In this article, I provide a systematic first-person account of my research into the thermal characteristics and aging behavior of the vehicle traction battery, focusing on a high-rate lithium cobalt oxide soft-pack power cell which is representative of the modern energy storage systems used in unmanned aerial vehicles. The vehicle traction battery is distinct from conventional cells in that it must function under stringent conditions such as rapid charge/discharge cycles, high ambient temperature variations, and mechanical and thermal constraints. My work integrates an extensive experimental program with a comprehensive set of physics-based models in order to gain a multi-scale understanding of heat generation, entropy-driven phenomena, and degradation behavior. In the study framework, I use the vehicle traction battery concept as a thread that links electrochemical modeling, thermal management, design optimization, and aging prediction.

Lithium-ion batteries stand out because of their high energy density, low self-discharge rates, outstanding cycle stability, and increasingly competitive cost. These advantages have consolidated their position as the principal power source for portable electronic devices, electrified vehicles, grid storage, and electric aviation systems. In particular, the demand for purely electric unmanned aerial vehicles has grown rapidly in both civilian and military sectors, introducing new requirements for the vehicle traction battery. For such applications, high-rate discharge capability is equally important as high energy content: the vehicle traction battery must provide short-duration high current for takeoff, acceleration, or payload hoisting. However, the very features that make these cells attractive also produce significant thermal loads, severe temperature gradients, and complex degradation pathways. In a standard battery pack, the vehicle traction battery is mounted tightly together, and any nonuniformity in temperature can lead to uneven state-of-charge distribution, accelerated localized aging, or thermal runaway risk.

Literature Context and Problem Identification

Numerous experimental studies have been performed to quantify the thermal behavior of lithium-ion batteries. Some researchers used accelerating rate calorimetry to measure the heat output of large-format cells, demonstrating that the heat generation rate in lithium iron phosphate cells at low temperature increases by more than a factor of two compared to room-temperature conditions. Other investigators designed experiments around DC resistance tests over a range of temperatures to quantify the reversible and irreversible heat components. These empirical studies, while valuable, are necessarily limited in their ability to reveal internal, spatially resolved states such as lithium concentration gradients, reaction current distribution, or local entropy generation. The vehicle traction battery has many internal layers—positive electrode, separator, negative electrode, and current collectors—each with its own thermophysical properties, and in-situ measurement of internal temperature remains extremely challenging.

Numerical simulation therefore becomes an indispensable complement to experimentation. Multiscale electrochemical-thermal models, most prominently those derived from the pseudo-two-dimensional (P2D) framework originally developed by Newman and co-workers, have been widely used to predict voltage profiles, capacity utilization, heat source distributions, and degradation behavior of lithium-ion cells. The vehicle traction battery provides an ideal application case for such modeling tools because of the wide range of operating conditions and the strong coupling between electrochemical kinetics, transport, and thermal field. I note that several previous publications coupled a one-dimensional electrochemical model to a three-dimensional thermal model for cylindrical cells, but fewer studies focused on the soft-pack geometry and even fewer addressed the interplay between thermal nonuniformity and aging. When modeling the vehicle traction battery, one must also account for the temperature dependence of parameters such as the solid-phase diffusion coefficient, electrolyte conductivity, reaction rate constants, and the entropy coefficient. The assumption of constant properties, although convenient, leads to significant errors under high-rate or low-temperature operation.

In the field of aging research, it is well documented that the vehicle traction battery degrades by calendar aging and cycling aging. The calendar aging mechanism proceeds even in the absence of current flow, driven by the thermodynamic instability of electrode materials in contact with the electrolyte. The cycling aging is accelerated by mechanical fatigue, localized overpotential, and repeated volume changes. A dominant aging pathway is the continuous growth of the solid electrolyte interphase (SEI) at the graphite negative electrode. The SEI film forms during the initial cycles as a passivation layer, but it cannot entirely prevent electrolyte transport. Solvent molecules slowly diffuse through the film and react with lithium ions and electrons at the carbon surface. This parasitic reaction consumes cyclable lithium inventory and increases the film thickness. The vehicle traction battery lacks lithium after such losses because no additional lithium reservoir exists in the cell design. The electrochemical-thermal coupling is therefore decisive: a temperature rise accelerates the SEI reaction, producing more heat, which in turn increases the film growth rate, creating a positive feedback that may ultimately lead to thermal runaway in extreme cases.

Upon reviewing the current state of research, I identified several gaps that motivated my work. Most studies that investigated battery thermal behavior used large-format prismatic cells or cylindrical cells intended for automotive applications, while the specific characteristics of a small-format, high-rate soft-pack cobalt-oxide cell for vehicle traction battery applications were insufficiently documented. Moreover, many in the literature that used the P2D model employed a simplified thermophysical representation of the cell, treating it as an isotropic and homogeneous solid. This approach cannot represent the internal thermal resistance of a stack composed of layers with vastly different thermal conductivities. Finally, despite the indisputable importance of aging in determining the thermal response of the vehicle traction battery, comparatively few studies have quantified how the heat generation distribution changes as a function of cycle number. My research aims to fill these gaps by constructing an experimentally validated, physics-based model that couples electrochemistry, heat transfer, and aging phenomena.

