The transition to electric mobility is inseparable from the development of reliable high-energy lithium-ion batteries. I have focused this work on understanding the thermal and aging behavior of a high-power soft-pack lithium-ion cell that can serve as one building unit of an EV battery pack. The cell is based on a lithium-cobalt-oxide positive electrode and a graphite negative electrode. I selected this type of cell because it is capable of delivering high discharge currents; this is also exactly the load pattern that appears in an EV battery pack during fast acceleration, hill climbing, or high-load operation. However, high-rate operation brings a serious challenge: increased heat generation, accelerated capacity fade, and eventually, non-uniform aging inside the pack. Therefore, I carried out a combined experimental and numerical study with the intention of linking internal electrochemical heat sources to the cell lifetime.
Lithium-ion batteries have many advantages, including high energy density, low self-discharge, and long cycle life. These advantages make them the most important energy storage technology for an EV battery pack. Many researchers have investigated the thermal behavior of cylindrical and prismatic automotive cells, but fewer studies have examined high-rate pouch cells, especially those used in aerial platforms. Since a small electric aircraft battery is discharged at current rates larger than those commonly seen in a passenger EV battery pack, I decided to use a representative small aerial-vehicle battery as the study object. The physical cell is a 2.25 Ah soft-package cell with nominal voltage 3.85 V and charge cutoff 4.4 V. Although the particular packaging is designed for an unmanned aerial vehicle, the electrochemical system is the same as a prismatic EV battery pack. Therefore, the conclusions are useful for pack-level thermal design.
In my research, I combined basic experiments, an electrochemically resolved cell model, a three-dimensional thermal model, and a side-reaction aging model. The experimental part included rate-capability tests, temperature-rise measurements, direct-current internal resistance measurement, entropy-coefficient measurement, and accelerated cycling aging. I then built an electrochemical-thermal coupling model in a finite-element environment and validated the model with measured voltage and surface temperature curves. After validation, I used the model to quantify reversible heat, irreversible heat, ohmic heat, polarization heat, electrode component contributions, and internal temperature gradients. Finally, I introduced a solid-electrolyte-interphase growth model into the coupled model so that I could calculate capacity fade, film resistance, film thickness, and heat generation changes during aging.
The central aim of this work is to answer three questions: how does an EV battery pack cell generate heat under different discharge rates and ambient temperatures, which design parameters control the heat-generation share, and how does negative-electrode film growth alter both capacity and thermal output? I believe that the answers will help engineers select better electrode dimensions, cooling conditions, and operating ranges for an EV battery pack.
2 Experimental Investigation of the EV Battery Pack Cell
I built a dedicated test platform for the pouch cell. The test bench consisted of a programmable charge-discharge tester, a temperature and humidity chamber, K-type thermocouples, a multi-channel thermometer, and a host computer for data acquisition. The cell specifications are summarized below. The cell was discharged with constant current to a lower cutoff voltage of 3.0 V. The charge procedure was constant-current constant-voltage charging up to 4.4 V, followed by a constant-voltage stage until the current decreased to 0.05 C.
| Specification | Value |
|---|---|
| Nominal capacity | 2.25 Ah at 0.5 C |
| Nominal voltage | 3.85 V |
| Upper cutoff voltage | 4.4 V |
| Lower cutoff voltage | 3.0 V |
| Maximum continuous discharge | 10 C |
| Positive electrode | LiCoO2 |
| Negative electrode | Graphite |
| Electrolyte | LiPF6 in carbonate solvent |
| Cell thickness | 7.8 mm |
| Cell width | 34 mm |
| Cell length | 61 mm |
| Weight | 33.7 g |
| Initial DC resistance | 4.8 mΩ |
Before every discharge test, I measured the actual capacity so that I could express the C-rate on a measured basis. The capacity-calibration step consisted of a 1 C discharge, a 1 C constant-current-constant-voltage charge, another 1 C discharge, and an average of three repetitions. After capacity calibration, I set the required ambient temperature, and then I applied the same full charge before each discharge experiment. I measured the cell surface temperature with a K-type thermocouple located at the center of the largest face. This schedule produced a reliable set of discharge voltage curves and temperature curves for later model validation.
