Initial Value and Initial Current Discrepancy in Simulating Lithium-Ion Battery Packs - Resolution from Dr. Ralph White’s Analytical Approach

Abstract

Battery models are useful tools that provide insight into electrochemical processes within an electrochemical device those can typically not be measured, either due to a lack of experimental methods or due to the transient nature of the phenomena in question. Irrespective of the complexity of the models involved, a general view is that a good model, once established for a single cell in terms of complexity of the physics, choice of simulation algorithm, value for the parameters, and mechanisms for fade, can be easily extended for pack simulations.1–3 This type of extension is critical to the virtual engineering efforts currently underway at OEMs which rely on accurate and representative battery models. In this work, pitfalls during scaling up approximate and detailed physics-based models developed for single-cell to pack-level simulations are highlighted using representative examples. Interesting mathematical nuances were found depending on the numerical simulation approach used. A discrepancy at initial times (t = 0) during the pack-level simulations was highlighted and resolved using the Laplace transform approach to get an analytical solution for the simplest model. A few thoughts on numerical challenges and the index of differential-algebraic equations (DAEs)4,5 while using the strong form and the weak form formulation of DAEs are also provided in the paper.6