I selected a high-rate pouch lithium-ion power battery designed for small unmanned aerial vehicles and studied its electrochemical behavior, thermal characteristics, and aging behavior through a combined experimental and modeling approach. The cell uses a lithium cobalt oxide positive electrode and a graphite negative electrode, and its operating conditions are much more aggressive than those of a conventional stationary cell. In many ways, the requirements resemble those of an electric vehicle battery pack, because both applications demand high energy density, high power capability, acceptable safety, and predictable degradation. However, the small pouch cell I studied experiences very frequent cycling and high-rate discharge, so its thermal and aging behavior must be understood in greater detail.
1. Motivation and Research Scope
I began from the practical observation that lithium-ion batteries have become central to clean transportation, portable electronics, aerospace systems, and electric vehicle battery pack architectures. Their advantages include high energy density, low self-discharge, zero local emissions, and relatively long cycle life. Nevertheless, temperature strongly controls their performance. A cell that operates at low temperature suffers from sluggish kinetics, reduced electrolyte conductivity, higher internal resistance, and lower available capacity. A cell that operates at high temperature may deliver higher power temporarily, but side reactions accelerate and the cell ages faster. In extreme cases, heat accumulation can lead to thermal runaway. Therefore, I focused on the coupled relationship among electrical current, heat generation, temperature distribution, and aging.
My study targeted a small UAV power battery because such batteries are often discharged at rates between 2C and 10C, while the cooling area is limited. The same concern appears in an electric vehicle battery pack, where high-rate charging, fast acceleration, and high ambient temperature can create non-uniform temperature fields. I therefore combined controlled experiments with an electrochemical-thermal coupling model and then extended the model to include solid electrolyte interphase growth. In this way, I could analyze not only terminal voltage and surface temperature but also internal heat sources, electrode-level contributions, and capacity fade.
2. Battery Structure, Working Principle, and Heat Generation
The cell I used is a wound pouch cell. Its main components are a positive electrode, a negative electrode, a separator, electrolyte, current collectors, tabs, and an aluminum-laminated film casing. The positive active material is lithium cobalt oxide, and the negative active material is graphite. During discharge, lithium ions leave the negative electrode, travel through the electrolyte and separator, and enter the positive electrode. During charge, the process reverses. I express the main reactions as follows:
$$LiCoO_2 + C_n \rightleftharpoons Li_{1-x}CoO_2 + Li_xC_n$$
$$LiCoO_2 \rightleftharpoons Li_{1-x}CoO_2 + xLi^+ + xe^-$$
$$C_n + xLi^+ + xe^- \rightleftharpoons Li_xC_n$$
In an ideal cell, only lithium intercalation and deintercalation occur. In a real cell, heat is produced by reversible and irreversible processes. I summarize the heat sources in the table below.
| Heat source | Physical origin | Sign in discharge | Key dependence |
|---|---|---|---|
| Reaction heat, \(Q_r\) | Entropy change of lithium intercalation and deintercalation | Can be positive or negative | Current, temperature, entropy coefficient |
| Ohmic heat, \(Q_o\) | Electronic and ionic resistance in electrodes, electrolyte, and tabs | Always positive | Current squared, resistance |
| Polarization heat, \(Q_p\) | Electrochemical and concentration polarization | Always positive | Overpotential, local current density |
| Side-reaction heat, \(Q_s\) | SEI growth, electrolyte decomposition, and other parasitic reactions | Usually positive | Temperature, SOC, cycle number |
The total heat generation rate can be written as
$$Q_{total}=Q_r+Q_o+Q_p+Q_s$$
The reversible heat is related to the entropy coefficient by
$$Q_r = I T \frac{\partial U}{\partial T}$$
where \(I\) is current, \(T\) is absolute temperature, and \(\partial U/\partial T\) is the entropy coefficient. The irreversible heat includes ohmic and polarization contributions and is always exothermic during both charge and discharge, although its magnitude changes with state of charge, temperature, and current.
I measured the entropy coefficient of the full cell and found that it varies between approximately \(-1.1\,\mathrm{mV\,K^{-1}}\) and \(0.29\,\mathrm{mV\,K^{-1}}\). It is negative from 0% to 35% depth of discharge, positive from 35% to 50% depth of discharge, and negative again with a rapidly increasing magnitude from 50% to 100% depth of discharge. This behavior is important because it explains why the surface temperature of the cell does not rise monotonically. In the middle of discharge, the reversible heat can become endothermic, so the surface temperature may pause or even decrease before rising again near the end of discharge.
