The pursuit of efficient energy storage solutions has propelled lithium-ion (Li-ion) batteries to the forefront of technologies powering mobile electronics, electric vehicles, and grid-scale storage. Their high energy density and long cycle life are unparalleled. In specialized fields such as aerospace, polar research, and emergency power systems for remote or high-altitude locations, the reliable operation of Li-ion batteries is critical. These applications often present extreme environmental challenges, particularly sub-zero temperatures. At low temperatures, the performance of a standard Li-ion battery degrades severely: electrolyte viscosity increases, ionic conductivity drops, and charge transfer at the electrodes becomes sluggish. This manifests as a dramatic increase in internal impedance, a significant reduction in usable capacity and deliverable power, and heightened risks such as lithium plating during charging. For mission-critical systems operating in harsh, off-grid environments, the ability for a Li-ion battery system to self-initiate and achieve operational temperature rapidly and efficiently without external auxiliary power is a paramount requirement. Therefore, developing rapid, effective, and self-sufficient low-temperature heating methods is essential for unlocking the full potential of Li-ion batteries in these demanding scenarios.
Existing heating strategies can be broadly categorized into internal, external, and composite methods. Internal heating relies on the battery’s own internal resistance ($$R_{int}$$) to generate heat through controlled current excitation, such as direct current (DC), alternating current (AC), or pulsed discharges. While elegant, these methods can induce large internal temperature gradients and may accelerate battery aging if not carefully controlled. External heating employs separate elements like silicon rubber heaters, air blowers, or liquid jackets to transfer heat to the battery. This approach, though straightforward, often requires additional system components, leads to slower heating rates due to thermal inertia and distance, and can result in poor temperature uniformity across a battery pack. Composite heating synergistically combines both principles, leveraging internal Joule heating from the battery and external heating from an integrated element, promising superior heating rates. A notable example is the All-Climate Battery (ACB), which embeds a nickel foil inside the cell. However, modifying the internal structure of a Li-ion battery raises non-trivial safety and manufacturability concerns. Most research has focused on single-cell heating or methods requiring external power buffers. There is a distinct lack of studies on auxiliary-free composite heating for multi-cell modules. Furthermore, existing approaches often prioritize surface temperature uniformity of cells within a module but pay less attention to the internal thermal gradient within each individual cell, which is crucial for health and safety.
To address these gaps, this research proposes and validates a novel, rapid composite heating method for Li-ion battery modules based on a pulsed discharge strategy. The core innovation lies in a module architecture where external heating elements are integrated into the electrical and thermal path, enabling heating solely from the module’s stored energy. A distributed thermal model is developed to accurately capture internal cell temperatures, and the method’s performance is rigorously evaluated under various operating conditions. This article details the module design, experimental platform, modeling efforts, and comprehensive analysis of key influencing factors, demonstrating a path toward practical, fast, and self-contained low-temperature startup for Li-ion battery systems.
Module Architecture and Experimental Platform for Li-Ion Battery Heating
The foundation of our composite heating approach is a purpose-built module architecture. We selected commercial 8 Ah soft-pack LiNiMnCoO2 (NMC) / Graphite Li-ion cells as the test subject. Key parameters are summarized in Table 1. To minimize the impact of cell-to-cell variations, nine cells were screened based on their room-temperature 1C discharge capacity, and the three most consistent units were chosen for module assembly.
| Parameter | Value |
|---|---|
| Nominal Voltage | 3.6 V |
| Nominal Capacity | 8 Ah |
| Internal Resistance | ≤ 1.5 mΩ |
| Charge/Discharge Cut-off Voltage | 2.75 V / 4.2 V |
| Dimensions (L×W×Th) | 142.0 × 115.0 × 8.5 mm |
| Discharge Operating Temperature | -20°C to 55°C |
The module consists of these three Li-ion battery cells connected in series with four thin, patterned heating plates, forming a single current loop. The heating plate design was optimized for this application. Based on a comparative analysis of density, resistivity, cost, and resistance temperature coefficient (see Table 2), aluminum was selected as the heating element material.
