As a key enabler of modern energy storage systems, lithium-ion batteries have revolutionized portable electronics, electric vehicles, and grid-scale storage due to their high energy density and long cycle life. However, the performance, safety, and longevity of lithium-ion batteries are intrinsically tied to their thermal behavior. Temperature fluctuations can trigger detrimental effects such as lithium plating at low temperatures or thermal runaway at high temperatures, leading to irreversible capacity loss or catastrophic failures. Therefore, accurately monitoring and managing the temperature state of lithium-ion batteries is paramount for advancing battery technology and ensuring reliable operation. This article delves into the comprehensive analysis of temperature state for lithium-ion batteries, covering its definition, detection methods, and estimation techniques, with an emphasis on practical applications and future directions.
The temperature state of a lithium-ion battery refers to the thermal condition that influences its electrochemical processes, including charge transfer, ion diffusion, and side reactions. Unlike other battery states like state of charge or health, the temperature state provides direct insight into the internal and external thermal environment, making it a critical parameter for intelligent battery management systems. In this review, we systematically explore the characterization metrics, detection technologies, and estimation approaches for the temperature state of lithium-ion batteries, integrating theoretical principles with practical implementations to offer a holistic perspective.
To begin, we define four primary temperature characterization metrics for a single lithium-ion battery cell: surface temperature (TOS), core temperature (TOC), bulk-average temperature (TOB), and temperature distribution (TOD). Additionally, at the module level, temperature extreme value (TEV) and temperature difference (TD) are discussed for assessing thermal uniformity and safety. These metrics are summarized in Table 1, highlighting their definitions, advantages, and limitations in the context of lithium-ion battery applications.
| Metric | Definition | Advantages | Limitations |
|---|---|---|---|
| Surface Temperature (TOS) | Temperature measured at the outer casing of the lithium-ion battery. | Easy to measure with low-cost sensors; non-invasive. | Does not reflect internal hot spots; delayed response due to thermal inertia. |
| Core Temperature (TOC) | Temperature at the geometric center of the lithium-ion battery. | Better indicator of internal thermal state; critical for safety. | Requires invasive sensor embedding; risk of damaging the lithium-ion battery. |
| Bulk-Average Temperature (TOB) | Volume-weighted average temperature of the entire lithium-ion battery. | Represents overall thermal condition; useful for system-level analysis. | May underestimate local temperatures in high-gradient scenarios. |
| Temperature Distribution (TOD) | Spatial variation of temperature within the lithium-ion battery. | Provides detailed thermal mapping; essential for hotspot detection. | Complex to measure or estimate; computationally intensive. |
| Temperature Extreme Value (TEV) | Maximum or minimum temperature within a lithium-ion battery module. | Identifies worst-case scenarios; crucial for thermal management. | Requires multiple sensors; may not capture gradients. |
| Temperature Difference (TD) | Difference in temperature between cells in a lithium-ion battery module. | Assesses thermal uniformity; prevents localized overheating. | Sensitive to sensor placement; threshold values vary with design. |
Moving to detection technologies, we categorize methods into invasive and non-invasive approaches. Invasive detection involves embedding sensors inside the lithium-ion battery, such as thermocouples, thermistors, resistance temperature detectors (RTDs), and fiber optic sensors. These methods offer high accuracy but pose risks of electrolyte leakage or structural damage. Non-invasive detection, including infrared thermal mapping and X-ray diffraction-computed tomography (XRD-CT), allows external monitoring without compromising the integrity of the lithium-ion battery. Table 2 compares these detection techniques based on principles, advantages, and challenges.
