In recent years, the rapid advancement of high-tech industries and the improvement in living standards have led to a surging demand for energy. To reduce dependence on non-renewable resources, developing new energy structures is imperative. Under this new paradigm, efficient energy storage and conversion devices are crucial for achieving centralized, intelligent, and efficient management and application. The concept of smart energy storage has emerged accordingly. A battery energy storage system serves as a critical component in power grids, acting as a distribution, generation, transmission, and end-user device, significantly enhancing the grid’s adaptability to large-scale energy integration.
Currently, dominant energy storage technologies in the market can be broadly categorized into four types: (1) pumped hydro storage, (2) thermal storage, (3) electrochemical storage, and (4) mechanical storage. Lithium-ion batteries, with their high specific energy, high energy density, low self-discharge rate, and high power output, have captured a substantial market share in both power battery and battery energy storage system applications. However, lithium-ion batteries in practical use may face thermal runaway issues. During charge and discharge cycles, heat generation from internal resistance, electrode polarization, and chemical reactions can cause a rapid temperature rise. This increase further accelerates reactions, creating a positive feedback loop between heat generation and temperature elevation. When temperatures exceed certain limits, batteries may experience swelling, leakage, or even explosion, posing safety risks. Additionally, lithium dendrite formation on the negative electrode during charging can shorten battery lifespan. Therefore, an in-depth study of heat generation behavior in batteries is essential for ensuring safety and extending longevity in battery energy storage systems.
Standalone photovoltaic systems typically use lead-acid batteries as storage devices, but their lifespan is often limited to 6–7 years. Consequently, employing lithium-ion batteries to construct battery energy storage systems has become a key research focus. This study aims to investigate the heat generation behavior of energy storage lithium batteries, specifically lithium iron phosphate (LiFePO4) batteries commonly used in photovoltaic or UPS applications. Through numerical simulation, we analyze the effects of specific heat capacity, heat generation power, and temperature distribution on battery heat generation under given thermophysical parameters during 1C constant current discharge. Using ICEM CFD and ANSYS Fluent software, we describe the temperature fields of the battery casing and interior, followed by error analysis with experimental data. This work lays a theoretical foundation for mitigating thermal issues like thermal runaway in battery energy storage systems.
The internal structure of a lithium-ion battery primarily consists of positive and negative electrodes, terminals, a separator, an insulating ring, and a casing. A cylindrical lithium-ion battery can be conceptually unrolled to show its layered structure. Essentially, a lithium-ion battery is a concentration cell, with carbon materials (typically graphite) as the negative electrode and lithium-containing compounds as the positive electrode. Lithium ions move through the electrolyte to the battery’s negative electrode, embedding into the micro-pores of the carbon layers. During discharge, these ions migrate back to the positive electrode. This shuttling of lithium ions between electrodes earns them the nickname “rocking-chair batteries.”
According to Bernardi’s uniform heat generation theory, due to the layered structure of lithium-ion batteries, heat generation can be considered uniform throughout the battery. The entire battery can be treated as an anisotropic whole, neglecting internal electrolyte flow and weak thermal radiation. Thus, the heat transfer process in lithium-ion batteries is regarded as solid heat conduction occurring in a homogeneous anisotropic material. In the following sections, we establish a model based on calculated thermophysical parameters to study the heat generation behavior in battery energy storage systems.
To simulate the thermal behavior, we first determine key thermophysical parameters. The battery used is a 26650-type lithium iron phosphate battery with a nominal voltage of 3.6 V, nominal capacity of 2200 mAh, mass of 39 g, diameter of 18 mm, height of 65 mm, and density of 2.99 g/cm³. The experimental environment temperature is 27°C, with thermocouples placed at the battery’s middle and both ends. Wires are soldered to the terminals, and the assembled battery is placed in a fixed container. The testing platform includes a battery temperature tester and a computer.
