Research PaperInvestigation on lithium-ion battery electrochemical and thermal characteristic based on electrochemical-thermal coupled model
Introduction
The worldwide energy shortage and environmental pollution stimulated the development of electric vehicles (EVs) and hybrid electric vehicle (HEVs). The trend of vehicle electrification will be to continue with the innovation of battery technology in the future. As the power source, the lithium-ion battery has attracted more attentions with the increasing number of EVs and HEVs. The performance of lithium-ion battery has a significant influence on the driving range, reliability and safety issues of EVs and HEVs. It has been known that the overall performance of battery depends not only on the material and physical parameters, but also on the operating conditions including discharge rate and temperature. Understanding the influence of operating conditions on electrochemical and thermal performance of battery is limited by experimental methods. Conversely, the numerical model and simulation are economic and convenient for understanding the information during the electrochemical process and thermal characteristics, such as the electrochemical reaction rate and heat generation distribution throughout the electrode layers can be obtained numerically while the data can’t be measured by experiment method.
In recent years, numerical simulation technology played an important role in the research of lithium-ion battery based on electrochemical-thermal coupled model. Compared with experimental method, the electrochemical characteristics (voltage and current density distribution) as well as thermal characteristics (heat generation rate and temperature distribution) can be obtained. The most famous and practical model for lithium-ion battery is the porous electrode model [1], [2], which was established according to the porous-electrode theory [3]. Coupling the thermal energy equation with electrochemical model and the heat generation and temperature-dependent physicochemical properties, an electrochemical-thermal coupled model was presented [4]. Zhao et al. [5], [6] numerically researched the thermal behavior of LiMn2O4 battery based on electrochemical-thermal coupled model, and they focused on the significance of reversible heat and analyzed the effect active material particle size and thickness of electrode on the heat generation. Most of the other researchers also focused on the battery with LiMn2O4 cathode material for simulating the electrochemical and thermal behavior based on electrochemical-thermal coupled model [7], [8], [9], [10]. Xu et al. developed two-dimensional [11] and three-dimensional [12] electrochemical-thermal coupled model of LiFePO4 battery to analyze the electrochemical performance, heat generation and temperature distribution. Du et al. [13] investigated the irreversible heat generation in lithium-ion battery and their results showed that the negative electrode particle size had more significant impact on heat production. Ye et al. [14] developed an electro-thermal cycle life model by incorporating the dominant capacity fading mechanism to analyze the capacity fading effect on the battery performance. Although previous work observed that phase change occurred in the LiFePO4 cathode material during lithium-ion intercalated and de-intercalated process [15], [16], these results demonstrated that the electrochemical-thermal coupled model without considering phase change were appropriate to simulate LiFePO4 battery.
A battery can be treated as the assembly of one dimensional (1D) cell unit [17]. As the basic unit, the thermal behavior and electrochemical behavior of cell unit directly determine performance of battery. In turn, the influence of temperature and discharge rate on battery ultimately showed as the different electrochemical reaction process and distribution in cell unit. Temperature has a significant effect on battery performance. For instance, Waldmann et al. [18] demonstrated two different aging mechanisms for the ranges of −20 °C to 25 °C and 25 °C to 70 °C. The aging rates increased with decrease of temperature below 25 °C, while above 25 °C aging was accelerated with increase of temperature. The battery performance both degraded when battery operated at higher [19], [20] or lower temperature [21], [22]. Most of the researches on temperature-dependent performance of battery were based on experiments in the macroscopic view. However, the mechanism of temperature affecting the electrochemical reaction and thermal behavior of battery in the microscopic view was rarely reported in public literatures.
