Parameter-identification method for fractional-order models of supercapacitors based on frequency-band division

doi:10.19799/j.cnki.2095-4239.2022.0236

Abstract

Abstract:

The resistance and capacitance of supercapacitors are not constant; they are affected by frequency and other factors. we realized that the fractional-order equivalent electrical-circuit models (ECMs) can describe the nonlinear characteristics of supercapacitors more accurately. To address the problem of solving the parameters of the fractional-order models (FOMs), a parameter-identification method based on frequency-band divisions is proposed. Based on the impedance characteristics of supercapacitors in different frequency bands, the equivalent impedance expressions at corresponding frequency bands are proposed. We found the unknown parameters in the impedance expressions at each frequency band using the impedance data at typical frequencies. Thus, the parameter identification of FOMs of supercapacitors in full-band is realized. This method reduces the FOM parameter identification difficulty. Finally, the dynamic-stress test (DST) and constant-current charge-discharge experiments at different frequencies are conducted on the supercapacitors. The output voltages of the solved FOMs are compared with the measured voltages of supercapacitors under DST. The results show that the mean relative error of the FOMs is 1.52%, and the maximum relative error is limited to 4%. Under the constant-current charge-discharge experiments, the maximum relative error is limited to 6%. The proposed method has high effectiveness and accuracy.

Key words: supercapacitor, fractional-order model, frequency characteristic, impedance characteristic, parameter identification

CLC Number:

TM 53

Qiao DENG, Dongyuan QIU, Wenchao GU, Yanfeng CHEN, Bo ZHANG. Parameter-identification method for fractional-order models of supercapacitors based on frequency-band division[J]. Energy Storage Science and Technology, 2022, 11(10): 3371-3380.

Figures/Tables 13

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 1

Table 2

Table 3

Parameters identification results of FOM of supercapacitor"

$α$	$β$	R_s/mΩ	R_p/mΩ	C/F	W/F
0.973	0.976	6	2	198	274

Table 3

Fig. 7

Fig. 8

Fig. 9

Table 4

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频段范围	频率取值	充放电频率f/Hz	阻抗参数/Ω
频段范围	频率取值	充放电频率f/Hz	Re(ω)	Im(ω)
主电容特性频段	ω_min	10.0 m	0.010 1	0.054 4
	ω_L	11.1 m	0.009 9	0.049 1
		16.7 m	0.009 3	0.033 2
		25.0 m	0.008 9	0.022 4
		33.3 m	0.008 6	0.017 0
		50.0 m	0.008 4	0.011 6
电荷扩散频段	ω_M	50	0.006 0	3.220 6×10^-5
电荷扩散频段	ω_M	100	0.006 0	1.640 9×10^-5
电阻特性频段	ω_H	100	0.006 0	1.640 9×10^-5

测试序号	充放电频率f/Hz	阻抗参数Im(ω_L)/Ω	拟合值/Ω	拟合结果
测试序号	充放电频率f/Hz	阻抗参数Im(ω_L)/Ω	拟合值/Ω	主电容系数W	分数阶阶数β
1	10.0 m	0.054 4	0.054 4	273.8	0.976
2	11.1 m	0.049 1	0.049 1
3	16.7 m	0.033 2	0.033 0
4	25.0 m	0.022 4	0.022 2
5	33.3 m	0.017 0	0.016 8
6	50.0	0.011 6	0.011 3

辨识方法	数据获取	辨识难度	建模精度	参考文献
阻抗辨识	通过专业的电化学仪器测量阻抗谱	需要拟合全频域内的阻抗谱	阻抗谱的测试条件和实际使用条件存在差距，可能造成辨识模型在实际应用过程中的模型精度下降	[27-28，30]
波形辨识	进行动态电压/电流测试	拟合电压电流波形，分数阶微积分方程推导复杂	误差范围小	[31-32]
分频段辨识法	进行几组典型频率的恒流充放电测试	仅需分步求解已化简的阻抗表达式	误差范围小	本文

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