2.1 Effect of Discharge C-Rate
At an ambient temperature of 25 °C, I discharged the cell at 1 C, 2 C, 3 C, and 4 C. The capacity values and terminal voltage curves clearly showed that an elevated discharge current reduced the initial terminal voltage and decreased the extractable capacity. The reason is that high current intensifies internal polarization, ohmic drops, and lithium-ion concentration gradients. Therefore, the cell reaches the cutoff voltage earlier. The measured surface temperature also increased with the current. During the discharge process, the sensitivity of temperature rise to current was large. With 1 C discharge, the peak surface temperature was about 29.2 °C; at 4 C it reached about 42.3 °C. The total excess temperature above ambient increased by more than 13 °C when the C-rate changed from 1 C to 4 C. I also observed that low-rate discharge curves often displayed a small dip or plateau in the middle region, caused by the reversible entropic heat characteristic of the cobalt-oxide electrode.
2.2 Effect of Ambient Temperature
I then performed 1 C discharges at ambient temperatures of -10 °C, 0 °C, 10 °C, 25 °C, and 40 °C. The discharge voltage curves shifted downward when the temperature was reduced. The initial voltage decreased, which means that a cold EV battery pack power module experiences a lower open-circuit plateau and more ohmic loss. At 40 °C, the discharge capacity was approximately 2280 mAh. At 25 °C the measured capacity was close to 2250 mAh, while at -10 °C it dropped to around 2179 mAh. This capacity loss is attributed to slower lithium diffusion, higher electrolyte viscosity, and lower electrolyte conductivity at low temperatures. These effects directly reduce the available capacity of an EV battery pack in cold weather.
I measured the surface temperature rise relative to the ambient temperature. At -10 °C, the peak absolute temperature rise reached about 7.5 °C, while at 40 °C, the peak absolute temperature rise was only about 3.4 °C. This agrees with the understanding that low temperature increases internal impedance and polarization, causing more Joule heat for the same current. The implication is that an EV battery pack operating in cold climates must implement preheating, not only to protect capacity, but also to reduce the internal heat concentration during high-power discharge.
| Condition | Discharge capacity relative to 25 °C 1 C value | Surface-temperature trend |
|---|---|---|
| 1 C, 25 °C | 100% | Slow increase; peak near 29.2 °C |
| 4 C, 25 °C | Approximately 96-98% | Fast increase; peak near 42.3 °C |
| 1 C, -10 °C | Approximately 96.8% | Increase; absolute rise 7.5 °C |
| 1 C, 40 °C | Approximately 101.3% | Weak rise; absolute rise 3.4 °C |
2.3 Direct-Current Internal Resistance
I measured the direct-current internal resistance with a hybrid pulse power characterization method. I applied a 10 s discharge pulse at different states of charge and at ambient temperatures of -10 °C, 0 °C, 10 °C, 25 °C, and 40 °C. The direct-current resistance is defined as the ratio of the voltage change to the pulse current:
$$R_{\mathrm{DC}} = \frac{U_A – U_C}{I}$$
where \(U_A\) is the voltage at the end of the preceding relaxation period, \(U_C\) is the voltage at the end of the 10 s discharge pulse, and \(I\) is the pulse current. I found that the cell resistance increased strongly when the ambient temperature was lower. In the middle state-of-charge range from 20% to 80%, the direct-current resistance was nearly independent of state of charge at temperatures above 10 °C. This behavior is useful for an EV battery pack because it permits a simple resistance-based state-of-health estimator at normal ambient temperatures.
2.4 Entropy Heat Coefficient
To separate reversible heat from irreversible heat, I measured the open-circuit voltage as a function of temperature at different depths of discharge. The cell was equilibrated at several temperature points, and I recorded the voltage response. The slope of the open-circuit voltage with respect to temperature is called the entropy coefficient, \(\partial U/\partial T\). For the full cell, I observed values between -1.1 mV/K and +0.29 mV/K. The entropy coefficient was negative in the 0-35% DOD window, became positive from about 35% to 50% DOD, and then became negative again and decreased rapidly after 50% DOD. This non-monotonic behavior strongly influences the discharge temperature curve. A negative entropy coefficient produces reversible exothermic heat during discharge; a positive value corresponds to a reversible endothermic process. This is why the measured temperature-rise curves sometimes show a characteristic N-shaped variation. It is important for an EV battery pack model because the reversible heat is often neglected in simplified thermal models.
2.5 Accelerated Cycling Aging
Since the practical endurance of the studied aerial power battery is short, the cells are cycled more often than typical automotive cells. I therefore carried out accelerated cycling aging using a 1 C constant-current-constant-voltage charge followed by a 3 C discharge at 25 °C. After every 50 cycles, I performed a 1 C capacity check and a performance check. After 450 cycles, the measured 1 C discharge capacity decreased to 92.6% of the initial value. The discharge curves shifted downward with increasing cycle number, meaning that aging increases cell overpotential. This capacity-fade data set was important for validating the aging model of the EV battery pack cell.
