超级电容器分数阶模型的分频段参数辨识方法

doi:10.19799/j.cnki.2095-4239.2022.0236

摘要/Abstract

摘要：

超级电容器的电阻与电容参数不是常数，受频率等因素影响。研究发现采用分数阶等效电路模型能够更加准确地描述超级电容器的非线性特性。针对超级电容器的分数阶模型参数难以获取的问题，提出一种分频段参数辨识方法。该方法根据不同频段下超级电容器的阻抗特性，提出了相应频段的等效阻抗表达式，进而根据典型频率的阻抗数据求解各频段阻抗表达式中的未知参数，实现超级电容器分数阶模型参数的全频段辨识，从而大大降低了分数阶模型参数辨识的难度。最后，对超级电容器进行动态应力(DST)测试和不同频率的恒流充放电实验，将辨识得到的超级电容器分数阶模型仿真输出电压与超级电容器的实测电压进行对比。结果显示在DST测试下，模型端电压的平均相对误差为1.52%，最大相对误差限制在4%以内；在恒流充放电实验中，最大相对误差限制在6%以内，验证了所提分频段参数辨识方法的有效性和准确性。

关键词: 超级电容器, 分数阶模型, 频率特性, 阻抗特性, 参数辨识

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

中图分类号:

TM 53

邓巧, 丘东元, 顾文超, 陈艳峰, 张波. 超级电容器分数阶模型的分频段参数辨识方法[J]. 储能科学与技术, 2022, 11(10): 3371-3380.

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.

图/表 13

图1

图2

图3

图4

图5

图6

表1

表2

表3

超级电容器分数阶模型的参数辨识结果"

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

表3

图7

图8

图9

表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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