3. Experimental Platform and Test Matrix
I built a battery test platform consisting of a multichannel battery cycler, a programmable temperature and humidity chamber, a multichannel temperature logger, and a computer for data acquisition. The temperature chamber provided ambient temperatures from \(-10^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\). K-type thermocouples were attached to the cell surface with high-temperature tape. The cell was connected to the cycler inside the chamber, and all cables passed through sealed ports to reduce thermal disturbance. I used constant-current constant-voltage charging and constant-current discharging. I also performed capacity calibration, direct-current internal resistance tests, entropy coefficient tests, and accelerated cycle aging tests.
| Test | Condition or variable | Purpose |
|---|---|---|
| Capacity calibration | 1C charge and 1C discharge at \(25^\circ\mathrm{C}\) | Determine initial usable capacity and state of health |
| Rate discharge | 1C, 2C, 3C, and 4C at \(25^\circ\mathrm{C}\) | Study rate effects on voltage, capacity, and temperature |
| Temperature discharge | \(-10^\circ\mathrm{C}\), \(0^\circ\mathrm{C}\), \(10^\circ\mathrm{C}\), \(25^\circ\mathrm{C}\), and \(40^\circ\mathrm{C}\) at 1C | Study ambient temperature effects |
| DCIR | HPPC pulses at different SOC and ambient temperatures | Measure ohmic and polarization resistance |
| Entropy coefficient | Open-circuit voltage at several temperatures and SOC values | Separate reversible heat from irreversible heat |
| Accelerated aging | 1C charge and 3C discharge at \(25^\circ\mathrm{C}\) | Obtain capacity fade and model validation data |
The direct-current internal resistance was calculated from the voltage response to a current pulse. I used the 10 s resistance, defined as
$$R_{DC}=\frac{U_A-U_C}{I}$$
where \(U_A\) is the voltage before the pulse, \(U_C\) is the voltage after the pulse, and \(I\) is the pulse current. The ohmic resistance and polarization resistance can be separated as
$$R_{\Omega}=\frac{U_A-U_B}{I},\qquad R_p=\frac{U_B-U_C}{I}$$
where \(U_B\) is the voltage at the beginning of the pulse. The entropy coefficient was obtained from the slope of open-circuit voltage with respect to temperature at a fixed state of charge:
$$\frac{\partial U}{\partial T}\approx \frac{U(T_2)-U(T_1)}{T_2-T_1}$$
4. Experimental Results and Interpretation
I first studied the effect of discharge rate. As the discharge rate increased from 1C to 4C, the initial discharge voltage decreased, the discharge capacity decreased, and the surface temperature increased. The reason is that higher current increases electrochemical polarization, concentration polarization, and ohmic loss. The cell cannot fully utilize its active material before the cutoff voltage is reached. I summarize the observed behavior below.
| Discharge rate at \(25^\circ\mathrm{C}\) | Initial voltage trend | Discharge capacity trend | Peak surface temperature |
|---|---|---|---|
| 1C | Highest | Highest | Approximately \(29.2^\circ\mathrm{C}\) |
| 2C | Lower | Lower | Higher than 1C |
| 3C | Lower | Lower | Higher than 2C |
| 4C | Lowest | Lowest | Approximately \(42.3^\circ\mathrm{C}\) |
The surface temperature curve often showed an N-shaped trend. In the early stage of discharge, heat generation is moderate, and heat dissipation can keep the surface temperature low. In the middle stage, the reversible heat may become endothermic or small, so the temperature may flatten or decrease. Near the end of discharge, polarization and irreversible heat increase sharply, so the temperature rises rapidly. This behavior is important for an electric vehicle battery pack because it shows that battery thermal behavior cannot be estimated from current alone.
