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Exploring the dependence of cell aging dynamics on thermal gradient in battery modules: A PDE-based time scale separation approach

There is an abundance of research dedicated to understanding lithium-ion batteries at the cell-level. However the cell-level models or estimation algorithms cannot be directly applied to battery modules or packs that are composed of tens to hundreds or thousands of cells. Pack or module-level modeling and estimation must take into consideration the temperature distribution manufacturing-induced parameter (impedance capacity) variances pack topology (electrical interconnections) and thermal interactions between cells. In this work we motivate the need for pack or module-level modeling by showing that the aging dynamics of a cell is influenced by the adjacent cells it is interacting with both electrically and thermally. The characteristic time-scale of the vital dynamics of an interconnected cell consisting of a high-fidelity coupled electrochemical- thermal-aging model are studied to reveal a three- time scale behavior. This distinct behavior is explored via singular perturbation theory to derive a reduced-order aging model for an interconnected cell that is shown to depend on the thermal gradient in a serially interconnected module.