Quantifying the Effects of Temperature and Depth of Discharge on Li-Ion Battery Heat Generation: An Assessment of Resistance Models for Accurate Thermal Behavior Prediction
Authors: Vashisht Sagar , Rakshit Dibakar , Panchal Satyam , Fowler Michael , Fraser Roydon 
Published: February 2024

Li-ion batteries (LiBs) are widely adopted in electric vehicles (EVs) owing to their superior properties, such as high energy density, low discharge rate, long lifespan, and lightweight construction. Since the battery pack is the sole energy source for an EV, its performance is critical for optimal vehicle operation. However, the battery's calendar life, cycle life, and overall performance are significantly affected by temperature variations. The Li-ion batteries used in EVs may encounter challenging working conditions, leading to thermal problems such as significant capacity and power loss. In contrast, thermal runaways can occur at temperatures above a specific threshold, leading to severe health deterioration and sometimes catastrophic safety hazards such as fires and explosions. As the temperature significantly impacts Li-ion batteries, a battery thermal management system that can efficiently dissipate heat is crucial to ensure the battery's optimal performance and longevity. Hence, it is crucial to develop accurate algorithms for battery thermal management systems to precisely and dynamically estimate the temperature dynamics of the batteries integrated within the battery pack.
While experimental data can be used to estimate battery temperatures, the dynamic and diverse operating conditions of electric vehicles (EVs) present a significant challenge. Therefore, accurately predicting thermal response within batteries is critical. Various thermal models have been developed to predict the thermal behavior of batteries and quantify the amount of heat generated. The simplified thermal model only considers joule heating and reversible entropic heating. However, more accurate physics-based models consider reversible heat caused by the side reactions, heat generated by mass transport loss, and even mixing-induced heat. The amount of heat generated inside a Li-ion battery is determined by its equivalent internal resistance, open circuit voltage, and entropy change, which are in turn influenced by temperature and depth of discharge (DoD). To the best of the authors' knowledge, previous research on the heat generation of Li-ion batteries has been limited in some respects. Specifically, there has been little investigation into the combined impact of temperature and depth of discharge (DoD) across a wide temperature range. Most studies have been conducted under ambient temperature conditions, and only a few have focused on high temperatures within a narrow range with low discharge rates.
Thus, this study aims to address the research gap regarding the impact of temperature and depth of discharge (DoD) on heat generation in Li-ion batteries by analyzing these parameters using a transient battery thermal model. The research intends to improve the accuracy and precision of battery thermal behavior prediction, which has broad implications for battery-powered applications. This study aims to evaluate the impact of different resistance models on heat generation in Li-ion batteries, explicitly comparing a constant resistance model with a model that considers resistance as a function of temperature and depth of discharge (DoD). Investigating the interdependent impact of battery temperature and DoD on heat generation is crucial to create an accurate battery thermal model with high fidelity. The current study uses a two-dimensional battery thermal model to comprehensively analyze thermal behavior of a LiFePO4-20Ah Li-ion pouch cell. In this research study, heat generation in a Li-ion battery is evaluated by estimating the internal resistance and entropic change obtained from experimentation. The energy equation is then solved using the finite difference method in MATLAB to obtain the transient thermal response of the battery. The developed transient electrothermal model is validated against experimental data under varying C rates to assess the accuracy and precision of the proposed model. The simulation results show that the thermal response obtained considering the effect of temperature and DoD on heat generation shows more accurate results than the constant resistance values. The thermal behavior of a LiFePO4 pouch cell, considering constant values for heat generation, has a maximum relative error of roughly 19.99% compared to experimental data at a 4C discharge rate. While this maximum relative error was reduced to 6.29% when considering the effect of temperature and DoD on heat generation. In the constant resistance model, more significant errors can be attributed to the fact that the resistance of a Li-ion battery varies with the depth of discharge (DoD). While the initial discharge phase of the battery exhibits minimal changes in resistance values, a substantial increase in resistance occurs during the final stages of discharge. This contrasts with the actual behavior of Li-ion batteries, which demonstrate significant variations in resistance values throughout the discharge process. Thus, coupling the effects of DoD and temperature on heat generation is necessary to accurately predict the thermal behavior of Li-ion battery.

Figure 1