I then studied ambient temperature. At lower ambient temperature, the initial voltage and discharge capacity decreased, while the absolute temperature rise increased. For example, at \(-10^\circ\mathrm{C}\), the 1C discharge capacity was approximately \(2179\,\mathrm{mAh}\), which is lower than the nominal capacity. At \(40^\circ\mathrm{C}\), the 1C discharge capacity was approximately \(2280\,\mathrm{mAh}\). The temperature rise above ambient was larger at low temperature because the internal resistance and polarization were larger.
| Ambient temperature | 1C discharge capacity | Temperature rise trend | Main reason |
|---|---|---|---|
| \(-10^\circ\mathrm{C}\) | Approximately \(2179\,\mathrm{mAh}\) | Largest rise, about \(7.5^\circ\mathrm{C}\) | High polarization and low electrolyte conductivity |
| \(0^\circ\mathrm{C}\) | Lower than room temperature | Large rise | Reduced kinetics |
| \(25^\circ\mathrm{C}\) | Reference | Moderate rise | Balanced kinetics and transport |
| \(40^\circ\mathrm{C}\) | Approximately \(2280\,\mathrm{mAh}\) | Smallest rise, about \(3.4^\circ\mathrm{C}\) | Improved kinetics and lower resistance |
The DCIR results showed that internal resistance increases significantly as ambient temperature decreases. At \(10^\circ\mathrm{C}\) and above, the DCIR was relatively stable over a wide SOC range. At lower temperature, the resistance increased, especially near low SOC. This observation matches the increased heat generation at low temperature. In an electric vehicle battery pack, low-temperature operation therefore requires either preheating or careful current limitation.
The accelerated aging test was performed with 1C charge and 3C discharge. After 450 cycles, the 1C discharge capacity decreased to approximately 92.6% of the initial value. The discharge voltage curve shifted downward as aging progressed, and the discharge time became shorter. This behavior resembles the low-temperature discharge response, but it is caused by irreversible capacity loss and impedance growth rather than by low temperature alone.
| Aging condition | Cycle number | Capacity retention | Observed voltage trend |
|---|---|---|---|
| 1C charge, 3C discharge, \(25^\circ\mathrm{C}\) | 0 | 100% | Reference discharge curve |
| Same | 450 | Approximately 92.6% | Lower voltage plateau and shorter discharge time |
5. Electrochemical Thermal Coupling Model
I established a pseudo-two-dimensional electrochemical model coupled with a three-dimensional thermal model. The electrochemical model describes lithium transport in solid particles and electrolyte, charge conservation, and interfacial reaction kinetics. The thermal model describes heat conduction inside the cell, heat convection and radiation at the surface, and heat generation from electrochemical reactions, ohmic loss, polarization, and tabs. I used COMSOL Multiphysics to solve the coupled system.
The solid-phase lithium diffusion in spherical active particles is described by 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
$$\left.\frac{\partial c_s}{\partial r}\right|_{r=0}=0$$
and at the particle surface it is
$$-D_s\left.\frac{\partial c_s}{\partial r}\right|_{r=R}=J$$
The interfacial reaction current density is calculated from the Butler-Volmer equation:
$$J=i_0\left[\exp\left(\frac{\alpha_a F\eta}{RT}\right)-\exp\left(-\frac{\alpha_c F\eta}{RT}\right)\right]$$
The overpotential is
$$\eta=\phi_s-\phi_l-U_{eq}-J R_{film}$$
The exchange current density is
$$i_0=Fk c_{s,max}^{1-\alpha_c}c_{s,surf}^{\alpha_c}\left(c_{s,max}-c_{s,surf}\right)^{\alpha_a}$$
Lithium transport in the electrolyte is described by
$$\varepsilon_e\frac{\partial c_e}{\partial t}=\frac{\partial}{\partial x}\left(D_e^{eff}\frac{\partial c_e}{\partial x}\right)+\frac{1-t_+}{F}a_v J$$
where the effective diffusion coefficient includes the Bruggeman correction:
$$D_e^{eff}=D_e\varepsilon_e^{b}$$
The temperature dependence of important parameters is included. For example, solid diffusion coefficients, reaction rate constants, electrolyte diffusion coefficients, electrolyte conductivity, and transference number are all functions of temperature. I used Arrhenius-type relations of the form
$$\Theta(T)=\Theta_{ref}\exp\left[\frac{E_a}{R}\left(\frac{1}{T_{ref}}-\frac{1}{T}\right)\right]$$
where \(\Theta\) represents a kinetic or transport parameter and \(E_a\) is its activation energy. This coupling is essential because the electrochemical model generates heat, while the thermal model changes the electrochemical parameters. The coupling is therefore two-way.
