Analytical transfer function for the blocked-diffusion warburg impedance with frequency dispersion. Simulation of the impedance spectrum and voltage response of a lithium-ion battery

Samuel Cruz-Manzo , Paul Greenwood
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Abstract

The frequency-impedance spectrum of the blocked-diffusion Warburg (BDW) impedance is represented by a 45-degree angle straight-line at high frequencies followed by a vertical line at low frequencies in the Nyquist plot. On the contrary, the impedance spectrum of the blocked-diffusion Warburg impedance with frequency dispersion (BDWf) is represented by a straight-line with slope < 45-degree angle at high frequencies followed by a constant phase element (CPE) response at low frequencies. In this study, the mathematical treatment reported in a previous study for the transfer function of the BDW impedance is extended for the derivation of a transfer function representing the BDWf impedance. The new transfer function representing the BDWf impedance is able to reveal the contribution of the diffusion process which is overlapped with the CPE behaviour in the BDWf impedance spectrum. The transfer function representing the BDWf impedance developed in this study and the transfer function representing the finite-length Warburg (FLW) impedance presented in a different study have been considered in an equivalent electrical circuit (EEC) configuration constructed in MATLAB/Simulink environment to simulate the frequency-impedance spectrum and output voltage response of a Lithium-ion battery. The effect of the electrode diffusion distance of lithium ions on the frequency-impedance spectrum and output voltage response of a Li-ion battery is simulated through the Simulink model of the battery. This study could assist other studies focusing on the simulation of the diffusion phenomena in modern batteries with different particle sizes considering the EIS measurements as a baseline.
具有频散的阻塞扩散warburg阻抗的解析传递函数。锂离子电池阻抗谱和电压响应的仿真
阻塞扩散Warburg (BDW)阻抗的频率-阻抗谱在Nyquist图中由高频处的45度角直线和低频处的垂直线表示。相反,具有频散的阻塞扩散Warburg阻抗(BDWf)的阻抗谱在高频处为斜率为<; 45度角的直线,在低频处为恒相元(CPE)响应。在本研究中,对先前研究中报道的BDWf阻抗传递函数的数学处理进行了扩展,以推导出表示BDWf阻抗的传递函数。新的传递函数表示BDWf阻抗,能够揭示与CPE行为重叠的扩散过程在BDWf阻抗谱中的贡献。在MATLAB/Simulink环境中构建等效电路(EEC)配置,模拟锂离子电池的频率-阻抗谱和输出电压响应,考虑本研究中提出的BDWf阻抗传递函数和另一项研究中提出的有限长度Warburg (FLW)阻抗传递函数。通过锂离子电池的Simulink模型,模拟了锂离子电极扩散距离对锂离子电池频率-阻抗谱和输出电压响应的影响。本研究可以为其他以EIS测量值为基准,着重模拟不同粒径现代电池中扩散现象的研究提供参考。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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