In modern energy storage systems, the lithium ion battery stands as a cornerstone technology, powering everything from portable electronics to electric vehicles and grid-scale storage. The thermal behavior of a lithium ion battery is critical, as temperature fluctuations directly impact its safety, longevity, and performance. Efficient thermal management system design hinges on accurate knowledge of key thermal parameters, notably the entropy thermal coefficient and the internal resistance. Traditionally, these parameters are measured using discrete-point methods such as the open-circuit voltage technique and hybrid pulse power characterization, which are time-consuming and offer limited resolution across the state of charge (SOC) range. In this article, I present a rapid, continuous measurement method based on isothermal calorimetry, which significantly enhances testing efficiency while maintaining high accuracy.
The widespread adoption of lithium ion battery technology brings forth challenges in thermal management. During operation, a lithium ion battery generates heat due to reversible entropy changes and irreversible losses from Joule heating and polarization. Excessive heat can accelerate aging or lead to thermal runaway, while low temperatures can induce lithium plating, compromising safety. Thus, precise thermal characterization is paramount. The entropy thermal coefficient, which governs reversible heat effects, and the internal resistance, dictating irreversible heat, are dynamic parameters that vary with SOC. Conventional methods for measuring these in a lithium ion battery involve separate experiments, each requiring substantial time and yielding only discrete data points at specific SOC levels. This discontinuity can obscure important trends and complicate thermal model development.
To address these limitations, I propose an integrated approach using isothermal calorimetry. This technique allows for real-time monitoring of heat generation during charge and discharge cycles of a lithium ion battery. By employing a custom-built isothermal calorimeter, I can maintain the battery at a constant temperature while measuring the compensatory power needed to offset its heat effects. The core innovation lies in a thermal hysteresis correction algorithm that refines the raw power data to obtain instantaneous heat generation rates. From these, both the entropy thermal coefficient and internal resistance can be derived continuously across the entire SOC range using the Bernardi heat generation equation. This method not only streamlines the measurement process but also provides a holistic view of the thermal dynamics in a lithium ion battery.
The foundation of this method rests on the principles of isothermal calorimetry. In an isothermal calorimeter, the lithium ion battery is housed within a chamber equipped with thermal sinks maintained at a constant boundary temperature. A flexible heater, controlled via a PID algorithm, adjusts its power output to keep the battery temperature steady at a set point above the sink temperature. When the lithium ion battery is idle, the heater power stabilizes at a baseline value. During charge or discharge, any heat produced or absorbed by the lithium ion battery causes a temperature deviation, prompting the control system to modulate the heater power accordingly. The change in heater power relative to the baseline directly corresponds to the battery’s heat generation rate.
The thermal model of the calorimeter can be represented by an equivalent electrical circuit, where temperatures are analogous to voltages, heat flows to currents, and thermal resistances and capacitances to electrical components. The governing equation for the system is:
$$ \tau \frac{dq_h}{dt} + q_h + q_b = q_{base} $$
where $\tau = R_{bh} C_b$ is the time constant (in seconds), $q_h$ is the heater power (in watts), $q_b$ is the battery heat generation power (in watts), and $q_{base} = (T_a – T_s)/R_{as}$ is the baseline power (in watts). Here, $R_{bh}$ is the thermal resistance between the battery and heater, $C_b$ is the battery thermal capacitance, $T_a$ is the uniform block temperature, $T_s$ is the sink temperature, and $R_{as}$ is the thermal resistance between the block and sink. For a lithium ion battery under test, the net heat generated over a period from $t_1$ to $t_2$ can be calculated as:
$$ \int_{t_1}^{t_2} q_b \, dt = \int_{t_1}^{t_2} (q_{base} – q_h) \, dt $$
However, due to thermal inertia from the lithium ion battery and attached components, the measured heater power exhibits a hysteresis effect, delaying the true heat generation signal. To correct this, I apply a thermal hysteresis correction algorithm. Defining $q = q_{base} – q_h$, the relationship is:
$$ q_b = q + \tau \frac{dq}{dt} $$
The time constant $\tau$ is determined experimentally by analyzing the decay of $q$ when the lithium ion battery is not generating heat ($q_b = 0$). In that case, $q$ follows an exponential decay:
$$ q = q(t_0) e^{-\frac{t – t_0}{\tau}} $$
Taking the natural logarithm:
$$ \ln(q) = \ln[q(t_0)] – \frac{t – t_0}{\tau} $$
By fitting a linear regression to $\ln(q)$ versus time, $\tau$ can be extracted. Once $\tau$ is known, the derivative $dq/dt$ is computed from filtered data to minimize noise, and the corrected battery heat generation power $q_b$ is obtained using the above equation. This correction is crucial for accurate transient analysis of a lithium ion battery.
