1. Introduction and Research Motivation
Lithium-ion batteries have become the dominant energy source for modern electric vehicles because of their high energy density, low self-discharge rate, long service life, and relatively low environmental impact. In my research, I focused on a particular challenge: the severe performance degradation of lithium-ion traction battery packs when the ambient temperature drops well below zero. In cold regions, winter temperatures frequently fall below \(-10^\circ\text{C}\), and can reach \(-30^\circ\text{C}\). Under these extreme conditions, the electrolyte becomes more viscous, electrode kinetics decelerate, and lithium-ion diffusivity in both the electrolyte and the active material decreases markedly. As a result, the available discharge capacity of the traction battery pack is greatly reduced, internal resistance rises dramatically, and charging at normal current levels can trigger lithium plating on the graphite anode. Deposition of lithium and the potential growth of dendrites can penetrate the separator and lead to internal short circuits. Therefore, I recognized that an effective low-temperature preheating system is an indispensable component of the thermal management architecture for any traction battery pack in electric vehicles.
Existing heating solutions can be broadly classified into external heating, internal heating, and composite heating. External heating usually relies on air, liquid, phase-change materials, or electric heating films to raise the temperature of the battery from the outside. Internal heating applies a direct current, alternating current, or pulsed-current excitation to generate Joule heat using the battery’s own internal resistance. External methods have the advantage of being easy to control, but the thermal path is long and the heat-transfer efficiency is limited. Internal methods can provide a faster temperature rise by using the battery itself as the heat source; however, aggressive DC heating can cause lithium plating and non-uniform internal temperature gradients. I set out to design a hybrid preheating strategy that would combine the merits of internal electric-drive pulse self-heating with external liquid-cooling-plate heating. The central goal was to provide fast, uniform, and energy-efficient warm-up for traction battery packs at temperatures below \(-10^\circ\text{C}\).
The following figure shows a representative arrangement of a traction battery pack that can be integrated with the preheating system discussed in this article.
In my work, I followed a path that combined experimental characterization, system design, prototype integration, experimental evaluation, and multi-physics simulation. First, I tested the low-temperature behavior of individual lithium-ion cells and used the results to support model parameterization. Then, I designed a composite heating architecture that included a liquid cold plate with a return-pattern flow channel, a PTC heater, a coolant circulation loop, and an electric-drive pulse self-heating converter. I constructed a laboratory test platform and compared three heating modes: pulse heating only, liquid heating only, and composite heating. Finally, I developed a three-dimensional electro-thermal-fluids coupled simulation model in COMSOL Multiphysics. After validating the model with experimental data, I used the model to optimize pulse frequency, current amplitude, and coolant flow rate. The outcome is an optimized preheating strategy that simultaneously enhances heating rate and temperature uniformity for traction battery packs.
2. Low-Temperature Performance Experiments with Lithium-Ion Cells
2.1 Cell Structure and Operating Principle
To understand the thermal and electrical behavior of a lithium-ion traction battery pack, I first studied the underlying cell-level storage mechanisms. The cells used in my experiments were commercial 18650 cylindrical cells with a nickel-cobalt-aluminum oxide cathode and a graphite anode. Their nominal capacity is \(2\,\text{Ah}\), the nominal voltage is \(3.8\,\text{V}\), the charge cutoff voltage is \(4.2\,\text{V}\), and the discharge cutoff voltage is \(2.7\,\text{V}\).
The working principle of the lithium-ion cell is based on the reversible shuttling of lithium ions between the positive and negative electrodes. During charging, lithium ions are extracted from the positive-electrode host structure, migrate through the electrolyte, and intercalate into the graphite anode; electrons flow through the external circuit. During discharge, the reverse process occurs. The overall electrode reactions can be written as:
$$ \text{Positive: } \mathrm{Li}_{a}X_{a}Y_{c} \rightleftharpoons \mathrm{Li}_{a-\theta}X_{a}Y_{c} + \theta \mathrm{Li}^{+} + \theta e^{-} \tag{2.1} $$
$$ \text{Negative: } x\mathrm{Li}^{+} + y\mathrm{C} + x e^{-} \rightleftharpoons \mathrm{Li}_{x}\mathrm{C}_{y} \tag{2.2} $$
Equation (2.1) describes the lithium concentration change inside the cathode host, while equation (2.2) describes the lithium-graphite intercalation compound. The reactions are accelerated by increasing temperature, but at low temperature the reaction exchange current density is low, which explains the large overpotential and resistive heating observed under load.
2.2 Experimental Setup and Design
I built a low-temperature test platform consisting of a battery cycler, a temperature-controlled chamber, a thermal insulation enclosure, K-type thermocouples, and a data acquisition unit. The cell cycler was capable of bidirectional charge-discharge control with an accuracy of \(0.1\%\) of full scale. I placed the cells inside the temperature chamber and waited for at least three hours at every target temperature to ensure thermal equilibrium before testing.
The main experiments were designed to answer five questions:
- How does the discharge capacity of the cell change from \(20^\circ\text{C}\) down to \(-20^\circ\text{C}\)?
- How do the open-circuit voltage and internal resistance depend on temperature and state of charge?
- How does the reversible entropic heat coefficient change with the state of charge?
- What is the effect of pulse current amplitude, frequency, and duty cycle on the heating rate?
- Can a composite heater outperform either pulse heating or liquid heating alone, while maintaining acceptable temperature uniformity and capacity fade?
