The transition towards electrified transportation is fundamentally dependent on the performance, safety, and longevity of the energy storage system—the electric vehicle (EV) battery pack. As market demands push for faster charging, higher discharge rates, and increased energy density, the thermal management of these high-power EV battery packs becomes a critical engineering frontier. Effective thermal control is not merely an ancillary system; it is a core enabler that dictates the boundaries of power output, cycle life, and operational safety. The primary challenge lies in managing the significant and rapid heat generation during high-current operations, which, if uncontrolled, leads to accelerated degradation, reduced efficiency, and in extreme cases, thermal runaway. This necessitates the development of sophisticated cooling strategies capable of maintaining the entire EV battery pack within a narrow, optimal temperature window while ensuring exceptional temperature uniformity from cell to cell.
Among the various cooling methodologies—passive air cooling, phase change material (PCM) cooling, and active liquid cooling—the latter has emerged as the predominant solution for high-performance automotive applications. Air cooling, while simple, suffers from low heat capacity and poor thermal conductivity, making it inadequate for managing the heat flux from high-power-density cells. PCM systems offer excellent temperature homogenization but are often burdened by weight, cost, and limited heat absorption capacity over continuous, high-load cycles. In contrast, active liquid cooling strikes an optimal balance, offering superior heat transfer coefficients, compact system packaging, and precise thermal control, making it indispensable for modern high-power EV battery packs. The cooling performance of a liquid-based system is governed by a complex interplay of multiple design parameters. This study undertakes a systematic, parametric optimization of a cold plate-based liquid cooling system for a high-power EV battery pack, employing a combined approach of electro-thermal coupling simulation, Design of Experiments (DOE), and experimental validation to identify the optimal configuration that minimizes maximum temperature and temperature differentials.
Thermal Management Imperatives and Electro-Thermal Coupling
The electrochemical processes within a lithium-ion cell during charge and discharge are inherently exothermic. The heat generation rate ($q$) is a function of irreversible Joule heating and reversible entropic heat, classically described by Bernardi’s equation:
$$ q = \frac{1}{V_b} \left[ I (E_{OC} – V_{terminal}) – I T_b \frac{dE_{OC}}{dT_b} \right] $$
This can be simplified for practical engineering modeling to:
$$ q = \frac{I}{V_b} \left( I R – T_b \frac{dE_{OC}}{dT_b} \right) $$
where $I$ is the operating current, $V_b$ is the cell volume, $E_{OC}$ is the open-circuit voltage, $V_{terminal}$ is the terminal voltage, $T_b$ is the cell temperature, and $R$ is the total internal resistance. The term $I^2R$ represents the irreversible Joule loss, while $I T_b (dE_{OC}/dT_b)$ accounts for the reversible entropic heat. For high-power cells operating at discharge rates of 3C or higher, the $I^2R$ term dominates, leading to substantial heat flux. The internal resistance $R$ itself is not a constant; it varies with the cell’s State of Charge (SOC) and temperature, adding a layer of complexity to accurate thermal modeling. A precise characterization of $R = f(SOC, T)$ is therefore foundational.
For an EV battery pack to operate reliably, its thermal state must be strictly controlled. The generally accepted optimal operating temperature range for lithium-ion cells is between 25°C and 45°C. Prolonged operation below this range increases internal resistance and reduces available capacity, while operation above it accelerates parasitic side reactions and degradation mechanisms. More critically, excessive temperature or severe temperature gradients within the pack lead to several detrimental effects:
- Reduced Lifetime and Power Capability: Cells at higher temperatures within a module age faster than their cooler neighbors. This divergence in State of Health (SOH) leads to capacity and power imbalance, causing the pack to be limited by its weakest cell.
- Safety Hazards: Localized overheating can initiate exothermic decomposition reactions, potentially cascading into thermal runaway—a critical safety failure mode for any EV battery pack.
- Performance Inconsistency: A large temperature differential ($\Delta T$) across the pack causes significant differences in cell impedance and voltage under load, complicating the Battery Management System’s (BMS) state estimation and reducing the usable energy.
Consequently, the dual objectives of thermal management for a high-power EV battery pack are to maintain the peak temperature ($T_{max}$) below a safe threshold (e.g., 45°C) and to minimize the maximum temperature difference ($\Delta T_{max}$) to within a tight band, typically less than 5°C. This ensures balanced performance, longevity, and safety.
