In recent years, lithium-ion batteries have become indispensable in various fields, including consumer electronics, electric vehicles, and energy storage systems, due to their high energy density, low self-discharge rate, and excellent cycle performance. However, the demand for faster charging and longer endurance has driven the development of power lithium-ion batteries, which face significant thermal safety challenges during high-rate charging and discharging processes. Excessive temperature can accelerate thermal runaway risks, making it crucial to optimize battery structural design to mitigate thermal effects. This study focuses on analyzing the impact of key structural parameters, such as tab position and aspect ratio, on the thermal behavior of lithium-ion batteries using a three-dimensional electrochemical-thermal coupling model. The goal is to provide insights for enhancing the thermal safety of power lithium-ion batteries through structural optimization.
The lithium-ion battery under investigation is an ultra-fast charging pouch cell with a nickel-cobalt-manganese oxide (NCM622) cathode and a soft/hard carbon composite anode. The nominal capacity is 800 mAh, with dimensions of 70 mm in length, 60 mm in width, and 3 mm in thickness. To manage computational complexity, a minimum cell unit is modeled, representing the stacked layers in a “Z-type” configuration. This approach has been validated in previous studies for accurately simulating thermal behavior in lithium-ion batteries.
The electrochemical model is based on the pseudo-two-dimensional (P2D) framework, which incorporates mass conservation, charge conservation, and electrode reaction kinetics. The governing equations are as follows:
The local exchange current density is given by:
$$ j_{ioc} = i_0 \left[ \exp\left(\frac{\alpha_a F}{RT} \eta\right) – \exp\left(\frac{\alpha_c F}{RT} \eta\right) \right] $$
where \( i_0 \) is the exchange current density, \( \alpha_a \) and \( \alpha_c \) are the transfer coefficients for anodic and cathodic reactions, \( F \) is Faraday’s constant, \( R \) is the gas constant, \( T \) is temperature, and \( \eta \) is the overpotential.
The charge conservation in the solid phase is:
$$ \frac{\partial}{\partial x} \left( -\sigma_1 \frac{\partial \phi_1}{\partial x} \right) = -i_1 $$
where \( \sigma_1 \) is the solid-phase conductivity, \( \phi_1 \) is the solid-phase potential, and \( i_1 \) is the solid-phase current.
In the liquid phase, the charge conservation equation is:
$$ \frac{\partial}{\partial x} \left[ \sigma_2 \left( -\frac{\partial \phi_2}{\partial x} + \frac{2RT}{F} \left(1 + \frac{\partial \ln f_{\pm}}{\partial \ln c_2}\right) (1 – t_+) \frac{\partial \ln c_2}{\partial x} \right) \right] = i_2 $$
where \( \sigma_2 \) is the liquid-phase conductivity, \( \phi_2 \) is the liquid-phase potential, \( f_{\pm} \) is the electrolyte activity coefficient, \( c_2 \) is the lithium-ion concentration in the electrolyte, and \( t_+ \) is the transference number.
The solid-phase diffusion is described by:
$$ \frac{\partial c_1}{\partial t} = \frac{D_1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial c_1}{\partial r} \right) $$
where \( c_1 \) is the lithium-ion concentration in the solid phase, \( D_1 \) is the solid-phase diffusion coefficient, and \( r \) is the particle radius.
The liquid-phase diffusion equation is:
$$ \varepsilon_2 \frac{\partial c_2}{\partial t} = \frac{\partial}{\partial x} \left( D_2 \frac{\partial c_2}{\partial x} \right) + \frac{(1 – t_+) S_a j_{ioc}}{F} $$
where \( \varepsilon_2 \) is the electrolyte volume fraction, \( D_2 \) is the liquid-phase diffusion coefficient, and \( S_a \) is the specific surface area.
The thermal model accounts for heat generation, conduction, convection, and radiation. The energy conservation equation is:
$$ \rho C_p \frac{\partial T}{\partial t} – \lambda \nabla^2 T = Q_{rea} + Q_{act} + Q_{ohm} $$
where \( \rho \) is density, \( C_p \) is specific heat capacity, \( \lambda \) is thermal conductivity, and \( Q_{rea} \), \( Q_{act} \), and \( Q_{ohm} \) are the reaction heat, activation heat, and ohmic heat, respectively.
The heat sources are defined as:
$$ Q_{rea} = S_a j_{ioc} T \frac{\partial U}{\partial T} $$
$$ Q_{act} = S_a j_{ioc} (\phi_1 – \phi_2 – U_{ref}) $$
$$ Q_{ohm} = -i_1 \nabla \phi_1 – i_2 \nabla \phi_2 – i_2 R_{Al,Cu} $$
where \( \frac{\partial U}{\partial T} \) is the entropy coefficient, \( U_{ref} \) is the open-circuit voltage, and \( R_{Al,Cu} \) is the internal resistance of the current collectors.