The thermal energy balance is
$$\rho C_p\frac{\partial T}{\partial t}=\nabla\cdot(\lambda\nabla T)+Q_{ohm}+Q_{pol}+Q_{rea}+Q_{tab}+Q_{Rfilm}$$
The polarization heat, ohmic heat, and reaction heat are written as
$$Q_{pol}=a_v J\eta$$
$$Q_{ohm}=\sigma_s^{eff}\left(\nabla\phi_s\right)^2+\sigma_e^{eff}\left(\nabla\phi_e\right)^2+\frac{2RT\sigma_e^{eff}}{F}\left(1-t_+\right)\nabla\ln c_e\cdot\nabla\phi_e$$
$$Q_{rea}=a_v J T\frac{\partial U}{\partial T}$$
The tab heat is approximated by
$$Q_{tab}=\frac{I^2}{A_{tab}}\left(\frac{1}{\sigma_{tab}}+\frac{1}{\sigma_c}\right)$$
The surface heat exchange is
$$Q_{diss}=hA_c(T-T_{amb})+\varepsilon\sigma A_c(T^4-T_{amb}^4)$$
Because a pouch cell is a layered structure, its thermal conductivity is anisotropic. I used different effective conductivities in the in-plane and through-plane directions:
$$k_x=k_y=\frac{L_p\lambda_p+L_n\lambda_n+L_{sep}\lambda_{sep}+L_{p,cc}\lambda_{p,cc}+L_{n,cc}\lambda_{n,cc}}{L_{bat}}$$
$$k_z=\frac{L_{bat}}{\frac{L_p}{\lambda_p}+\frac{L_n}{\lambda_n}+\frac{L_{sep}}{\lambda_{sep}}+\frac{L_{p,cc}}{\lambda_{p,cc}}+\frac{L_{n,cc}}{\lambda_{n,cc}}}$$
The electrochemical and thermal parameters I used are summarized below. I obtained some values from my own measurements and estimated others from published models for similar lithium cobalt oxide and graphite systems.
| Parameter | Negative electrode | Separator | Positive electrode | Negative current collector | Positive current collector |
|---|---|---|---|---|---|
| Material | Graphite | Polymer separator | LiCoO2 | Cu | Al |
| Thickness | \(34.5\,\mu\mathrm{m}\) | \(8\,\mu\mathrm{m}\) | \(26\,\mu\mathrm{m}\) | \(6\,\mu\mathrm{m}\) | \(13\,\mu\mathrm{m}\) |
| Particle radius | \(5\,\mu\mathrm{m}\) | Not applicable | \(1\,\mu\mathrm{m}\) | Not applicable | Not applicable |
| Solid volume fraction | 0.58 | Not applicable | 0.48 | Not applicable | Not applicable |
| Electrolyte volume fraction | 0.332 | 0.45 | 0.30 | Not applicable | Not applicable |
| Maximum solid concentration | \(31507\,\mathrm{mol\,m^{-3}}\) | Not applicable | \(56250\,\mathrm{mol\,m^{-3}}\) | Not applicable | Not applicable |
| Initial solid concentration | \(25330\,\mathrm{mol\,m^{-3}}\) | Not applicable | \(19020\,\mathrm{mol\,m^{-3}}\) | Not applicable | Not applicable |
| Initial electrolyte concentration | \(1200\,\mathrm{mol\,m^{-3}}\) | Not applicable | Not applicable | ||
| Solid conductivity | \(100\,\mathrm{S\,m^{-1}}\) | Not applicable | \(10\,\mathrm{S\,m^{-1}}\) | \(6\times10^7\,\mathrm{S\,m^{-1}}\) | \(3.8\times10^7\,\mathrm{S\,m^{-1}}\) |
| Density | \(1347\,\mathrm{kg\,m^{-3}}\) | \(900\,\mathrm{kg\,m^{-3}}\) | \(2500\,\mathrm{kg\,m^{-3}}\) | \(8910\,\mathrm{kg\,m^{-3}}\) | \(2700\,\mathrm{kg\,m^{-3}}\) |
| Specific heat capacity | \(1437.4\,\mathrm{J\,kg^{-1}\,K^{-1}}\) | \(1842.44\,\mathrm{J\,kg^{-1}\,K^{-1}}\) | \(745.76\,\mathrm{J\,kg^{-1}\,K^{-1}}\) | \(386\,\mathrm{J\,kg^{-1}\,K^{-1}}\) | \(905\,\mathrm{J\,kg^{-1}\,K^{-1}}\) |
| Thermal conductivity | \(1.04\,\mathrm{W\,m^{-1}\,K^{-1}}\) | \(0.344\,\mathrm{W\,m^{-1}\,K^{-1}}\) | \(1.58\,\mathrm{W\,m^{-1}\,K^{-1}}\) | \(401\,\mathrm{W\,m^{-1}\,K^{-1}}\) | \(238\,\mathrm{W\,m^{-1}\,K^{-1}}\) |
I validated the model against charge and discharge voltage curves and surface temperature curves. The maximum voltage error was about 5.56%, and the maximum temperature error was about 4.25%. Both errors occurred at the highest rate, 4C. The agreement at 1C, 2C, and 3C was better. I therefore concluded that the model is accurate enough to analyze internal heat generation and temperature distribution.