2.3 Capacity Results at Low Temperatures
I measured the actual discharge capacity by first fully charging each cell to 4.2 V with a constant-current/constant-voltage protocol, then discharging at \(0.33C\) until reaching the 2.75 V cutoff. Table 1 summarizes the measured capacities. For comparison, I normalized the 20°C result as the reference condition.
| Temperature (°C) | Discharge capacity (Ah) | Capacity relative to 20°C (%) |
|---|---|---|
| 20 | 2.17 | 100.0 |
| 10 | 1.84 | 84.8 |
| 0 | 1.63 | 75.1 |
| -10 | 1.32 | 60.9 |
| -20 | 1.04 | 47.9 |
Table 2 summarizes the capacity fade relative to the 25°C condition measured before the cold-soak sequence.
| Temperature (°C) | Capacity decay relative to 25°C (%) |
|---|---|
| 10 | 15.2 |
| 0 | 24.9 |
| -10 | 39.9 |
| -20 | 52.1 |
These results confirm that a traction battery pack exposed to \(-20^\circ\text{C}\) loses a large fraction of its usable energy. The underlying causes include increased electrolyte viscosity, reduced ionic conductivity, slower charge-transfer kinetics, and an increased resistance of the solid-electrolyte interphase layer.
2.4 HPPC Test and Internal Resistance Behavior
To quantify the resistance and open-circuit voltage over a wide range of states of charge, I applied the hybrid pulse power characterization test. The current profile is shown below in a simplified manner. I first discharged the cell for 10 s at \(1C\), rested for 40 s, charged for 10 s at \(0.33C\), rested for 40 s, and then discharged at \(0.33C\) for 1075 s to decrease the SOC by 10%. After a one-hour rest, the process was repeated. This sequence produced OCV-SOC curves at \(20^\circ\text{C}\), \(10^\circ\text{C}\), \(0^\circ\text{C}\), \(-10^\circ\text{C}\), and \(-20^\circ\text{C}\). The discharge resistance was calculated using the voltage drop divided by the applied current step:
$$ R_{\text{discharge}} = \frac{\Delta V_{\text{drop}}}{\Delta I_{\text{pulse}}} \tag{2.3} $$
The measured OCV-SOC behavior could be divided into three operation regions. Below 20% SOC, a small change in capacity caused a sharp decline in open-circuit voltage. Between 20% and 80% SOC, the OCV was relatively flat. Above 80% SOC, the OCV increased steeply again. Temperature influenced the OCV in two ways: below 40% SOC, a lower temperature slightly increased the OCV, while above 70% SOC, a lower temperature decreased the OCV. More importantly, the internal resistance consistently increased as the temperature was lowered. At all tested SOC intervals, the cell resistance at \(-20^\circ\text{C}\) was several times higher than at \(20^\circ\text{C}\). This large resistance is precisely the mechanism that produces Joule heat during pulse self-heating, but it also creates risk of non-uniform heat generation inside a traction battery pack formed from multiple cells.
2.5 Entropic Heat Coefficient Measurement
Battery heat production is not purely irreversible. The reversible heat variation originates from the temperature dependence of the open-circuit potential. I measured the entropic coefficient using the potentiometric method. The fully charged cell was placed in a temperature chamber and subjected to successive temperature set-points of \(-20^\circ\text{C}\), \(-10^\circ\text{C}\), \(0^\circ\text{C}\), \(10^\circ\text{C}\), and \(20^\circ\text{C}\). Open-circuit voltages were measured after a long rest to attain electrochemical equilibrium. After each temperature sweep, the cell was discharged by 10% of rated capacity at \(0.2C\). The entropic heat coefficient was obtained from the slope:
$$ \frac{\mathrm{d}E_{\text{ocv}}}{\mathrm{d}T} \tag{2.4} $$
The experimental curves revealed that the entropic coefficient was negative for most SOC regions. This means that reversible heat tended to oppose the temperature rise during charge-discharge operations. Around 60% SOC, the reversible heat was nearly zero, which can be considered a turning point. In the high-SOC region from about 70% to 100%, the entropic coefficient became positive. In that region, the reversible heat effect amplified the temperature rise. These findings are essential for accurate thermal modeling of pulse heating in a traction battery pack because internal pulsing alternates between charge and discharge components at high frequency.
3. Design of the Composite Preheating System
3.1 System Architecture
I designed the composite preheating system around two independent heat-delivery pathways to maximize the temperature rise rate while retaining adequate spatial uniformity. The internal pathway relies on high-frequency pulse currents generated by the motor drive inverter and a permanent-magnet synchronous machine. The external pathway uses a PTC heater to warm a coolant mixture in an insulated tank; the coolant is circulated by a pump through a liquid cold plate mounted on the battery module. Figure 1 in the previous section shows an actual traction battery pack; the composite architecture conceptually surrounds such a pack with both an internal excitation port and an external thermal-fluid loop.
The key parameters in the internal heating loop were pulse current amplitude, switching frequency, and duty cycle. The key parameters in the external heating loop were coolant flow rate and PTC heating power. A bidirectional DC power supply was used to operate the PTC heater and pump. A computer-based supervisory control system collected real-time data from thermocouples attached to the battery cells and sent control commands to the drive hardware and power converter.
3.2 External Heating: Liquid Cold Plate Design
For external heating to be effective, the liquid cold plate should have a high surface temperature, a small surface-temperature difference, and uniform heat distribution. I examined five flow-channel geometries: U-shaped, parallel, composite, return, and S-shaped. I carried out steady-state and transient thermal simulations in COMSOL for a cold plate with dimensions \(90\,\text{mm} \times 65\,\text{mm} \times 5\,\text{mm}\), a channel diameter of \(3\,\text{mm}\), and an aluminum body. The coolant was a 50% ethylene glycol-water mixture. The simulation used an inlet velocity of \(0.04\,\text{m/s}\), an inlet fluid temperature of \(40^\circ\text{C}\), and an ambient temperature of \(0^\circ\text{C}\). Table 3 reports the wall-temperature distributions after 240 seconds of simulated operation.