Experimental Platform and Basic Performance Tests

In this section I describe the experimental framework that I used to characterize a vehicle traction battery sample with nominal capacity of 2250 mAh and nominal voltage of 3.85 V. The cell has a soft-pouch format with external dimensions of approximately 61 mm × 34 mm × 7.8 mm. The positive electrode is lithium cobalt oxide (LiCoO2), while the negative electrode is graphite. The electrolyte comprises LiPF6 dissolved in a mixture of ethylene carbonate and dimethyl carbonate. According to the manufacturer’s datasheet, the maximum continuous discharge current is 10 C and the recommended operating temperature spans from –20 °C to 60 °C. The cell mass is about 33.7 g, and the measured DC internal resistance is approximately 4.8 mΩ.

I constructed a test bench that included a programmable charge-discharge system (model CT-4008T-5V12A-S1), a temperature and humidity chamber (BPS-50CL), a multi-channel temperature recorder (TA612C), and a data acquisition station. The battery was placed inside the chamber, and K-type thermocouples were attached to the cell surface to record temperature evolution. The charge/discharge system was controlled through a host computer that logged current, voltage, capacity, and time. To ensure reproducibility and stable initial conditions, the battery was subjected to a standard preconditioning procedure before each test: a constant-current discharge at 1 C down to the cutoff voltage of 3.0 V, followed by a 30-minute rest, then a constant-current constant-voltage charge at 1 C and 4.4 V, until the current decreased to 0.05 C, and again a rest period.

Through these experiments, I evaluated the performance of the vehicle traction battery at discharge rates of 1 C, 2 C, 3 C, and 4 C, all at an ambient temperature of 25 °C. Figure 2-8 in the original work and the associated voltage-capacity curves show that increasing the discharge current causes a notable drop in the initial voltage plateau and a moderate decrease in delivered capacity. At 4 C, the battery discharges to 3.0 V more quickly, and the voltage drop at the end of discharge becomes sharper. This behavior can be attributed to the polarization effect: at high current densities, the slow solid-state diffusion in the electrode particles and the limited ionic conductivity in the electrolyte cannot maintain the required thermodynamic potential at the particle surface. The overpotential increases with current, so the terminal voltage reaches the cutoff value before all active material has been utilized.

In parallel with discharge-rate tests, I varied the ambient temperature over a wide range. The vehicle traction battery was discharged at 1 C in environments regulated to –10 °C, 0 °C, 10 °C, 25 °C, and 40 °C. The cell was allowed to rest for 30 minutes at the target temperature before discharge. The voltage curves reveal a clear positive correlation between temperature and delivered capacity. At –10 °C, the discharge capacity dropped to approximately 2179 mAh, while at 40 °C it rose to approximately 2280 mAh, relative to the nominal 2250 mAh. The explanation lies primarily in the temperature dependence of transport properties: at low temperature, the electrolyte viscosity increases sharply, the ionic diffusion coefficient drops, and the solid-phase diffusion kinetics slow down. This raises the internal impedance and voltage polarization, which manifests as a depressed voltage curve and reduced accessible capacity. In extreme cold conditions, the negative graphite electrode becomes increasingly susceptible to lithium plating, which would consume cyclable lithium and may cause internal shorts over time. These results underline why thermal management is essential to achieve reliable performance of the vehicle traction battery in unmanned aerial vehicle operations.

In addition, I performed HPPC (Hybrid Pulse Power Characterization) tests to measure the DC internal resistance of the vehicle traction battery across a range of SOC values and at different temperatures. The applied pulse sequence consisted of a 10-second discharge at 1 C, a 40-second rest, then a 10-second charge at 1 C, followed by 40 seconds of open-circuit relaxation. The DC resistance was calculated as the voltage change divided by the pulse current. The results indicate that the internal resistance increases gradually as the ambient temperature drops from 40 °C to –10 °C. Over the SOC interval of 20% – 80%, the DC resistance is relatively flat at high temperatures. This finding is useful because it suggests that under moderate climate conditions, the DC resistance can be treated as a single representative value in the reduced-order model.

I further measured the entropy coefficient dU/dT of the cell to evaluate the reversible heat generation rate. In this test, the vehicle traction battery was charged to a specific SOC and placed in the temperature chamber. The chamber temperature was then sequentially set to 5 °C, 15 °C, 25 °C, 35 °C, and 45 °C, and the open-circuit voltage was recorded after a minimum rest of 2 hours at each temperature. Plotting the cell voltage as a function of temperature produced a series of straight-line segments whose slopes correspond to the full-cell entropy coefficient at that SOC. I repeated this protocol over a SOC sweep from 0% to 100% with increments of 10% discharge depth. The measured full-cell entropy coefficient varied between –1.1 mV/K and +0.29 mV/K. It starts negative in the range from 0% to 35% DOD, becomes positive between 35% and 50% DOD, and then turns strongly negative in the final portion of discharge. This behavior follows from the staging transitions in the graphite electrode and the ordered-disordered phase transitions of the LiCoO2 cathode. The sign of dU/dT determines whether the reaction heat term is endothermic or exothermic during discharge. For a vehicle traction battery, being aware of these transitions is important because the temperature evolution of the cell surface can exhibit a non-monotonic “N-shape” during a constant-current discharge.

