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 correlatio...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.展开更多
Rate capability,peak power,and energy density are of vital importance for the capacitive energy storage(CES)of electrochemical energy devices.The frequency response analysis(FRA)is regarded as an efficient tool in stu...Rate capability,peak power,and energy density are of vital importance for the capacitive energy storage(CES)of electrochemical energy devices.The frequency response analysis(FRA)is regarded as an efficient tool in studying the CES.In the present work,a bi-scale impedance transmission line model(TLM)is firstly developed for a single pore to a porous electrode.Not only the TLM of the single pore is reparameterized but also the particle packing compactness is defined in the bi-scale.Subsequently,the CES properties are identified by FRA,focused on rate capability vs.characteristic frequency,peak power vs.equivalent series resistance,and energy density vs.low frequency limiting capacitance for a single pore to a porous electrode.Based on these relationships,the CES properties are numerically simulated and theoretically predicted for a single pore to a porous electrode in terms of intra-particle pore length,intra-particle pore diameter,inter-particle pore diameter,electrolyte conductivity,interfacial capacitance&exponent factor,electrode thickness,electrode apparent surface area,and particle packing compactness.Finally,the experimental diagnosis of four supercapacitors(SCs)with different electrode thicknesses is conducted for validating the bi-scale TLM and gaining an insight into the CES properties for a porous electrode to a single pore.The calculating results suggest,to some extent,the inter-particle pore plays a more critical role than the intra-particle pore in the CES properties such as the rate capability and the peak power density for a single pore to a porous electrode.Hence,in order to design a better porous electrode,more attention should be given to the inter-particle pore.展开更多
基金support from the National Science Foundation of China(22078190)the National Key R&D Plan of China(2020YFB1505802).
文摘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.
基金financial support from the National Science Foundation of China(22078190)the National Key R&D Plan of China(2020YFB1505802)。
文摘Rate capability,peak power,and energy density are of vital importance for the capacitive energy storage(CES)of electrochemical energy devices.The frequency response analysis(FRA)is regarded as an efficient tool in studying the CES.In the present work,a bi-scale impedance transmission line model(TLM)is firstly developed for a single pore to a porous electrode.Not only the TLM of the single pore is reparameterized but also the particle packing compactness is defined in the bi-scale.Subsequently,the CES properties are identified by FRA,focused on rate capability vs.characteristic frequency,peak power vs.equivalent series resistance,and energy density vs.low frequency limiting capacitance for a single pore to a porous electrode.Based on these relationships,the CES properties are numerically simulated and theoretically predicted for a single pore to a porous electrode in terms of intra-particle pore length,intra-particle pore diameter,inter-particle pore diameter,electrolyte conductivity,interfacial capacitance&exponent factor,electrode thickness,electrode apparent surface area,and particle packing compactness.Finally,the experimental diagnosis of four supercapacitors(SCs)with different electrode thicknesses is conducted for validating the bi-scale TLM and gaining an insight into the CES properties for a porous electrode to a single pore.The calculating results suggest,to some extent,the inter-particle pore plays a more critical role than the intra-particle pore in the CES properties such as the rate capability and the peak power density for a single pore to a porous electrode.Hence,in order to design a better porous electrode,more attention should be given to the inter-particle pore.