3 Electrochemical-Thermal Coupling Model
The porous-electrode model used in this thesis follows the classic pseudo-two-dimensional approach. I model the positive electrode, separator, and negative electrode along the thickness direction, while lithium transport inside each spherical active-material particle is described in the radial direction. The cell is divided into 20 electrode layers in the real structure, but for simulation I used an equivalent single-layer representation so that the three-dimensional thermal model remains computationally manageable. The electrochemical model provides local heat-generation rates, while the thermal model returns the local temperature to update the electrochemical parameters. This is the fundamental coupling in my EV battery pack cell model.
3.1 Governing Equations
The solid-phase lithium concentration inside an active material sphere follows Fick’s second law:
$$\frac{\partial c_s}{\partial t} = \frac{D_s}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial c_s}{\partial r}\right)$$
The boundary condition at the particle center is a zero concentration gradient:
$$\left.\frac{\partial c_s}{\partial r}\right|_{r=0}=0$$
At the particle surface, the flux is related to the local pore-wall current density \(j_{\mathrm{Li}}\):
$$-D_s\left.\frac{\partial c_s}{\partial r}\right|_{r=R_s}=j_{\mathrm{Li}}$$
The charge-transfer reaction is described by the Butler-Volmer equation:
$$j_{\mathrm{Li}}=a_s i_0\left[\exp\left(\frac{\alpha_a F}{RT}\eta\right)-\exp\left(-\frac{\alpha_c F}{RT}\eta\right)\right]$$
where \(a_s\) is the specific surface area, \(i_0\) is the exchange current density, and \(\eta\) is the local overpotential. I assumed that the apparent transfer coefficients are both 0.5. The exchange current density is:
$$i_0=F k_{\mathrm{eff}}\sqrt{c_e\left(c_{s,\max}-c_{s,\mathrm{surf}}\right)c_{s,\mathrm{surf}}}$$
The overpotential at the negative electrode includes the solid-electrolyte-interphase film resistance:
$$\eta=\phi_s-\phi_e-U_{\mathrm{eq}}-j_{\mathrm{Li}}R_{\mathrm{film}}$$
The electrolyte concentration field in the liquid phase is governed by the concentrated-solution equation:
$$\varepsilon_e\frac{\partial c_e}{\partial t}=\frac{\partial}{\partial x}\left(D_e^{\mathrm{eff}}\frac{\partial c_e}{\partial x}\right)+\frac{1-t_+^0}{F}j_{\mathrm{Li}}$$
where \(\varepsilon_e\) is the electrolyte volume fraction, \(t_+^0\) is the lithium-ion transference number, and \(D_e^{\mathrm{eff}}\) is the effective electrolyte diffusion coefficient corrected by the Bruggeman tortuosity exponent.
3.2 Temperature-Dependent Parameters
The solid diffusion coefficients, reaction rate constants, electrolyte conductivity, and electrolyte diffusion coefficients depend strongly on temperature. I implemented Arrhenius-type equations for the solid diffusion coefficient:
$$D_s(T)=D_{s,\mathrm{ref}}\exp\left[\frac{E_{a,D}}{R}\left(\frac{1}{T_{\mathrm{ref}}}-\frac{1}{T}\right)\right]$$
Similar temperature corrections were applied to the reaction rate constants and electrolyte properties. The use of dynamic parameters is essential if the model is to predict the discharge performance of an EV battery pack at -10 °C and 40 °C. The main electrode and electrolyte parameters are listed in the following table.