| Validation item | Condition | Maximum relative error |
|---|---|---|
| Charge voltage | 0.5C at \(25^\circ\mathrm{C}\) | Small, within model tolerance |
| Discharge voltage | 1C to 4C at \(25^\circ\mathrm{C}\) | Approximately 5.56% at 4C |
| Surface temperature | 1C to 4C at \(25^\circ\mathrm{C}\) | Approximately 4.25% at 4C |
6. Thermal Characteristics under Different Conditions
Using the validated electrochemical thermal coupling model, I analyzed the internal heat generation of the cell. At 25°C, I compared 1C, 2C, and 4C discharge. The total heat generation rate increased with discharge rate. The reversible heat fraction decreased, while the irreversible heat fraction increased. At 1C, the electrochemical reaction heat accounted for about 58% of the total heat, whereas at 4C it decreased to about 31%. At the same time, the polarization heat increased significantly. This means that at low rate the thermal behavior is strongly influenced by reversible heat, while at high rate the thermal behavior is dominated by irreversible heat.
| Discharge rate at \(25^\circ\mathrm{C}\) | Reaction heat fraction | Ohmic heat fraction | Polarization heat fraction | Dominant heat source |
|---|---|---|---|---|
| 1C | Approximately 58% | Small | Moderate | Reaction heat and irreversible heat balanced |
| 2C | Lower | Higher | Higher | Irreversible heat increasing |
| 4C | Approximately 31% | Approximately 6% | Approximately 63% | Irreversible heat dominated |
I also compared the contributions of the positive electrode, negative electrode, and separator. The positive electrode was the main heat source over the range I studied. However, as the discharge rate increased, the negative electrode and separator contributions increased. The separator contribution was small because it mainly generated ohmic heat. The negative electrode generated more irreversible heat than the positive electrode, while the positive electrode generated much more reversible heat. Near the end of discharge, the negative reversible heat changed sign and became exothermic because lithium accumulation and local over-discharge effects became more important.
When I varied ambient temperature at 2C discharge, I found that lower ambient temperature increased both the average heat generation rate and the temperature rise. For example, when ambient temperature decreased from 25°C to 5°C, the average heat generation rate increased from about \(190.4\,\mathrm{kW\,m^{-3}}\) to about \(235.4\,\mathrm{kW\,m^{-3}}\). When ambient temperature increased from 25°C to 45°C, the average heat generation rate decreased to about \(173.7\,\mathrm{kW\,m^{-3}}\). The irreversible heat fraction was larger at low temperature, while the reaction heat fraction increased at high temperature. This again shows that an electric vehicle battery pack must consider ambient temperature when designing cooling and heating strategies.
| Ambient temperature at 2C | Average heat generation rate | Temperature rise trend | Dominant heat fraction |
|---|---|---|---|
| \(5^\circ\mathrm{C}\) | Approximately \(235.4\,\mathrm{kW\,m^{-3}}\) | Largest | Irreversible heat |
| \(25^\circ\mathrm{C}\) | Approximately \(190.4\,\mathrm{kW\,m^{-3}}\) | Moderate | Mixed |
| \(45^\circ\mathrm{C}\) | Approximately \(173.7\,\mathrm{kW\,m^{-3}}\) | Smallest | Reaction heat increasing |
I next studied structural parameters. Increasing positive and negative electrode thickness increased the total heat generation rate and the irreversible heat fraction. The ohmic heat fraction increased most clearly, because longer transport paths increase ionic and electronic resistance. Increasing particle radius also increased heat generation. The irreversible heat was more sensitive to particle size than the reversible heat. Before about 25% depth of discharge, the reversible heat was almost independent of particle size. These results are useful for designing high-energy cells and for understanding the thermal behavior of an electric vehicle battery pack.
