一种求解锂离子电池单粒子模型液相扩散方程的新方法

电解液中的锂离子浓度表达是锂离子电池电化学模型求解的基本任务之一.为了平衡单粒子模型的液相动态性能和计算效率,假设反应仅发生在集电极和电解质界面上,为此,提出一种基于液相扩散方程无穷级数解析解的界面浓度求解新方法.在恒流工况下,利用数列单调收敛准则将解析解转化为一个收敛和函数.在动态工况下,将该解析解简化为输入与和函数的无限离散卷积.利用和函数随时间单调衰减并收敛至零的特性对其进行截断,从而得到有限离散卷积求解算法.对比专业有限元分析软件,该方法在恒流工况和动态工况下均能以较少的计算时间获得相当好的精度.而且,该方法仅有一个配置参数.因此,所提方法将有效减小应用于实时电池管理系统上的电化学模型计算负担.

A new method to solve electrolyte diffusion equations for single particle model of lithium-ion batteries

It is one of basic tasks to solve the electrochemical model of lithium-ion batteries for obtaining the lithium-ion concentration in the electrolyte.In order to balance the computational efficiency and electrolyte dynamic property,it is assumed that reactions occur only at interfaces between the collector and the electrolyte.Based on the analytical solution to the liquid diffusion equations,which is in the form of infinite series,a new method is proposed to solve it.Under galvanostatic profiles,the analytic solution is an infinite time series transformed into a converged sum function by using the monotone convergence theorem.Under the dynamic profiles,the infinite series solution is simplified into an infinite discrete convolution of both the input and the sum function.The sum function is truncated by its characteristic of monotonic decay approaching to zero over time,thus obtaining a finite discrete convolution algorithm.Reference to the results from a professional finite element analysis software,the proposed algorithm can produce high accuracy with less computation time under both galvanostatic profiles and dynamic profiles.Also,there is only one parameter to be configured.Therefore,our algorithm will reduce the computation burden of the electrochemical model applied to a real-time battery management system.