| Parameter | Negative electrode | Separator | Positive electrode |
|---|---|---|---|
| Thickness / μm | 34.5 | 8 | 26 |
| Particle radius / μm | 5 | – | 1 |
| Solid volume fraction | 0.58 | – | 0.48 |
| Electrolyte volume fraction | 0.332 | 0.45 | 0.30 |
| Maximum solid concentration / mol m-3 | 31507 | – | 56250 |
| Initial solid concentration / mol m-3 | 25330 | – | 19020 |
| Solid conductivity / S m-1 | 100 | – | 10 |
| Bruggeman exponent | 4.1 | 2.3 | 1.5 |
3.3 Thermal Model
The thermal model is a three-dimensional transient heat-conduction equation for the pouch cell. I assumed that the cell is an anisotropic homogeneous composite because it is composed of many stacked layers. The energy equation is:
$$\rho C_p\frac{\partial T}{\partial t}=\nabla\cdot\left(k\nabla T\right)+\dot{q}_{\mathrm{tot}}$$
The total heat-generation rate contains reversible reaction heat, polarization heat, ohmic heat, tab heat, and SEI-film heat:
$$\dot{q}_{\mathrm{tot}}=\dot{q}_{\mathrm{rev}}+\dot{q}_{\mathrm{pol}}+\dot{q}_{\mathrm{ohm}}+\dot{q}_{\mathrm{tab}}+\dot{q}_{\mathrm{SEI}}$$
The reversible or entropic heat production is calculated from the local current density and the temperature derivative of the equilibrium potential:
$$\dot{q}_{\mathrm{rev}}=a_s i_{\mathrm{loc}}T\frac{\partial U_{\mathrm{eq}}}{\partial T}$$
The polarization heat is produced by the surface overpotential:
$$\dot{q}_{\mathrm{pol}}=a_s i_{\mathrm{loc}}\eta$$
The ohmic heat includes ionic conduction in the electrolyte and electronic conduction in the solid matrix. In a simplified form, I express it as:
$$\dot{q}_{\mathrm{ohm}}=\sigma_s^{\mathrm{eff}}\nabla\phi_s\cdot\nabla\phi_s+\sigma_e^{\mathrm{eff}}\nabla\phi_e\cdot\nabla\phi_e$$
In addition to the cell body, the tabs produce heat because of tab resistance and contact resistance. The tab heat is:
$$\dot{q}_{\mathrm{tab}}=\frac{I^2}{A_{\mathrm{tab}}^2}\left(\frac{1}{\sigma_{\mathrm{tab}}}+\frac{1}{\sigma_c}\right)$$
Because the pouch cell has a large in-plane thermal conductivity and a small through-plane conductivity, I calculated the equivalent anisotropic thermal conductivity from the series and parallel resistances of the layers:
$$k_x=k_y=\frac{\sum_i L_i k_i}{\sum_i L_i},\qquad k_z=\frac{\sum_i L_i}{\sum_i \left(L_i/k_i\right)}$$
Natural convection and radiation were applied on the external surfaces:
$$-k\left.\frac{\partial T}{\partial n}\right|_{\mathrm{surface}}=h\left(T_{\mathrm{amb}}-T_s\right)+\varepsilon\sigma_{\mathrm{SB}}\left(T_{\mathrm{amb}}^4-T_s^4\right)$$
I set the ambient convection coefficient to 25 W m-2 K-1 for the natural-convection validation case. For the forced-convection sensitivity analysis, I increased this coefficient from 50 to 200 W m-2 K-1. The values are relevant to air-cooled EV battery pack designs.
3.4 Model Validation
I solved the coupled model in finite-element software and compared the simulated voltage curves and temperature curves with the experimental measurements. The validation was performed at ambient temperature 25 °C for charge rates of 0.5 C and for discharge rates of 1 C, 2 C, 3 C, and 4 C. The simulated voltage curves agreed well with the experimental data. The maximum voltage error was 5.56%, located in the middle-stage of the 4 C discharge. The surface temperature simulation also matched the measured data; the maximum temperature error was 4.25% at the late stage of the 4 C discharge. These errors are acceptable for a coupled electrochemical thermal model. The remaining error is caused by model-parameter uncertainty, heat losses from the test fixture, and thermocouple attachment.
| Quantity | Maximum relative error | Condition |
|---|---|---|
| Voltage | 5.56% | 4 C discharge middle part |
| Surface temperature rise | 4.25% | 4 C discharge middle-late part |
| Capacity fade after 200 cycles | 1.10% | Accelerated cyclic aging |
| Capacity fade from 200 to 450 cycles | 0.68% | Accelerated cyclic aging |
After validation, I used the model to perform a series of virtual experiments for a representative EV battery pack cell. In these numerical experiments, I could separate the positive electrode, negative electrode, separator, and tab heat sources, which is not possible from external measurements. This is the greatest advantage of the electrochemical-thermal coupling model.
4 Thermal Characteristics Discussed from the Model
4.1 Heat Generation under Different Discharge Rates
I simulated 1 C, 2 C, and 4 C discharges at 25 °C. The total volumetric heat-generation rate increased with the discharge current. At 1 C, the reversible reaction heat contributed approximately 58% of the total heat. At 4 C, the reversible share decreased to roughly 31%, while the polarization heat and ohmic heat increased to about 63% and 6%, respectively. In other words, the irreversible heat dominates an EV battery pack operating at high C-rates. This result can be explained by the growth of concentration overpotential and charge-transfer overpotential at high current. If the cooling system is designed only from reversible-heat assumptions, it will fail under hard acceleration because the irreversible heat has become the largest heat source.
