Analytical Solution for Thermal Runaway of Li-Ion Battery with Simplified Thermal Decomposition Equation

Analytical solutions for the temperature change of a lithium-ion battery during thermal runaway were derived by the equation of linearizing thermal decomposition reaction. This study focuses on the representative temperature of the battery cell (zero-dimensional) during the heating test. First, the thermal decomposition reaction was modeled from DSC tests data of the electrode assuming Arrhenius-type temperature dependency. Subsequently, the reaction was simplified by a linear function of temperature and the analytical solution was derived as the exponential function with respect to time. The validity and applicability of the analytical solution are discussed by comparing it with a one-dimensional thermal runaway simulation. Further study was carried out for multiple batteries in consideration of cell-to-cell propagation of the thermal runaway and the applicability was discussed. As results, the single-cell predictions agreed generally with numerical results, especially with higher heating and lower latent heat. A delay in thermal runaway onset in multiple cells, linearly dependent on inter-cell conductivity, was quantified analytically. Parameter adjustments improved the alignment of analytical and numerical results for multiple cells, enabling quick thermal assessments. While numerical simulation is needed for high accuracy, this analytical framework offers new insights and facilitates initial analyses.