Lithium-ion batteries are one of the most developing categories of batteries on the market these days because of their high energy density and capacity. A large amount of energy is stored inside them and they have great sensitivity to the operating conditions. Therefore, safety is an important issue in lithium-ion batteries. In addition, demands on safety of these batteries is increasing with their utilization in more applications.
With the intention of reaching out to safety requirements of the lithium-ion batteries on electronic device applications, researchers are resuming to do supplementary investigations on the essential issues in relation to the lithium-ion batteries.
System safety, cycle life, and cell performance are influenced by temperature distribution in the cell. Consecutively, it depends on heat dissipation rate at surface of the cell and heat generation rate within the cell.
Although lithium-ion batteries are susceptible to extreme heat load under severe or abnormal functional conditions, thermal management has been one of the considerable issues in developing lithium-ion batteries in hybrid electric vehicle and battery system applications.
A pseudo 2D electrochemical model for modelling electrochemical systems subject to realistic automotive operation situations was proposed [1
]. The model was developed for a lithium ion battery. It consists of complicated electrochemical phenomena, which were generally eliminated in online battery performance forecasters such as over potentials owing to mass transport restrictions and the full current-over potential relation and variable double layer capacitance. The model was able to simulate battery cell behaviour under dynamic procedures [1
Electrochemical characteristics of layered transition metal oxide cathode materials for lithium ion batteries were investigated by considering different parameters such as thermal properties, surface, and bulk behaviour [2
The electrochemical behaviour of vapour grown carbon nanofibers was optimized for lithium-ion batteries by hydrothermal and thermal treatments and impregnation [3
]. It was concluded that the surface of the untreated carbon nanofibers experiences an aging process during the earliest cycles [3
In recent years, research on lithium-ion batteries heat loss has become very popular. However, most of the previous studies did not quantify the reversible and irreversible heat sources in lithium-ion batteries. A simple transformation of coordinates was proposed which simplifies the efficient simulation of the non-isothermal lithium-ion pseudo 2D battery cell model [4
Model reformulation and efficient simulation of two-dimensional electrochemical thermal behaviour of lithium-ion batteries were investigated [5
]. The two dimensional battery model was presented and developed by using Chebyshev-based orthogonal collocation. It was concluded that great changes in internal variables could appear, even under approximately mild situations [5
A coupled continuum formulation for the mechanical processes—thermal, chemical, and electrostatic—in battery materials was proposed [6
]. The main improvement was to model the evolution of porosity because of strains, which was induced by mechanical stresses, thermal expansion, and intercalation [6
A mathematical model was developed to anticipate the time dependent behaviour of a cell [7
]. It was concluded that the reaction current was concentrated neighbouring the terminals at the start of the discharging process, continuously became more homogeneous over the electrode surface, and developed into a concentrated situation underneath the electrode neighbouring the ending of the discharge process [7
A 1D model appertaining to electrochemical and physical processes of a lithium ion cell was employed to explain hybrid pulse power characterization and constant current data from a battery cell [8
]. It was designed for hybrid electric vehicle utilization. It was concluded that depending on battery cell operating situation and design, the end of discharge pulse might be attributable to positive electrode solid phase Li saturation, electrolyte phase Li discharge, or negative electrode solid phase Li discharge [8
Electrodes modelling was accomplished for three different battery cell geometries to investigate the influence of the positioning of current collecting tabs and the aspect ratio of the electrodes on the discharge behaviours of the battery [9
]. In addition, with the intention of predicting the thermal behaviour of the lithium-polymer battery cell the heat generation rate as a function of the location on the electrodes and discharge time was determined. The modelling outcomes were compared with the experimental discharge curves at different discharge rates [9
]. It was concluded that that the parameters, which were adjusted for the electrodes of one geometry, could be used for the electrodes of other geometries. It should be noted that to accomplish this the manufacturing processes, compositions, and materials of the electrodes should be the same [9
Four distinct battery cell designs were investigated to appraise the effects of cell stack aspect ratio, size, and tab configuration for similar electrode-level designs [10
]. The model outcomes demonstrated that the internal battery cell kinetics is considerably affected by the macroscopic battery cell design for heat transport and electrical current [10
The current density and potential distribution on the electrodes of a lithium-polymer battery were investigated by employing the finite element procedure [11
]. The outcomes demonstrated that the placing and size of current collecting tabs and the aspect ratio of the electrodes have a considerable impact on the current density and potential distribution on the electrodes to affect the SOC distribution on the electrodes, hence influencing the homogeneous usage of the active material of electrodes [11
A procedure was designed for dependency modelling of the discharge behaviour of a lithium-ion battery cell on the environmental temperature [12
]. The two-dimensional modelling of the potential was validated by the modelling outcomes. The heat generation rates as a function of the position on the electrodes and the discharge time were determined in order to anticipate the temperature distributions of the lithium-ion battery [12
]. This was according to the modelling outcomes of current density and the potential distributions. The temperature distributions, which were achieved from experimental measurements, were in good agreement with the modelling [12
A battery cell model, which is flexible to investigate the thermal, electrochemical, physical phenomena, and advance over extensive length scales in battery cell systems of different assemblies, is necessary.