The convective heat transfer at the battery surface is given by:
$$ -\lambda \left( \frac{\partial}{\partial x} + \frac{\partial}{\partial y} + \frac{\partial}{\partial z} \right) T = h (T_{amb} – T) $$
where \( h \) is the convective heat transfer coefficient and \( T_{amb} \) is the ambient temperature.
The electrochemical-thermal coupling is achieved by modifying temperature-dependent parameters using the Arrhenius equation:
$$ \phi = \phi_{ref} \exp\left[ \frac{E_{\phi}}{R} \left( \frac{1}{T_{ref}} – \frac{1}{T} \right) \right] $$
where \( \phi_{ref} \) is the reference value at temperature \( T_{ref} \), and \( E_{\phi} \) is the activation energy. The coupling framework ensures that the electrochemical model computes heat generation, which is then used in the thermal model to solve for temperature distribution, creating a feedback loop that accurately represents the behavior of lithium-ion batteries.
To validate the model, experimental tests were conducted on the lithium-ion battery at various discharge rates (4 C, 6 C, 8 C, and 10 C) under an ambient temperature of 298.15 K. The battery surface temperature was measured using thermocouples, and the average temperature was compared with simulation results. The voltage and temperature curves showed good agreement, with errors within 3%, confirming the model’s accuracy for thermal analysis of lithium-ion batteries.
The aspect ratio, defined as the width-to-length ratio (W/L), is a critical parameter in battery design. To analyze its impact on thermal characteristics, two tab configurations were considered: counter tab (CT), where tabs are on opposite sides, and nominal tab (NT), where tabs are on the same side. The aspect ratio was varied while maintaining a constant capacity for the lithium-ion battery. The thermal effects were evaluated based on maximum temperature and temperature difference at the end of discharge.
Table 1 summarizes the temperature and temperature difference for different aspect ratios under CT and NT configurations at a 10 C discharge rate.
| Aspect Ratio | CT Max Temp (K) | CT Temp Diff (K) | NT Max Temp (K) | NT Temp Diff (K) |
|---|---|---|---|---|
| 4.66 | 313.6 | 2.2 | 313.5 | 2.16 |
| 2.62 | 313.3 | 1.9 | 313.4 | 2.06 |
| 1.16 | 313.25 | 1.8 | 313.7 | 2.3 |
| 0.86 | 313.4 | 1.85 | 314.0 | 2.5 |
| 0.38 | 313.8 | 1.9 | 315.2 | 3.1 |
| 0.21 | 314.1 | 2.1 | 316.5 | 3.8 |
The results indicate that for CT configuration, the lithium-ion battery exhibits lower thermal effects when the aspect ratio is between 0.38 and 2.62, with the minimum at 1.16. For NT configuration, better thermal performance is observed at aspect ratios above 2.62. This is attributed to the uniformity of electrode material utilization, which can be quantified using the uneven utilization index \( \beta \):
$$ \beta = \frac{SOC_{max} – SOC_{min}}{SOC_{avg}} $$
where \( SOC_{max} \), \( SOC_{min} \), and \( SOC_{avg} \) are the maximum, minimum, and average state of charge in the battery plane, respectively. A lower \( \beta \) value indicates more uniform heat generation in the lithium-ion battery.
Table 2 shows the uneven utilization index \( \beta \) for different aspect ratios.
| Aspect Ratio | CT \( \beta \) (%) | NT \( \beta \) (%) |
|---|---|---|
| 4.66 | 0.86 | 0.70 |
| 2.62 | 0.75 | 0.63 |
| 1.16 | 0.72 | 0.85 |
| 0.86 | 0.74 | 1.10 |
| 0.38 | 0.73 | 1.95 |
| 0.21 | 0.80 | 2.67 |
The potential gradient in the current collectors also influences thermal behavior. A higher potential gradient increases ohmic resistance and heat generation. For CT configuration, the potential gradient is lower at aspect ratios around 1.16, contributing to reduced thermal effects in the lithium-ion battery.