| Detection Method | Principle | Advantages | Challenges |
|---|---|---|---|
| Thermocouple | Seebeck effect: voltage generated by temperature difference between two metals. | Wide temperature range; fast response; cost-effective. | Invasive; potential corrosion in lithium-ion battery environment. |
| Thermistor | Resistance change with temperature (NTC or PTC). | High sensitivity; compact size. | Non-linear response; limited temperature range for lithium-ion batteries. |
| RTD | Resistance change of pure metals (e.g., platinum) with temperature. | High accuracy and stability; linear over ranges. | Expensive; invasive for lithium-ion battery integration. |
| Fiber Optic Sensor | Wavelength shift in fiber Bragg grating due to temperature-induced strain. | Immune to electromagnetic interference; multi-point sensing. | Complex installation; high cost for lithium-ion battery systems. |
| Infrared Thermal Mapping | Detection of infrared radiation emitted from the lithium-ion battery surface. | Non-contact; full-field temperature distribution. | Affected by surface emissivity; cannot measure internal temperature of lithium-ion battery. |
| XRD-CT | X-ray diffraction to analyze lattice expansion; computed tomography for 3D imaging. | Non-invasive; provides internal temperature maps of lithium-ion battery. | High equipment cost; limited to laboratory settings. |
For estimation techniques, we focus on model-based and data-driven approaches that infer the temperature state of lithium-ion batteries without direct sensor measurements. These include methods based on electrochemical impedance spectroscopy (EIS), thermal models, ultrasonic sensing, and machine learning algorithms. Each method leverages specific physical or empirical relationships to estimate temperature, as detailed below.
Electrochemical impedance spectroscopy relies on the temperature dependence of impedance parameters in lithium-ion batteries. The impedance \(Z\) at a frequency \(\omega\) is given by:
$$Z(\omega) = \frac{V(\omega)}{I(\omega)} = |Z| e^{j\phi},$$
where \(|Z|\) is the magnitude and \(\phi\) is the phase shift. For lithium-ion batteries, the real part \(Z’\) or phase \(\phi\) at selected frequencies can be correlated with temperature through calibration curves. The relationship is often expressed as:
$$T = f(Z’, Z”, \phi),$$
where \(f\) is a polynomial or linear function derived from experimental data. This method enables non-invasive temperature estimation but requires precise impedance measurements, which can be affected by state of charge and health of the lithium-ion battery.
Thermal models describe the heat generation, accumulation, and dissipation in lithium-ion batteries using energy conservation laws. The general heat conduction equation for a lithium-ion battery is:
$$\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q,$$
where \(\rho\) is density, \(C_p\) is specific heat capacity, \(k\) is thermal conductivity, \(T\) is temperature, and \(Q\) is the heat generation rate. For lithium-ion batteries, \(Q\) is commonly modeled using the Bernardi equation:
$$Q = I \left( U_{ocv} – V \right) – I T \frac{\partial U_{ocv}}{\partial T},$$
where \(I\) is current, \(U_{ocv}\) is open-circuit voltage, and \(V\) is terminal voltage. This equation accounts for irreversible and reversible heat effects in lithium-ion batteries. Thermal models can be full-order (solved numerically), reduced-order lumped (using thermal equivalent circuits), or reduced-order distributed (using basis function approximations). For instance, a lumped thermal model for a cylindrical lithium-ion battery might represent it as a network of resistors and capacitors, with temperature estimated at key nodes.
Ultrasonic estimation exploits the temperature dependence of sound speed in lithium-ion battery materials. The time-of-flight \(\tau\) of an ultrasonic wave through a battery of thickness \(d\) is measured, and the sound speed \(c\) is calculated as:
$$c = \frac{d}{\tau}.$$
Since \(c\) varies with temperature \(T\), a calibration curve \(T = g(c)\) is established for the lithium-ion battery. This method offers real-time, non-invasive estimation but requires high-frequency sensors and is sensitive to battery geometry and state.
Data-driven approaches, particularly machine learning, have gained traction for estimating the temperature state of lithium-ion batteries. These methods use historical data from sensors (e.g., voltage, current, ambient temperature) to train models such as artificial neural networks (ANNs), long short-term memory (LSTM) networks, or physics-informed neural networks (PINNs). For example, an LSTM model can capture temporal dependencies in thermal behavior of lithium-ion batteries, with the output being estimated temperature \(\hat{T}\):
$$\hat{T}(t) = \text{LSTM}(I(t), V(t), T_{\text{amb}}(t), \ldots),$$
where inputs include time-series data. Hybrid models combine physical principles with data-driven techniques to enhance accuracy and generalizability for lithium-ion batteries. Table 3 summarizes these estimation methods, highlighting their key equations and applications.