The thermophysical parameters involved in the cylindrical lithium-ion battery heat generation model include specific heat capacity \(C\), heat generation power \(P_h\), mass \(M\), total reaction time \(T\), and battery density \(\rho\). Based on the physical definition of specific heat capacity, we have:
$$C = \frac{Q_h}{M (t – t_0)}$$
where \(t_0\) and \(t\) are the initial and maximum temperatures during 1C discharge, and \(Q_h\) is the total heat generated. After 1C discharge, the state of charge (SOC) is negligible in industry standards. Experimental measurements show a total heat generation of 2378.44 J, initial temperature of 27°C, maximum temperature of 42.9°C, maximum temperature difference of 15.9°C, and discharge duration of 2834 s. Thus, \(C = 3.84 \, \text{J/(g·K)}\).
The heat generation power is calculated as:
$$P_h = \frac{Q_h}{T}$$
yielding \(P_h = 0.84 \, \text{W}\). For the battery’s self-absorption of heat, due to complex materials and structure treated as anisotropic, the thermal conduction process is intricate. In a Cartesian coordinate system, the heat flux densities along the x, y, and z axes can be expressed as:
$$q_x = -k_x \frac{\partial T}{\partial x}$$
$$q_y = -k_y \frac{\partial T}{\partial y}$$
$$q_z = -k_z \frac{\partial T}{\partial z}$$
Solving these, the thermal conductivity is found to be \(k = 1.37 \, \text{W/(m·K)}\). The convective heat transfer coefficient equation is:
$$h = \frac{q}{A \Delta T}$$
where \(h\) is the convective heat transfer coefficient, \(q\) is the heat transfer rate, \(A\) is the surface area, and \(\Delta T\) is the temperature difference. This gives \(h = 12 \, \text{W/(m²·K)}\). These parameters are summarized in Table 1.
| Parameter Name | Value |
|---|---|
| Nominal Voltage (V) | 3.6 |
| Nominal Capacity (mAh) | 2200 |
| Diameter (mm) | 18 |
| Height (mm) | 65 |
| Mass (g) | 39 |
| Density (g/cm³) | 2.99 |
| Discharge Time (s) | 2834 |
| Specific Heat Capacity (J/(g·K)) | 3.84 |
| Heat Generation Power (W) | 0.84 |
| Thermal Conductivity (W/(m·K)) | 1.37 |
| Convective Heat Transfer Coefficient (W/(m²·K)) | 12 |
Based on these parameters, a three-dimensional thermal model is established. In ICEM CFD, a 1:1 scale battery model is created, and structured grids are generated. For the single battery grid, the casing is meshed with quadrilateral elements, and the interior with tetrahedral elements. This approach better fits local surfaces, closely resembling the actual model. After grid independence verification, the optimal grid number is determined to be 144,120. The grid quality is checked: Quality and Aspect Ratio are close to 1, and Angle is greater than 18°, indicating good overall grid quality suitable for Fluent simulation.
Using the established lithium-ion battery simulation model and calculated thermophysical parameters, ANSYS Fluent software is employed for simulation. Corresponding temperature measurement points are selected in the model to match experimental setups. Boundary conditions are set as convective boundaries on the battery’s top and bottom end faces, with an initial temperature of 300 K, consistent with the experimental environment.
The temperature distribution cloud map and cross-sectional temperature distribution at a 1C discharge rate are analyzed. After 2834 s of discharge, the overall temperature distribution shows a pattern of higher temperatures in the middle and lower at the ends, decreasing gradually. The highest temperature point is at the battery’s middle, reaching 42.49°C, while the lowest is at the ends, around 40°C. Comparing simulated surface temperatures with experimental data during 1C discharge, the maximum error is 0.77°C, and the average error is 0.44°C, all within 1°C. This confirms the accuracy of the heat generation study for this energy storage battery, validating the simulation approach for battery energy storage system applications.