| Metal | Density (g/cm³) | Resistivity at 20°C (Ω·m) | Temp. Coefficient (°C⁻¹) |
|---|---|---|---|
| Nickel (Ni) | 8.85 | 6.84 × 10⁻⁸ | 0.00690 |
| Aluminum (Al) | 2.7 | 2.655 × 10⁻⁸ | 0.00429 |
| Copper (Cu) | 8.9 | 1.678 × 10⁻⁸ | 0.00393 |
Prior single-cell optimization work suggested an optimal equivalent discharge heating resistance of approximately 47.8 mΩ. For our three-cell module, this translated to a target resistance of about 36 mΩ per heating plate. The plates were fabricated by patterning 0.1 mm thick aluminum foil, with tabs designed for robust electrical connection to the cell tabs. A key safety and insulation feature was the lamination of the main plate area with polyimide (PI) film. The final resistance of the fabricated plates was characterized as a function of temperature, yielding the linear relationship:
$$R_m(T) = 37.196 + 0.169T$$
where $$R_m$$ is in mΩ and $$T$$ is in °C. The resistance at 20°C was measured at 40.57 mΩ, satisfactorily close to the design target.
The physical assembly of the Li-ion battery module is shown schematically in cross-section. The stack sequence is: insulation board, heating plate, thermal grease, Li-ion battery cell, thermal grease, heating plate, Li-ion battery cell, thermal grease, heating plate, Li-ion battery cell, thermal grease, heating plate, insulation board. The entire assembly is clamped, and thermal grease ensures good thermal contact. The module is wrapped in aerogel insulation to mimic practical pack conditions and placed in an environmental chamber. Thermocouples are strategically embedded between layers to measure temperatures of both the heating plates and the surfaces of the Li-ion battery cells.
A comprehensive experimental platform was established. It comprises three main subsystems: 1) The Heating Control Module: A microcontroller generates a Pulse Width Modulation (PWM) signal which drives a MOSFET, periodically connecting the series loop of Li-ion battery cells and heating plates to create a pulsed discharge current. 2) The Data Acquisition Module: A high-speed data acquisition card records current and voltage, while a separate data logger records temperatures from all embedded thermocouples. 3) The Battery Module & Environmental Chamber: The assembled module is housed in a temperature-controlled chamber. A professional battery cycler is used for initial conditioning and state-of-charge (SOC) setting. This platform enables precise control and monitoring of the pulsed heating process for the Li-ion battery module.
Development and Validation of a Distributed Thermal Model for the Li-Ion Battery Module System
To understand and predict the thermal behavior of the Li-ion battery module during heating, a lumped-parameter distributed thermal model was developed. The core idea is to model heat generation and transfer in the through-plane direction of the module stack.
First, each soft-pack Li-ion battery cell is discretized into seven isothermal nodes along its thickness, connected by thermal resistances ($$R_b$$) and each node having a thermal capacitance ($$C_b$$). This captures the internal temperature gradient. The heat generation within each segment of the Li-ion battery is approximated as the product of the pulse current ($$I$$) and the overpotential ($$U_{OV}$$):
$$P_b \approx I \cdot U_{OV} = I \cdot (U_{OCV} – U_k)$$
where $$U_{OCV}$$ is the open-circuit voltage and $$U_k$$ is the terminal voltage of the Li-ion battery.
Second, the heating plate is modeled as a single thermal mass ($$C_c$$) with its Joule heating power:
$$P_c = I^2 \cdot R_m(T)$$
The Polyimide (PI) insulation layer on each side is represented by a thermal resistance ($$R_c$$). The thermal grease layers are modeled as three-node thermal RC ladders (resistance $$R_d$$, capacitance $$C_d$$). Convective/conductive heat loss from the outermost surfaces to the ambient ($$T_a$$) is modeled via a resistance ($$R_a$$).
Finally, by assembling the models for the three Li-ion battery cells, four heating plates, and six thermal grease layers in their physical stack order and applying symmetry assumptions for simplification, a complete state-space model for the module is derived. The governing equations for a generic internal node follow the form:
$$C_j \frac{dT_j}{dt} = \sum \frac{T_i – T_j}{R_{ij}} + P_j$$
where the summation is over all adjacent nodes $$i$$ connected to node $$j$$ through thermal resistance $$R_{ij}$$, and $$P_j$$ is the heat generation at node $$j$$ (nonzero for Li-ion battery and heating plate nodes).
