Model reduction of fractional impedance spectra for time-frequency analysis of batteries, fuel cells, and supercapacitors

Joint time-frequency analysis is an emerging method for interpreting the underlying physics in fuel cells, batteries, and supercapacitors. To increase the reliability of time-frequency analysis, a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required. The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high- to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process. The following work has been carried out: (i) the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique, respectively; (ii) the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time-frequency analysis; (iii) the results of time-frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured; and (iv) the results of time-frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries, supercapacitors, and solid oxide fuel cells. In turn, the numerical validation has demonstrated the powerful function of the joint time-frequency analysis. The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time-frequency analysis for electrochemical energy devices.

Automated summary

In order to increase the reliability of time-frequency analysis, it is essential to establish a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis. This study formulates a thorough model reduction of fractional impedance spectra for electrochemical energy devices, including the reduction from fractional-order models to integer-order models and from high- to low-order RC circuits, as well as the evolution of characteristic time constants. The results of time-frequency analysis are found to be useful for determining the reduction order and have been validated for various electrochemical energy devices.