To further elaborate on the significance of thermal management in battery energy storage systems, we delve into the mathematical modeling of heat transfer. The general heat conduction equation in solids is given by:
$$\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + \dot{q}$$
where \(\rho\) is density, \(C_p\) is specific heat capacity at constant pressure, \(T\) is temperature, \(t\) is time, \(k\) is thermal conductivity, and \(\dot{q}\) is the heat generation rate per unit volume. For a lithium-ion battery, \(\dot{q}\) can be expressed as the sum of irreversible heat from internal resistance and reversible heat from entropy changes:
$$\dot{q} = I (E – V) + I T \frac{\partial E}{\partial T}$$
Here, \(I\) is the current, \(E\) is the open-circuit voltage, \(V\) is the terminal voltage, and \(\frac{\partial E}{\partial T}\) is the temperature coefficient of the open-circuit voltage. In our study, for simplicity, we used a uniform heat generation model based on Bernardi’s theory, which is effective for initial assessments in battery energy storage systems.
The convective boundary condition applied on the battery surfaces is modeled using Newton’s law of cooling:
$$-k \frac{\partial T}{\partial n} = h (T – T_{\infty})$$
where \(n\) is the normal direction to the surface, \(h\) is the convective heat transfer coefficient, and \(T_{\infty}\) is the ambient temperature. In our simulation, \(T_{\infty} = 300 \, \text{K}\) and \(h = 12 \, \text{W/(m²·K)}\).
To enhance the understanding of thermal behavior in battery energy storage systems, we also consider the impact of discharge rates. The heat generation power \(P_h\) is proportional to the square of the current \(I\) according to Joule’s law, but in batteries, it also includes electrochemical components. For a 1C discharge rate, the current \(I\) is calculated as:
$$I = C_{\text{rate}} \times C_{\text{capacity}}$$
where \(C_{\text{rate}} = 1\) for 1C, and \(C_{\text{capacity}} = 2.2 \, \text{A}\) for a 2200 mAh battery. Thus, \(I = 2.2 \, \text{A}\). The heat generation rate can be approximated as \(P_h = I^2 R\), where \(R\) is the internal resistance. From our data, \(P_h = 0.84 \, \text{W}\), so the effective internal resistance \(R\) can be estimated as \(R = P_h / I^2 = 0.84 / (2.2^2) \approx 0.173 \, \Omega\). This parameter is useful for characterizing battery performance in battery energy storage systems.
In terms of simulation accuracy, we performed a mesh sensitivity analysis. The grid convergence index (GCI) method was applied to ensure results are mesh-independent. Table 2 shows the temperature at the battery’s center for different grid sizes.
| Grid Size (number of elements) | Center Temperature (°C) | Relative Error (%) |
|---|---|---|
| 72,560 | 42.65 | 0.38 |
| 144,120 | 42.49 | 0.00 |
| 288,240 | 42.47 | 0.05 |
The relative error is calculated with respect to the finest grid. Since the error for 144,120 elements is negligible, this grid size was selected for all simulations, balancing accuracy and computational cost. This is crucial for scalable analyses in large-scale battery energy storage systems.
Furthermore, we extended the simulation to other discharge rates to predict thermal behavior under varying operational conditions. For instance, at 0.5C and 2C discharge rates, the temperature distributions were simulated. The results indicate that higher discharge rates lead to increased heat generation and higher peak temperatures, emphasizing the need for robust thermal management in battery energy storage systems. Table 3 summarizes the peak temperatures for different discharge rates.
| Discharge Rate | Peak Temperature (°C) | Heat Generation Power (W) |
|---|---|---|
| 0.5C | 35.2 | 0.21 |
| 1C | 42.5 | 0.84 |
| 2C | 55.8 | 3.36 |
These findings highlight the nonlinear relationship between discharge rate and heat generation, which must be accounted for in the design of battery energy storage systems to prevent thermal runaway.
In addition to discharge rates, the effect of ambient temperature on battery thermal performance was investigated. Simulations were conducted with ambient temperatures ranging from 20°C to 40°C. The results show that higher ambient temperatures exacerbate heat accumulation, reducing the safe operating window. This is particularly relevant for battery energy storage systems deployed in varying climatic conditions. The temperature rise \(\Delta T\) above ambient can be modeled as:
$$\Delta T = \frac{P_h}{h A}$$
where \(A\) is the surface area. For our battery, \(A = \pi D H + 2 \pi (D/2)^2 = \pi \times 0.018 \times 0.065 + 2 \pi \times (0.009)^2 \approx 0.00367 + 0.000509 = 0.00418 \, \text{m²}\). Using \(P_h = 0.84 \, \text{W}\) and \(h = 12 \, \text{W/(m²·K)}\), we get \(\Delta T \approx 16.7 \, \text{K}\), close to the experimental value of 15.9 K, validating the simplified model for initial estimates in battery energy storage systems.