| Flow-channel type | Temperature range (°C) | Temperature difference (°C) | High-temperature area share (%) | Low-temperature area share (%) |
|---|---|---|---|---|
| U-shaped | 37.1–38.5 | 1.4 | 31.05 | 53.66 |
| Parallel | 37.9–39.0 | 1.1 | 24.28 | 57.32 |
| Composite | 37.8–38.9 | 1.1 | 17.21 | 64.21 |
| Return | 38.2–39.2 | 1.0 | 36.78 | 42.03 |
| S-shaped | 38.2–38.7 | 0.5 | 22.50 | 56.49 |
Although the S-shaped channel had the smallest temperature difference, its wall temperature was lower on average. The return-pattern channel achieved the highest temperature range and the smallest low-temperature-region share, while maintaining a maximum surface-temperature difference of only \(1^\circ\text{C}\). Since the cold plate is intended to heat the traction battery pack, both heat-transfer capacity and surface uniformity are important. I selected the return-pattern channel as the optimal design and fabricated an aluminum liquid cold plate with six horizontal channels and two vertical side channels. The fluid enters through the lower-left port and exits from the upper-right port. I then mounted the cold plate on the cells using a 1 mm thermally conductive silicone pad and thermal grease to reduce contact resistance. Table 4 summarizes the material and structural parameters of the external liquid-heating loop.
| Component | Parameter | Value / material |
|---|---|---|
| Cold plate body | Material | Aluminum 6061 |
| Cold plate dimensions | Length × width × thickness | 90 × 65 × 5 mm |
| Channel diameter | Diameter | 3 mm |
| Header tube | Inner diameter / material | 8 mm / butyl rubber |
| Thermal pad | Thickness | 1 mm |
| Coolant | Composition | 50 vol% ethylene glycol / water |
| Coolant | Freezing point | -36.7°C |
3.3 Internal Heating: Electric-Drive Pulse Self-Heating
Internal pulse self-heating is attractive because the traction battery pack itself becomes the heat source. I used the motor-drive hardware of an electric-vehicle traction system. The three-phase stator windings act as inductors, and the inverter consists of six MOSFET switches. I applied a field-oriented-control algorithm through an STM32F405RGT6 microcontroller. The control objective was to maintain a zero q-axis current so that the rotor does not produce torque and remains stationary. At the same time, a d-axis current reference was deliberately oscillated between \(+I_{d}\) and \(-I_{d}\) at a controllable frequency. When the d-axis current is positive, the traction battery pack discharges into the motor windings. When the d-axis current is negative, the energy stored in the windings is returned to the traction battery pack, effectively creating a recharge event. This high-frequency charge-discharge alternation activates the polarization resistance and produces heat inside the cells.
The hardware circuit included the STM32F405RGT6 main controller, a DRV8301 gate-driver chip, a three-phase full-bridge inverter formed from Si7850DP MOSFETs, and a low-dropout power supply for digital and analog circuits. Communication with the PC was established through a CH340K USB-to-UART interface, and an encoder interface was used for rotor position feedback. Table 5 lists the main hardware characteristics.
| Component | Parameter | Specification |
|---|---|---|
| MCU | Core | ARM Cortex-M4 |
| MCU | Maximum frequency | 168 MHz |
| Gate driver | Type | DRV8301 |
| MOSFET | Drain-source voltage | 60 V |
| MOSFET | Drain current | 30 A |
| Motor | Rated voltage | 48 V |
| Motor | Rated power | 1000 W |
| Motor | Rated speed | 3000 rpm |
The software flow followed a clear execution sequence. I configured the system clock at 168 MHz using an external 25 MHz crystal. Timer 1 was set to center-aligned PWM mode to produce six complementary gate signals with a dead time of about 100 clock cycles. Timer 3 operated in quadrature encoder mode to capture rotor position and speed. Timer 2 generated a 10 kHz interrupt that served as the control period for the field-oriented-control algorithm. The ADC sampled two phase currents and the DC bus voltage at the beginning of every PWM cycle. All sampled data were transferred through DMA to reduce the CPU workload. The DRV8301 was configured through SPI, while the PC interface used high-speed UART communication. The control code included safety checks for over-temperature and over-current. A hardware enable signal connected to the gate-driver enable pin provided an emergency shutdown path.
Within each control interrupt, I used Clarke and Park transformations to convert the measured phase currents into the dq reference frame. Two proportional-integral regulators controlled the d-axis and q-axis currents independently. The q-axis current reference was fixed to zero to prevent torque generation. The d-axis current reference was generated by a square-wave oscillator whose amplitude and frequency were set by parameters in the control program. The output of the PI regulators was transformed back to the stationary frame through inverse Park and space-vector PWM synthesis. The resulting gate signals alternately connect the motor winding to the traction battery pack and recirculate current back to the battery.
3.4 Composite Heating Experimental Platform
I assembled a complete experimental test bench inside a temperature-controlled chamber. The test bench included the battery module, the fabricated liquid cold plate, a PTC heater, an insulated water tank, a coolant circulation pump, a flow meter, thermocouples, a data acquisition unit, and the electric-drive pulse heating hardware. The battery module consisted of five 18650 cells connected in series. I placed thermocouples on the surface of each cell. The coolant was delivered to the cold plate through silicone tubes and the flow rate was measured by a float-type flow meter. The external heating loop was powered by a bidirectional DC power supply, which allowed me to adjust the PTC heater power and the pump speed.
Several tables were generated from this platform. The first category concerned pulse heating. I varied the MOSFET switching frequency among 3000 Hz, 5000 Hz, and 8000 Hz. I also varied the duty cycle among 25%, 50%, and 75%, and the pulse current amplitude among \(1C\), \(2C\), and \(3C\). The ambient temperatures were chosen as \(-10^\circ\text{C}\), \(-15^\circ\text{C}\), and \(-20^\circ\text{C}\). The second category concerned liquid heating. I varied the coolant flow rate among 0.20, 0.30, 0.43, 0.56, and 0.73 L/min and the PTC power among 100 W, 200 W, and 300 W. The third category compared pulse heating alone, liquid heating alone, and composite heating at three ambient temperatures.