The thermal parameters for the Li-ion battery ($$R_b$$, $$C_b$$) were taken from prior characterization of identical cells. The heating plate heat capacity ($$C_c$$) was calculated from its material properties and volume. The remaining parameters—thermal contact resistances ($$R_d$$, $$R_c$$) and the external heat transfer resistance ($$R_a$$)—were identified using experimental data. An Adaptive Particle Swarm Optimization (APSO) algorithm was employed to minimize the error between measured and simulated surface temperatures of the Li-ion battery cells and heating plates. The fitness function was:
$$F = \frac{1}{N} \left[ \sum_{i=1}^{N} (T_{b,meas}^i – T_{b,sim}^i)^2 + \sum_{i=1}^{N} (T_{c,meas}^i – T_{c,sim}^i)^2 \right]$$
The identified parameters are listed in Table 3.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| $$R_a$$ | 18.45 K/W | $$R_{d1}$$ | 0.014 K/W |
| $$R_{d2}$$ | 0.035 K/W | $$R_{d3}$$ | 0.011 K/W |
| $$C_{d1}$$ | 48.33 J/K | $$C_{d2}$$ | 6.33 J/K |
| $$C_{d3}$$ | 23.33 J/K | $$R_c$$ | 0.002 K/W |
The model’s accuracy was validated under a wide range of conditions: different PWM duty cycles (D), different initial SOCs of the Li-ion battery, and different ambient temperatures. Figure 1 shows exemplary validation results for different duty cycles at -20°C and 100% SOC. The model closely tracks the experimental temperature rise. Across all validation tests, the maximum Root Mean Square Error (RMSE) between the model simulations and experimental measurements for surface temperatures was less than 1.3°C. This confirms that the distributed thermal model can accurately predict the thermal dynamics of the Li-ion battery module heating system.
Experimental Investigation of Heating Performance and Influencing Factors for the Li-Ion Battery Module
With the experimental platform and validated model, we systematically investigated the performance of the pulsed composite heating method for the Li-ion battery module. Key performance metrics were defined:
- Temperature Rise Rate (TSR): $$TSR = \frac{T_{end} – T_0}{t_{end} – t_0}$$, where $$T_0$$ and $$T_{end}$$ are the average module temperatures at start and end.
- Maximum Temperature Difference (MDT) within the central Li-ion battery cell: $$MDT = \max(T_{b,i}) – \min(T_{b,i})$$, where $$T_{b,i}$$ are the modeled internal node temperatures.
- Energy Consumption Rate (ECR): $$ECR = \frac{\int_{t_0}^{t_{end}} U_{OCV} \cdot I \cdot dt}{E_{cell}} \times 100\%$$, where $$E_{cell}$$ is the total stored energy of the Li-ion battery module.
Based on prior frequency analysis, a fixed pulse frequency of 1 Hz was used for all tests, as it offered a good compromise between heating rate and temperature uniformity. Three main experimental campaigns were conducted.
1. Effect of Pulse Duty Cycle (D)
Tests were performed at -20°C with the Li-ion battery module at 100% SOC, varying D from 10% to 90%. Results are summarized in Table 4.
| Duty Cycle (D) | Heating Time (s) | TSR (°C/min) | ECR (%) | MDT (°C) |
|---|---|---|---|---|
| 90% | 40.25 | 28.38 | 6.24 | 12.45 |
| 70% | 52.08 | 21.93 | 6.46 | 10.57 |
| 50% | 75.59 | 15.11 | 6.82 | 7.46 |
| 30% | 122.93 | 9.29 | 6.95 | 4.96 |
| 10% | 441.77 | 2.59 | 8.67 | 1.34 |
The TSR increases monotonically with D due to higher average current and thus higher average heating power from both the Li-ion battery’s internal resistance and the heating plates. However, MDT also increases significantly with D because the shorter off-time in the pulse cycle provides less opportunity for heat to conduct from the surfaces to the core of the Li-ion battery, leading to larger internal gradients. The ECR is lowest at high D because the heating process is faster, reducing the time for parasitic heat loss to the environment. A duty cycle of D=50% was selected as a balanced operating point, offering a high TSR (>15°C/min) while maintaining MDT below 7.5°C and a reasonable ECR.
