In this paper, the equivalent small parameter method (ESPM) is used to establish the nonlinear mathematical model of the fractional‐order buck–boost converter in continuous current mode (CCM), and the analytical expression of approximate steady‐state period of converter state variable is obtained by using equivalent small parameter method and combining with harmonic balance principle. The Matlab/Simulink is used to construct the fractional‐order capacitance and inductance and to build the circuit model as well as the simulation model of fractional‐order buck–boost converter. Moreover, the simulation results of Oustaloup circuit model and numerical simulation model are compared with those of ESPM model to verify the validity and accuracy of the ESPM. The model is simulated by changing the orders of the capacitor and inductor to obtain the influence rule of the order of fractional element on harmonic characteristics of the state variables.

中文翻译：

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分数阶降压-升压转换器的建模和分析方法

本文采用等效小参数方法（ESPM）建立了连续电流模式（CCM）的分数阶降压-升压变换器的非线性数学模型，以及变换器状态的近似稳态周期的解析表达式。通过使用等效的小参数方法并结合谐波平衡原理获得变量。Matlab / Simulink用于构建分数阶电容和电感，并建立电路模型以及分数阶降压-升压转换器的仿真模型。此外，将Oustaloup电路模型和数值仿真模型的仿真结果与ESPM模型的仿真结果进行比较，以验证ESPM的有效性和准确性。