| Structural change | Effect on voltage | Effect on total heat | Effect on irreversible heat fraction |
|---|---|---|---|
| Increase electrode thickness | Lower voltage plateau | Higher heat rate | Increases |
| Increase particle radius | Higher polarization | Higher heat rate | Increases |
| Increase positive electrode thickness | More capacity but higher resistance | Higher heat rate | Increases |
| Increase negative electrode thickness | Similar trend | Higher heat rate | Increases |
Temperature uniformity is another critical issue. I used the difference between core temperature and surface temperature as an indicator. I studied the effects of surface convection coefficient, cell thickness, and through-plane thermal conductivity. A higher convection coefficient reduces surface temperature but increases the core-to-surface temperature difference. At 10C discharge with \(h=50\,\mathrm{W\,m^{-2}\,K^{-1}}\), the maximum temperature difference was about 3.5°C. At \(h=200\,\mathrm{W\,m^{-2}\,K^{-1}}\), it increased to about 4.8°C. Increasing cell thickness also increased both peak temperature and temperature difference. At 8C discharge, every 1 mm increase in thickness raised the peak temperature by about 1°C and the maximum temperature difference by about 0.6°C. When the through-plane thermal conductivity was increased from 1.11 to \(3\,\mathrm{W\,m^{-1}\,K^{-1}}\), the core-to-surface temperature difference decreased. At 10C and \(h=200\,\mathrm{W\,m^{-2}\,K^{-1}}\), the maximum difference decreased to about 2.6°C.
| Factor | Condition | Effect on peak temperature | Effect on core-to-surface difference |
|---|---|---|---|
| Convection coefficient | 10C, \(h=50\) to \(200\,\mathrm{W\,m^{-2}\,K^{-1}}\) | Decreases surface temperature | Increases from about 3.5°C to 4.8°C |
| Cell thickness | 8C, thickness increase of 1 mm | Increases by about 1°C | Increases by about 0.6°C |
| Through-plane conductivity | 10C, \(k_z=1.11\) to \(3\,\mathrm{W\,m^{-1}\,K^{-1}}\) | Smaller gradient | Decreases to about 2.6°C |
| Discharge rate | 1C to 10C | Strong increase | Strong increase |
7. Aging Model and Aging Behavior
After validating the electrochemical thermal model, I extended it to include solid electrolyte interphase growth on the negative electrode. This is a major aging mechanism at moderate and high temperature. The SEI layer consumes lithium inventory and increases impedance. I modeled the SEI growth as a parasitic electrochemical reaction:
$$S+Li^++e^-\rightarrow P_{SEI}$$
The SEI reaction current density is
$$J_{SEI}=-\frac{c_{EC}Fk_{SEI}\exp\left(-\frac{\alpha_{c,SEI}F\eta_{SEI}}{RT}\right)}{1+\frac{k_{SEI}\delta_{film}}{D_{EC}}\exp\left(-\frac{\alpha_{c,SEI}F\eta_{SEI}}{RT}\right)}$$
The SEI overpotential is
$$\eta_{SEI}=\phi_s-\phi_l-U_{SEI}-\frac{J_{total}R_{film}}{a_{v,neg}}$$
The total negative electrode current density is the sum of the intercalation current and the SEI current:
$$J_{total}=J+J_{SEI}$$
To account for graphite particle expansion and SEI cracking, I included an expansion factor:
$$J_{SEI}=HK J_{SEI,0}$$
where \(K\) depends on the negative electrode state of charge:
$$K=
\begin{cases}
2, & 0.0<soc_n<0.3\\ &="" 0,="" 0.3\leq="" 0.7\leq="" 1,="" <p="" \end{cases}$$="" soc_n<0.7\\="" soc_nThe SEI concentration and film thickness evolve as
$$\frac{\partial c_{SEI}}{\partial t}=-\frac{a_{v,neg}J_{SEI}}{F}$$
$$\frac{\partial \delta_{film}}{\partial t}=-\frac{J_{SEI}M_{SEI}}{F\rho_{SEI}a_{v,neg}}$$
The film resistance is
$$R_{film}=\frac{\delta_{0,SEI}+\delta_{film}}{\kappa_{SEI}}$$
The heat generated by the SEI film is
$$Q_{Rfilm}=a_{v,neg}J_{total}^2R_{film}$$
The total heat generation in the aging model becomes
$$Q_{total}=Q_{ohm}+Q_{pol}+Q_{rea}+Q_{tab}+Q_{Rfilm}$$
| SEI parameter | Value |
|---|---|
| Electrolyte EC concentration | \(4541\,\mathrm{mol\,m^{-3}}\) |
| SEI reaction transfer coefficient | 0.5 |
| SEI molar mass | \(0.16\,\mathrm{kg\,mol^{-1}}\) |
