A new solution to the spherical particle surface concentration of lithium-ion battery electrodes

• Published in: Electrochimica acta 2021-12, Vol.399, p.139391, Article 139391
• Main Authors: Xie, Yizhan, Cheng, Ximing
• Format: Article
• Language: English
• Subjects: Algorithms; Convergence; Convolution; Discrete convolution; Electrochemical model; Exact solutions; Finite element method; Infinite series; Ion concentration; Ion diffusion; Lithium; Lithium-ion batteries; Lithium-ion battery; Management systems; Partial differential equations; Power management; Rechargeable batteries; Solid phase diffusion; Solid phases; Sum function
• ISSN: 0013-4686; 1873-3859
• DOI: 10.1016/j.electacta.2021.139391

•An analytic solution is derived by using the Laplace transformation.•A converged sum function is used to solve the solid diffusion equation under galvanostatic profiles.•A finite discrete convolution is used to accurately and efficiently solve the solid diffusion equation under dynamic profiles.•Compared with a finite element method, the discrete convolution algorithm is validated by using different profiles.•By comparison with two approximations, the proposed algorithm has intermediate error with the least operation time. The lithium-ion concentration of a solid phase is essential to solve the electrochemical model of a lithium-ion battery. Based on the analytic solution of a convolution infinite series, a new algorithm is proposed to efficiently and accurately solve the partial differential equation for the lithium-ion diffusion behavior of electrode particles. Under galvanostatic profiles, the analytic solution is an infinite time series transformed into a converged sum function by using the monotone convergence theorem. Under dynamic profiles, the infinite series solution is simplified to a finite discrete convolution of both the input and the sum function. Meanwhile, the discrete step is determined by the amplitude-frequency characteristic curve, and the sum function is truncated by its characteristic monotonic decay approaching zero over time. Compared with using a professional finite element analysis software, it takes less time to use this discrete convolution algorithm, and it yields less error. And, it has the least solution time with medium accuracy in comparison with two commonly used approximations. Not only that, the proposed algorithm has only two parameters to be determined with little computation, thus promoting the electrochemical models built in battery management systems.