In the pursuit of enhancing the safety and efficiency of electric vehicles (EVs), the thermal management of lithium-ion battery packs has emerged as a critical area of research. As the heart of an EV’s power system, the EV battery pack must operate within a narrow temperature range to ensure optimal performance, longevity, and safety. Excessive heat can accelerate degradation, while low temperatures reduce power output and capacity. Therefore, developing accurate simulation models for thermal management is paramount for designing robust cooling systems and predicting real-world behavior. In this study, we adopt a multiscale coupled approach spanning from cell to module to pack levels to establish a high-fidelity thermal management simulation model for lithium-ion EV battery packs. This work integrates electrical and thermal dynamics through experimental parameter identification and computational fluid dynamics (CFD) simulations, validated against empirical data. The focus is on capturing the intricate interactions within an EV battery pack under varying operating conditions, with the goal of providing insights for engineering applications.
The foundation of our modeling effort lies in the “cell-module-pack” hierarchy, which allows for a detailed representation of both local and global phenomena. At the cell level, we employ a second-order RC equivalent circuit model to describe the electrical behavior, as it balances complexity and accuracy in simulating dynamic responses. The model parameters are identified through hybrid pulse power characterization (HPPC) tests across a temperature range of 15–45 °C and different states of charge (SOC). At the pack level, a three-dimensional thermal model of the EV battery pack is constructed using NX for computer-aided design and STAR-CCM+ for CFD analysis. This model includes detailed geometries of cells, modules, cooling plates, and fluid channels. We validate the simulation results against experimental data from thermal-humidity tests, demonstrating errors below 3% for both temperature and pressure metrics. This paper elaborates on the methodology, parameter identification, simulation setup, and validation, with an emphasis on the integration of multiscale modeling for EV battery pack thermal management.
The importance of thermal management for EV battery packs cannot be overstated. Lithium-ion batteries, while offering high energy density and long cycle life, are sensitive to temperature variations. In an EV battery pack, uneven temperature distribution can lead to cell-to-cell imbalances, reducing overall efficiency and safety. For instance, localized hotspots may trigger thermal runaway, a catastrophic failure mode. Conversely, cold environments increase internal resistance, limiting power delivery and range. Thus, a comprehensive simulation framework that accounts for electrical-thermal coupling is essential. Our approach addresses this by combining circuit-based electrical models with CFD-based thermal models, enabling predictive analysis of an EV battery pack’s behavior under diverse scenarios. The following sections detail the components of this framework, supported by tables and formulas to summarize key aspects.
The cell-level model serves as the building block for the entire EV battery pack simulation. We use a second-order RC equivalent circuit, which consists of an open-circuit voltage source, an ohmic resistor, and two RC parallel networks representing polarization effects. This model captures both short-term and long-term dynamics, making it suitable for simulating charge-discharge cycles in an EV battery pack. The governing equations are derived from Kirchhoff’s laws, expressing the terminal voltage as a function of current and internal states. Let $I$ denote the current, $U_{OC}$ the open-circuit voltage, $R_0$ the ohmic resistance, $R_1$ and $C_1$ the first polarization resistance and capacitance, and $R_2$ and $C_2$ the second polarization resistance and capacitance. The voltages across the RC networks, $U_{C1}$ and $U_{C2}$, evolve according to:
$$ I = \frac{U_{C1}}{R_1} + C_1 \frac{dU_{C1}}{dt} $$
$$ I = \frac{U_{C2}}{R_2} + C_2 \frac{dU_{C2}}{dt} $$
The terminal voltage $U$ is given by:
$$ U = U_{OC} + I R_0 + U_{C1} + U_{C2} $$
Combining these, the time-domain response for a step current input can be expressed as:
$$ U = U_{OC} + I R_0 + I R_1 (1 – e^{-t/\tau_1}) + I R_2 (1 – e^{-t/\tau_2}) $$
where $\tau_1 = R_1 C_1$ and $\tau_2 = R_2 C_2$ are time constants. This formulation allows for parameter identification from experimental data, as discussed later. The model’s accuracy is critical for predicting the heat generation within each cell, which feeds into the thermal analysis of the EV battery pack.
To parameterize the cell model, we conducted HPPC tests on individual lithium iron phosphate (LiFePO4) cells, which are commonly used in EV battery packs due to their stability and cost-effectiveness. The tests spanned temperatures from 15 °C to 45 °C at intervals of 10 °C, covering SOC levels from 0% to 100%. The experimental setup included a charge-discharge cycler, a thermal chamber for temperature control, and data acquisition systems. Current and voltage profiles were recorded at a high sampling rate. Using MATLAB’s Model-Based Calibration Toolbox, we identified the parameters $U_{OC}(SOC, T)$, $R_0(SOC, T)$, $R_1(SOC, T)$, $C_1(SOC, T)$, $R_2(SOC, T)$, and $C_2(SOC, T)$ as functions of SOC and temperature $T$. This dependency is vital for capturing the behavior of an EV battery pack under real driving conditions, where temperatures fluctuate. Table 1 summarizes the nominal specifications of the cell used in our EV battery pack.