Unfortunately, thermal parameter measurement explanations and electrical parameters determination for lithium-ion batteries were not conveniently found in the literature. Many researchers commonly address the thermal parameters without reporting measurement procedures. A detailed description of thermal parameter measurement is reported in this investigation. Notwithstanding, to the author’s best knowledge, only very few publications [13
] are available in the literature that discuss the thermal simulation of lithium-ion batteries by considering all of the influential parameters such as thermal, electrical, and chemical processes on the thermal behaviour of the lithium-ion batteries. In addition, most of the previous studies did not take into account all of the electrochemical phenomena. In this investigation, the Multi-Scale Multi-Dimensional (MSMD) battery module was used for a lithium titanate oxide battery, which to the author´s best knowledge, it has not been done yet. The investigated model is able to determine the surface temperature distribution of the battery cell at various operating conditions with high accuracy.
7. Simulation Results and Discussion
In this investigation, several quantities for the volumetric heat generation were considered. The values were measured by an isothermal battery calorimeter for various load profiles. The model is simulated in both time dependent and steady state environment to determine the temperature spatial distribution over the battery surface. In addition, the modelling is able to show the maximum value of surface temperature of the battery as a function of time for different environment temperature and discharge current rates.
The temperature distributions of the battery cell were determined as a function of time at different discharge rates. As could be seen in Figure 12
and Figure 13
, the overall temperature distributions, which were achieved from the model and experiment, are in good agreement with each other.
The heat, which is dissipated from the battery, and the heat generated inside it are approximately equal during low current rates. Therefore, fast equilibrium could be reached. In another word, most of generated heat will be transferred to the surrounding through free or forced convection. The evolution of the uttermost temperature of the battery cell is confined at low current rates. The phenomenon demonstrates the minor rises in the surface temperature. Notwithstanding, the difference among the maximum temperatures, which were attained, from the modelling and experiment was lower than that between the corresponding minimum ones.
The simulation was accomplished at different discharge current rates ranging from 0.25 C to 9 C with 0.25 C interval. The modelling discharge profiles agree good with those, which were gained from experimental. The corresponding heat loss from the battery cell was shown in Figure 11
. In accordance with the findings, the temperature increase sharply to a specific point. As anticipated, the position of the hottest area is seen near the negative tab of the battery cell throughout the discharge process. In addition, non-uniform temperature propagation was observed.
Temperature distribution of the battery cell at different discharge rates ranging from 0.25 C to 9 C is illustrated in Figure 14
. As could be seen from the distributions of temperature over the volume of the battery cell, the temperature contours showed moderate slopes at low current rates. On the contrary, the temperature contours demonstrate sharper slopes at higher current rates. It demonstrates quicker temperature increase during the discharge of the battery cell, which is due to the higher heat generation inside the battery cell. At high current rates, achieving equilibrium occurs in a longer time. This phenomenon demonstrates that the modelling discharge curves agree well with those which were achieved from the experiments.
Although the current flows in the neighbourhood of the tabs of both the negative and positive electrodes are correspondingly great, the electrical conductivity of the active material of the negative electrode is much higher than that of the positive electrode. This phenomenon leads to lower temperatures in the neighbourhood of the current collecting tab of the positive electrode compared to the negative electrode [21
Electrochemical reaction rate was increased due to higher temperature gradient. This phenomenon could be described by higher current rates in some parts of the cell owing to high temperature gradient. The minimum and maximum temperatures, which, were collected from the modelling and experiment, are in good agreement with each other over the entire scope of battery cell surface at the different discharge rates. Notwithstanding, some difference was seen among the discharge curves, which were achieved from the experiment and model in close proximity to the end period of discharge. The highest discrepancy was seen for high discharge rates.