Approximate Solutions for Determining Electrolyte Concentrations in Electrochemical Models of Lithium-Ion Batteries

The pseudo two-dimensional (P2D) model and its reduced order models, such as the single particle model (SPM), are widely used in electrochemical modeling and simulating lithium-ion batteries. Although the SPM has a low computational burden, its accuracy is poor under high-rate discharge conditions. Therefore, to balance accuracy and efficiency, the SPM with one-dimensional spatial electrolyte dynamics (SPMe) has been proposed. However, due to the complex diffusion equations for electrolyte dynamics, calculating the lithium-ion concentration in the electrolyte is still difficult. Therefore, we propose the cosine approximation (CA) method to efficiently calculate lithium-ion concentrations. We first use the Laplace transform to analytically solve the diffusion equations, and then, the complete transfer function from the discharge rate to lithium-ion concentration is obtained. In addition, the proposed method is obtained by both truncating the time-domain analytical solution of an infinite series and using error compensation. Moreover, compared to the finite volume method, the new method is verified under the galvanostatic and dynamic profiles, where the higher the order of the method, the higher the accuracy. Finally, the second-order CA shows a higher degree of accuracy compared to the widely used second-order polynomial approximation.