The safety and performance of modern electric vehicles and energy storage systems are intrinsically linked to the behavior of their core component: the li-ion battery. During operation, electrical energy conversion is accompanied by heat generation. If this heat is not managed effectively, it can lead to accelerated degradation, reduced efficiency, and in extreme cases, thermal runaway—a critical safety hazard. Therefore, developing an accurate predictive model that couples the electrical and thermal behaviors of a li-ion battery is paramount for designing robust battery management and thermal management systems. This study focuses on establishing and validating a high-fidelity electro-thermal coupled model for a commercial 10 Ah pouch-type li-ion battery, providing a reliable tool for performance analysis and system optimization.
The internal structure of a li-ion battery is complex, comprising a cathode, anode, separator, and electrolyte. For modelling purposes, an equivalent circuit model (ECM) offers an effective compromise between computational complexity and accuracy for simulating external electrical characteristics. Among various ECMs, the second-order RC model is widely adopted for its ability to capture both the fast and slow polarization dynamics of a li-ion battery. This model consists of an open-circuit voltage (OCV) source, an ohmic resistor (R0), and two parallel resistor-capacitor (RC) branches (R1C1 and R2C2), as shown in the schematic. The governing equations based on Kirchhoff’s laws are:
$$U_t = U_{OC} – IR_0 – U_{p1} – U_{p2}$$
$$\frac{dU_{p1}}{dt} = -\frac{U_{p1}}{R_1 C_1} + \frac{I}{C_1}$$
$$\frac{dU_{p2}}{dt} = -\frac{U_{p2}}{R_2 C_2} + \frac{I}{C_2}$$
where \(U_t\) is the terminal voltage, \(U_{OC}\) is the open-circuit voltage, \(I\) is the current (positive for discharge), \(R_0\) is the ohmic resistance, and \(U_{p1}\), \(U_{p1}\), \(R_1\), \(C_1\), \(R_2\), \(C_2\) are the voltages, resistances, and capacitances of the two RC branches, respectively. This electrical model forms the foundation of our coupled framework.
Electrical Parameter Identification via HPPC Testing
The parameters of the second-order RC model for the li-ion battery are not constant; they vary with the battery’s state of charge (SOC) and temperature. To accurately capture these dependencies, Hybrid Pulse Power Characterization (HPPC) tests were conducted. The test platform integrated a high-precision battery cycler, a thermal chamber for precise temperature control, and a data acquisition system. The 10 Ah pouch li-ion battery (NCM811/Si-C chemistry) was first capacity-calibrated at different temperatures (25°C, 35°C, 45°C) to determine its actual capacity \(C_0\) at each condition. The HPPC test sequence involved stabilizing the battery at a specific SOC point, applying a 1C discharge pulse for 10 seconds, a rest period, followed by a 1C charge pulse for 10 seconds, and another rest. This sequence was repeated at SOC intervals from 100% down to nearly 0% at each target temperature. A sample voltage response from the 35°C test is illustrated below, showing the characteristic voltage steps during pulses and the relaxation thereafter.
The voltage response curves from the discharge pulses were analyzed using a least-squares fitting algorithm in MATLAB to extract the model parameters \(U_{OC}(SOC,T)\), \(R_0(SOC,T)\), \(R_1(SOC,T)\), \(C_1(SOC,T)\), \(R_2(SOC,T)\), and \(C_2(SOC,T)\). The identified parameters revealed clear trends: The \(U_{OC}\) profile was largely independent of temperature in the tested range. However, the resistances \(R_0\), \(R_1\), and \(R_2\) exhibited a strong temperature dependence, decreasing as temperature increased, which is characteristic of enhanced ion mobility and charge transfer kinetics in the li-ion battery. The polarization capacitances \(C_1\) and \(C_2\) generally increased with temperature. The variation with SOC was also distinct; for instance, \(R_0\) typically showed a U-shaped curve versus SOC. A summary of the parameter identification results is presented in the table below, showing values at selected SOC points for 25°C.
| Parameter | Symbol | Unit | SOC 90% | SOC 50% | SOC 10% |
|---|---|---|---|---|---|
| Open-Circuit Voltage | \(U_{OC}\) | V | 4.12 | 3.68 | 3.45 |
| Ohmic Resistance | \(R_0\) | mΩ | 2.1 | 1.8 | 2.5 |
| Polarization Resistance 1 | \(R_1\) | mΩ | 1.5 | 2.0 | 3.8 |
| Polarization Capacitance 1 | \(C_1\) | kF | 12.5 | 9.8 | 5.2 |
| Polarization Resistance 2 | \(R_2\) | mΩ | 3.0 | 4.5 | 8.0 |
| Polarization Capacitance 2 | \(C_2\) | kF | 120.0 | 150.0 | 95.0 |
Thermal Property Characterization
Accurate thermal parameters are equally critical for the electro-thermal model of the li-ion battery. The key properties include specific heat capacity (\(c_p\)) and anisotropic thermal conductivity (\(k_x\), \(k_y\), \(k_z\)).
