Lithium-ion batteries have become the dominant energy source for modern electric vehicles, mainly because of their high energy density, low self-discharge rate, long cycle life, and comparatively low environmental impact. In recent years, the vehicle traction battery has evolved from a simple energy-storage unit into a highly engineered subsystem that determines vehicle range, dynamic response, and safety. However, the working temperature of the vehicle traction battery is far from uniform across climates. When the ambient temperature drops below 0 °C, the behavior of the lithium-ion cell changes drastically. The electrolyte viscosity increases, the lithium-ion diffusion coefficient in the graphite anode decreases, and the charge-transfer resistance at the electrode–electrolyte interface rises. These changes lead to serious consequences: capacity loss during discharge, limited regenerative braking acceptance, drastic power decrease, and, most dangerously, lithium plating during charging. Lithium dendrites may grow through the separator and cause internal short circuits, which can result in thermal runaway and catastrophic failure.
The challenge is particularly severe in high-latitude regions where winter temperatures may remain below −20 °C for weeks. For a vehicle traction battery, the low-temperature limitation is not only a comfort issue, but also an energy-security issue. Field data from northern China show that the actual driving range can drop by more than 40% at −20 °C compared with the range at 25 °C. Even when the vehicle is parked outdoors overnight, the battery temperature may drop far below the acceptable threshold for fast charging. Therefore, an effective low-temperature preheating system is indispensable for a vehicle traction battery. The preheating system must raise the cell temperature from an extremely cold state to the normal operating window within a few minutes, while maintaining adequate thermal uniformity inside the pack and minimizing extra energy consumption.
Various approaches have been proposed for lithium-ion battery preheating, and they can be divided into external heating methods and internal heating methods. External heating uses air, liquid, phase-change material, or an electric heating film as the heat transfer medium. In these methods, heat is first generated outside the battery, then transferred through the surface of the cell. External heating is usually easy to integrate into the vehicle thermal management loop, but its heating rate is limited by the thermal resistance between the heat source and the core of the battery. The internal heating method, by contrast, applies current through the battery itself. The internal resistance of the cell generates Joule heat directly inside the electrode stack. As a result, internal heating can achieve a much higher temperature rise rate, but an improper current waveform may accelerate the degradation of the vehicle traction battery. A more promising route is to combine internal and external heating. The composite heating strategy can exploit the advantages of both methods: the internal pulsed current produces heat from the inside, while the external liquid loop provides a boundary heat source and improves the uniformity of the final temperature distribution.
In my research, I address the low-temperature preheating problem of the vehicle traction battery from four perspectives. First, I characterize the low-temperature performance of a commercial 18650 lithium-ion cell and extract the parameters needed for thermal modeling. Second, I design a composite preheating system that is composed of an internal electric-drive pulse self-heating loop and an external liquid-cooling-plate heating loop. Third, I experimentally study the influence of key parameters, including pulse amplitude, pulse frequency, duty cycle, coolant flow rate, and heating power, on the behavior of the vehicle traction battery under cold conditions. Finally, I build a three-dimensional electro-thermal coupled simulation model in COMSOL Multiphysics, validate the model against experimental data, and use the model to search for an optimized set of operating parameters. The main contribution of this work is a carefully optimized composite-preheating solution for a low-temperature vehicle traction battery, and its positive effect on heating rate and thermal uniformity is quantitatively confirmed.
1. Low-Temperature Characterization of the Studied Cell
The test cell used in this study is a commercial 18650-format lithium-ion battery with a rated capacity of 2 Ah and a nominal voltage of 3.8 V. The positive electrode uses nickel-cobalt-aluminate, the negative electrode uses graphite, the charging cut-off voltage is 4.2 V, and the discharging cut-off voltage is 2.7 V. The dimensions of the cell are 65 mm in height and 18 mm in diameter. The primary properties of the cell are listed in Table 1.