| SEI density | \(1690\,\mathrm{kg\,m^{-3}}\) |
| SEI ionic conductivity | \(5\times10^{-6}\,\mathrm{S\,m^{-1}}\) |
| Graphite expansion factor | 6.7 |
| Initial SEI thickness | \(1\,\mathrm{nm}\) |
| SEI equilibrium potential | \(0.4\,\mathrm{V}\) |
I validated the aging model against the measured capacity fade and discharge voltage curves. The simulated capacity retention matched the experimental data well over 450 cycles. The maximum relative error was about 1.1% in the first 200 cycles and about 0.68% between 200 and 450 cycles. The discharge voltage curves at the beginning, after 50 cycles, and after 400 cycles also followed the measured trends, with the largest deviation around the middle voltage plateau.
| Aging validation item | Cycle range | Maximum relative error |
|---|---|---|
| Capacity retention | 0 to 200 cycles | Approximately 1.1% |
| Capacity retention | 200 to 450 cycles | Approximately 0.68% |
| Discharge voltage | Beginning, 50, and 400 cycles | Largest near middle plateau |
I then analyzed heat generation during aging. The negative electrode polarization heat increased with aging, while the positive electrode polarization heat remained relatively stable. This is because the SEI layer grows on the negative electrode, so the negative electrode interface becomes more resistive. As a result, the total heat generation rate increased. The average heat generation rate at 2C increased from about \(190.4\,\mathrm{kW\,m^{-3}}\) for the fresh cell to about \(278.4\,\mathrm{kW\,m^{-3}}\) for the aged cell. The reaction heat fraction decreased from about 48.4% to 33.3%, while the polarization heat fraction increased from about 48.2% to 64.7%. The negative electrode heat fraction increased from about 45% to 60%, so the negative electrode became the main heat source. This is a critical finding for an electric vehicle battery pack, because aged cells generate more heat and may require more aggressive cooling.
| Cell state | Average heat generation rate at 2C | Reaction heat fraction | Polarization heat fraction | Negative electrode heat fraction |
|---|---|---|---|---|
| Fresh cell | Approximately \(190.4\,\mathrm{kW\,m^{-3}}\) | Approximately 48.4% | Approximately 48.2% | Approximately 45% |
| Aged cell after 450 cycles | Approximately \(278.4\,\mathrm{kW\,m^{-3}}\) | Approximately 33.3% | Approximately 64.7% | Approximately 60% |
I also studied how cycle rate and ambient temperature influence aging. Higher cycle rate accelerated capacity fade. At 1C, 2C, and 3C cycling, the 3C case showed the fastest fade. After 450 cycles, the difference between 1C and 3C was about 2% in relative capacity. The SEI resistance and SEI thickness followed the same trend: they grew quickly in the early cycles and then slowed down. Higher cycle rate increased both SEI resistance and SEI thickness. This occurs because high-rate operation increases polarization, stress, and local reaction heterogeneity, which promotes SEI growth and can also damage the SEI layer.
| Cycle rate at \(25^\circ\mathrm{C}\) | Capacity fade after 450 cycles | SEI resistance trend | SEI thickness trend |
|---|---|---|---|
| 1C | Slowest fade | Lowest increase | Lowest increase |
| 2C | Moderate fade | Moderate increase | Moderate increase |
| 3C | Fastest fade | Highest increase | Highest increase |
Ambient temperature had an even stronger effect. At 450 cycles, the relative capacity was about 92.6% at 25°C but only about 78.9% at 40°C. When the temperature increased from 25°C to 40°C, the SEI resistance increased by about \(0.073\,\Omega\,\mathrm{m^2}\), and the SEI thickness increased by about \(363\,\mathrm{nm}\). Thus, the aging behavior was more sensitive to ambient temperature than to discharge rate in my study. For an electric vehicle battery pack, this means that thermal management should not only limit peak temperature during fast charging or acceleration but also control long-term average temperature.
