As an important supplementary part of experiment, multi-scale modeling and simulation plays an important role in reasonable design and performance prediction of lithium-ion batteries. Due to the complexity of spherical diffusion equation, the calculation error of Li-ion diffusion process in solid spherical active particles is an important factor restricting the accuracy of the simplified mechanism model of Li-ion batteries. In this study, based on the quasi-steady state of spherical active particles in Li-ion diffusion processes, the concepts of zero-state response, zero-input response, and total response in the discipline of circuit analysis are introduced to expand the spherical diffusion equation, the analytical solution of Li-ion diffusion process in active particles is solved by using the variable-separation method, and an error-controllable method for solving the approximate solution of diffusion process in spherical particles is proposed and verified. Besides, the computational complexity of the algorithm is very low, therefore, this study is of great significant to construct the high-precision simplified mechanism model of Li-ion batteries and to realize the high-accuracy battery management algorithm on microprocessor systems.

作为实验的重要补充部分，多尺度建模和仿真在锂离子电池的合理设计和性能预测中起着重要作用。由于球形扩散方程的复杂性，固体球形活性颗粒中锂离子扩散过程的计算误差是限制锂离子电池简化机理模型精度的重要因素。在这项研究中，基于锂离子扩散过程中球形活性粒子的准稳态，在电路分析学科中引入了零状态响应，零输入响应和总响应的概念来扩展球形扩散方程，采用变分离法求解了锂离子在活性颗粒中扩散过程的解析解，提出并验证了一种误差控制方法，用于求解球形颗粒扩散过程的近似解。此外，该算法的计算复杂度很低，因此，对于建立锂离子电池的高精度简化机构模型，并在微处理器系统上实现高精度的电池管理算法具有重要的意义。