Accelerated Aging Protocol and Capacity Loss Trends

The deployment scenario of a small-scale electric drone typically involves a high discharge current during the flight phase, often greater than 2 C, while charging is limited to 1 C by the onboard charger. To assess long-term stability within a manageable experimental time frame, I designed an accelerated ageing test in which the charge step was fixed at 1 C constant-current constant-voltage (CCCV) and the discharge step was performed at 3 C constant current down to 3.0 V. Each charge-rest-discharge-rest sequence constituted one cycle. I performed a capacity check and DC resistance measurement after every 50 cycles to track the degradation of the vehicle traction battery. The cell was maintained at an ambient temperature of 25 °C throughout the entire cycling test.

After 450 cycles, the cell retained only 92.6% of its initial capacity. The capacity decay curve appears almost linear over the whole range of cycles, with a slight decrease in the decay rate in later cycles. The discharge voltage curves at 1 C, recorded at different cycle numbers, shift downward as the cell ages. This voltage fade mirrors the increase in internal impedance and the growing overpotential required to drive the intercalation reaction. A similar trend appears when the cell is discharged in a cooler environment: aged cells resemble cold cells in that they reach the cutoff voltage earlier and thus deliver less discharge capacity. The measured DC internal resistance after cycling also increases, confirming that power capability and peak-current handling of the vehicle traction battery are gradually compromised.

I considered several degradation modes to interpret the observed capacity loss. In a graphite/LiCoO2 chemistry subjected to moderate current and temperature, active material loss can occur through particle cracking and loss of electrical contact, but these effects are typically less pronounced than SEI growth. Lithium inventory loss associated with SEI growth is consistently identified as a major cause of capacity fade under these conditions. Because the cell was cycled at room temperature rather than at sub-ambient cold temperatures, lithium plating is likely not the dominant ageing mechanism. Thus, the SEI thickness increase is the most appropriate degradation model to reproduce the measured capacity fade of the vehicle traction battery.

Governing Equations of the Electrochemical Thermal Coupling Model

The electrochemical model that I used in this work is the pseudo-two-dimensional formulation. This model represents each porous electrode as a superposition of spherical active material particles and an electrolyte-filled pore network. The first pseudo-dimension is the macroscopic coordinate through the cell thickness (from negative current collector to positive current collector), while the second pseudo-dimension is the radial coordinate inside the spherical particles. The model accounts for solid-phase diffusion, electrolyte-phase diffusion and migration, charge conservation, and electrochemical kinetics. I summarize the essential governing equations here.

The active surface area per unit volume of the electrode is calculated as:

$$a_v=\frac{3 \varepsilon_s}{R_p}$$

In the above equations, \(c_s\) is the lithium concentration inside the spherical particle, \(c_e\) denotes the electrolyte concentration, \(D_s\) and \(D_e\) are the solid-phase and liquid-phase diffusion coefficients, \(\sigma_s\) and \(\kappa_e\) are the solid and electrolyte conductivities, \(t_+\) is the lithium-ion transference number, \(R_p\) is the particle radius, and \(\alpha_a\) and \(\alpha_c\) are the anodic and cathodic charge-transfer coefficients, taken to be 0.5 for both electrodes in this study.

The temperature dependence of key material parameters is critical for accurately modeling the vehicle traction battery. I adopted Arrhenius-type relationships for the solid-phase diffusion coefficient and the electrochemical reaction rate constant, as shown above. The electrolyte diffusion coefficient, ionic conductivity, and transference number were taken as functions of both temperature and salt concentration, following expressions commonly reported for LiPF6 in carbonate-based solvents. By incorporating these dependencies, the model is able to capture the increase in internal resistance at low temperature and the acceleration of chemical reactions at elevated temperature.

Thermal Model and Heat Generation Source Terms

The thermal model used to track the temperature distribution inside the vehicle traction battery is based on the energy conservation equation in three dimensions. I assumed that the pouch cell is composed of alternating electrode, separator, and current collector layers that are stacked repetitively. Owing to the large number of layers and the computational cost of resolving the full stacked geometry, I homogenized the cell into a single macroscopic continuum with anisotropic thermal conductivity. The volumetric heat capacity and density were obtained by volume-averaging the corresponding values of each component. The thermal conductivity in the plane direction and through-thickness direction was determined using the thermal resistance network model. The resulting values are: \(k_x = k_y = 63.76\ \mathrm{W/(m\cdot K)}\) in the in-plane direction and \(k_z = 1.11\ \mathrm{W/(m\cdot K)}\) in the through-thickness direction. The large anisotropy arises because the aluminum and copper foils provide excellent conductive paths in the plane, while the coating layers and separator dominate the heat conduction across the thickness.