| Estimation Method | Key Equations/Principles | Applications for Lithium-Ion Batteries |
|---|---|---|
| Electrochemical Impedance Spectroscopy (EIS) | $$T = a Z’ + b \phi + c$$ (linear fit) or higher-order polynomials. | Online temperature monitoring; non-invasive but requires frequency sweep. |
| Thermal Models (Full-Order) | $$\rho C_p \frac{\partial T}{\partial t} = k \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + Q$$ with boundary conditions. | Detailed temperature distribution simulation; used in design and safety analysis of lithium-ion batteries. |
| Thermal Models (Reduced-Order Lumped) | $$C \frac{dT}{dt} = \frac{T_{\text{core}} – T_{\text{surface}}}{R} + Q$$ for a two-node model. | Real-time temperature estimation in BMS; low computational cost for lithium-ion batteries. |
| Ultrasonic Estimation | $$T = \alpha \tau^2 + \beta \tau + \gamma$$ based on time-of-flight calibration. | Internal temperature sensing; emerging technique for lithium-ion battery packs. |
| Data-Driven (Machine Learning) | $$\hat{T} = \text{NN}(\mathbf{x})$$ where \(\mathbf{x}\) is input feature vector (e.g., current, voltage). | Adaptive temperature prediction; handles nonlinearities in lithium-ion battery systems. |
| Hybrid Models (Physics-Informed) | Combine PDE constraints (e.g., heat equation) with neural network loss functions. | Robust estimation under varying conditions; enhances generalizability for lithium-ion batteries. |
In practice, the choice of detection or estimation method for lithium-ion batteries depends on factors such as cost, accuracy, invasiveness, and application context. For instance, electric vehicles may prioritize non-invasive estimation via EIS or machine learning to avoid battery modification, while laboratory studies might use embedded sensors for validation. The integration of multiple methods, such as combining fiber optic sensors with thermal models, can provide comprehensive thermal management for lithium-ion battery systems.
Looking ahead, several challenges and future directions emerge for the temperature state of lithium-ion batteries. First, the development of solid-state lithium-ion batteries introduces new thermal phenomena due to different electrolyte properties, requiring revised temperature metrics and estimation models. Second, unifying temperature characterization across battery modules remains an open issue, as thermal boundaries vary with design and cooling strategies. Third, hardware advancements, like multi-sensor integration and flexible electronics, will enable smarter lithium-ion batteries with real-time thermal monitoring. Fourth, algorithm optimization, including large-scale deep learning and digital twins, can improve the accuracy and efficiency of temperature estimation for lithium-ion batteries. Finally, system-level applications, such as real-time thermal warning systems that jointly estimate state of charge, health, and temperature, will enhance the safety and reliability of lithium-ion battery deployments.
In conclusion, the temperature state is a fundamental aspect of lithium-ion battery performance and safety. This review has detailed the definitions, detection technologies, and estimation techniques for lithium-ion battery temperature, emphasizing the need for a holistic approach that combines physical insights with advanced sensing and modeling. As lithium-ion battery technology evolves towards higher energy densities and broader applications, continuous innovation in thermal management will be crucial to unlocking their full potential while mitigating risks. By addressing the outlined challenges, we can pave the way for more efficient, durable, and safe lithium-ion battery systems in the future.
To further illustrate the principles discussed, consider the following formula for heat generation in a lithium-ion battery under dynamic loads, which incorporates both irreversible and reversible components:
$$Q_{\text{total}} = I^2 R_{\text{int}} + I T \frac{dU_{ocv}}{dT},$$
where \(R_{\text{int}}\) is the internal resistance of the lithium-ion battery. This equation highlights how temperature affects and is affected by electrochemical processes, underscoring the importance of accurate temperature state management. Additionally, the thermal time constant \(\tau_{\text{thermal}}\) for a lithium-ion battery can be approximated as:
$$\tau_{\text{thermal}} = \frac{\rho C_p V}{h A},$$
where \(V\) is volume, \(h\) is heat transfer coefficient, and \(A\) is surface area, providing insights into thermal response times for lithium-ion battery designs. Through such analytical tools and empirical methods, we can advance our understanding and control of the temperature state in lithium-ion batteries, driving progress in energy storage technology.