The local heat source was not uniform along the cell thickness. The negative electrode produced more irreversible heat than the positive electrode, while the positive electrode produced much more reversible heat. The separator produced only a small amount of ohmic heat because it has no active material but a relatively high ionic resistance. In terms of total heat contribution, the positive electrode was the largest heat source at moderate rates. When the discharge rate was increased from 1 C to 4 C, the percentage of heat generated in the positive electrode decreased, while the negative electrode and separator percentages increased. These results suggest that reducing positive-electrode kinetic resistance and positive-electrode entropy variations can be an effective way to improve the thermal behavior of an EV battery pack.
4.2 Effect of Ambient Temperature on Heat Generation
I simulated 2 C discharges at ambient temperatures of 5 °C, 25 °C, and 45 °C. The discharge-temperature rise increased when the ambient temperature decreased. At 5 °C, the irreversible heat occupied more than 60% of the total heat. At 45 °C, the reversible heat share increased to about 56%. A cold EV battery pack therefore not only loses electrical performance, but also produces more heat per unit of delivered energy. The higher temperature, on the other hand, enhances electrolyte conductivity, solid diffusion, and reaction kinetics, reducing the irreversible resistance. Thus, temperature control is a compromise for an EV battery pack: elevated temperature improves kinetics but accelerates aging; low temperature increases heat production and polarization.
4.3 Effects of Electrode Thickness and Particle Size
I varied the electrode design parameters to study how the internal heat sources change. When the positive electrode thickness was increased from 26 μm to 56 μm, while keeping the capacity ratio balanced, the discharge voltage decreased and the average cell temperature increased. A thicker electrode increases lithium diffusion distances and current-path lengths, so the cell impedance rises. The share of ohmic heat in the total heat increased with electrode thickness, while the reversible heat share decreased. This outcome shows that high-energy electrodes, obtained by thick coatings, may create a more serious thermal burden for an EV battery pack.
I also changed the active-material particle radius. Larger particles reduce the specific surface area and increase solid-diffusion resistance, which consequently raises the irreversible heat. The total heat-generation rate, the irreversible heat, and the reaction heat all increased when the particle size was larger, but the reversible heat was less affected by particle size. During the first 25% depth of discharge, the reversible heat was almost independent of particle radius. This is because reversible heat is related to entropy change rather than to transport resistance. Therefore, if an EV battery pack cell is designed with large particles to improve energy density, its discharge thermal behavior will be more irreversible and more sensitive to current.
4.4 Temperature Uniformity Inside the Cell
In a real EV battery pack, forced air convection is often applied on the cold plates or on the module surfaces. I therefore investigated the surface-to-core temperature difference under forced convection coefficients from 50 to 200 W m-2 K-1. The discharge rates were 1 C, 4 C, 7 C, and 10 C. At 25 °C ambient temperature and a convection coefficient of 50 W m-2 K-1, the core temperature at the end of a 10 C discharge reached about 54.9 °C. This is above the recommended working range of the cell. When the convection coefficient was increased to 200 W m-2 K-1, the surface temperature was reduced, but the temperature difference between the core and the surface became larger. At 10 C and \(h=50\) W m-2 K-1, the maximum core-to-surface temperature difference was about 3.5 °C; at \(h=200\) W m-2 K-1, this difference increased to about 4.8 °C.
These results are important for EV battery pack cooling. Increasing the external heat-transfer coefficient cools the surface but does not remove heat fast enough from the center. The internal temperature gradient may lead to non-uniform reaction rates and non-uniform SEI growth. If each cell in an EV battery pack is cooled too aggressively at the surface, the center of the cell may still age faster than the edge. This phenomenon emphasizes the role of internal thermal conductivity.
I evaluated two possible remedies. The first is reducing the cell thickness. I changed the total cell thickness by scaling the width at a constant volume. The temperature rise increased with cell thickness because the heat-conduction path became longer. For an 8.6 mm cell, 8 C discharge produced a smaller core-to-surface difference than for an 11.6 mm cell. In the 8 C discharge simulation with a convection coefficient of 100 W m-2 K-1, each 1 mm increase in thickness increased the peak temperature by roughly 1 °C and the maximum core-to-surface difference by about 0.6 °C. EV battery pack cells with fewer thick layers therefore offer better thermal uniformity.