During battery operation, the total heat generation rate per unit volume is decomposed into four contributions: polarization heat, ohmic heat, reaction heat, and SEI film heat. The polarization heat originates from the activation and concentration overpotentials and is calculated as the product of the local electrochemical reaction current density and the overpotential:

$$Q_{pol} = a_v \, J \, \eta$$

The ohmic heat arises from the finite conductivity of both the solid matrix and the electrolyte:

$$Q_{ohm} = \sigma_s^{eff} (\nabla\phi_s)^2 + \kappa_e^{eff} (\nabla\phi_l)^2 + \kappa_D^{eff} \nabla\ln c_e \cdot \nabla\phi_l$$

The reversible (reaction) heat is related to the entropy change of the electrochemical reaction:

$$Q_{rev} = a_v \, J \, T \, \frac{\partial U_{eq}}{\partial T}$$

The heat generated at the current-collector tabs was considered separately:

$$Q_{tab}= \frac{I^2}{A_{tab}^2} \left(\frac{1}{\sigma_{tab}}+\frac{1}{\sigma_c}\right)$$

where \(\sigma_{tab}\) is the conductivity of the tab material, \(\sigma_c\) is the contact conductivity between the tab and the current collector, and \(A_{tab}\) is the tab cross-sectional area. Finally, the heat lost by convection and radiation from the external surfaces of the pouch cell is:

$$Q_{diss} = h A_c (T – T_{amb}) + \epsilon \sigma A_c (T^4 – T_{amb}^4)$$

The above heat generation terms are embedded into the energy balance as follows:

$$\rho C_p \frac{\partial T}{\partial t} = \nabla\cdot(k \nabla T) + Q_{pol} + Q_{ohm} + Q_{rev} + Q_{tab}$$

Model Parameterization and Boundary Conditions

A central contribution of my work is the careful parameterization of the electrochemical-thermal model for the soft-pouch vehicle traction battery. I measured the physical dimensions of the cell by disassembling a fully discharged cell and using a digital micrometer. The measured thickness values are listed in the table below. I confirmed through X-ray inspection (reference from datasheet) that the cell is produced by a wound process with 20 layers. The active area per layer was determined from the electrode area, and the total active surface area is around 0.125 m².

Since the soft-pack vehicle traction battery has no rigid casing and is typically clamped between lightweight support plates in the UAV frame, I applied a convective heat transfer boundary condition on all external surfaces. The natural convective heat transfer coefficient in still air is \(h = 25\ \mathrm{W/(m^2\cdot K)}\), and I additionally considered forced-air conditions with coefficients up to 200 W/(m²·K) for sensitivity studies. The emissivity was set to 0.95.

Model Validation

Before using the model for predictive analysis, I validated it against a comprehensive set of test data for the vehicle traction battery. The first validation case was a constant-current constant-voltage charge at 0.5 C, for which the simulated full-cell voltage curve almost overlays the measured curve. The second validation case was constant-current discharge at 1 C, 2 C, 3 C, and 4 C at 25 °C. For each discharge, I extracted the terminal voltage profile and the surface temperature profile from simulation and compared them to the experimental records. The maximum absolute error between model and experiment is about 5.56% in voltage, which appears in the middle of the 4 C discharge. The temperature error on the surface is larger for the 4 C rate with a maximum relative error of 4.25%. These deviations are expected, because the model parameters, especially the electrolyte transport properties at high concentrations, may differ from the actual values of the commercial material. Nevertheless, the overall agreement confirms that the electrochemical-thermal model can reliably reproduce the external performance of the vehicle traction battery.

The model was further used to shed light on the experimentally observed “N-shape” of the temperature curve. In the middle of discharge, the cell surface temperature may show a small dip even though the heat generation rate is positive. The results show that the sign and magnitude of the entropy coefficient dominate the reaction heat in the middle portion of the discharge. When the full-cell entropy coefficient is positive at approximately 35%–50% DOD, the reaction heat turns endothermic, absorbing heat from the cell and reducing the rate of temperature rise. This effect is sufficiently strong to produce the local minimum in the temperature profile. The “N-shaped” curve is therefore a direct consequence of reversible thermodynamic phenomena rather than an instrumentation artifact.

Simulation-Based Analysis of Heat Generation under Various Operating Conditions

After validation, the numerical model was used to quantify heat generation and predict the thermal performance of the vehicle traction battery in higher detail than possible in the experiments alone. In this section I summarize the findings obtained when varying the discharge rate and ambient temperature. To compare heat generation across different electrodes and cycles, it is useful to define the share of each heat source as a fraction of the total heat production.

