Including double-layer capacitance in lithium-ion battery mathematical models

A fundamental model of lithium-ion battery cell based on Newman's works is presented in this article, including migration and diffusion of species and charges in electrodes and electrolyte. The particularity of our work is that the double layer capacitance, which is commonly neglected, is integrated in the model. We especially emphasize how to include correctly, in a physical point of view, the double layer capacitance in the electrochemical lithium-ion cell model. It is first demonstrated that the widely used mathematical formulation of the model leads to a physical error when the double layer capacitance is included, and a new formulation free of this error is proposed. Then are given the conditions for which the physical error mentioned before may cause appreciable inaccuracy in the prediction. Simulations have been carried out to validate the present analysis, and the results obtained show that the difference in cell voltage can attain several tens of millivolts.