The spatial non-uniformity of current and state of charge (SOC) within a battery monomer, have become the key concern for both manufacturers and designers with the increase of battery size. The larger temperature gradient within battery results from the decrease of surface-to-volume ratio with the increase of battery size, and the higher heat generation rate is another key factor in causing larger temperature non-uniformity. For instance, Xu et al. [11] and Zhang et al. [23] demonstrated that there existed a certain temperature gradient within the battery, and Li et al. [24] showed that the distribution of electrochemical parameters was also location-related. But the interaction of temperature gradient and distribution of electrochemical parameters were not focused on in these researches. A battery is formed by a multitude of cells connected in series or/and in parallel to satisfy the desired power and capacity. The uneven temperature distribution will lead to mismatch of the internal resistance among cells, which induces unbalanced discharging and aging performance. This divergence of different cells will significantly shorten the total deliverable capacity and battery lifespan. It also should be noted that a larger temperature gradient also would be generated in the cross-plane direction during discharge process even though an external cooling system is installed, because the thermal management system (TMS) only cool the surface of the battery and the thermal conductivity in cross-plane direction is low duo to the layer to layer configuration. The temperature-dependent electrochemical performance is supposed to vary due to the temperature gradient, which makes the cells at different layer operating at different temperature. Meanwhile, the non-uniformity in laminated direction will increase with the increase of thickness of battery.
Although plenty of scholars have studied battery performance based on electrochemical-thermal coupled model, they almost focused on the overall electrochemical behavior or the heat generation at a certain temperature. Few of researches concerned about the heat generation distribution and electrochemical reaction process across the cell under different operating temperature and discharge rate, as well as the relationship between heat generation characteristic and electrochemical characteristic in the cell unit. In addition, most of electrochemical-thermal coupled model studies on lithium-ion battery behavior were based on LiMn2O4 chemistry. For battery with LiFePO4 electrode material, only a handful of kinetic model studies have been conducted, even though these battery have many performance superiority compared with the other battery. For a whole battery, the effect of temperature gradient in the battery on the electrochemical performance also should be investigated due to the sensibility of electrochemical reaction on temperature, and provide suggestions for the design of large scale battery to avoid undesirable loss of battery performance.
This study aims to shed some light on the electrochemical reaction process and heat generation characteristic in the cell, as well as the temperature distribution in the laminated direction in a battery monomer. In this study, a one dimensional electrochemical-thermal coupled model was established. The thermal behavior and the dynamic evolution of electrochemical reaction in the cell at different discharge rate and temperature were simulated and the mechanism of temperature affecting the battery performance were discussed. Furthermore, the relationship between heat generation distribution and electrochemical reaction process in a cell was also analyzed. The one cell model was extended to multi-cells and the temperature distribution in the laminated direction at different discharge rates was obtained. The influence of temperature gradient on the electrochemical performance inside a lithium-ion battery was studied.
Section snippets
Model assumption and calculation domain
A 1D electrochemical-thermal coupled model for a single cell in LiFePO4/graphite battery was established based on the energy, mass and charge conservation as well as electrochemical kinetics. The main model assumption were showed as follow [1], [2], [7]:
Active materials in positive and negative electrodes are considered as spherical shape of uniform sizes;
Gas possibly generated in the charge/discharge process is neglected, and only solid and liquid phase in the battery are considered;
All kinds
Model parameters
The parameters in the model included constant parameters and temperature/concentration dependent parameters, which were from literature and estimation. All the parameters used in this model were summarized in Table 1 [11], [24], [26], [27]. The temperature/concentration dependent parameters will be analyzed below.
Results and discussion
The discharge rate and operating temperature play an important role on battery electrochemical behavior and heat generation characteristic, and they determines the local current density in the electrode, lithium-ion concentration distribution in liquid and solid phase and the process of electrochemical reaction. The simulated heat distribution and the constitution of heat generation in cell unit combined with the electrochemical behavior were analyzed in detail.
Conclusions
In this paper, a one-dimension electrochemical thermal couple model was proposed to simulate several galvanostatic discharge process on one cell and multi-cell under different physical condition. The electrochemical characteristic and thermal characteristic were studied and some conclusions were obtained as below.
- (1)
Discharge rate not only affects the total heat generation rate, but also the proportion of different mechanism heat. At lower discharge rate, reversible dominants the heat generation,
Acknowledgement
This research was supported by National Natural Science Foundation of China (No. 51776015).
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