Time-frequency Analysis Of The Spatial Distribution Of Lithium Concentration Throughout The Full Battery Operating In Different Modes

Lithium-ion batteries have become the core of energy storage and supply for electric vehicles and hybrid electric vehicle applications as they have ideal performance in terms of energy density,power density and cycle life,which directly contributing to the technological advancement from portable electronic devices to energy-efficient vehicles.However,lithium-ion batteries will encounter potential safety hazards and degradation mechanisms during operation.In order to improve the safety and cycle life of lithium-ion batteries,variables such as state of charge,state of health,state of power and state of energy should be estimated and predicted.These parameter values can be calculated by the solid phase concentration and the electrolyte concentration in the pseudo two dimensional battery model.Therefore,accurate prediction of the concentration is particularly important for improving the economy and battery performance of electric vehicles for different operating modes.This paper studies the diffusion of solid phase concentration and electrolyte concentration for different operating modes batteries.(1)Three different excitation signals are applied to simulate the transient process of lithium concentration distribution for power battery switched in different operating modes.On one hand,the exact solution of the solid state diffusion equation is resolved in the time domain and frequency domain respectively.On the other hand,the calculation precision,computing cost,and applicable range are compared under four excitation signals for solid surface concentration profile,calculated with different approximation methods,such as diffusion length method,polynomial profile approximation method,Padéapproximation method,pseudo steady state method,eigenfunction based Galerkin collocation method,and separation of variables method.The simulated solid phase concentration profiles indicate the calculation precision,time cost,and effective range not only rely on calculation methods but also excitation signals.Hence,in order to obtain concentration profiles in higher precision and for a wider applicable range,it is necessary to optimize calculation algorithms in terms of excitation signals related to operation modes of lithium ion batteries.The analyzing results in the present work for different algorithms under various excitation signals offer a theoretical basis on how to obtain an optimal estimation of solid phase concentration profiles.In turn,this optimal estimation benefit to predict safe operating regime and maximum power density of automotive batteries.(2)A pseudo-two-dimensional electrochemical model is used as the lithium battery physicochemcial model,which can provide the complete information about the spatial distribution of Li~+concentration in the electrolyte throughout the full battery.Regarding solution algorithm,which normally takes lots of time for the traditional finite difference method to discretize the diffusion partial differential equation,a new algorithm combining the finite element method andθmethod is proposed and a simple and efficient linear basis function is introduced into the finite element method in this paper,aiming at a quick calculation on the spatial distribution of Li~+concentration in the electrolyte throughout the full battery under different charging/discharging modes.Results of numerical calculation show:(1)in the frequency domain,the numerical solution obtained by the finite element method is highly consistent with the analytical solution obtained by the parameter transformation method;(2)in the time domain,the numerical solution obtained by the combination of finite element method andθmethod is also in good agreement with that obtained by the finite difference method.The algorithm proposed in this study provides a new method for obtaining the spatial distribution of Li~+concentration in the electrolyte throughout the full battery with a high speed and accuracy.