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

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

Abstract

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

CLC Number:

TN711.4

CHEN Yanfeng, CHEN Sheng, ZHANG Bo, et al. Analysis of Transient and Steady-State Characteristics of Fractional-Order Cuk Converter[J]. Journal of South China University of Technology(Natural Science Edition), 2023, 51(3): 1-12.

Figures/Tables 12

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Comparison of DC components of state variables obtained by the method in this paper and simulation"

阶次 $α, β$	ESPM				仿真结果
阶次 $α, β$	$I L 1$ /A	$I L 2$ /A	$V C 1$ /V	$V C 2$ /V	$I L 1$ /A	$I L 2$ /A	$V C 1$ /V	$V C 2$ /V
（1，1）	0.150 0	0.150 0	6.000 0	3.000 0	0.150 0	0.150 0	6.000 6	2.999 9
（1，0.95）	0.149 5	0.149 4	5.999 5	2.988 9	0.149 5	0.149 5	5.991 4	2.990 1
（0.95，1）	0.151 5	0.150 0	6.001 5	3.000 0	0.151 3	0.150 0	5.999 9	2.999 8
（0.95，0.95）	0.150 9	0.149 4	6.000 9	2.988 9	0.150 8	0.149 5	5.990 0	2.989 8
（0.95，0.9）	0.149 5	0.148 0	5.999 4	2.959 6	0.149 5	0.148 2	5.963 6	2.963 8
（0.95，0.85）	0.146 0	0.144 5	5.996 0	2.889 6	0.146 5	0.145 2	5.907 2	2.903 3
（0.9，0.95）	0.154 8	0.149 4	6.004 8	2.988 8	0.154 2	0.149 5	5.989 8	2.989 3
（0.9，0.9）	0.153 5	0.148 0	6.003 5	2.959 3	0.153 0	0.148 2	5.963 9	2.962 1
（0.9，0.85）	0.150 1	0.144 4	6.000 1	2.887 9	0.150 0	0.145 0	5.902 6	2.898 4
（0.85，0.95）	0.164 2	0.149 4	6.014 2	2.988 8	0.162 5	0.149 5	5.988 9	2.988 8
（0.85，0.9）	0.163 0	0.147 9	6.013 0	2.958 6	0.161 6	0.148 2	5.959 9	2.959 9
（0.85，0.85）	0.160 0	0.144 2	6.009 9	2.884 4	0.158 8	0.144 7	5.895 4	2.887 5

Table 1

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 2

Comparison of methods in this paper，simulations and experimental results"

变量	方法	稳定时间/ms	纹波峰-峰值/A	直流分量/A
$i L 2$	ESPM	1.52	0.059	0.148
	仿真	1.52	0.073	0.148
	实验	1.56	0.052	0.112
$v C 2$	ESPM	1.60	0.109	2.959
	仿真	1.60	0.130	2.962
	实验	1.64	0.096	2.110

Table 2

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