Journal of South China University of Technology(Natural Science) >

2023 , Vol. 51 >Issue 3: 1 - 12

DOI: https://doi.org/10.12141/j.issn.1000-565X.220161

Energy, Power & Electrical Engineering

Analysis of Transient and Steady-State Characteristics of Fractional-Order Cuk Converter

  • CHEN Yanfeng ,
  • CHEN Sheng ,
  • ZHANG Bo ,
  • QIU Dongyuan
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  • School of Electric Power Engineering，South China University of Technology，Guangzhou 510640，Guangdong，China
陈艳峰（1970-），女，教授，博士生导师，主要从事非线性系统与电力电子建模与控制研究。

Received date: 2022-03-29

  Online published: 2022-10-21

Supported by

the National Natural Science Foundation of China(52077085);the Natural Science Foundation of Guangdong Province(2019A1515011133)

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Abstract

This paper established the nonlinear equivalent circuit model and nonlinear mathematical model of the fractional-order Cuk converter operating in Continuous Conduction Mode (CCM), and obtained the equivalent mathematical model by using the equivalent small parameter (ESP) symbolic analysis method. Then, based on the principle of harmonic balance, it iteratively obtained the transient and steady-state approximate periodic solutions of the transients and steady-state variables of the transformer state variables. Furthermore, it analyzed the influence of fractional inductance and capacitance on the DC operating point and periodic declosing orbit and ripple component of the state variable, and the accuracy of the transient solution and steady-state solution of the state variable obtained by the proposed method was verified by simulation. Finally, an experimental verification was carried out on a fractional-order Cuk converter with an inductor and capacitor order of 0.9. The settling times of the state variables (output voltage and inductor current) obtained by the experiment and the method are 1.56 ms and 1.52 ms, the average output voltage is 2.110 V and 2.959 V, the peak ripple voltage is 96 mV and 109 mV, the average inductor current is 0.112 A and 0.148 A, and the peak ripple current is 52 mA and 59 mA, respectively. It can be seen that for the transient and steady-state characteristics of state variables, the results obtained in the method and experiments are relatively close. The study further verified the effectiveness of the method and the accuracy of the transient and steady-state solutions of the obtained state variables. The steady-state period solution of the fractional-order converter obtained in this method is related to the order of the fractional energy storage element, so it can be used to analyze the influence of fractional-order on circuit characteristics. In addition, the stability of the converter system can also be analyzed according to obtained analytical expression of obtained steady-state solution.

Key words： fractional-order; equivalent small parameter method; steady-state analytical solution; Cuk converter; transient analytical solution

Cite this article

CHEN Yanfeng , CHEN Sheng , ZHANG Bo , QIU Dongyuan . Analysis of Transient and Steady-State Characteristics of Fractional-Order Cuk Converter[J]. Journal of South China University of Technology(Natural Science), 2023 , 51(3) : 1 -12 . DOI: 10.12141/j.issn.1000-565X.220161

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