The tab position is another key factor affecting thermal characteristics. Four tab placement schemes were designed for both CT and NT configurations, as shown in Table 3.
| Scheme | Positive Tab Position | Negative Tab Position |
|---|---|---|
| CT-1 | Center | Center |
| CT-2 | Left Edge | Center |
| CT-3 | Center | Right Edge |
| CT-4 | Left Edge | Right Edge |
| NT-1 | Center | Center |
| NT-2 | Left Edge | Center |
| NT-3 | Center | Right Edge |
| NT-4 | Left Edge | Right Edge |
The thermal performance was evaluated using the optimal temperature index (OPTD), which normalizes maximum temperature and temperature difference:
$$ OPTD(i) = T_{max-N}(i) + \Delta T_{max-N}(i) $$
$$ T_{max-N}(i) = \frac{T_{max}(i)}{\max(T_{max})} $$
$$ \Delta T_{max-N}(i) = \frac{\Delta T_{max}(i)}{\max(\Delta T_{max})} $$
where \( T_{max}(i) \) and \( \Delta T_{max}(i) \) are the maximum temperature and temperature difference for scheme \( i \), respectively. A lower OPTD value indicates better thermal design for the lithium-ion battery.
Table 4 presents the OPTD values for different tab placement schemes across various aspect ratios.
| Scheme | Aspect Ratio 4.66 | Aspect Ratio 2.62 | Aspect Ratio 1.16 | Aspect Ratio 0.86 | Aspect Ratio 0.38 | Aspect Ratio 0.21 |
|---|---|---|---|---|---|---|
| CT-1 | 1.381 | 1.309 | 1.271 | 1.273 | 1.308 | 1.406 |
| CT-2 | 1.411 | 1.347 | 1.307 | 1.298 | 1.320 | 1.409 |
| CT-3 | 1.721 | 1.594 | 1.496 | 1.472 | 1.479 | 1.542 |
| CT-4 | 1.523 | 1.467 | 1.466 | 1.465 | 1.470 | 1.533 |
| NT-1 | 1.332 | 1.312 | 1.367 | 1.407 | 1.638 | 1.925 |
| NT-2 | 1.288 | 1.279 | 1.352 | 1.408 | 1.648 | 1.938 |
| NT-3 | 1.633 | 1.533 | 1.518 | 1.547 | 1.732 | 1.986 |
| NT-4 | 1.523 | 1.471 | 1.502 | 1.542 | 1.743 | 2.000 |
The results show that for CT configuration, scheme CT-1 (tabs at center) consistently yields the lowest OPTD values, especially at an aspect ratio of 1.16. For NT configuration, schemes with tabs symmetrically placed about the cell domain center improve temperature uniformity in the lithium-ion battery at higher aspect ratios.
Based on the optimal structure (CT-1 with aspect ratio 1.16), further size optimization was conducted for tab width and current collector thickness. The total tab width and current collector thickness were kept constant to maintain energy density. Table 5 and Table 6 summarize the optimization schemes.
| Group | Positive Tab Width (mm) | Negative Tab Width (mm) |
|---|---|---|
| A | 11 | 9 |
| B | 10 | 10 |
| C | 9 | 11 |
| D | 8 | 12 |
| E | 7 | 13 |
| Group | Positive Current Collector Thickness (μm) | Negative Current Collector Thickness (μm) |
|---|---|---|
| A | 11 | 3.5 |
| B | 10 | 4.5 |
| C | 9 | 5.5 |
| D | 8 | 6.5 |
| E | 7 | 7.5 |
The thermal performance was evaluated after optimization. For tab width, Group C (positive tab width 9 mm, negative tab width 11 mm) showed the lowest maximum temperature and temperature difference: 312.82 K and 1.3 K, respectively, representing reductions of 1.12% and 48% compared to the initial design. For current collector thickness, Group C (positive thickness 9 μm, negative thickness 5.5 μm) also achieved the best results: 313.79 K and 1.51 K, with reductions of 9.4% and 34.3%. This optimization enhances the thermal safety and stability of the lithium-ion battery without compromising energy density.
In conclusion, this study demonstrates the significant impact of structural parameters on the thermal behavior of power lithium-ion batteries. The aspect ratio and tab position are critical factors influencing temperature distribution and heat generation. For lithium-ion batteries with aspect ratios above 2.62, the NT configuration (tabs on the same side) is preferable due to better uniformity in electrode material utilization. For aspect ratios below 0.86, the CT configuration (tabs on opposite sides) offers superior thermal performance. Symmetric tab placement about the cell domain center improves temperature uniformity across all aspect ratios. Size optimization further reduces thermal effects, with optimal tab widths and current collector thicknesses identified. These findings provide valuable guidelines for designing safer and more efficient power lithium-ion batteries, contributing to the advancement of energy storage technology. Future work could explore dynamic operating conditions and multi-objective optimization to enhance the thermal management of lithium-ion batteries in practical applications.