The second remedy is increasing the through-plane thermal conductivity. I increased the equivalent thickness-direction thermal conductivity from 1.11 W m-1 K-1 to 3 W m-1 K-1. At 10 C discharge and a convection coefficient of 200 W m-2 K-1, the maximum core-to-surface temperature difference dropped from about 4.8 °C to about 2.6 °C. Such an improvement can be achieved by using thinner current collectors, carbon coatings, or thermally conductive separators. Therefore, pack-level thermal design must not focus only on the cooling fluid; the internal anisotropic conduction path is also a crucial design variable.
5 SEI Growth Aging Model
Battery aging is an unavoidable phenomenon in every EV battery pack. In my accelerated aging test, the cell lost 7.4% of initial capacity after 450 cycles. The dominant capacity-loss mechanism at 25 °C is generally the growth of the solid-electrolyte interphase on the graphite surface. During storage and cycling, solvent molecules diffuse through the SEI layer and react with lithium ions and electrons, forming a thicker film. This parasitic reaction consumes lithium inventory, increases the film resistance, and thereby increases polarization and heat generation.
I built the aging model on the foundation of the validated electrochemical-thermal model. The simplified parasitic reaction is written as
$$S+\mathrm{Li}^{+}+e^{-}\rightarrow P_{\mathrm{SEI}}$$
where \(S\) is the solvent and \(P_{\mathrm{SEI}}\) denotes the solid-electrolyte interphase products. I added a side-reaction current density \(j_{\mathrm{SEI}}\) at the graphitic negative electrode. The magnitude of this current depends on the solvent concentration, diffusion coefficient, kinetic constant, film thickness, and overpotential:
$$j_{\mathrm{SEI}}=-\frac{c_{\mathrm{EC}}F}{\frac{1}{k_{\mathrm{SEI}}}+\frac{\delta_{\mathrm{film}}}{D_{\mathrm{EC}}}}\exp\left(\frac{\alpha_{\mathrm{SEI}}F}{RT}\eta_{\mathrm{SEI}}\right)$$
The overpotential of the SEI reaction is defined as the difference between solid and electrolyte potential, the reversible potential of SEI, and the ohmic drop across the existing film. I also included the breakage of SEI when graphite particles expand. The coefficient \(K\) is set to zero when the local negative-particle state of charge is less than 0.3, zero between 0.3 and 0.7, and one between 0.7 and 1.0. This simple formulation lets the model artificially accelerate SEI formation at high negative-electrode state of charge. The side-reaction current also alters the total current balance on the negative particle:
$$j_{\mathrm{neg,total}}=j_{\mathrm{intercalation}}+j_{\mathrm{SEI}}$$
The growth rate of the SEI film is proportional to the parasitic current density:
$$\frac{\partial \delta_{\mathrm{film}}}{\partial t}=-\frac{j_{\mathrm{SEI}}M_{\mathrm{SEI}}}{\rho_{\mathrm{SEI}}F}$$
The film resistance terms in the electrochemical model are then updated as follows:
$$R_{\mathrm{film}}=\frac{\delta_{\mathrm{film},0}+\delta_{\mathrm{film}}}{\kappa_{\mathrm{SEI}}}$$
Finally, the heat produced by the SEI film is computed from the local current and the film resistance:
$$\dot{q}_{\mathrm{SEI}}=\frac{j_{\mathrm{neg,total}}^2R_{\mathrm{film}}}{a_{s,\mathrm{neg}}}$$
I inserted this additional heat-source term into the global energy balance. In this way, as the SEI film grows, the model simultaneously accounts for capacity loss, impedance rise, and extra heat generation. Many EV battery pack models ignore this term, but during aging, the film-resistance contribution can become significant.
| Parameter | Value |
|---|---|
| EC concentration / mol m-3 | 4541 |
| Charge-transfer coefficient for SEI | 0.5 |
| SEI molar mass / kg mol-1 | 0.16 |
| SEI density / kg m-3 | 1690 |
| SEI ionic conductivity / S m-1 | 5.0e-6 |
| Initial SEI thickness / nm | 1 |
| SEI equilibrium potential / V | 0.4 |
5.1 Aging Model Validation
I validated the coupled aging model by simulating the same accelerated cycling procedure that I used in the experiment. The input cycle schedule was a 1 C constant-current-constant-voltage charge and a 3 C constant-current discharge at 25 °C. The simulated relative capacity at 450 cycles was very close to the measured value. During the first 200 cycles, the maximum relative error between simulation and experiment was 1.1%; from cycle 200 to 450, the maximum error decreased to 0.68%. I also compared the 1 C discharge curves at cycle 0, cycle 50, and cycle 400. The agreement was satisfactory, with the largest discrepancies appearing around the voltage knee near 3.6 V. These validations prove that the SEI-growth model is suitable for predicting the capacity fade of this EV battery pack cell under nominal cycling conditions.