Development and Validation of an Electro-Thermal Simulation Model
To explore the design space efficiently, a high-fidelity three-dimensional electro-thermal coupled simulation model of a battery module was developed. The module consisted of five high-power pouch cells connected in a series-parallel configuration, with a liquid-cooled cold plate positioned between adjacent cells. The cold plate featured a simple, straight, dual-channel design. The model solves the coupled physics of electrical current distribution and conjugate heat transfer.
The heat generation within each cell, calculated using the modified Bernardi equation, served as a volumetric heat source in the energy equation. The heat transfer within the cell and through the various components (cell, thermal interface material, cold plate) is governed by Fourier’s law of conduction. The cooling fluid flow and convective heat transfer within the cold plate channels are modeled using the Navier-Stokes equations and energy equation. The thermo-physical properties of all materials are crucial inputs. The parameters for the cell and cooling system components are summarized in the table below.
| Component | Property | Value | Units |
|---|---|---|---|
| Lithium-ion Cell | Density ($\rho$) | 1646 | kg/m³ |
| Specific Heat Capacity ($C_p$) | 1118 | J/(kg·K) | |
| Thermal Conductivity ($k_x$, $k_y$, $k_z$) | 20, 20, 2 | W/(m·K) | |
| Nominal Voltage / Capacity | 3.7 / 210 | V / Ah | |
| Coolant (50% Glycol-Water) | Density ($\rho$) | 1072 | kg/m³ |
| Specific Heat Capacity ($C_p$) | 3201 | J/(kg·K) | |
| Thermal Conductivity ($k$) | 0.379 | W/(m·K) | |
| Dynamic Viscosity ($\mu$) | 0.00338 | Pa·s | |
| Aluminum Cold Plate | Density ($\rho$) | 2603 | kg/m³ |
| Specific Heat Capacity ($C_p$) | 904 | J/(kg·K) | |
| Thermal Interface Material | Density ($\rho$) | 1199 | kg/m³ |
| Specific Heat Capacity ($C_p$) | 1701 | J/(kg·K) | |
| Thermal Conductivity ($k$) | 2.0 | W/(m·K) |
Prior to module-level analysis, the single-cell electro-thermal model was rigorously calibrated and validated against experimental data. A High-Precision Pulse Characterization (HPPC) test was performed to map the internal resistance $R$ as a function of SOC at 25°C. Subsequently, discharge tests at 1C, 2.5C, and 5C rates were conducted in a controlled environmental chamber, with surface temperatures monitored using high-accuracy thermocouples. The simulation results for cell surface temperature evolution showed excellent agreement with experimental measurements across all discharge rates, with a maximum error of less than 7%, well within acceptable engineering tolerances. This validation established high confidence in the predictive capability of the modeling framework.
The full module simulation under a 3C continuous discharge rate, with initial baseline cooling parameters (coolant inlet temperature $T_{in}$ = 25°C, flow rate $V$ = 0.05 m/s), revealed the need for optimization. The predicted $T_{max}$ reached 50.6°C, and $\Delta T_{max}$ was 6.2°C, both exceeding the target specifications for a high-performance EV battery pack. The hot spot was localized at the central region of the cell surface, while the coolest area was near the tabs, highlighting an uneven cooling distribution.
Parametric Study via Orthogonal Experimental Design
Optimizing a multi-parameter system like a liquid-cooled EV battery pack through a full-factorial experiment (testing every possible combination of parameters) is computationally prohibitive. The orthogonal experimental design (OED) method provides a statistically sound framework to evaluate the influence of multiple factors and their interactions with a minimal number of simulation runs. Four critical design parameters were selected as factors for optimization:
- Coolant Inlet Temperature ($T$): Directly affects the temperature potential for heat transfer.
- Coolant Volumetric Flow Rate ($V$): Influences the convective heat transfer coefficient and the coolant’s temperature rise along the channel.
- Cooling Channel Width ($W$): Impacts flow distribution, pressure drop, and contact area with the cold plate.
- Cooling Channel Height ($H$): Affects the hydraulic diameter, flow velocity for a given flow rate, and structural space.