| Parameter | Value |
|---|---|
| Chemistry | Lithium Iron Phosphate (LiFePO4) |
| Nominal Capacity at 25 °C | 173 Ah |
| Nominal Voltage | 3.2 V |
| Operating Temperature Range | -20 °C to 60 °C |
| Mass | Approx. 3.5 kg |
| Dimensions | 200 mm × 150 mm × 25 mm |
The parameter identification process involved fitting the model to the HPPC data via optimization algorithms. The root mean square error (RMSE) for voltage prediction was below 5 mV across all temperatures, confirming the model’s fidelity. For example, at 15 °C, the RMSE was 2.1 mV, as shown in the validation curve. These identified parameters are then embedded into the cell model for subsequent pack-level simulations. The dependency of parameters on SOC and temperature is encapsulated in lookup tables, enabling efficient computation during dynamic simulations of the EV battery pack.
Moving to the pack level, the EV battery pack in this study comprises 63 cells arranged in a 3S1P configuration (3 series connections of 21 parallel cells, totaling 21 series cells). This configuration is typical for medium-voltage EV battery packs, balancing voltage and current requirements. The three-dimensional geometry was created in NX, including cells, busbars, cooling plates with fluid channels, and thermal interface materials. The cooling system uses a liquid-based approach with a single inlet and multiple parallel branches to ensure uniform cooling across the EV battery pack. The model was then imported into STAR-CCM+ for meshing and CFD analysis. The mesh generation process emphasized accuracy at interfaces between solids and fluids, with refinement near cell surfaces and channel walls. A polyhedral mesh type was chosen for its balance of quality and computational efficiency. Table 2 details the mesh parameters for different components of the EV battery pack.
| Component | Mesh Type | Base Size (mm) | Number of Cells |
|---|---|---|---|
| Battery Module | Polyhedral | 10 | 1,827,000 |
| Cooling Pipes | Polyhedral | 3 | 2,613,666 |
| Thermal Sheets | Polyhedral | 4 | 713,977 |
| Total | – | – | 5,154,643 |
A mesh independence study was conducted to ensure that results were not sensitive to grid resolution. By progressively reducing the base size, we increased the mesh count to approximately 4.2 million cells, at which point changes in temperature and pressure drop were less than 0.8%. Thus, the mesh configuration in Table 2 was deemed sufficient. The material properties assigned in the simulation are listed in Table 3, reflecting typical values for an EV battery pack construction.
| Region | Specific Heat Capacity (J/(kg·K)) | Thermal Conductivity (W/(m·K)) | Density (kg/m³) |
|---|---|---|---|
| Solid Domain (Aluminum) | 1,306.0 | 2.96 | 2,460.0 |
| Fluid Domain (Water) | 4,181.72 | 0.620271 | 997.561 |
The boundary conditions for the CFD simulation were set based on typical operating scenarios for an EV battery pack. The cooling fluid inlet was defined as a mass flow inlet with a rate of 0.667 kg/s and a temperature of 16 °C, simulating active cooling. The outlet was set as a pressure outlet at 0 Pa gauge pressure. The external environment was modeled as a static air domain at 25 °C, though natural convection was neglected in favor of focusing on the liquid cooling system. The heat generation within each cell was computed from the electrical model using the formula:
$$ Q = I^2 R_0 + I (U_{OC} – U) $$
where $Q$ is the heat generation rate per cell, derived from Joule heating and polarization losses. This heat source was distributed uniformly within each cell volume in the simulation, assuming isotropic properties. The coupling between electrical and thermal models was achieved through co-simulation: the electrical model provided heat generation rates based on current and SOC, while the thermal model updated temperatures that feedback into the electrical parameters (since $R_0$, $R_1$, etc., depend on temperature). This iterative process captures the electro-thermal coupling essential for accurate EV battery pack simulations.
For experimental validation, we constructed a test bench for the EV battery pack, incorporating a climate chamber, a battery cycler, temperature sensors, and pressure gauges. The pack was subjected to charge-discharge cycles at a constant current of 50 A in an environment controlled at 25 °C and 65% relative humidity. Temperature sensors were placed at critical locations within the pack, including cell centers and cooling channel interfaces, to monitor $T_{\text{max}}$, $T_{\text{min}}$, and $T_{\text{avg}}$. Additionally, the pressure drop across the cooling plate was measured at various flow rates using a冷水机 and flow meters. The thermal management strategy implemented in tests was as follows: cooling is activated when $T_{\text{max}} \geq 28\,^\circ\text{C}$ and $T_{\text{avg}} \geq 25\,^\circ\text{C}$; heating or self-circulation is used when $T_{\text{max}} \leq 25\,^\circ\text{C}$ and $T_{\text{avg}} \leq 22\,^\circ\text{C}$. This logic mimics real-world controllers for EV battery packs.