I did not include low-temperature lithium plating in this aging model because the experimental aging matrix was limited to 25 °C. Therefore, all conclusions about aging in this thesis should be interpreted within the window of SEI-dominated aging. This is still the most relevant mechanism for moderate and warm environments where an EV battery pack usually operates.
5.2 Heat Generation after Aging
One critical issue is whether an aged EV battery pack generates more heat than a fresh cell. I used the aging model to simulate a new cell and a cell after 450 cycles. At a 2 C discharge rate, the aged cell was unable to reach the same depth of discharge because part of the lithium inventory had been consumed and its capacity was reduced. The average volumetric heat-generation rate increased from 190.4 kW m-3 for the fresh cell to 278.4 kW m-3 for the aged cell. This means that an aged EV battery pack cell not only provides less energy, but also becomes a stronger heat source for the same current.
I separated the heat-generation components after aging. The reversible reaction-heat share declined from 48.4% to 33.3%, while the polarization-heat share increased from 48.2% to 64.7%. The negative-electrode heat share increased from 45% to 60%, while the positive-electrode share dropped from 54.3% to 39.3%. These numbers show that the negative electrode becomes the main heat source after aging. This is consistent with the growth of the SEI film and the associated impedance rise on the negative electrode. I also found that the negative-electrode polarization heat increased with battery aging, whereas the positive-electrode polarization heat stayed almost unchanged. Therefore, an EV battery pack state-of-health estimator should consider the increasing polarization heat when predicting the thermal load of a degraded battery.
| Heat source or electrode share | Fresh cell / 450 cycles |
|---|---|
| Reversible heat share | 48.4% to 33.3% |
| Polarization heat share | 48.2% to 64.7% |
| Positive-electrode total heat share | 54.3% to 39.3% |
| Negative-electrode total heat share | 45.0% to 60.0% |
5.3 Effect of Cycle Rate on Aging
I investigated the effect of charge-discharge current on capacity fade by simulating 1 C, 2 C, and 3 C cycling at 25 °C. The term “cycle rate” means the rate during both charging and discharging, while the total discharged energy is the same for every cycle. The simulation showed that a higher cycle rate accelerates capacity fade. After 450 cycles, the 1 C-cycled cell retained a higher fraction of capacity than the 3 C-cycled cell. The difference in relative capacity between the two cells was about 2%. The capacity-fade curve was not linear. In the first 80 cycles, the capacity decrease was relatively fast because the initial SEI film grows rapidly. Later, the film becomes thicker and creates a larger diffusion resistance for solvent molecules, so the SEI-growth rate and the capacity-loss rate slow down.
The same trend was observed for the SEI film resistance and film thickness. Both quantities increased rapidly during the initial cycles and then gradually approached a more linear, but slower, increase. A higher cycle rate produces more film resistance and film thickness after the same number of cycles. This effect is caused by greater polarization, higher local overpotential, and more side-reaction driving force at high current. Therefore, a high-rate application is more punishing for the EV battery pack than a moderate-rate application, not only because of instantaneous heat generation but also because of faster SEI growth.
5.4 Effect of Ambient Temperature on Aging
Ambient temperature has a strong influence on SEI growth. I simulated 1 C cycling at 25 °C, 32 °C, and 40 °C. The capacity-fade rate increased as the ambient temperature increased. After 450 cycles at 40 °C, the relative capacity was about 78.9%, which is already below the commonly accepted end-of-life criterion of 80%. In comparison, the cell cycled at 25 °C retained about 92.6% of initial capacity. The SEI film resistance grew by about 0.073 Ω m² when the cycling temperature was increased from 25 °C to 40 °C. The corresponding film-thickness increase was 363 nm. These values clearly demonstrate that temperature is more critical than cycle rate for SEI-driven aging of this high-rate pouch cell. When designing thermal management of an EV battery pack, keeping the temperature near 25-30 °C is not only beneficial for instantaneous electrical performance, but also essential to slow down the chemical aging reaction.