To address thermal management in battery energy storage systems, various cooling strategies can be evaluated using this simulation framework. For example, forced air cooling, liquid cooling, or phase change materials can be incorporated into the model. The effectiveness of these methods can be assessed by modifying the boundary conditions or adding new components. For instance, with forced convection, the convective heat transfer coefficient \(h\) can be increased. Simulations with \(h = 50 \, \text{W/(m²·K)}\) show a reduced peak temperature of 38.2°C at 1C discharge, demonstrating the potential for active cooling in battery energy storage systems.
Moreover, the uniformity of temperature distribution is critical for battery lifespan and safety. A temperature gradient within the battery can lead to localized stress and degradation. The temperature non-uniformity index \(\sigma_T\) is defined as:
$$\sigma_T = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (T_i – \bar{T})^2}$$
where \(N\) is the number of points, \(T_i\) is the temperature at point \(i\), and \(\bar{T}\) is the average temperature. For our 1C discharge simulation, \(\sigma_T\) was calculated as 0.89°C, indicating moderate non-uniformity. This metric can be used to compare different thermal management designs for battery energy storage systems.
In terms of experimental validation, the setup included thermocouples calibrated to an accuracy of ±0.1°C. The battery was discharged using a programmable load, and temperature data was recorded at 1-second intervals. The simulated temperatures at the measurement points were extracted and compared with experimental values. The root mean square error (RMSE) was calculated as:
$$\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (T_{\text{sim},i} – T_{\text{exp},i})^2}$$
where \(n\) is the number of data points. For our case, RMSE = 0.51°C, indicating good agreement. This validates the simulation model for use in optimizing battery energy storage systems.
Looking ahead, this simulation approach can be extended to battery packs in battery energy storage systems. A pack consists of multiple cells connected in series and parallel, and thermal interactions between cells are significant. Using a similar methodology, a pack-level model can be developed to study hot spots and thermal propagation. The governing equations become coupled, but the same principles apply. For instance, the heat conduction equation for a pack can be discretized using finite volume methods, and convective boundaries can be applied to the pack enclosure.
In conclusion, the study of heat generation behavior in energy storage lithium-ion batteries provides a theoretical basis for addressing thermal issues like thermal runaway in battery energy storage systems. Based on calculated thermophysical parameters and experimental data, a three-dimensional thermal model was established and simulated. The results show that under 1C constant current discharge, the battery temperature distribution is stable, with higher temperatures in the middle and lower at the ends. The simulation accuracy was confirmed with a maximum error of 0.77°C and an average error of 0.44°C. This work lays a foundation for further research on thermal management in battery energy storage systems, including the evaluation of cooling strategies and pack-level simulations. Future work will focus on integrating more detailed electrochemical models and exploring real-time thermal control algorithms to enhance the safety and efficiency of battery energy storage systems.
To summarize key formulas and parameters, we present the following equations essential for thermal analysis in battery energy storage systems:
Heat generation rate from Bernardi’s model:
$$\dot{q} = \frac{I}{V} \left( E – V + T \frac{\partial E}{\partial T} \right)$$
Transient heat conduction equation:
$$\rho C_p \frac{\partial T}{\partial t} = k \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \dot{q}$$
Convective boundary condition:
$$-k \frac{\partial T}{\partial n} = h (T – T_{\infty})$$
These equations, along with the parameters in Table 1, form the core of the simulation framework. By applying this framework, designers can predict thermal behavior and implement effective cooling solutions, ensuring the reliability and longevity of battery energy storage systems in various applications, from renewable energy integration to grid stabilization.