Evaluation of Order Reduction Techniques for Porous Electrode Diffusion Equation in Lithium Ion Model

Models for lithium ion batteries based on electrochemical thermal principles approximate electrodes with spheres. Ion concentration in the spheres is described using Fick's second law with partial differential equations (PDE), which can be solved numerically. The model calculation time, especially the electrode ion concentration part, should be reduced as less as possible for real time control purposes. Several mathematical methods have been proposed to reduce the complexity of PDE in electrode particles which include polynomial approximation, proper orthogonal decomposition (POD), Padé approximation, Galerkin reformulation and etc. These methods are compared to each other with different input current density. Then, selected method is further integrated into a reduced order model (ROM) for a complete battery that considers Li ion concentration, potentials in electrode and electrolyte. Evaluation of simulation results reveal that the 3^rd order Padé approximation serves as a better computationally efficient replacement for the diffusion equation in lithium ion battery model.