| Ambient temperature at 1C cycling | Capacity retention after 450 cycles | SEI resistance increase | SEI thickness increase |
|---|---|---|---|
| \(25^\circ\mathrm{C}\) | Approximately 92.6% | Reference | Reference |
| \(32^\circ\mathrm{C}\) | Lower than at 25°C | Higher | Higher |
| \(40^\circ\mathrm{C}\) | Approximately 78.9% | Approximately \(0.073\,\Omega\,\mathrm{m^2}\) higher | Approximately \(363\,\mathrm{nm}\) higher |
8. Discussion and Practical Implications
My results show that lithium-ion power batteries must be understood as coupled electrochemical, thermal, and aging systems. The electrochemical reactions generate heat, the heat changes transport and kinetic parameters, and the changed parameters alter both performance and degradation. In an electric vehicle battery pack, this coupling becomes even more important because many cells are connected in series and parallel, and cell-to-cell variations can cause uneven current and temperature distributions. A cell that is slightly hotter or more aged may generate more heat, which can further increase its temperature and accelerate its aging.
I found that positive electrode heat generation dominates in the fresh cell, but negative electrode heat generation becomes more important after aging because of SEI growth. This means that aging diagnosis should not rely only on total capacity fade. It should also consider changes in internal resistance and heat generation. For an electric vehicle battery pack, a battery management system should estimate not only state of charge and state of health but also the thermal state. If the pack operates at high rate or low temperature, the irreversible heat fraction increases, and the risk of local overheating becomes larger.
From a design perspective, I identified several practical directions. First, increasing the through-plane thermal conductivity can reduce the core-to-surface temperature difference. Second, reducing cell thickness can shorten the heat conduction path and improve temperature uniformity, although it may reduce volumetric energy density. Third, surface cooling should be designed together with internal thermal conductivity. Strong surface cooling alone can lower the surface temperature but may increase the internal temperature gradient. Fourth, avoiding operation above about 80% depth of discharge can reduce the high heat generation rate near the end of discharge. Fifth, limiting average temperature and high-rate cycling can slow SEI growth and extend life. These conclusions apply to electric vehicle battery pack design as well as to high-power UAV batteries.
9. Conclusions
I studied a high-rate pouch lithium-ion power battery by combining experiments and electrochemical thermal coupling simulations. I built a test platform and measured discharge performance, temperature rise, DCIR, entropy coefficient, and capacity fade. I then established a coupled electrochemical thermal model, validated it against voltage and temperature data, and used it to analyze internal heat generation. I further extended the model with SEI growth to study aging behavior and heat generation after aging.
My main conclusions are as follows. First, increasing discharge rate or decreasing ambient temperature reduces initial voltage and usable capacity while increasing surface temperature rise. Second, the entropy coefficient causes the surface temperature to show an N-shaped trend, and reversible heat is important at low rate or high temperature. Third, irreversible heat dominates at high rate or low temperature, and the positive electrode is the main heat source in the fresh cell. Fourth, increasing electrode thickness or particle radius increases total heat generation and the irreversible heat fraction. Fifth, temperature uniformity is worsened by high convection, high rate, and large cell thickness, but it can be improved by increasing through-plane thermal conductivity. Sixth, SEI growth increases negative electrode polarization heat and makes the negative electrode the primary heat source after aging. Seventh, higher cycle rate and higher ambient temperature accelerate capacity fade and SEI growth. Among these factors, ambient temperature had a stronger effect than cycle rate in my aging study.
Overall, my work provides a detailed understanding of the thermal and aging behavior of a high-rate lithium-ion power battery. The findings can support thermal management, electrode design, and lifetime prediction for UAV batteries and for an electric vehicle battery pack. In future work, I would include additional aging mechanisms such as lithium plating, expand the model to cell modules and full packs, and validate the model under more extreme high-rate and low-temperature conditions.
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