When the battery is discharged at 1 C, 2 C, and 4 C in a 25 °C environment, the simulated results show that the reaction heat fraction is 58%, 44%, and 31%, respectively. As the discharge rate increases, the irreversible heat contributions from polarization and ohmic heating increase, until at 4 C the irreversible components dominate more than 60% of the total heat production. This quantitative shift is the reason why the battery surface temperature increase is much more rapid at high C-rates. At low discharge rates, the reaction heat controls the temperature change, producing a plateau or dip in the middle of discharge, whereas at high rates, the irreversible heat masks the reversible signature.

The internal component-level analysis shows that, for a fresh vehicle traction battery, the positive electrode is the largest source of heat generation at moderate discharge rates. The negative electrode becomes increasingly important as the discharge proceeds and as the rate increases. The separator contributes the least to total heat generation because it only transports ions and thus generates no reaction heat, producing only ohmic heat. This finding has implications for electrode design: to reduce the heat generation of the vehicle traction battery, improving the ionic transport inside the positive electrode and adjusting its active material loading are more effective than targeting the separator or the negative electrode alone.

When the ambient temperature changes from 25 °C down to 5 °C at the same discharge rate of 2 C, the total heat release rate increases by about 24%. This response is caused primarily by the temperature dependence of the electrolyte conductivity and the solid-state diffusion coefficients. Likewise, when the temperature is raised from 25 °C to 45 °C, the total heat release rate decreases. Simultaneously, the contribution of irreversible heat decreases while that of the reaction heat increases. At 5 °C, the irreversible heat fraction is around 60% or more; at 45 °C, the reversible reaction term becomes dominant.

Design Parameter Sensitivity and Effect on Heat Generation

I employed the validated electrochemical-thermal model of the vehicle traction battery as a virtual design tool to investigate the influence of geometric parameters on heat generation. The electrode thickness and active-material particle diameter are decisive parameters because they determine the diffusion length and the active surface area. To isolate the effect of electrode thickness, I adjusted the loading while keeping the n/p ratio constant so that the theoretical capacity remains unchanged.

The simulations reveal that, as the positive electrode thickness is increased from 16 μm to 56 μm, both the total heat generation and the cell temperature increase. This trend can be explained by the increased diffusion path length in the liquid phase and solid phase, leading to greater concentration polarization. The voltage profile is slightly lower for thicker electrodes, while the discharge capacity slightly decreases. At the same time, the ohmic heat fraction rises significantly with the electrode thickness, confirming that ohmic losses in the electrode stack grow when the transport path is longer. These findings are highly relevant for designers who want to increase energy density by using thick electrodes in the vehicle traction battery.

Increasing the particle radius of either positive or negative electrode material reduces the active surface area and thus increases the true current density at the particle interface. The model shows that both the irreversible heat and the reversible heat increase when the particles are larger. The effect on irreversible heat is stronger than the effect on reversible heat. In the first 25% of discharge depth, the reversible heat is almost insensitive to particle size. However, larger particles cause a visible delay in the peak of the reversible heat production. The total heat production rate follows the same trend: larger particles lead to higher peak heat release and a less uniform heat source distribution. These results confirm the importance of microstructural design for thermal performance of the vehicle traction battery.

Temperature Uniformity of the Vehicle Traction Battery

The temperature distribution inside a soft-pouch vehicle traction battery is a crucial indicator of reliability and durability. When some regions of the cell become hotter than others, the hotter regions will age faster and may accumulate more internal resistance. This nonuniform aging process is self-accelerating, because higher local temperature increases the SEI growth rate, which increases the local resistance and heat release, further raising the temperature. Thermal uniformity must therefore be considered during the design of the battery pack for drone applications.

Using the anisotropic thermal model, I determined the steady-state temperature distribution at the end of discharge at different C-rates. The results show that the core of the cell is consistently hotter than the surface because the in-plane thermal conductivity is about fifty times larger than the through-thickness conductivity. Heat generated inside the core must travel through the entire thickness before being removed by convective cooling. For a moderate discharge rate of 2 C and a convective coefficient of 25 W/(m²·K), the core-to-surface difference is only on the order of 1 °C. However, when the drone performs a high-power maneuver with a discharge current corresponding to 10 C and the surface is exposed to forced airflow, the interior excess temperature can be as high as 4.5 °C.

In this work, I systematically simulated several factors that affect the core-to-surface temperature difference: the surface heat transfer coefficient \(h\), the cell thickness \(L_{bat}\), and the through-thickness thermal conductivity \(k_z\). Increasing the convective heat transfer coefficient is beneficial for lowering the absolute cell temperature, but it simultaneously increases the temperature difference between the core and the surface. This is because the surface temperature drops faster while the core heat dissipation path length remains unchanged. At \(h=200\ \mathrm{W/(m^2\cdot K)}\), the temperature gradient is more significant than at \(h=50\ \mathrm{W/(m^2\cdot K)}\). The vehicle traction battery thus presents a thermal-management trade-off: aggressive air cooling keeps the average temperature low but introduces stronger internal temperature gradients.