| Parameter | Value |
|---|---|
| Rated capacity | 2 Ah |
| Nominal voltage | 3.8 V |
| Cell dimension | 18 mm in diameter, 65 mm in height |
| Cathode material | LiNiCoAlO2 |
| Anode material | Graphite |
| Charge cut-off voltage | 4.2 V |
| Discharge cut-off voltage | 2.7 V |
All characterization tests were performed in a programmable temperature chamber. The chamber provides a stable thermal environment whose fluctuation is less than ±0.3 °C and whose deviation is less than ±2 °C over the desired operating range. A battery cycler was used to load the cell with a pre-programmed current profile, while thermocouples attached to the cell surface measured the temperature. The experimental platform is briefly described in Table 2.
| Device | Main function | Key specification |
|---|---|---|
| Temperature chamber | Maintains the cell at the target temperature | −40 °C to +80 °C |
| Battery cycler | Charges and discharges the cell according to a designed pattern | Voltage range up to 5 V, current range adjustable |
| Data acquisition unit | Records voltage, current, and surface temperature | Measurement accuracy ±0.1% of range |
| Thermocouples | Measure surface temperature at different locations | Measurement range −30 °C to 110 °C |
During a lithium-ion battery’s operation, the overall electrochemical reaction can be summarized by equations that describe the transfer of lithium ions between the cathode and the anode. At the positive electrode, lithium ions are released during charging and reinserted during discharging:
$$ \mathrm{LiMO_2} \rightleftharpoons \mathrm{Li_{1-x}MO_2} + x\mathrm{Li^+} + x e^- . $$
At the negative graphite electrode, lithium ions are inserted during charging and removed during discharging:
$$ x\mathrm{Li^+} + x e^- + 6\mathrm{C} \rightleftharpoons \mathrm{Li_xC_6}. $$
In cold conditions, the kinetics of both reactions slows down remarkably. The exchange current density decreases because the charge-transfer activation energy is difficult to overcome at low temperatures. Consequently, the internal resistance and the polarization resistance of the vehicle traction battery increase, limiting its power throughput.
1.1 Capacity tests at different temperatures
To evaluate the temperature sensitivity of usable energy, the cell was first charged to 4.2 V using a constant-current constant-voltage protocol at room temperature, and then discharged at 0.33 C until the voltage reached 2.75 V. The discharge process was repeated at 20 °C, 10 °C, 0 °C, −10 °C, and −20 °C after the cell was soaked for three hours at the target temperature. The measured discharge capacity and the capacity retention relative to the value at 25 °C are summarized in Table 3.
| Temperature (°C) | Discharge capacity (Ah) | Capacity retention relative to 25 °C (%) |
|---|---|---|
| 25 | ≈ 2.17 | 100.0 |
| 20 | 2.17 | ≈ 100.0 |
| 10 | 1.84 | 84.8 |
| 0 | 1.63 | 75.1 |
| −10 | 1.32 | 60.1 |
| −20 | 1.04 | 47.9 |
Compared with the capacity at 25 °C, the discharge capacity of the 18650 cell decreases by more than 50% at −20 °C. The result is even worse when the discharge current is increased. A vehicle traction battery in a cold climate therefore loses a significant portion of its usable energy, and the only practical solution is to raise the battery temperature before the main discharge event.
1.2 Hybrid pulse power characterization
Hybrid pulse power characterization (HPPC) tests were carried out to measure the open-circuit voltage (OCV) and the direct-current internal resistance at different SOC levels. The HPPC test consists of repeated pulse sequences at different states of charge. At each SOC point, a 10-second discharge pulse is applied, followed by a 40-second rest, a 10-second charge pulse, and another rest period. The direct-current resistance was calculated from the voltage response and the applied current:
$$ R_{\rm dc} = \frac{\Delta U}{\Delta I}. $$
The OCV-SOC relationship of the cell at several temperatures is illustrated by the measured data. When the SOC is below 20%, a sharp decrease in OCV is observed as the SOC approaches zero. In the intermediate SOC window from 20% to 80%, the OCV changes only gradually. Above 80% SOC, the OCV rises quickly. The influence of temperature is coupled with the SOC level: below approximately 40% SOC, the OCV decreases as the temperature increases; above approximately 70% SOC, the opposite trend appears. The internal resistance of the vehicle traction battery also depends on both temperature and SOC. At SOC levels lower than 20%, the resistance increases sharply when the SOC decreases; in the middle SOC range, the resistance is relatively flat; above 80%, it increases again as the SOC approaches full charge. For every tested SOC point, the internal resistance grows significantly as the temperature drops. The HPPC results confirm that thermal management of the vehicle traction battery cannot rely only on averaged parameters; a coupled electro-thermal model is required.