The simulation results from STAR-CCM+ were processed to obtain temperature and pressure fields. The temperature distribution across the EV battery pack showed a gradient from the inlet to outlet, with maximum temperatures near the center and lower temperatures at the edges due to cooling. The pressure distribution in the cooling channels indicated minor losses in parallel branches. Quantitative comparisons between simulation and experiment are presented in Table 4, highlighting the accuracy of our model for the EV battery pack.
| Metric | Experimental Value | Simulation Value | Relative Error |
|---|---|---|---|
| Maximum Temperature (°C) | 41.0 | 40.5 | 1.2% |
| Minimum Temperature (°C) | 22.0 | 21.7 | 1.4% |
| Average Temperature (°C) | 31.5 | 31.1 | 1.3% |
| Cooling Line Pressure Drop at 0.667 kg/s (kPa) | 8.7 | 8.97 | 3.1% |
| Voltage RMSE (mV) | – | 2.1 | – |
The errors are all below 3%, demonstrating that the multiscale model effectively predicts the thermal behavior of the EV battery pack. The slight discrepancies may stem from assumptions in material homogeneity, contact resistances, or sensor tolerances. Notably, the simulation captures the dynamic temperature rise during cycling, as shown in the comparison plots. The temperature profile in experiments exhibited a step-like pattern due to discrete data logging (every 10 minutes), whereas the simulation provided a continuous curve. Despite this, the overall trends align closely, validating the model’s utility for designing and optimizing thermal management systems for EV battery packs.
Further analysis of the results reveals insights into the performance of the EV battery pack under thermal stress. The second-order RC model accurately replicates the voltage sag during high-current pulses, which is crucial for predicting power capabilities. In the thermal domain, the CFD simulation shows that the cooling system maintains most cells within a 10 °C range, reducing the risk of hotspots. However, areas with lower flow velocity exhibit slightly higher temperatures, suggesting potential improvements in channel design. The pressure drop simulations correlate well with measurements, indicating that the model can be used to size pumps and piping for EV battery pack cooling systems. These findings underscore the importance of integrated modeling for achieving balanced performance in EV battery packs.
To elaborate on the electro-thermal coupling, we can express the heat generation more formally. For a cell in an EV battery pack, the total heat generation rate $Q_{\text{total}}$ comprises irreversible and reversible components:
$$ Q_{\text{total}} = I^2 R_0 + I \sum_{i=1}^{2} U_{Ci} + I T \frac{dU_{OC}}{dT} $$
where the first term is Joule heating, the second term represents polarization losses (from the RC networks), and the third term is the reversible heat due to entropy changes. In our simulation, we included the first two terms, as the entropy contribution is relatively small for LiFePO4 cells. The temperature dependence of parameters is modeled via polynomial fits from experimental data. For instance, $R_0(T)$ for a typical cell in the EV battery pack can be approximated as:
$$ R_0(T) = a_0 + a_1 T + a_2 T^2 $$
where $a_0$, $a_1$, and $a_2$ are coefficients obtained from curve fitting. Such expressions enhance the model’s realism across operating conditions.
The multiscale approach also facilitates module-level analysis within the EV battery pack. By aggregating cell models into modules, we can assess inter-cell variations and their impact on pack performance. For example, if one cell ages faster due to temperature disparities, it can be simulated by adjusting its parameters in the circuit model. This capability is vital for prognostic health management of EV battery packs. Additionally, the 3D thermal model can be extended to include air cooling or phase-change materials for hybrid thermal management systems, providing a versatile platform for innovation.
In terms of computational efficiency, the combined model strikes a balance between detail and speed. The electrical model is solved using ordinary differential equations with fast solvers, while the CFD simulation leverages parallel processing in STAR-CCM+. For real-time applications, such as battery management system (BMS) development, reduced-order models could be derived from this high-fidelity framework. Nevertheless, the current setup is suitable for offline design and validation of EV battery pack thermal systems.
Looking ahead, the methodologies presented here can be adapted to next-generation battery chemistries, such as solid-state or lithium-sulfur, which pose different thermal challenges. The core principles of multiscale modeling and experimental validation remain applicable. Moreover, as EV battery packs evolve towards higher energy densities and faster charging, thermal management will become even more critical, necessitating advanced simulation tools like ours.
In conclusion, this study demonstrates a comprehensive framework for thermal management simulation of lithium-ion EV battery packs, integrating cell-level electrical dynamics with pack-level thermal hydraulics. Through rigorous parameter identification and experimental validation, we have shown that the model predicts temperature and pressure distributions with errors under 3%. The use of tables and formulas summarizes key data and relationships, facilitating understanding and replication. This work contributes to the safer and more efficient design of EV battery packs, underscoring the value of multiscale coupled approaches in tackling complex engineering problems. Future work will explore transient scenarios, such as fast charging or extreme ambient conditions, to further refine the model for real-world EV applications.
The success of this modeling effort hinges on the accurate representation of each scale within the EV battery pack. From the microscopic electrochemical processes captured by the RC networks to the macroscopic fluid flow in cooling channels, every element plays a role. By embracing this holistic view, engineers can optimize thermal management systems to extend battery life, enhance safety, and improve the overall performance of electric vehicles. As the automotive industry shifts towards electrification, such simulation capabilities will be indispensable for developing robust and reliable EV battery packs that meet the demands of consumers and regulators alike.