Cell thickness is another major factor that determines the uniformity of temperature. I simulated battery packs with the same total volume and capacity but different thicknesses by changing the ratio of cell thickness to width. The model results show that the maximum temperature and the difference between core and surface increase proportionally with the cell thickness. For every additional millimeter of thickness, the peak temperature rises by approximately 0.5 °C at 4 C and 1 °C at 8 C. Concurrently, the core-surface temperature difference increases by about 0.3 °C at 4 C and 0.6 °C at 8 C. If the battery design is constrained by the available space inside the UAV frame, minimizing the thickness can significantly improve the durability of the vehicle traction battery.

Finally, I considered the possibility of enhancing the through-thickness thermal conductivity by material modification or by inserting a thermally conductive interlayer between the battery layers. When \(k_z\) is increased from the baseline value of 1.11 W/(m·K) to 3 W/(m·K), the core-to-surface temperature difference at 10 C under forced-air cooling drops by approximately 1.2 °C. This finding underlines the importance of designing composite electrodes and separator coatings with higher thermal conductivity. In conclusion, for the vehicle traction battery intended for unmanned aerial vehicle applications, achieving good temperature uniformity requires balancing the convective cooling coefficient, geometric aspect ratio, and internal thermal conductance.

Extension to the Electrochemical-Thermal-Aging Coupled Model

Building upon the validated electrochemical-thermal model, I extended the framework for the vehicle traction battery by introducing a negative-electrode side reaction that represents the formation and growth of the SEI film. This aging mechanism is widely considered to be the dominant capacity fade pathway for graphite-based lithium-ion cells during nominal cycling at moderate temperature. I assumed that ethylene carbonate as solvent molecules diffuse through the existing SEI layer and react with lithium ions at the carbon surface to form lithium alkyl carbonate species. The simplified reaction is:

$$\text{EC} + 2 e^- + 2 Li^+ \rightarrow \text{(CH}_2\text{OCO}_2\text{Li})_2 + \text{C}_2\text{H}_4$$

Since the active material is graphite, both the main lithium intercalation reaction and the SEI formation reaction consume lithium ions. The total current density at the negative electrode particle surface is therefore:

$$J_{total} = J_{main} + J_{SEI}$$

where \(J_{main}\) is the intercalation current density described by the Butler-Volmer equation, and \(J_{SEI}\) is the parasitic current density driving the SEI growth:

$$J_{SEI} = -\, \frac{a_v^{SEI} \, i_{0,SEI} \, c_{EC}}{c_{EC,ref}} \exp\left( -\frac{\alpha_{c,SEI} F}{RT} \eta_{SEI} \right)$$

The SEI overpotential \(\eta_{SEI}\) is given by the potential difference between the solid and electrolyte phases at the negative electrode surface relative to the equilibrium of the SEI formation reaction:

$$\eta_{SEI} = \phi_s – \phi_l – U_{SEI} – \frac{J_{SEI} \, R_{film}}{a_{v,neg}}$$

where \(R_{film}\) is the total resistance of the SEI film. The film resistance is related to the film thickness \(\delta_{film}\) and to the SEI ionic conductivity \(\kappa_{SEI}\):

$$R_{film} = \frac{\delta_{film}}{\kappa_{SEI}}$$

The rate of growth of the film thickness is proportional to the parasitic current density:

$$\frac{\partial \delta_{film}}{\partial t} = -\, \frac{M_{SEI}\, J_{SEI}}{a_{v,neg}\, \rho_{SEI}\, F}$$

In the above expressions, \(M_{SEI}\) is the molar mass of the SEI product, \(\rho_{SEI}\) is its density, and \(\kappa_{SEI}\) is the SEI ionic conductivity. The parameters that were used for the aging model are summarized below.

The SEI side reaction generates additional heat due to the internal resistance of the film. The heat generation rate from the film is denoted by \(Q_{film}\) and is added to the total energy balance:

$$Q_{film} = J_{SEI,\,total}^2 \, R_{film}$$

The modified energy equation for the aging model is therefore:

$$\rho C_p \frac{\partial T}{\partial t} = \nabla\cdot(k\nabla T) + Q_{pol} + Q_{ohm} + Q_{rev} + Q_{tab} + Q_{film}$$

By incorporating the above equations, the model predicts both the evolution of the SEI film thickness and the resulting capacity fade. The capacity fade is calculated from the loss of cyclable lithium inventory in the negative electrode.

Validation of the Aging Model

I validated the electrochemical-thermal-aging coupled model by comparing the simulated capacity retention to the accelerated aging test results of the vehicle traction battery. The comparison was performed for up to 450 cycles under the same 1 C charge/3 C discharge protocol and at 25 °C ambient temperature. The simulated capacity fade curve has a relative error of less than 1.1% for the first 200 cycles and below 0.68% over the subsequent cycles. The excellent agreement demonstrates that the SEI formation model accurately describes the degradation rate of this cell under the specified cycling scheme.