With the corrected heat generation profiles, the key thermal parameters for a lithium ion battery are derived from the Bernardi heat generation equation, which simplifies to:
$$ q_b = I T \frac{dU_{ocv}}{dT} + I^2 R $$
where $I$ is the current (in amperes, positive for discharge), $T$ is the absolute battery temperature (in kelvin), $dU_{ocv}/dT$ is the entropy thermal coefficient (in volts per kelvin), and $R$ is the internal resistance (in ohms). For a lithium ion battery undergoing charge and discharge at the same current magnitude $|I|$ and temperature $T$, the heat generation powers during charge ($q_{ch}$) and discharge ($q_{dch}$) are:
$$ \begin{cases} q_{ch} = I^2 R_{ch} + |I| T \frac{dU_{ocv}}{dT} \\ q_{dch} = I^2 R_{dch} – |I| T \frac{dU_{ocv}}{dT} \end{cases} $$
Assuming the internal resistance is symmetric ($R = R_{ch} = R_{dch}$) for a lithium ion battery under moderate conditions, solving these equations yields continuous expressions as functions of SOC:
$$ R(SOC) = \frac{q_{ch} + q_{dch}}{2 I^2} $$
and
$$ \frac{dU_{ocv}}{dT}(SOC) = \frac{q_{ch} – q_{dch}}{2 |I| T} $$
Thus, by performing a single pair of charge and discharge experiments at a constant current rate, I can obtain both parameters simultaneously across all SOC points for a lithium ion battery.
To validate this method, I conducted experiments using a commercial NCM ternary lithium ion battery. The specifications are summarized in Table 1.
| Parameter | Value |
|---|---|
| Rated Capacity | 53 Ah |
| Nominal Voltage | 3.7 V |
| Charge Cut-off Voltage | 4.2 V |
| Discharge Cut-off Voltage | 2.5 V |
| Charge Termination Current | 2.65 A |
| Dimensions | 148 mm × 29 mm × 98 mm |
The experimental setup centers on a self-developed isothermal calorimetry system. The calorimeter chamber is constructed with acrylic panels for insulation and houses two symmetric thermal sinks connected to an external恒温油浴 (constant-temperature oil bath) to maintain a stable boundary at 22°C. Inside, a uniform block with embedded temperature sensors ensures even heat distribution. A flexible heater is attached to the block and controlled via a PID algorithm to keep the lithium ion battery at an isothermal target temperature of 25°C. The battery is connected to a cycler for charge-discharge operations, and all data—including heater power, temperatures, current, and voltage—are logged at 1 Hz using a LabVIEW-based interface.
In the rapid measurement procedure, the lithium ion battery is first conditioned to 0% SOC and then charged to 100% SOC using constant-current constant-voltage (CCCV) mode at rates of 0.5C, 0.75C, and 1C (where C denotes the current rate relative to capacity). After a 1.5-hour rest, it is discharged back to 0% SOC at the same constant current rate. The heater power data during these cycles are recorded, corrected for thermal hysteresis, and then used to compute $q_b$. Applying the formulas above, the entropy thermal coefficient and internal resistance are calculated as continuous functions of SOC for each current rate.
For comparison, traditional methods are also employed on the same lithium ion battery. The entropy thermal coefficient is measured via the open-circuit voltage method: the battery is equilibrated at different temperatures (from 12°C to 20°C) at each 10% SOC interval, and $dU_{ocv}/dT$ is derived from the linear slope of open-circuit voltage versus temperature. The internal resistance is measured using hybrid pulse power characterization (HPPC): at each 10% SOC, a 1C discharge pulse of 10 seconds is applied, and the immediate voltage drop gives the ohmic resistance, while the subsequent slow change gives the polarization resistance, summing to total internal resistance.