2. Effect of Initial State of Charge (SOC)
Using the selected D=50% at -20°C, the Li-ion battery module was heated from different initial SOC levels. Results are in Table 5.
| Initial SOC (%) | Heating Time (s) | TSR (°C/min) | ECR (%) | MDT (°C) |
|---|---|---|---|---|
| 100 | 75.59 | 15.11 | 6.82 | 7.46 |
| 80 | 87.08 | 13.11 | 6.97 | 6.41 |
| 60 | 99.97 | 11.42 | 7.03 | 5.61 |
| 40 | 111.99 | 10.20 | 7.02 | 4.75 |
A higher initial SOC results in a higher TSR. This is primarily because the average terminal voltage of the Li-ion battery is higher at high SOC, leading to a larger discharge current for a given circuit resistance (dominated by the heating plates). Consequently, the Joule heating power ($$P=I^2R$$) is greater. The internal resistance of a Li-ion battery typically exhibits a “U”-shape vs. SOC, being higher at very high and very low SOC. This is reflected in the slightly higher ECR at mid-SOC (60%), where the lower battery impedance allows more voltage drop across the fixed heating plates, consuming slightly more energy for the same temperature rise. MDT is positively correlated with SOC because higher current induces a greater heat generation rate, exacerbating the core-surface gradient. Importantly, even at 40% SOC, the Li-ion battery module achieved a TSR exceeding 10°C/min with an MDT under 5°C, demonstrating the method’s effectiveness across a useful SOC range.
3. Effect of Ambient Temperature
The performance of the D=50% strategy was evaluated at different sub-zero ambient temperatures with the Li-ion battery module at 100% SOC. Results are in Table 6.
| Ambient Temp. (°C) | Heating Time (s) | TSR (°C/min) | ECR (%) | MDT (°C) |
|---|---|---|---|---|
| -30 | 132.79 | 13.83 | 10.98 | 7.34 |
| -20 | 78.68 | 15.11 | 7.12 | 7.55 |
| -10 | 37.02 | 17.51 | 3.62 | 8.51 |
As ambient temperature decreases, the TSR also decreases. This is because the internal resistance of the Li-ion battery increases exponentially with decreasing temperature, which limits the discharge current despite the higher voltage potential of a cold battery. The lower current reduces the total heating power. The ECR increases significantly at lower temperatures for two reasons: 1) more energy is required to raise the module from a lower temperature to the target, and 2) the higher battery impedance leads to greater voltage sag, meaning more of the module’s energy is dissipated as heat within the Li-ion battery itself rather than in the external heating plates. Interestingly, the MDT is somewhat lower at -30°C than at -10°C. At colder temperatures, the Li-ion battery’s own internal resistance constitutes a larger fraction of the total circuit resistance, making its self-heating proportionally more significant compared to the heating plate contribution. This leads to a more distributed heat generation profile within the Li-ion battery, slightly improving internal temperature uniformity. Remarkably, at -30°C, the method still achieved a TSR of 13.83°C/min, demonstrating robust ultra-low-temperature capability.
Conclusion and Outlook
This research successfully developed and validated a rapid, auxiliary-free composite heating method for Li-ion battery modules based on a pulsed discharge strategy. A novel module architecture integrating patterned aluminum heating plates was designed and built. A distributed thermal model was constructed and accurately parameterized, achieving a maximum RMSE of less than 1.3°C against experimental data. Comprehensive experimental analysis revealed the effects of key operational parameters. The pulsed heating method, operating at 1 Hz with a 50% duty cycle, enabled the Li-ion battery module to achieve temperature rise rates exceeding 10°C/min across a wide SOC range (40-100%) at -20°C, with energy consumption below 7.05% and a maximum internal temperature difference kept under 7.5°C. Even under a severe -30°C environment, the Li-ion battery module was heated at 13.83°C/min with an internal gradient of 7.34°C, proving the method’s effectiveness in extreme cold.
The primary advantage of this method is its self-sufficiency and speed. By cleverly integrating the heating element into the discharge path, it utilizes the stored energy of the Li-ion battery module itself, eliminating the need for any external power buffer or auxiliary heating system—a critical feature for remote or emergency applications. Compared to continuous heating, the pulsed operation introduces intermittent periods where heat can conduct inward from the hot heating plates and battery surfaces to the cooler core, mitigating the accumulation of large internal thermal gradients and thus improving temperature uniformity and potentially safety.
For specialized applications where rapid low-temperature startup is paramount and some cycle life degradation may be acceptable, this method presents a compelling solution. Future work will focus on extending this study to evaluate the long-term impact of repeated heating cycles on the health and safety boundaries of the Li-ion battery, particularly investigating how the internal temperature gradients influence aging mechanisms. Optimization of the heating plate resistance and pulse pattern for different module configurations and cell types also remains an important avenue for further research to enhance the practicality and efficiency of this promising approach for safeguarding Li-ion battery performance in the cold.