I also cross-checked the voltage profiles at selected cycle numbers, including cycle 1, cycle 50, and cycle 400. The comparison confirms that the model reproduces the progressive downward shift in voltage during discharge. The error between the simulated and measured discharge voltage is largest around 3.6 V, which corresponds to the region where the negative electrode undergoes staging phase transitions. In spite of this, the model captures the key aspects of the voltage fade and the capacity loss of the vehicle traction battery.

Thermal and Degradation Analyses of the Aged Cell

One of the main goals of my research was to clarify how the heat generation of the vehicle traction battery changes with aging. I extracted the heat generation components at different stages of the aging process. The polarization heat at the negative electrode increases significantly as the cell ages, while the polarization heat at the positive electrode remains largely unchanged. This is a direct consequence of the fact that the SEI film grows at the negative electrode, increasing the surface film resistance and activation overpotential there. The film resistance hinders lithium-ion transfer across the electrode/electrolyte interface, thereby increasing the local polarization losses.

In contrast, the positive electrode does not experience SEI growth, so its polarization heat is almost independent of cycle number. This finding has important consequences for cell design and thermal management. For example, if an aged vehicle traction battery is discharged at high rate, the negative electrode becomes the dominant heat source, gradually overtaking the positive electrode in heat contribution. Whereas in a fresh cell the positive electrode is the largest contributor, after prolonged cycling the negative electrode can generate more heat because of the thicker film. This transition was quantified in my model: the share of negative electrode heat generation rises from about 45% (fresh) to 60% after 450 cycles. Simultaneously, the total heat production rate of the cell increases by about 46%, from an area-averaged value of roughly 190.4 kW/m³ for a fresh cell to 278.4 kW/m³ for the aged cell during a 2 C discharge in a 25 °C environment.

When examining the evolution of heat components, I found that the reversible heat fraction declines from about 48.4% (fresh) to 33.3% after 450 cycles. In contrast, the polarization heat fraction grows from about 48.2% to 64.7%. These data show that the aging process is intrinsically linked to increasing irreversibility. The vehicle traction battery in the aged state converts a larger fraction of its chemical energy directly into heat, which increases the thermal management burden and reduces the energy efficiency.

These trends are depicted through the component-specific comparison of heat production rates for fresh and aged cells, confirming that the SEI film growth induced by cycle aging is the primary driver of the increase in total heat generation. The quantitative information is critical for establishing when a battery pack needs to be derated: as the vehicle traction battery ages, the maximum allowable discharge current must be reduced to avoid exceeding the thermal limit of the system.

Influence of Cycling Rate and Ambient Temperature on Degradation

Having presented the model and its validation, I used it as a virtual tool to examine the effects of cycling current and ambient temperature on the degradation process of the vehicle traction battery.

Effect of cycling C-rate

The vehicle traction battery in an electric drone may be cycled at a high C-rate if the flight duration is short and the battery must be recharged quickly after each mission. I simulated the long-term cycling performance under 1 C, 2 C, and 3 C charging/discharging rates while keeping all other conditions identical at 25 °C. The capacity retention curves show that the degradation rate increases with higher cycling current. At 450 cycles, the relative capacity difference between 1 C and 3 C cycling is approximately 2%. In the first 100 cycles, the difference is small because the cell is still fresh and the SEI film has not yet built up to a level that causes significant resistance. In the later stages, the gap widens. The model predicts that the SEI film resistance and thickness follow a trend that is qualitatively identical to the capacity fade curve, namely a fast initial increase followed by a gradual slowdown. Higher cycling currents produce a larger SEI film thickness after any given cycle number.

These observations can be interpreted from a mechanistic standpoint. High discharge currents intensify the concentration polarization in the electrolyte, leading to a locally negative potential at the graphite surface and a higher driving force for the SEI reaction. Additionally, rapid charging can induce mechanical stress in the negative electrode particles because of large volume changes, which may crack the existing SEI film and expose fresh surface for further parasitic reactions. Thus, high-rate operation of the vehicle traction battery must be balanced against its long-term durability.

Effect of ambient temperature

I further simulated the cycling of the vehicle traction battery at 25 °C, 32 °C, and 40 °C at a constant current rate of 1 C. The result is unequivocal: the cell degrades faster at higher ambient temperatures. The capacity retention after 450 cycles is about 92.6% at 25 °C, in agreement with the measured data, but only 78.9% at 40 °C. If 80% capacity retention is taken as the end-of-life criterion, the cell at 40 °C would have exceeded its useful life just after about 430 cycles, whereas at 25 °C it still has considerable remaining life. The SEI film resistance after 450 cycles at 40 °C is about 0.073 Ω·m² higher than that at 25 °C, and the corresponding film thickness is about 363 nm thicker.

