In recent years, the rapid development of renewable energy and the increasing demand for grid stability have highlighted the importance of efficient energy storage solutions. Among various technologies, the battery energy storage system (BESS) has emerged as a critical component due to its high energy density, long cycle life, and flexibility in application. However, the thermal management of large-capacity lithium iron phosphate batteries within a BESS remains a significant challenge, as maintaining optimal operating temperatures and minimizing temperature variations between cells are essential for ensuring safety, performance, and longevity. In this study, we propose a composite thermal management approach that integrates liquid cooling with phase change materials (PCM) to address these issues in a BESS. We begin by developing a three-dimensional electro-thermal coupling model for a 280Ah battery, extending it to a module comprising 52 series-connected cells to analyze temperature distribution under high discharge rates. Our results demonstrate that the composite system effectively reduces the maximum temperature difference and average temperature compared to standalone liquid cooling, thereby enhancing the thermal performance of the BESS.
The electro-thermal coupling model for the battery energy storage system (BESS) is based on a lumped parameter approach that simplifies the complex electrochemical processes into key parameters influencing voltage and heat generation. The battery voltage, \( E_{\text{lib}} \), is expressed as:
$$ E_{\text{lib}} = E_{\text{OCV}}(SOC_{\text{ave}}) + \eta_{\text{IR}} + \eta_{\text{act}} + \eta_{\text{conc}} $$
where \( E_{\text{OCV}} \) is the open-circuit voltage as a function of the average state of charge (SOC), \( \eta_{\text{IR}} \) represents the ohmic overpotential, \( \eta_{\text{act}} \) denotes the activation overpotential, and \( \eta_{\text{conc}} \) accounts for the concentration overpotential. The ohmic overpotential is given by:
$$ \eta_{\text{IR}} = \eta_{\text{IR,1C}} \frac{I_{\text{cell}}}{I_{\text{1C}}} $$
Here, \( \eta_{\text{IR,1C}} \) is the ohmic loss at 1C rate, \( I_{\text{cell}} \) is the actual current, and \( I_{\text{1C}} \) is the standard 1C current. The activation overpotential is modeled as:
$$ \eta_{\text{act}} = \frac{2RT}{F} \sinh^{-1} \left( \frac{I_{\text{cell}}}{2J_{\text{1C}}} \right) $$
where \( R \) is the universal gas constant (8.314 J/(mol·K)), \( T \) is the temperature, \( F \) is Faraday’s constant (96485.33289 C/mol), and \( J_{\text{1C}} \) is the exchange current density at 1C rate. The concentration overpotential is derived from:
$$ \eta_{\text{conc}} = -\tau \frac{\partial E_{\text{OCV}}}{\partial SOC} \frac{dSOC}{dt} $$
with \( \tau \) as the diffusion time constant, and \( SOC_{\text{surf}} \) and \( SOC_{\text{ave}} \) representing the surface and average SOC, respectively.
The thermal model incorporates heat generation from both ohmic losses in connectors and electrochemical reactions within the battery. The total heat generation rate, \( Q \), is:
$$ Q = Q_{\text{ohm}} + Q_{\text{ech}} $$
where \( Q_{\text{ohm}} = I_{\text{cell}}^2 R_s \) (with \( R_s \) as the internal resistance) and \( Q_{\text{ech}} = I_{\text{cell}} \left( T \frac{\partial E_{\text{OCV}}}{\partial T} + \eta_{\text{act}} + \eta_{\text{conc}} \right) \). The energy balance equation for the battery is:
$$ \rho_p C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q $$
Here, \( \rho_p \) is the density, \( C_p \) is the specific heat capacity, and \( k \) is the thermal conductivity tensor.
For the liquid cooling system in the battery energy storage system (BESS), we consider a serpentine channel design within a cold plate attached to the module base. The cooling fluid, a 50% ethylene glycol-water mixture, operates in turbulent flow conditions, as determined by the Reynolds number:
$$ Re = \frac{\rho_l v L}{\mu} $$
where \( \rho_l \) is the fluid density, \( v \) is the velocity, \( L \) is the characteristic length, and \( \mu \) is the dynamic viscosity. Given the high Reynolds numbers (exceeding 4000), the k-ω turbulence model is employed. The governing equations for fluid flow and heat transfer include the continuity equation:
$$ \nabla \cdot (\rho_l \mathbf{u}) = 0 $$
the Reynolds-averaged Navier-Stokes equation:
$$ \rho_l (\mathbf{u} \cdot \nabla) \mathbf{u} = \nabla \cdot \left[ -P \mathbf{I} + \mu (\nabla \mathbf{u} + (\nabla \mathbf{u})^T) – \frac{2}{3} \mu (\nabla \cdot \mathbf{u}) \mathbf{I} \right] + \mathbf{F} $$
and the energy equation for the fluid:
$$ \rho_l C_l \frac{\partial T}{\partial t} + \rho_l C_l \mathbf{u} \cdot \nabla T = \nabla \cdot (k_l \nabla T) $$
For the cold plate, the heat conduction equation is:
$$ \rho_s C_s \frac{\partial T}{\partial t} = \nabla \cdot (k_s \nabla T) $$
In the PCM-based thermal management for the battery energy storage system (BESS), we utilize a paraffin-based material that undergoes solid-solid phase transitions. The energy equation for the PCM is:
$$ \rho_p \frac{\partial H_p}{\partial t} = \nabla \cdot (k_p \nabla T_p) $$
where \( H_p = L_p \beta + h_p \) is the enthalpy, \( L_p \) is the latent heat, \( \beta \) is the liquid fraction, and \( h_p = \int_{T_0}^{T_p} C_p \, dT \) is the sensible enthalpy. The liquid fraction \( \beta \) is defined as:
$$ \beta = \begin{cases} 0 & T_p < T_s \\ \frac{T_p – T_s}{T_l – T_s} & T_s \leq T_p \leq T_l \\ 1 & T_p > T_l \end{cases} $$
with \( T_s \) and \( T_l \) as the solidus and liquidus temperatures, respectively.