The results demonstrate the efficacy of the isothermal calorimetry method. Figure 1 (though not explicitly labeled, referring to the data trends) shows the entropy thermal coefficient and internal resistance profiles obtained from the rapid method across SOC for different current rates, alongside discrete points from traditional methods. The curves exhibit strong agreement in trend and magnitude, validating the accuracy of the continuous measurements. Specifically, the entropy thermal coefficient for a lithium ion battery typically ranges from -0.3 to 0.3 mV/K, reflecting reversible heat absorption or release during phase transitions, while the internal resistance varies from 1 to 5 mΩ, influenced by factors like SOC and temperature.
To quantify accuracy, the absolute errors between the rapid method (at 0.5C, 0.75C, and 1C) and traditional methods are computed at corresponding SOC points. The maximum absolute errors are summarized in Table 2.
| Current Rate | Entropy Thermal Coefficient Error (mV/K) | Internal Resistance Error (mΩ) |
|---|---|---|
| 0.5C | 0.0593 | 0.4696 |
| 0.75C | 0.0406 | 0.2341 |
| 1C | 0.0668 | 0.2954 |
These errors are minimal, with the entropy thermal coefficient error staying below 0.0668 mV/K and internal resistance error below 0.4696 mΩ. Slight discrepancies may arise from assumptions like symmetric internal resistance in the lithium ion battery during charge and discharge, or from noise in the calorimetric baseline at low heat generation rates. Nevertheless, the consistency across current rates underscores the robustness of the method for a lithium ion battery.
A key advantage is the dramatic reduction in measurement time. Traditional methods require approximately 22 hours per SOC point for entropy coefficient and 2.3 hours per point for internal resistance, totaling around 218.7 hours to cover 10% to 90% SOC in 10% increments. In contrast, the rapid method using isothermal calorimetry completes both parameter measurements in a single charge-discharge cycle. For example, at 0.5C rate, the experiment takes about 6 hours—a time saving of over 97%. This efficiency gain is pivotal for rapid characterization of lithium ion battery thermal properties, especially when screening multiple cells or optimizing thermal management systems.
The continuous data provided by this method offers deeper insights into the behavior of a lithium ion battery. For instance, the entropy thermal coefficient often shows peaks near phase transitions in electrode materials, which can be critical for managing reversible heat effects. Similarly, the internal resistance profile can reveal details about polarization losses at different SOC levels. By capturing these variations seamlessly, the method enhances the fidelity of thermal models used in battery management systems for a lithium ion battery.
In terms of experimental considerations, the isothermal calorimeter must be carefully calibrated to minimize errors. The time constant $\tau$ is a critical parameter that depends on the thermal mass and contact resistances of the setup. For a typical lithium ion battery, $\tau$ values ranged from 336 to 354 seconds in my experiments, as determined from the logarithmic decay fits. Ensuring stable boundary temperatures and precise temperature control is essential for reproducible results with a lithium ion battery. Additionally, the current rates should be chosen to generate sufficient heat for accurate measurement while avoiding excessive heating that could deviate from isothermal conditions.
Looking forward, this rapid measurement approach can be extended to other battery chemistries beyond the lithium ion battery, such as lithium-sulfur or solid-state batteries, where thermal management is equally important. The integration of real-time data acquisition and advanced correction algorithms could further automate the process, enabling high-throughput thermal characterization. For the lithium ion battery industry, this means faster development cycles and more reliable thermal designs, ultimately contributing to safer and more efficient energy storage solutions.
In conclusion, I have presented a novel method for rapid measurement of thermal parameters in a lithium ion battery using isothermal calorimetry. By leveraging a thermal hysteresis correction algorithm and the Bernardi heat generation equation, this method simultaneously provides continuous profiles of entropy thermal coefficient and internal resistance across the entire SOC range. Validation against traditional techniques confirms high accuracy, with absolute errors within tight bounds, while measurement time is reduced by over 97%. This advancement not only streamlines the characterization process for a lithium ion battery but also enriches the understanding of its thermal dynamics, supporting the design of effective thermal management systems. As the demand for high-performance lithium ion batteries grows, such efficient testing methodologies will play a crucial role in ensuring their safety and longevity.