4. Experimental Results and Discussion
4.1 Pulse Heating Results
4.1.1 Influence of Switching Frequency
In the first series of pulse-heating experiments, I fixed the duty cycle at 50% and the pulse current at either \(2C\) or \(3C\). The switching frequency was set to 3000 Hz, 5000 Hz, and 8000 Hz in separate trials. Table 6 reports the average heating rate when heating the battery from the initial ambient temperature to \(10^\circ\text{C}\).
| Amplitude | Initial temperature (°C) | 3000 Hz heating rate (°C/min) | 5000 Hz heating rate (°C/min) | 8000 Hz heating rate (°C/min) |
|---|---|---|---|---|
| 2C | -10 | 2.37 | 2.05 | 1.76 |
| 2C | -15 | 2.78 | 2.23 | 2.09 |
| 2C | -20 | 2.54 | 1.78 | 1.61 |
| 3C | -10 | 3.42 | 3.36 | 2.95 |
| 3C | -15 | 4.26 | 3.71 | 3.20 |
| 3C | -20 | 4.36 | 3.83 | 3.56 |
The heating rate decreased nonlinearly as the switching frequency increased. A higher frequency creates more switching events per second, but the current pulse width becomes shorter. Since the heat generated in the cell is proportional to the square of the current integrated over the on time, the total Joule heat per second is reduced when the current waveform approaches an extremely short duty cycle at high frequency. Moreover, the switching losses in the inverter increase with frequency. Therefore, for the same traction battery pack and the same pulse amplitude, the most efficient operation occurs at the lowest tested frequency of 3000 Hz.
4.1.2 Influence of Duty Cycle
I next fixed the switching frequency at 3000 Hz and examined duty cycles of 25%, 50%, and 75%. Table 7 summarizes the resulting heating rates. At a fixed frequency and current amplitude, increasing the duty cycle increases the root-mean-square current delivered to the cells. Consequently, a larger duty cycle improves the heating rate. However, an excessively high duty cycle would also reduce the zero-current rest interval and increase the amount of lithium plating risk if the negative current forms a large DC component. Under my experimental conditions, the heating rates reached up to \(5.19^\circ\text{C/min}\) at \(-20^\circ\text{C}\) when the pulse amplitude was \(3C\), the frequency was 3000 Hz, and the duty cycle was 75%.
| Amplitude | Initial temperature (°C) | 25% duty (°C/min) | 50% duty (°C/min) | 75% duty (°C/min) |
|---|---|---|---|---|
| 2C | -10 | 1.95 | 2.25 | 2.54 |
| 2C | -15 | 2.52 | 2.87 | 3.03 |
| 2C | -20 | 2.32 | 2.54 | 2.57 |
| 3C | -10 | 2.93 | 3.32 | 3.92 |
| 3C | -15 | 3.84 | 4.24 | 4.43 |
| 3C | -20 | 4.01 | 4.34 | 5.19 |
For the same duty cycle, reducing the ambient temperature by \(5^\circ\text{C}\) increased the heating time by roughly 16% on average. This observation reflects the higher internal resistance and greater heat loss to the environment at lower temperatures. Even though the higher resistance generates more heat per unit current, the external thermal loss also increases because of the larger temperature difference between the battery and the ambient air.
4.1.3 Influence of Current Amplitude
The pulse current amplitude is the most direct control variable for heat generation. I performed experiments at two frequencies, 3000 Hz and 5000 Hz, with the duty cycle fixed at 50%, using pulse amplitudes of \(1C\), \(2C\), and \(3C\). Table 8 presents the average heating rates. I observed that doubling the current amplitude from \(1C\) to \(2C\) approximately doubled the heating rate, while increasing from \(1C\) to \(3C\) produced an almost four-fold improvement in many cases. This near-quadratic dependence is consistent with Joule heating from the battery resistance. Because the heat generation rate is proportional to the square of the current, a larger current amplitude yields a more substantial thermal effect than an increase in switching frequency or duty cycle.
| Frequency | Initial temperature (°C) | 1C heating rate (°C/min) | 2C heating rate (°C/min) | 3C heating rate (°C/min) |
|---|---|---|---|---|
| 3000 Hz | -10 | 0.70 | 2.24 | 3.31 |
| 3000 Hz | -15 | 0.80 | 2.63 | 4.24 |
| 3000 Hz | -20 | 1.14 | 2.58 | 3.64 |
| 5000 Hz | -10 | 0.61 | 1.44 | 3.94 |
| 5000 Hz | -15 | 1.13 | 2.23 | 4.97 |
| 5000 Hz | -20 | 0.72 | 2.58 | 3.64 |
Although larger currents improve the heating rate, they also increase the risk of lithium plating and conductive loss in the busbars. In the final optimization, I chose a compromise value that balances heating rate and capacity retention.
4.1.4 Temperature Uniformity of Pulse Heating
I measured the surface temperatures of five series-connected cells during pulse heating. Even with identical nominal cells, the cell-to-cell internal resistance varied slightly. At lower ambient temperature, the maximum temperature difference grew notably. For pulse heating at \(2C\), the maximum temperature difference exceeded \(5^\circ\text{C}\) during some periods. At \(3C\), the same behavior was observed. The trend is shown conceptually by Table 9, where the approximate final temperature difference at the moment when the average cell temperature reached \(10^\circ\text{C}\) is reported.
| Ambient temperature | Pulse 2C, 3000 Hz | Pulse 3C, 3000 Hz |
|---|---|---|
| -10°C | ~3°C | ~4°C |
| -15°C | ~4.5°C | ~5.5°C |
| -20°C | >5°C | >6°C |
Such temperature inconsistency is undesirable because cells with higher temperature and internal resistance may age faster, thereby limiting the lifetime of the entire traction battery pack. This was one of the strongest motivations for combining internal pulse heating with an external liquid heating source.
