Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs).On one hand,the quasi-exact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand,calculation errors and application range of approx-imate solutions not only rely on approximate algorithms but also on discharge modes.For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range,it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles.In this study,approximation methods,such as diffusion length method,polynomial profile approximation method,Padé approximation method,pseudo steady state method,eigenfunction-based Galerkin collocation method,and separation of vari-ables method for solving Li solid-phase diffusion in spherical active particles are compared from calcula-tion fundamentals to algorithm implementation.Furthermore,these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes,i.e.,start-up,slow-down,and speed-up.The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range.In turn,optimal solu-tions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.

Institute for Sustainable Energy/College of Science,Shanghai University,Shanghai 201800,China;Shaanxi Key Laboratory of Nanomaterials and Nanotechnology,School of Mechanical and Electrical Engineering,Xi'an University of Architecture and Technology,Xi'an 710055,Shaanxi,China;Institute of Materials/School of Materials Science and Engineering,Shanghai University,Shanghai 200072,China;Xi'an Key Laboratory of New Energy Materials and Devices,Institute of Advanced Electrochemical Energy&School of Materials Science and Engineering,Xi'an University of Technology,Xi'an,Shaanxi 710048,China

[1]Qiu-An Huang;Yuxuan Bai;Liang Wang;Juan Wang;Fangzhou Zhang;Linlin Wang;Xifei Li;Jiujun Zhang-.Time-frequency analysis of Li solid-phase diffusion in spherical active particles under typical discharge modes)[J].能源化学,2022(04):209-224

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