One dimensional fast computational partial differential model for heat transfer in lithium-ion batteries

Abstract The temperature and heat produced within lithium-ion batteries (LIBs) is an important field of research as it affects the power, voltage, and degradation of the battery. Models quickly and accurately predict the temperature and voltage based on operating conditions and can prevent thermal runaway, increase charging speed, prevent lithium plating, and increase cycle life. This paper presents mathematical models that allow for fast calculation which are used in the battery management system (BMS) and battery thermal management system (BTMS) for these goals. This paper presents two distinct models: 1) Internal resistance ( R i n t ) model, and 2) Physio-chemical diffusion/Butler-Volmer based partial differential 1-D model. In addition to this, the internal resistance in the R i n t model is also modeled as a function of the state of charge (SOC) and C-rate. In the experiments, thermocouples are placed on the tabs as well as the surface of the battery, and it is observed that temperature increases with the C-rate at both the surface and the tabs. It is noted that at 4C, the battery temperature increased from 22.00°C to 47.40°C and the tab temperature increased from 22°C to 52.94°C. The simulation results are compared with experimental data at C-rates of 1C, 2C, 3C, and 4C at 22°C. Overall, the simulation results show that the temperature is predicted accurately with a simple R i n t model. We also find that the simplified physio-chemical model of only 3 partial differential equations (PDEs) also produces satisfactory results compared to the usual 8-PDE model and is of similar accuracy as the Rint model. Finally, we find that the internal resistance of the battery, in the case of the R i n t model, is accurately predicted by a function of current and SOC through the use of a Pearson curve and hyperbolic sine function. These findings aid in accurate thermal design and thermal management of LIBs.