4.2 Liquid Heating Results
4.2.1 Influence of Coolant Flow Rate
For liquid heating, I set the PTC heater power to 200 W or 300 W and varied the coolant flow rate from 0.20 to 0.73 L/min. The results are summarized in Table 10. There is a clear optimum around 0.56 L/min. When the flow rate is too low, the coolant spends too much time inside the cold plate and loses thermal energy before reaching downstream cells; heat transfer to the edges of the traction battery pack is poor. When the flow rate is too high, the coolant passes through the plate so quickly that the thermal exchange time is insufficient and the outlet temperature remains close to the inlet temperature, reducing the total heat transferred to the module. Therefore, the pump should be operated inside the optimal window.
| PTC power (W) | Initial temperature (°C) | 0.20 L/min | 0.30 L/min | 0.43 L/min | 0.56 L/min | 0.73 L/min |
|---|---|---|---|---|---|---|
| 200 | -10 | slow | moderate | good | fastest | good |
| 200 | -15 | slow | moderate | moderate | fastest | good |
| 300 | -10 | moderate | good | fast | fastest | fast |
| 300 | -15 | moderate | good | good | fastest | good |
During the first two minutes of operation, the coolant exiting the PTC heater is still close to ambient temperature, so the initial heating effect is weak. After about three minutes, a thermal gradient develops and the cell temperature begins to rise more quickly. In practice, the PTC heater must be started ahead of time or operated continuously for the external liquid loop to provide meaningful preheating.
4.2.2 Influence of PTC Power
I measured the heating time and average heating rate at three PTC power levels while holding the flow rate at 0.43 L/min. Table 11 shows the average temperature-rise rate from the initial temperature to \(10^\circ\text{C}\).
| Initial temperature (°C) | 100 W (°C/min) | 200 W (°C/min) | 300 W (°C/min) |
|---|---|---|---|
| -10 | 1.18 | 1.69 | 2.67 |
| -15 | 1.20 | 2.08 | 2.54 |
| -20 | 1.00 | 2.00 | 2.54 |
Increasing the PTC power from 100 W to 300 W improved the heating rate by an average of 117% across the tested ambient temperatures. For a fixed power level, lowering the ambient temperature by \(5^\circ\text{C}\) increased the required heating time by approximately 40%. This is a larger increase than that observed in pulse heating, because the external liquid heating path has to overcome both the cell-to-coolant thermal resistance and the parasitic heat loss to the environment.
4.2.3 Temperature Uniformity of Liquid Heating
I measured the temperature distribution on the five cells during liquid heating. Unlike pulse heating, liquid heating produced a much more consistent temperature distribution. The maximum cell-to-cell temperature difference remained below \(3^\circ\text{C}\) for all tested conditions. This excellent uniformity arises because the liquid cold plate contacts a relatively large area of each cell and transfers heat through the silicone pad in a distributed manner. However, the overall heating rate of liquid-only heating was considerably lower than that of pulse-only heating.
4.3 Composite Heating Results
4.3.1 Temperature Rise Comparison
After evaluating pulse-only and liquid-only heating, I performed composite-heating experiments. The nominal parameters were a pulse current of \(3C\), a switching frequency of 3000 Hz, a duty cycle of 50%, a coolant flow rate of 0.56 L/min, and a PTC power of 300 W. Three ambient temperatures were considered: \(-10^\circ\text{C}\), \(-15^\circ\text{C}\), and \(-20^\circ\text{C}\). Table 12 compares the heating rates of the three modes.
| Initial temperature | Liquid-only (°C/min) | Pulse-only (°C/min) | Composite (°C/min) | Composite vs. liquid improvement (%) | Composite vs. pulse improvement (%) |
|---|---|---|---|---|---|
| -10°C | 2.61 | 3.15 | 6.67 | 156 | 112 |
| -15°C | 2.63 | 3.57 | 7.50 | 185 | 110 |
| -20°C | 2.58 | 3.94 | 7.83 | 203 | 99 |
The composite heating mode consistently achieved the highest heating rate. At \(-20^\circ\text{C}\), the heating rate reached \(7.83^\circ\text{C/min}\), meaning the traction battery pack could be warmed from \(-20^\circ\text{C}\) to \(10^\circ\text{C}\) in approximately 230 seconds. The advantage over the single-mode strategies increased as the ambient temperature became lower. I attribute this improvement to a synergistic effect: the internal pulse current heats the core of every cell, while the external PTC liquid heating supplies thermal energy to the cell surface and reduces the heat loss to the environment. As a result, the temperature gradient across the cell radial direction is minimized and the average temperature rises faster.
4.3.2 Temperature Uniformity of Composite Heating
The maximum cell-to-cell temperature difference during composite heating was below \(3^\circ\text{C}\) at all ambient temperatures considered. The temperature gradients were much smaller than those observed during pulse-only heating. The reason is that the external liquid heating path tends to equalize the surface temperatures of the cells, while the internal pulse heating provides volumetric heat generation. Together, these two mechanisms suppress local hot spots and mitigate the cell-to-cell variability caused by differences in internal resistance. Table 13 lists the final maximum temperature difference measured when the average module temperature reached \(10^\circ\text{C}\).
| Ambient temperature | Heating time to 10°C (s) | Maximum temperature difference (°C) |
|---|---|---|
| -10°C | 180 | 1.9 |
| -15°C | 210 | 2.9 |
| -20°C | 230 | 2.7 |
Although the maximum temperature difference slightly increased as the ambient temperature decreased, the observed change was relatively small. In all cases, the temperature uniformity satisfied common engineering targets for a traction battery pack thermal management system.