In Figure 5-10 of the original work, I plotted the temporal growth of the SEI film thickness at different temperatures. The film growth is faster in high-temperature environments because the parasitic reaction follows an Arrhenius-type temperature dependence. Although high temperature also enhances the main intercalation reaction and temporarily improves the cell performance, the negative side effect is accelerated electrolyte decomposition and lithium inventory loss. Consequently, thermal management of the vehicle traction battery must aim not only to keep the maximum temperature below safety limits but also to minimize the time spent in high-temperature environments, especially at high SOC.

In contrast, the effect of cycle rate is relatively weaker than that of temperature within the tested range. This result emphasizes that ambient temperature control should be prioritized in battery management systems. For a vehicle traction battery, equal to the consideration of discharge current, the temperature conditioning strategy has a first-order effect on extending service lifetime.

Summary of Findings

From this comprehensive study on the thermal characteristics and aging behavior of the vehicle traction battery, I summarize the main conclusions as follows:

1. The electrochemical-thermal model that I established, which accounts for the temperature-dependent transport and kinetic parameters and the layered anisotropic thermal structure of the soft-pouch cell, reproduces the voltage curves and surface temperature of the vehicle traction battery over a wide range of discharge rates and ambient temperatures. The maximum relative errors are below 5.6% for voltage and 4.3% for surface temperature, which supports the predictive use of the model.

2. The heat generation analysis reveals that the reaction reversibility plays a dominating role at low C-rates and at elevated temperatures. At high C-rates or low temperature, irreversible heat, especially polarization heat, dominates. The positive electrode is the primary heat source in a fresh cell, but the negative electrode gradually becomes more important when the discharge rate is increased. The reversible heat generated at the positive electrode controls the “N-shape” temperature profile during discharge, which appears as a plateau or even a small dip at moderate state of charge.

3. The design parameter sensitivity study shows that increasing the electrode thickness or the particle size of the active material increases the total heat generation and the proportion of irreversible heat. Therefore, an energy-dense design of the vehicle traction battery must integrate thermal modeling in its optimization to keep the core temperature within an acceptable range.

4. The temperature uniformity analysis indicates that a high surface heat transfer coefficient has the unintended consequence of increasing the core-to-surface temperature difference. The cell geometry, particularly its thickness, plays a more decisive role in temperature uniformity than the surface cooling coefficient in certain ranges. The utilization of materials with higher through-thickness thermal conductivity can dramatically improve the thermal uniformity of the vehicle traction battery without changing the external dimensions.

5. The accelerated aging experimental campaign on the vehicle traction battery produced a linear capacity fade trend, and the cell retained 92.6% of its initial capacity after 450 cycles of 1 C charge/3 C discharge at 25 °C. The discharge voltage curves shifted downward as the cell aged, indicating increased internal resistance.

6. The electrochemical-thermal-aging coupled model that introduces SEI film growth as the principal degradation mechanism is able to reproduce the measured capacity fade with an error of under 1.1%. According to the simulation, the SEI film thickness and resistance increase rapidly during the first phase of cycling, then gradually slow down in later cycles. This is a result of the protective nature of the SEI layer, which limits the transport of solvent molecules to the reaction interface.

7. The thermal analysis of the aged vehicle traction battery shows that capacity fade is necessarily accompanied by increased heat production. After 450 cycles, the total heat generation rate at 2 C is about 46% higher than that of a fresh cell, and the negative electrode contributes the majority of the heat. The increase in heat generation is mainly caused by the enhancement of polarization heat at the negative electrode due to the SEI layer resistance. If uncorrected, this increased heat release further accelerates the SEI growth and may lead to thermal instability.

8. Finally, I quantitatively evaluated the effects of cycling rate and ambient temperature on the degradation rate. High ambient temperature was identified as the most damaging factor among the tested conditions. Therefore, the battery management system for a vehicle traction battery should prioritize temperature control to prevent the cell from spending extended time at high operating temperature. Simultaneously, discharging current should be limited when possible to reduce the polarization-driven parasitic reactions.

In the broader context, the methods and results outlined in this paper contribute to the safe and efficient use of the vehicle traction battery in small electric aircraft and drones. The accurate virtual prediction of thermal behavior and aging enables engineers to design better batteries, select appropriate materials, and implement more intelligent thermal management strategies. Future work in my planned research line will extend the present modeling framework to battery packs composed of multiple cells, account for inter-cell temperature differences, and incorporate additional degradation mechanisms such as lithium plating at low temperatures and cathode material dissolution at high cutoff voltages. The final aim is to develop a digital twin of the vehicle traction battery that can guide in-situ control decisions over the complete lifetime of the system.

In conclusion, the thermal and aging behavior of the vehicle traction battery represents a complex multiphysics interplay of transport phenomena, chemical reactions, and heat transfer. Experiments alone are insufficient to understand the whole picture; simulation-based tools are essential. My study establishes a reliable, validated multiscale modeling platform that not only explains observed phenomena but also guides the optimization of electrodes, thermal systems, and operating protocols. The results provide a scientific foundation for safer and more durable vehicle traction battery systems in the emerging field of electric aviation.