Thermal analysis of lithium-ion batteries
Introduction
The secondary lithium-ion battery with its high specific energy, high theoretical capacity and good cycle-life is a prime candidate as a power source for electric vehicles (EVs) and hybrid electric vehicles (HEVs). Safety is especially important for large-scale lithium-ion batteries, so thermal analysis is essential for their development and design. In order to provide sufficient capacity, a large-scale lithium-ion battery generally consists of many individual cells that are connected in parallel. This configuration inherently increases the thermal resistance of a battery, so thermal management becomes critical for operation.
Thermal modelling is an effective way to understand how the design and operating variables affect the thermal behaviour of the lithium-ion battery during charging and discharging. Bernardi et al. [1] have presented a general energy balance for battery systems. Chen and Evans [2], [3], [4] introduced several two-dimensional and three-dimensional thermal models. Lee et al. [5] also formulated a three-dimensional thermal model for electric vehicle batteries. These models were developed based on the transient heat-transfer equation and the heat generation equation proposed by Bernardi et al. [1]. The convective and radiative heat transfers on the surface were considered to be the boundary conditions, and the container of the battery was incorporated into a part of the boundary equations to facilitate the calculation. Pals and Newman [6] presented a one-cell model and a cell-stack model [7] to examine the effect of temperature variation on the heat-generation rate and the cell discharge behaviour. They showed that the heat-generation rate is much larger for lower temperatures than for higher temperatures. Song and Evans [8] also developed an electrochemical-thermal model, which was coupled with a two-dimensional thermal model and a one-dimensional electrochemical model, to examine the relationship between thermal and electrochemical behaviour.
In order to obtain a precise simulation of the thermal behaviour of a battery, the geometry, configuration, physical, chemical and electrochemical properties should be delineated as accurately as possible in the model. It may be impractical to describe completely the complicated behaviour of a lithium battery with existing theoretical expressions. Besides, an unacceptable amount of calculation time could be required if the model is too complicated. Thus, it is common to adopt some simplified strategies such as neglecting the radiative heat transfer on the boundaries, taking the layered-structure of the cells as the homogeneous materials, transferring the container to be a part of the boundary equations, and degrading a three-dimensional system to a two-dimensional model. It should be recognized that proper assumptions greatly enhance the value of the thermal model, whereas any improper assumption can lead to inaccurate or incorrect simulation results. It is important to ascertain the critical factors that significantly affect the thermal behaviour and together with the minor elements that can be neglected in the thermal model. Hence, in the present work, a detailed thermal model has been developed to verify the correctness of the assumptions and to determine the optimal approach to simplify the thermal model. The manner in which battery design parameters and operating variables affect thermal behaviour is also analyzed.
Section snippets
Detailed three-dimensional thermal model
A schematic diagram of the rectangular lithium-ion battery is shown in Fig. 1. It is divided into three major portions, namely, the core region, the case, and the contact layer. The core region consists of individual cells that are connected in parallel. Within an individual cell, the bi-cell configuration shown in Fig. 2 is one of the preferred designs and is chosen in this study. The case is the container of the battery. The contact layer stands for a narrow gap between the core region and
Results and discussion
The thermal behaviour of a typical large-scale lithium-ion battery is examined in accordance with the detailed thermal model proposed here. Information on the simulation is summarized in Table 4, Table 5. The default value of emissivity is 0.25, and the natural convection with radiation is the default condition at the boundaries. The cell potential as a function of utilization at different discharge rates, which is obtained from the experiment, is shown in Fig. 4. The simulation is terminated
Conclusions
A detailed three-dimensional thermal model has been developed to simulate the thermal behaviour of a lithium-ion battery. The layer-structured core region, the contact layer and the battery case are all included without simplification. In addition, this model considers the location-dependent convection and the radiation simultaneously to enhance the accuracy at the boundaries. Hence, some important phenomena such as the asymmetric temperature profile and the anomaly of temperature distribution
Acknowledgements
This work has been supported by the Materials Research Laboratories of Industrial Technology Research Institute. The authors would especially like to thank Dr. M.H. Yang for helpful assistance.
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