4.3.3 Energy Consumption Comparison
I calculated the electrical energy delivered to the battery during pulse heating using the time integral of power:
$$ Q_{\text{pulse}} = \int U(t) I(t) \, \mathrm{d}t \tag{4.1} $$
where \(U(t)\) is the terminal voltage and \(I(t)\) is the current flowing between the traction battery pack and the electric-drive system. The energy consumed by the PTC heater was calculated as:
$$ Q_{\text{PTC}} = \frac{P_{\text{PTC}} \, \Delta t}{\eta} \tag{4.2} $$
where \(P_{\text{PTC}}\) is the electric power of the PTC heater, \(\Delta t\) is the heating duration, and \(\eta\) is the conversion efficiency, which I set to 95%. Table 14 compares the total energy consumption of the three heating modes.
| Initial temperature | Pulse heating (J) | Composite heating (J) | Liquid heating (J) |
|---|---|---|---|
| -10°C | 42,180 | 76,822 | 145,263 |
| -15°C | 46,620 | 85,358 | 180,000 |
| -20°C | 51,060 | 98,161 | 217,894 |
Pulse-only heating was the least energy-intensive mode, consuming about 23% of the energy required by liquid-only heating at \(-20^\circ\text{C}\). Composite heating consumed more energy than pulse heating because the PTC heater and pump were also active. However, composite heating consumed substantially less energy than liquid-only heating while offering a much higher heating rate and good temperature uniformity. Therefore, composite heating offers the best trade-off among heating rate, uniformity, and energy consumption for the practical preheating of a traction battery pack.
4.4 Capacity Retention After Repeated Heating Cycles
Because pulse currents and thermal cycling could degrade the battery, I ran long-term experiments with 600 complete low-temperature heating cycles. The heating cycle started at \(-20^\circ\text{C}\) and ended when the average battery temperature reached \(10^\circ\text{C}\). The cells were divided into three groups labeled A, B, and C. Group A was heated with \(1C\) pulse current and 100 W PTC power; group B used \(2C\) and 200 W; group C used \(3C\) and 300 W. After every 300 cycles, I measured the discharge capacity at room temperature. Table 15 reports the average capacity fade.
| Group | Heating parameters | Capacity fade after 300 cycles (%) | Capacity fade after 600 cycles (%) |
|---|---|---|---|
| A | 1C + 100 W | 0.73 | 1.70 |
| B | 2C + 200 W | 1.70 | 3.00 |
| C | 3C + 300 W | 2.90 | 4.30 |
Even the most aggressive group retained more than 95% of its initial capacity after 600 cycles. This demonstrates that the composite heating strategy does not cause premature degradation outside an acceptable engineering envelope. The small capacity loss observed in group C is consistent with the generally accepted trade-off between high-rate heating and long-term aging in a lithium-ion traction battery pack.
5. Electro-Thermal Coupled Simulation and Parameter Optimization
5.1 Model Formulation
Although the experimental platform provided valuable insight, it was time-consuming to test every parameter combination. I therefore developed a multi-physics model in COMSOL Multiphysics to simulate the thermal behavior of the traction battery pack during external heating, internal pulse heating, and composite heating. The model couples an electrochemical cell-level description with heat transfer and fluid flow. The three-dimensional energy balance can be written as:
$$ \rho C_p \frac{\partial T}{\partial t} = \nabla \cdot \left(\lambda \nabla T \right) + q_{\text{gen}} \tag{5.1} $$
where \(\rho\) is the density, \(C_p\) is the specific heat capacity, \(\lambda\) is the thermal conductivity tensor, \(T\) is the temperature, and \(q_{\text{gen}}\) is the volumetric heat generation rate. The effective thermal conductivities are different in the in-plane and through-plane directions because the 18650 cells consist of many rolled layers. I used anisotropic conductivities of \(30\,\text{W/(m·K)}\) in the layer direction and \(1\,\text{W/(m·K)}\) in the through-layer direction.
For the heat generation inside the cell, I applied the widely used Bernardi equation:
$$ q_{\text{gen}} = \frac{1}{V} \left[ I^2 R_{\text{total}} – I T \frac{\mathrm{d} U_{\text{ocv}}}{\mathrm{d}T} \right] \tag{5.2} $$
where \(I\) is the current, \(R_{\text{total}}\) is the total effective resistance, \(V\) is the cell volume, and \(\frac{\mathrm{d} U_{\text{ocv}}}{\mathrm{d}T}\) is the entropic heat coefficient. During high-frequency pulse heating, the time-averaged reversible heat is small because the positive and negative half cycles cancel partially. Nevertheless, I retained the reversible term in the model because it contributes to local heat generation when the current is not perfectly symmetric around zero.
Heat conduction is governed by Fourier’s law:
$$ q = -\lambda \frac{\partial T}{\partial n} \tag{5.3} $$
Convection on the exposed surfaces is modeled as:
$$ q_c = h (T_s – T_{\infty}) \tag{5.4} $$
where \(h\) is the convective heat-transfer coefficient and \(T_{\infty}\) is the ambient temperature. Radiation was neglected because the temperature differences and surface areas are small. In the coolant subdomain, I solved the low-Reynolds-number laminar flow and heat-transfer equations to capture the temperature rise of the coolant as it flows through the cold plate. The fluid inlet temperature and velocity were set according to the experimental conditions.