Each factor was assigned four levels, reflecting a realistic design range constrained by vehicle system capabilities (e.g., chiller capacity, pump power, packaging space). The $L_{16}(4^4)$ orthogonal array was chosen, requiring only 16 simulations to study the four factors at four levels each.
| Factor | Level 1 | Level 2 | Level 3 | Level 4 | Units |
|---|---|---|---|---|---|
| A: Coolant Temp. ($T$) | 15 | 20 | 25 | 30 | °C |
| B: Flow Rate ($V$) | 0.40 | 0.20 | 0.10 | 0.05 | m/s |
| C: Channel Width ($W$) | 4 | 5 | 6 | 7 | mm |
| D: Channel Height ($H$) | 4 | 5 | 6 | 7 | mm |
The 16 simulation runs were executed according to the orthogonal array, and the response variables $T_{max}$ and $\Delta T_{max}$ for the module were extracted. The results were then analyzed using range analysis ($R$-analysis) to determine the primary and secondary order of influence of each factor on the response targets. The principle is straightforward: for a given factor, calculate the average response ($k_i$) at each of its four levels. The range $R$ for that factor is the difference between the maximum and minimum $k_i$ values. A larger $R$ indicates that the factor has a greater influence on the response target.
| Factor | $k_1$ | $k_2$ | $k_3$ | $k_4$ | Range $R$ | Order of Influence |
|---|---|---|---|---|---|---|
| $T$ (Coolant Temp.) | 46.25 | 48.58 | 52.70 | 53.90 | 7.65 | 1 (Most Influential) |
| $V$ (Flow Rate) | 50.78 | 50.20 | 51.80 | 48.65 | 3.15 | 2 |
| $W$ (Channel Width) | 49.23 | 51.48 | 51.65 | 49.08 | 2.58 | 3 |
| $H$ (Channel Height) | 50.98 | 50.68 | 49.03 | 50.75 | 1.95 | 4 (Least Influential) |
The analysis for $T_{max}$ clearly shows that the coolant inlet temperature ($T$) is the overwhelmingly dominant factor, with a range $R_T = 7.65$ °C. This underscores the fundamental principle that the coolant temperature sets the lower bound for the cell temperature. The flow rate ($V$) is the second most significant factor. Based on the level means, the optimal combination for minimizing $T_{max}$ (denoted as Optimal Combination I) is derived by selecting the level for each factor that yields the lowest average $k_i$ value: $T_1$ (15°C), $V_4$ (0.05 m/s), $W_1$ (4 mm), $H_3$ (6 mm).
| Factor | $k_1$ | $k_2$ | $k_3$ | $k_4$ | Range $R$ | Order of Influence |
|---|---|---|---|---|---|---|
| $V$ (Flow Rate) | 6.23 | 5.98 | 9.40 | 6.20 | 3.43 | 1 (Most Influential) |
| $T$ (Coolant Temp.) | 5.98 | 7.93 | 6.85 | 7.05 | 1.95 | 2 |
| $H$ (Channel Height) | 6.70 | 6.33 | 6.65 | 8.13 | 1.80 | 3 |
| $W$ (Channel Width) | 7.13 | 6.93 | 6.48 | 7.28 | 0.80 | 4 (Least Influential) |
For $\Delta T_{max}$, the coolant flow rate ($V$) emerges as the most influential factor ($R_V = 3.43$ °C). This is logical because the flow rate determines the coolant’s temperature rise as it absorbs heat along the channel. A low flow rate leads to significant coolant warming, creating a large temperature gradient from the inlet to the outlet side of the EV battery pack, which translates into a high cell $\Delta T$. The coolant temperature ($T$) is the second key factor. The optimal combination for minimizing $\Delta T_{max}$ (Optimal Combination II) is: $V_2$ (0.20 m/s), $T_1$ (15°C), $H_2$ (5 mm), $W_3$ (6 mm).
To statistically confirm the significance of these findings, an Analysis of Variance (ANOVA) was performed on the orthogonal experimental data. The F-test confirmed that for $T_{max}$, factor $T$ (Coolant Temperature) had a statistically significant effect ($F_T > F_{critical}$ at the 0.1 level). Similarly, for $\Delta T_{max}$, factor $V$ (Flow Rate) was shown to have a statistically significant effect. This mathematical validation reinforces the conclusions drawn from the range analysis.