1.3 Entropy coefficient measurement
The reversible heat of a lithium-ion cell is related to the temperature derivative of the open-circuit voltage, usually called the entropic heat coefficient. This coefficient can be measured by recording the OCV at several well-defined temperatures after the cell has reached thermodynamic equilibrium. In my test, the cell was charged to a given SOC, left at rest for twelve hours, and then exposed to alternating temperature steps of −20 °C, −10 °C, 0 °C, 10 °C, and 20 °C. The open-circuit voltage was recorded after each temperature step, and the entropic heat coefficient was approximated as
$$ \frac{d E_{\rm OCV}}{dT} \approx \frac{\Delta E_{\rm OCV}}{\Delta T}. $$
The measured entropic coefficient is negative for most of the SOC range, which means that the reversible heat during charging tends to absorb energy and therefore suppresses the temperature rise. Around 60% SOC, the reversible heat is close to zero. In the high-SOC region from approximately 70% to 100% SOC, the coefficient becomes positive, and the reversible reaction heat reinforces the total heat generation. The measured behavior is listed qualitatively in Table 4.
| SOC interval | Entropic heat coefficient | Effect on temperature |
|---|---|---|
| 10%–50% | Negative | Reversible heat during discharge enhances heating; reversible heat during charge absorbs energy |
| ≈ 60% | Near zero | Negligible reversible contribution |
| 70%–100% | Positive | Reversible heat raises the effective heating rate |
These data provide the necessary thermal parameters for the dynamic model of the vehicle traction battery used later in this thesis.
2. Architecture and Design of the Composite Heating System
I design a composite heating architecture that combines an external liquid-loop heating system with an internal electric-drive pulse-heating system. The proposed layout is shown in the experimental process diagram of the composite system. In the internal heating loop, a three-phase permanent-magnet synchronous motor and an inverter are used to generate a high-frequency alternating current in the battery pack, so that the battery can self-heat through its internal impedance. In the external heating loop, a bidirectional DC power source supplies electric energy to a positive-temperature-coefficient (PTC) heater. The PTC heater heats the coolant stored in an insulated water tank. A pump then circulates the heated coolant through a liquid cooling plate that is in contact with the battery module. In my design, the heating parameters can be independently adjusted, including the amplitude and frequency of the pulse current, the PTC heating power, and the coolant flow rate.
2.1 External heating: selection of the liquid cooling plate flow channel
The liquid cooling plate is one of the most important components of the external heating circuit. In order to obtain a compact and efficient cooling plate, I compared five different flow-channel configurations: U-shaped, parallel-channel, compound-channel, serpentine-return-channel, and S-shaped. The plate is made of aluminum, whose density is much lower than that of copper while its thermal conductivity is sufficient for a plate thickness of several millimeters. The dimensions of the plate are 90 mm × 65 mm × 5 mm, and the channel diameter is 3 mm. The coolant is a 50%-volume ethylene glycol-water solution. Table 5 lists the physical properties of the aluminum plate and the coolant.
| Property | Aluminum plate | Coolant (50% EG/water) |
|---|---|---|
| Density (kg/m³) | 2719 | 1100 |
| Specific heat (J/kg·K) | 891 | 3300 |
| Thermal conductivity (W/m·K) | 202.4 | 0.43 |
| Dynamic viscosity (Pa·s) | — | 0.00339 |
| Freezing point (°C) | — | −36.7 |
I first simulated the five flow-channel designs with a coolant inlet velocity of 0.04 m/s and an inlet temperature of 40 °C. The transient simulation ran for 240 s until the flow and thermal fields reached an approximately steady state. The temperature-distribution results are summarized in Table 6. The serpentine-return channel exhibits the best combination of a small temperature span and a high wall temperature. The parallel channel and the compound channel display improved uniformity but a smaller area of high temperature, which implies a weaker heating capability for the battery module. The U-shaped channel shows the largest temperature spread. Therefore, the serpentine-return channel was selected as the optimal design for the external heating circuit.