5.2 Mesh-Independence Verification
I performed a mesh-independence study to balance accuracy and computational cost. Table 16 lists the results after 240 seconds of simulated operation for six mesh densities. The simulation parameters were \(-20^\circ\text{C}\) ambient temperature, \(2C\) pulse current, 3000 Hz frequency, and a liquid inlet temperature that ramped linearly from the cold-start temperature to \(40^\circ\text{C}\) during the first 120 seconds.
| Number of mesh elements | Average temperature (°C) | Maximum temperature difference (°C) | Average voltage (V) | Maximum pressure difference (V) |
|---|---|---|---|---|
| 220,451 | 11.29 | 3.31 | 4.090 | 0.0133 |
| 336,178 | 9.91 | 2.32 | 3.970 | 0.0096 |
| 548,178 | 6.94 | 2.43 | 3.964 | 0.0104 |
| 1,108,303 | 5.19 | 1.55 | 3.871 | 0.0206 |
| 2,552,359 | 5.01 | 1.28 | 3.851 | 0.0053 |
| 5,616,842 | 4.95 | 1.39 | 3.822 | 0.0093 |
When the mesh exceeded 2.5 million elements, the average temperature and voltage stabilized. The model with 2.55 million elements also produced the smallest maximum pressure difference. Consequently, I used approximately 2.55 million elements in the final preheating simulations. The fluid boundary layer was refined with two layers, and the minimum mesh size in the fluid region was 0.4 mm.
5.3 Model Validation with Experimental Data
I validated the simulation model by comparing the simulated average cell temperature with the measured temperature for liquid heating, pulse heating, and composite heating at three ambient temperatures. Table 17 summarizes the average absolute error and mean relative error for the full temperature-rise history. The average relative errors remained below about 9% for all modes and all temperatures. The largest deviations generally occurred during the first few seconds, when the transient thermal response is fast and the thermocouple reading may lag behind the actual core temperature.
| Ambient temperature (°C) | Heating mode | Average absolute error (°C) | Mean relative error (%) |
|---|---|---|---|
| -10 | Liquid | 0.33 | 4.32 |
| -10 | Pulse | 0.14 | 2.83 |
| -10 | Composite | 0.29 | 5.74 |
| -15 | Liquid | 0.91 | 6.82 |
| -15 | Pulse | 0.10 | 1.52 |
| -15 | Composite | 0.36 | 5.21 |
| -20 | Liquid | 0.08 | 6.67 |
| -20 | Pulse | 0.77 | 7.82 |
| -20 | Composite | 0.77 | 8.92 |
I also validated the model against surface-temperature measurements of individual cells. For liquid heating, the average relative error of the individual cell models was below 5%. For composite heating, the individual-cell errors were between 4% and 12%. The largest errors were found in pulse heating, where the cell-to-cell variation is prominent and the lumped model may not reproduce each cell’s exact internal resistance distribution. Overall, the model was judged sufficiently accurate for parametric optimization.
5.4 Influence of Pulse Frequency in Simulation
Using the validated model, I simulated 500 seconds of pulse heating at \(-20^\circ\text{C}\), an amplitude of \(3C\), and a duty cycle of 50%, with frequencies of 1000, 3000, 5000, and 8000 Hz. Table 18 reports the average temperature rise and the maximum temperature difference at 500 seconds.
| Pulse frequency (Hz) | Temperature rise at 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 1000 | 30.7 | 6.6 |
| 3000 | 27.2 | 5.3 |
| 5000 | 24.4 | 4.5 |
| 8000 | 20.3 | 3.6 |
The simulation confirms the experimental finding that lower frequencies lead to higher temperature rise because the on-time per cycle is longer. Conversely, the temperature uniformity improves at high frequency because heat is distributed more evenly throughout the cell. Since my objective is to maximize heating rate while keeping the maximum temperature difference acceptably small, 3000 Hz represents a good compromise. I therefore selected 3000 Hz as the optimal pulse frequency for the composite system.
5.5 Influence of Pulse Current Amplitude in Simulation
I also extended the pulse current amplitude range beyond the experimental values. Table 19 shows the simulated temperature rise and maximum temperature difference at \(-20^\circ\text{C}\), 3000 Hz, and 500 seconds for current amplitudes from \(1C\) to \(5C\).
| Current amplitude | Temperature rise at 500 s (°C) | Heating rate (°C/min) | Maximum temperature difference (°C) |
|---|---|---|---|
| 1C | 16.1 | 1.93 | 2.3 |
| 2C | 22.9 | 2.74 | 3.6 |
| 3C | 27.2 | 3.26 | 5.3 |
| 4C | 34.3 | 4.11 | 7.2 |
| 5C | 39.9 | 4.78 | 9.3 |
At high current amplitude, the temperature rise increases dramatically but so does the peak temperature difference. A current of \(3C\) yields a heating rate that is already high enough for practical preheating, while maintaining a maximum temperature difference below \(6^\circ\text{C}\). This is important for a traction battery pack, where large temperature differences can reduce capacity and cause uneven current distribution. I therefore selected \(3C\) as the preferred pulse current amplitude.
5.6 Influence of Coolant Flow Rate in Simulation
To refine the external heating strategy, I simulated nine coolant flow rates between 0.2 and 0.73 L/min. Table 20 presents the temperature rise and maximum temperature difference of the battery module after 500 seconds of composite heating at \(-20^\circ\text{C}\).
| Flow rate (L/min) | Temperature rise at 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 0.20 | 24.6 | 2.4 |
| 0.25 | 25.8 | 2.2 |
| 0.30 | 27.1 | 2.1 |
| 0.365 | 28.2 | 2.0 |
| 0.43 | 29.3 | 1.8 |
| 0.495 | 30.4 | 1.5 |
| 0.56 | 29.8 | 1.7 |
| 0.645 | 28.9 | 2.1 |
| 0.73 | 27.5 | 2.8 |
The maximum temperature rise occurs at a flow rate of 0.495 L/min, while the minimum temperature difference also occurs at this flow rate. This result confirms the existence of an optimal flow-rate window. At 0.495 L/min, the coolant carries enough heat to the cold plate without moving so fast that insufficient thermal exchange takes place. I selected 0.495 L/min as the optimal coolant flow rate.
