基于相似理论的锂电池三维电化学跨尺度建模

从抛物线型偏微分方程基本形式出发，利用量纲为一分析法推导了抛物线型偏微分方程的相似准则，并推广得到电化学过程的相似准则，从而确定原型与模型之间的电化学过程参数相似关系.利用Comsol Multiphysics软件进行了锂离子电池单元电化学过程的有限元建模与计算，验证了所建立相似准则和相似关系的正确性.模型验证结果表明电化学有限元建模方法能实现锂离子电池三维电化学过程的一致模拟，同时，高倍率充放电工况下电池内部不均匀性加剧，导致传统的通用准二维模型预测结果具有较大误差.因此，在电池单体设计及系统集成与管理过程中，有必要对基于准二维模型的状态估计算法进行修正，以避免电池局部过充过放而导致安全隐患.
A dimensional analysis method was performed to derive similarity criteria and the similarity coefficients of parabolic partial differential equation, and then it was further generalized to deduce the similarity coefficients of the electrochemical process. To validate the similarity criteria and the similarity coefficients, three dimension finite element models of electrochemical process of lithium ion battery under specified conditions were established with the software of Comsol Multiphysics. The simulation results show that the similarity criteria and the similarity coefficients are certified to be correct and the modelling method based on the similarity theory can achieve equivalent simulation. Moreover, the simulation results reveal that the inner state of the battery tends to be uneven under high rate operation, thus corresponding measurements in design and management based on conventional Pseudo 2D model should be modified to avoid safety issues due to a local over charge or over discharge