Model order reduction for solid-phase diffusion in physics-based lithium ion cell models

A model order reduction method is developed and applied to the solid-phase diffusion problem used in physics-based lithium ion cell models. The reduced order model is in the form of a state space model. Model identification is performed in the frequency-domain using the vector fitting method. The method allows the user to control the order of the model, the frequency band for model identification, and optionally a weight function to give a certain frequency band more weight. The model can be used for spherical and non-spherical particles. For spherical particles, the results from using the reduced order model are compared with those from analytical solutions, and excellent agreement is achieved using 3rd and 5th order models. When the approach is applied to non-spherical particles, the transfer functions need to be calculated numerically. Two methods, step response and complex exponential, are proposed to calculate the required transfer function. While the step response method is more suitable for low frequencies, the exponential method is more accurate for high frequencies. © 2012 Elsevier B.V.