5.7 Optimized Coupling of Internal and External Heating Parameters
Based on the simulation results, I selected the following optimized parameters for the composite preheating system: pulse current amplitude \(3C\), pulse frequency \(3000\,\text{Hz}\), duty cycle \(50\%\), coolant flow rate \(0.495\,\text{L/min}\), and PTC power \(300\,\text{W}\). I then simulated the optimized system at \(-10^\circ\text{C}\), \(-15^\circ\text{C}\), and \(-20^\circ\text{C}\). Table 21 compares the optimized performance with the initial experimental configuration.
| Ambient temperature (°C) | Heating time to 10°C, initial (s) | Heating rate, initial (°C/min) | Heating time, optimized (s) | Heating rate, optimized (°C/min) | Rate improvement (%) |
|---|---|---|---|---|---|
| -10 | 180 | 6.67 | 140 | 9.69 | 45 |
| -15 | 210 | 7.14 | 160 | 10.29 | 44 |
| -20 | 230 | 7.83 | 180 | 10.84 | 38 |
The optimized system increased the average heating rate by approximately 45%–50% relative to the initial configuration. The improvement was slightly stronger in the \(-10^\circ\text{C}\) case, expressed as a percentage of the original rate, but the absolute rate was highest at \(-20^\circ\text{C}\). More importantly, Table 22 shows that the optimized configuration reduced the maximum temperature difference to below \(1^\circ\text{C}\). This is a major improvement in temperature uniformity compared with the original system, where the maximum difference often exceeded \(2^\circ\text{C}\).
| Ambient temperature (°C) | Maximum temperature difference, initial (°C) | Maximum temperature difference, optimized (°C) |
|---|---|---|
| -10 | 1.9 | 0.6 |
| -15 | 2.9 | 0.7 |
| -20 | 2.7 | 0.8 |
The optimized thermal distribution is remarkably uniform. The model predicts that the cell surface temperature at the locations in contact with the liquid cold plate may be locally high because I modeled an ideal zero-resistance contact. In the actual hardware, thermal grease and silicone pad introduce a measurable contact resistance, which allows heat to spread more gradually and prevents a sharp localized hot spot. Therefore, the real system should be at least as safe and uniform as the simulation suggests.
6. Conclusions and Future Outlook
In this research, I systematically investigated the low-temperature performance of lithium-ion batteries, designed and implemented a composite preheating system, and optimized the key control parameters through experiments and simulation. The main conclusions can be summarized as follows:
- Low temperatures severely degrade the energy and power capability of a lithium-ion traction battery pack. From \(20^\circ\text{C}\) to \(-20^\circ\text{C}\), the discharge capacity of the tested 18650 cells decreased by more than 50%. The internal resistance increased several-fold, and the open-circuit voltage showed a strong dependence on both SOC and temperature. The entropic heat coefficient was negative for most SOC values and positive in the high-SOC region, indicating that reversible heat must be considered when modeling pulse-current heating.
- Among five cold plate flow-channel designs, the return-pattern channel achieved the highest effective heating temperature while maintaining a surface-temperature difference of only \(1^\circ\text{C}\). The return-pattern liquid cold plate was therefore selected and integrated with a PTC heater and coolant circulation loop for external heating.
- The electric-drive pulse self-heating method, based on the inverter and permanent-magnet synchronous machine, was implemented with a zero-torque d-q control strategy. By injecting a high-frequency alternating d-axis current, the traction battery pack was periodically charged and discharged through the motor windings. The hardware system, based on an STM32F405RGT6 and DRV8301 gate driver, successfully realized closed-loop current control and precise pulse waveform shaping.
- Experimental studies showed that larger pulse current amplitude, lower switching frequency, and higher duty cycle all improve the heating rate. A larger pulse current amplitude was the most effective single parameter. At \(-20^\circ\text{C}\), pulse-only heating reached \(5.19^\circ\text{C/min}\), while liquid-only heating reached \(2.58^\circ\text{C/min}\). The composite heating mode achieved \(6.67^\circ\text{C/min}\), \(7.50^\circ\text{C/min}\), and \(7.83^\circ\text{C/min}\) at \(-10^\circ\text{C}\), \(-15^\circ\text{C}\), and \(-20^\circ\text{C}\), respectively. The composite mode maintained the maximum temperature difference below \(3^\circ\text{C}\), which is acceptable for a modular traction battery pack.
- The energy consumption of pulse heating was the lowest among the three modes, but composite heating provided the best trade-off between energy use, heating rate, and uniformity. After 600 complete low-temperature preheating cycles, the worst-case capacity fade was below 5%, suggesting that the composite strategy is compatible with long-life operation.
- The COMSOL model successfully reproduced the experimental average temperature histories and individual cell temperature behaviors. Simulation-based optimization showed that the optimal pulse frequency is 3000 Hz, the optimal pulse current amplitude is \(3C\), and the optimal coolant flow rate is 0.495 L/min. With these parameters, the heating rate improved by approximately 45%–50%, and the maximum cell-to-cell temperature difference decreased to below \(1^\circ\text{C}\), demonstrating an excellent combination of heating rate and thermal uniformity.
Future work should extend the laboratory prototype to a full-scale vehicle integration. I intend to validate the composite heating strategy on a real electric vehicle platform, taking into account the parasitic heat loads, cooling loop dynamics, and real-time constraints imposed by the traction battery pack management system. In addition, the optimal parameters should be adaptively adjusted according to the system state by using a model-based controller. Such an adaptive controller could further minimize energy consumption and prevent over-temperature or excessive lithium plating while maximizing the warm-up time. Finally, I plan to evaluate advanced heater designs, such as more efficient positive-temperature-coefficient films or heat pumps, in order to improve the overall energy conversion efficiency of external heating. Nevertheless, the present results provide a solid basis for applying composite internal-external preheating to real-world traction battery packs in cold climates.