The aging model also suggests that the growth rate of the SEI film is not constant. Initially, both the film thickness and capacity fade change rapidly. In the later period, the growth rate becomes slower because the diffusion of the solvent through the existing film becomes the limiting process. This behavior is beneficial for the EV battery pack because it prevents an immediate end of life, but it also makes capacity-fade prediction difficult using linear extrapolation. A physical side-reaction model is therefore more suitable than a simple empirical lifetime law when extrapolating from laboratory aging tests to real EV battery pack usage.
| Cycling temperature | Relative capacity after 450 cycles | SEI growth behavior |
|---|---|---|
| 25 °C | 92.6% | Slow film growth |
| 32 °C | Intermediate | Moderate film growth |
| 40 °C | 78.9% | Fast film growth; end-of-life reached |
6 Discussion for EV Battery Pack Design
The numerical and experimental results in this thesis provide several recommendations for EV battery pack design. First, the cooling system must be designed for the worst-case internal heat source, not only the steady-state low-rate source. During high-rate discharge, polarization heat is the dominant irreversible source. The thermal mass of the cell and the through-plane thermal conductivity determine the temperature difference between the core and the surface. Because high convection coefficients can increase the internal temperature gradient, a successful EV battery pack cooling design must combine high heat transfer on the surface with an internal thermally conductive path.
Second, the operating range of depth of discharge should be carefully selected. My model showed that the heat-generation rate accelerates rapidly above 80% DOD. This is partly caused by the coefficient of entropy becoming strongly negative and partly by the increasing overpotential at the end of discharge. In an EV battery pack, limiting the operational window to a middle state-of-charge range can reduce heat generation and improve thermal uniformity.
Third, high ambient temperatures are particularly detrimental to the life of the cell. The simulation shows that an increase from 25 °C to 40 °C can reduce the life of the cell from more than 450 cycles to less than 450 cycles under the same cycling schedule. Because the capacity fade is driven by SEI thickening, an EV battery pack should be kept at a moderate temperature even when high power is not needed. This can be achieved by using an active liquid thermal management system or by coupling with phase-change materials.
Fourth, the aged cell is not the same as the fresh cell from the heat-generation point of view. If the thermal model of the EV battery pack is calibrated only on fresh data, it will underestimate the polarization heat and negative-electrode heat when the battery has aged. The increased heat generation at end of life may push the cell into a thermal runaway region that was not considered in the original design. Therefore, thermal engineers should simulate not only the beginning-of-life condition but also the end-of-life heat-generation profile.
I also discussed the effect of electrode thickness and particle radius. Increasing electrode thickness is an efficient way to increase cell energy density, but it increases ohmic heat and impedance. Increasing particle size has a similar effect on irreversible heat. For a high-discharge-rate aerial or automotive application, the cell designer should select moderately thin electrodes and small enough particles to keep the reaction rate uniform. This trade-off between energy density and polarization is a central challenge in developing the next-generation EV battery pack.
7 Conclusions
This thesis studied the thermal characteristics and aging behavior of a LiCoO2/graphite high-rate soft-pack power battery. I used experiments and a coupled electrochemical-thermal aging model to draw the following main conclusions.
First, increasing the discharge rate or reducing the ambient temperature lowered the initial voltage and reduced the available discharge capacity. At the same time, the surface temperature rise increased. The discharge capacity was more sensitive to ambient temperature than to discharge current. The measured entropy coefficient explains the non-monotonic temperature-rise curve, especially the N-shaped pattern observed during discharge. This reversible-heat effect must be included in any accurate EV battery pack model.
Second, the electrochemical-thermal model was validated by discharge curves and temperature curves. The model showed that the positive electrode is the largest heat source in a fresh cell during normal-rate discharge. At lower discharge rates, reversible heat dominates the temperature response, while at high rates and low temperatures, irreversible heat dominates. The model further showed that an increase in electrode thickness or particle radius increases the irreversible heat share. In a forced-convectively cooled cell, the core-to-surface temperature difference is increased by improving the surface cooling coefficient, but it is decreased by raising the through-plane thermal conductivity. A thinner cell is also beneficial for reducing temperature gradients.
Third, the SEI film growth model successfully reproduced capacity fade under accelerated cycling. I found that the capacity fade and SEI film growth are rapid in the initial period and then slow down. Both high cycle rate and high ambient temperature accelerate the aging process. The ambient temperature is even more critical than the discharge rate in the range considered here. As the cell ages, the total heat-generation rate rises, and the negative-electrode irreversible heat becomes dominant. Therefore, end-of-life thermal behavior should be included in EV battery pack thermal safety assessment.
I hope that the quantitative relations obtained in this work will guide the design of safer and longer-lasting lithium-ion cells and modules. The multidimensional electrochemical-thermal aging model can be extended to pack-level simulations by coupling a finite-volume thermal-fluid model with the cell model. In the future, I recommend including lithium plating at low temperature and active-material loss at high state of charge to give a more complete lifetime prediction for an EV battery pack. My current results already provide a useful foundation for such extensions because the experimental and modeling system has been rigorously validated for the high-rate cell representative of an EV battery pack unit.