractional-order CCM Boost converter using R-L definition is more in line with the actual working condition of the converter,which verify the correctness of the theoretical analysis,the method proposed in this paper can be generalized to other fractional-order DC-DC converters.