Comprehensive Optimization and Experimental Verification
The analysis yielded two distinct optimal combinations: one for lowest peak temperature (Combination I: $T_1V_4W_1H_3$) and one for best temperature uniformity (Combination II: $T_1V_2W_3H_2$). A holistic evaluation is required to select the single best configuration for the EV battery pack. Comparing the simulated performance of all 16 orthogonal trials plus these two derived combinations revealed that Combination I and Trial #1 (which happened to be $T_1V_1W_1H_1$) offered the best overall performance, both achieving a $T_{max}$ below 45°C.
A deeper dive into the temperature distribution was conducted. The surface temperature profile of the cells was analyzed by calculating the percentage of cell area within specific temperature bins. This analysis showed that while both Combination I and Trial #1 had similar $T_{max}$ and average temperature, Combination I exhibited a tighter temperature distribution and a lower average temperature. Its temperature profile was more concentrated around the mean, indicating superior thermal homogeneity. Given that the primary risk for a high-power EV battery pack is localized overheating, a design that minimizes both $T_{max}$ and $\Delta T_{max}$ is preferable, even if one metric is not the absolute minimum. Combination I excelled in this balanced approach, maintaining a low $T_{max}$ (44.8°C) while keeping $\Delta T_{max}$ at a manageable 4.8°C, thus meeting both key thermal specifications.
To validate the simulation-based optimization, a physical prototype of the battery module with cooling system parameters set to Optimal Combination I was fabricated. The module was instrumented with thermocouples at strategic locations: the coolant inlet, the geometric center of the top cell surface, and the front face center. The module was preconditioned and subjected to a continuous 3C discharge test within a thermal chamber set to 25°C. The experimentally measured temperatures were then compared to the simulation predictions for the same operational conditions.
| Measurement Point | Simulation Value (°C) | Experimental Value (°C) | Relative Error (%) |
|---|---|---|---|
| Point 1 (Top Surface Center) | 43.9 | 41.8 | 5.02 |
| Point 2 (Front Surface Center) | 42.8 | 40.9 | 4.65 |
| Point 3 (Coolant Inlet Region) | 40.8 | 38.1 | 7.09 |
The results demonstrate strong agreement between the simulated and experimental thermal behavior. The maximum error observed was 7.09%, which is acceptable for complex multi-physics engineering simulations involving electrochemical systems. The minor discrepancies can be attributed to simplifications in the model (e.g., homogeneous material properties for the layered cell, ideal thermal contact resistance), uncertainties in boundary conditions, and measurement instrument tolerances. The successful correlation validates the entire methodology—from the electro-thermal coupling model to the orthogonal experimental design and optimization process—as a reliable and effective tool for developing thermal management solutions for high-power EV battery packs.
Conclusion
This study presents a systematic framework for optimizing the liquid cooling system of a high-power electric vehicle battery pack. By integrating high-fidelity electro-thermal coupling simulation with the statistical rigor of orthogonal experimental design, the complex, multi-parameter optimization problem was efficiently solved. The key findings are:
- The coolant inlet temperature ($T$) is the most significant factor influencing the maximum temperature ($T_{max}$) of the EV battery pack. Lowering the coolant temperature is the most direct and effective way to reduce peak cell temperatures.
- The coolant flow rate ($V$) is the most significant factor influencing the maximum temperature difference ($\Delta T_{max}$) within the pack. A sufficiently high flow rate is necessary to limit the coolant temperature rise along the channel, thereby promoting temperature uniformity.
- While geometric parameters of the cooling channel (width $W$ and height $H$) have an effect, their influence on thermal performance is secondary compared to the operational parameters ($T$ and $V$) within the studied design space.
- The optimal configuration identified through this process (Combination I: $T=15°C$, $V=0.05 m/s$, $W=4 mm$, $H=6 mm$) successfully maintained the module within the target operational window ($T_{max} < 45°C$, $\Delta T_{max} < 5°C$) under a demanding 3C discharge, a critical requirement for any high-performance EV battery pack.
- The methodology was conclusively validated through experimental testing, with simulation results showing strong correlation to measured data.
This work demonstrates that a principled, parametric approach grounded in simulation and statistical design can rapidly converge on optimal thermal management designs. It provides engineers with a clear understanding of parameter sensitivity, enabling informed trade-offs between cooling performance, parasitic pump power, chiller load, and packaging constraints during the development of advanced, high-power EV battery packs. Future work could extend this approach to include transient driving cycles, incorporate aging effects on heat generation, and explore more complex cold plate topologies or hybrid cooling strategies.