The specific heat capacity was measured using an accelerated rate calorimeter (ARC) under near-adiabatic conditions. A heating foil was used to impart a known constant power \(P\) to the battery package. By measuring the temperature rise over time in the absence of significant heat loss, the specific heat capacity can be derived from the energy balance:
$$P = m c_p \frac{dT}{dt}$$
where \(m\) is the mass of the li-ion battery. The recorded temperature-time profile was fitted, and its derivative \(dT/dt\) was calculated. The results showed that \(c_p\) is temperature-dependent. A polynomial function was fitted to the data, and the average \(c_p\) over the 25-60°C range was calculated to be 1342.3 J/(kg·K).
$$c_p(T) = 0.00108T^2 + 0.89697T + 1309.82372 \quad \text{[J/(kg·K)]}$$
The thermal conductivity of the pouch li-ion battery is anisotropic due to its layered structure. The through-plane conductivity (\(k_z\)) is typically much lower than the in-plane conductivity (\(k_x = k_y\)). \(k_z\) was determined using a steady-state heat flux method based on a one-dimensional slab model:
$$k_z = \frac{q \cdot h}{\Delta T}$$
where \(q\) is the applied heat flux, \(h\) is the battery thickness, and \(\Delta T\) is the measured temperature difference across the thickness. The in-plane conductivity was identified inversely by combining experimental temperature data from a localized heating test with a finite element simulation. An optimization algorithm adjusted \(k_x\) in the simulation until the simulated temperature profile matched the experimental data. The final measured thermal properties for the li-ion battery are summarized below.
| Thermal Property | Symbol | Value | Unit |
|---|---|---|---|
| Average Specific Heat Capacity | \(c_p\) | 1342.3 | J/(kg·K) |
| Through-plane Thermal Conductivity | \(k_z\) | 0.86 | W/(m·K) |
| In-plane Thermal Conductivity | \(k_x\), \(k_y\) | 23.75 | W/(m·K) |
| Density | \(\rho\) | \(\sim 2200\) | kg/m³ |
Electro-Thermal Coupled Model Implementation
With all necessary parameters characterized, the electro-thermal coupled model was implemented. A three-dimensional geometric model of the pouch li-ion battery, including its tabs, was created in ANSYS Discovery. The volume was discretized into a polyhedral mesh of approximately 160,000 cells, ensuring mesh-independent results. The electrical behavior was governed by the second-order RC model, where the parameter lookup tables (functions of SOC and temperature) were integrated using a user-defined function. The heat generation rate (\(Q_{gen}\)) within the li-ion battery during operation is calculated from the electrical model outputs:
$$Q_{gen} = I(U_{OC} – U_t) – I T \frac{dU_{OC}}{dT}$$
The first term \(I(U_{OC} – U_t)\) represents the total irreversible Joule and polarization losses. The second term \(I T (dU_{OC}/dT)\) accounts for the reversible entropic heat. This \(Q_{gen}\) is introduced as a volumetric heat source in the thermal model. The thermal response is solved via the three-dimensional heat conduction equation:
$$\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q_{gen}$$
where \(k\) is the anisotropic thermal conductivity tensor. The model was solved in ANSYS Fluent, with the electrical and thermal solutions coupled at each time step: the temperature affects the ECM parameters, which in turn affect the heat generation rate.
Model Validation Under Adiabatic Discharge
To validate the coupled model without the uncertainty of external convection boundaries, an adiabatic discharge test was used as the benchmark. The li-ion battery was discharged at a 1/3 C rate from 100% SOC in a highly insulated environment at an initial temperature of 25°C. The simulation was set up with adiabatic boundary conditions on all surfaces.
First, the voltage discharge curve was compared. The simulated terminal voltage closely tracked the experimental data throughout the discharge process, from the initial drop, through the plateau, to the final rapid decrease. The average relative error between the simulated and experimental voltage was only 1.38%, demonstrating high electrical fidelity.
Second, the thermal response was validated. Temperature was monitored at two points on the battery surface: Point 1 at the center and Point 2 offset from the center. The simulated temperature rise at both points showed excellent agreement with the experimental measurements. The average relative error was 3.55% for Point 1 and 3.98% for Point 2. These errors are well within the acceptable range for engineering analysis of li-ion battery behavior. The close match validates the accuracy of the characterized thermal properties (\(c_p\), \(k\)) and the coupling methodology. The temperature contours from the simulation also provided insights into the thermal gradient within the li-ion battery, which is minimal under low-rate adiabatic discharge but becomes crucial for higher rate scenarios.
Conclusion
This work successfully established and validated a comprehensive electro-thermal coupled model for a 10 Ah pouch-type li-ion battery. The core achievements include the detailed experimental characterization of both electrical (via HPPC tests) and thermal (specific heat, anisotropic conductivity) parameters essential for modelling the li-ion battery. The implementation of a second-order RC electrical model, coupled with a three-dimensional thermal model using empirically derived properties, resulted in a high-fidelity simulation framework. Validation under adiabatic 1/3 C discharge conditions confirmed the model’s accuracy, with voltage prediction errors around 1.4% and temperature prediction errors below 4%. This model serves as a powerful virtual tool for analyzing the thermal behavior of li-ion batteries under various operating conditions, optimizing cell design, and developing effective thermal management strategies, thereby contributing significantly to the advancement of safe and efficient energy storage systems.