单端初级电感变换器的分数阶建模与仿真分析  

Modeling and simulation analysis of fractional-order single ended primary inductor converter

作　　者：谢玲玲[1] 蒙远杰 Xie Lingling;Meng Yuanjie(School of Electrical Engineering,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学电气工程学院,广西南宁530004

出　　处：《南京理工大学学报》2023年第5期587-595,共9页Journal of Nanjing University of Science and Technology

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

摘　　要：出于电感和电容本质上是分数阶的实际情况考虑,针对单端初级电感变换器(Single ended primary inductor converter,SEPIC)的分数阶建模问题进行研究,建立了更准确的分数阶模型。在分数阶微积分的理论基础上,使用状态空间平均法,建立了电流连续模式下SEPIC的分数阶数学模型,推导了分数阶模型的静态工作点、电感电流纹波、电容电压纹波和传递函数表达式。采用分抗电路拟合的方法,实现0.9阶电感和0.9阶电容,用它们替换变换器中的整数阶元件,得到了SEPIC的分数阶电路模型。在MATLAB/Simulink仿真软件中,对SEPIC的分数阶数学模型和电路模型进行了仿真,并与理论计算值进行比较,仿真结果与理论计算基本一致,充分验证了分数阶模型的正确性。对比了分数阶模型与整数阶模型的差异,分数阶模型会产生更大的纹波,但具有更好的动态性能:响应速度更快,超调量更小,到达稳态的时间更短。Considering the fact that inductance and capacitance are fractional order in nature,a more accurate fractional order model of single ended primary inductor converter(SEPIC)converter is established.On the basis of fractional calculus theory,the fractional mathematical model of SEPIC converter in continuous current mode is established by using state space averaging method,and the static operating point,inductance current ripple,capacitor voltage ripple and transfer function expressions of the fractional model are derived.Using the fitting method of fractance circuit,the 0.9-order inductance and 0.9-order capacitance are realized.They are used to replace the integer order components in the converter,and the fractional order circuit model of SEPIC converter is obtained.In MATLAB/Simulink simulation software,the fractional mathematical model and circuit model of SEPIC converter are simulated and compared with the theoretical calculation value.The simulation results are basically consistent with the theoretical calculation,which fully verifies the correctness of the fractional model.The difference between the fractional model and the integer model shows that the fractional model produces larger ripple but has better dynamic performance:faster response speed,smaller overshoot and shorter time to steady state.

关 键 词：分数阶理论 单端初级电感变换器 电流连续模式 状态空间平均法 

分 类 号：TM46[电气工程—电器]