To validate our model, we established an experimental platform for a 280Ah lithium iron phosphate battery, which is a key component of the BESS. The test setup includes a battery cycler, a thermal chamber, voltage and temperature sensors, and an accelerating rate calorimeter (ARC). The battery was subjected to 1C charge-discharge cycles at a constant temperature of 25°C, and parameters such as voltage, current, and surface temperature were recorded. The measured properties are summarized in Table 1.
| Parameter | Value |
|---|---|
| Capacity (Ah) | 296.3 |
| Specific Heat Capacity (J/kg·K) | 965 |
| Density (kg/m³) | 2091 |
| Thermal Conductivity (W/m·K) | 10.63, 7.74, 2.55 (anisotropic) |
The simulation results for the single battery under natural convection at 1C rate show close agreement with experimental data. The voltage and temperature profiles were compared using error metrics such as root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), as detailed in Table 2. The formulas for these metrics are:
$$ \text{RMSE} = \sqrt{\frac{1}{n} \sum_{t=1}^{n} (y_t – \hat{y}_t)^2} $$
$$ \text{MAE} = \frac{1}{n} \sum_{t=1}^{n} |y_t – \hat{y}_t| $$
$$ \text{MAPE} = \frac{100\%}{n} \sum_{t=1}^{n} \left| \frac{y_t – \hat{y}_t}{y_t} \right| $$
where \( y_t \) and \( \hat{y}_t \) are the experimental and simulated values, respectively, and \( n \) is the number of samples.
| Parameter | RMSE | MAE | MAPE (%) |
|---|---|---|---|
| Voltage (V) | 0.03354 | 0.02768 | 0.890 |
| Center Surface Temperature (°C) | 1.63269 | 1.37506 | 3.556 |
| Vent Temperature (°C) | 1.36035 | 1.19267 | 2.948 |
Extending the model to a 52-cell series-connected module in the BESS, we analyzed the temperature distribution under natural convection during 1C and 1.5C discharge. The results indicate that cells in the central region experience higher temperatures due to limited heat dissipation, with maximum temperature differences reaching 9.76°C and 12.98°C for 1C and 1.5C rates, respectively. This underscores the necessity for effective thermal management in a BESS to prevent thermal runaway and ensure uniformity.
For the liquid cooling system, we evaluated different inlet velocities (0.1 m/s, 1 m/s, and 2 m/s) of the cooling fluid. The performance metrics, including average temperature, maximum temperature difference, and pressure drop across the channel, are summarized in Table 3. The pressure drop \( \Delta P \) is calculated based on the Darcy-Weisbach equation for turbulent flow:
$$ \Delta P = f \frac{L}{D} \frac{\rho_l v^2}{2} $$
where \( f \) is the friction factor, \( L \) is the channel length, and \( D \) is the hydraulic diameter.
| Inlet Velocity (m/s) | Average Temperature (°C) | Max Temperature Difference (°C) | Pressure Drop (Pa) |
|---|---|---|---|
| 0.1 | 63.15 | 3.97 | Low |
| 1.0 | 54.94 | 2.64 | Moderate |
| 2.0 | 54.13 | 2.45 | High |
At 1 m/s, the cooling effect is nearly optimal, with a significant reduction in temperature compared to natural convection. Increasing the velocity to 2 m/s only marginally improves cooling but substantially increases the pressure drop, leading to higher energy consumption for pumping. Thus, for the BESS, a velocity of 1 m/s is chosen as a balance between performance and cost.
In the composite thermal management approach, PCM is incorporated into the gaps between cells in the module, replacing air. The PCM’s phase change behavior absorbs heat during discharge, reducing temperature peaks and improving uniformity. Under 1.5C discharge, the composite system achieves an average temperature of 51.93°C and a maximum temperature difference of 1.4°C, which are lower than those of standalone liquid cooling by 3.01°C and 1.1°C, respectively. The temperature evolution of the PCM at different heights shows distinct phases: pre-phase change (sensible heating), phase change (latent heat absorption), and post-phase change (temperature rise). This highlights the PCM’s role in enhancing thermal inertia and uniformity in the BESS.
In conclusion, our study demonstrates that the composite thermal management system, integrating liquid cooling and PCM, effectively addresses the thermal challenges in a battery energy storage system (BESS). By leveraging the strengths of both active and passive cooling, it ensures operational safety and efficiency, particularly under high discharge rates. Future work could explore PCMs with broader phase change intervals and enhanced thermal conductivity to further optimize the BESS performance. This approach provides a robust framework for thermal management in large-scale energy storage applications, contributing to the reliability and longevity of BESS installations.