| Channel type | Temperature range (°C) | Maximum deviation (°C) | High-temperature area share (%) | Low-temperature area share (%) |
|---|---|---|---|---|
| U-shaped | 37.1–38.5 | 1.4 | 31.1 | 53.7 |
| Parallel channel | 37.9–39.0 | 1.1 | 24.3 | 57.3 |
| Compound channel | 37.8–38.9 | 1.1 | 17.2 | 64.2 |
| Serpentine return | 38.2–39.2 | 1.0 | 36.8 | 42.0 |
| S-shaped | 38.2–38.7 | 0.5 | 22.5 | 56.5 |
After thermal simulation, the serpentine-return flow channel was machined from an aluminum block. The external liquid loop also includes a PTC heater, an insulated water tank, a coolant pump, a flow meter, and flexible hoses. The cooling plate is mounted in good thermal contact with the bottom of the vehicle traction battery module through a thermally conductive silicone pad with a thickness of 1 mm.
2.2 Internal heating: electric-drive pulse self-heating
The internal self-heating method relies on the resistance of the vehicle traction battery to generate heat. However, continuous DC self-heating can cause serious lithium plating at low temperature, especially on the graphite anode. A more effective solution is to generate a high-frequency alternating pulse current through the battery. If the frequency is chosen properly, the current changes the direction of lithium insertion and extraction quickly, which reduces the concentration polarization and avoids prolonged lithium deposition. The heat generation can be described by the Joule heating expression
$$ Q_{\rm Joule} = I_{\rm rms}^{2} R_{\rm cell}, $$
where \(R_{\rm cell}\) is the total equivalent resistance of the battery, including ohmic resistance and polarization resistance.
In an electric vehicle, the inverter and the stator winding of the traction motor are already available hardware. If the vehicle is stationary, the rotor can be locked. Under this condition, the motor torque is proportional to the q-axis current. If the q-axis current is controlled to zero, the motor does not produce any torque, while the d-axis current remains controllable. The d-axis current can therefore be used as a pulse current flowing through the inverter and the motor winding. When the d-axis current is positive, the battery delivers energy. When the d-axis current is negative, the stored magnetic energy in the motor winding is returned to the battery. As a result, the vehicle traction battery is charged and discharged alternately in a controlled high-frequency pattern.
I implemented the control algorithm on an STM32F405-based controller. The controller generates six PWM signals with a programmed dead time and sends them to a gate driver. The gate driver drives six power MOSFETs arranged as a three-phase full bridge. Two phase currents and the DC-bus voltage are sampled synchronously with the PWM carrier. The field-oriented control algorithm calculates the current error in the d-q reference frame and outputs the voltage reference. Space-vector pulse-width modulation is then used to synthesize the required voltage vector.
The main hardware parameters of the permanent-magnet synchronous motor are listed in Table 7. This motor is used as the electromagnetic load in the internal self-heating circuit.
| Motor parameter | Value |
|---|---|
| Rated voltage | 48 V |
| Rated output power | 1000 W |
| Rated current | 30 A |
| q-axis inductance | 0.15 mH |
| d-axis inductance | 0.08 mH |
| Rated speed | 3000 rpm |
| Line-to-line resistance | 0.07 Ω |
The controller software contains a current closed-loop routine. The q-axis current reference is set to zero to guarantee zero torque output, and the d-axis current reference alternates between \(+I_{d,\rm ref}\) and \(-I_{d,\rm ref}\) with a programmable switching frequency and a variable duty cycle. This control strategy is the foundation of the internal pulse self-heating system.
2.3 Construction of the composite heating platform
After assembling the components, I built a complete experimental platform for the composite preheating study. The platform is composed of a battery module with five 18650 cells, a serpentine-return liquid cooling plate, a PTC heater, a water tank, a pump, a flow meter, an STM32 control board, a three-phase motor, a bidirectional DC power supply, a data acquisition unit, and a high-low temperature chamber. The battery module and the external liquid loop are installed inside the temperature chamber, while the DC power supply, pump, and controller are located outside. Thermocouples are attached to the surface of each cell to record the temperature evolution during the heating tests. The platform permits precise adjustment of the most important heating parameters: the pulse amplitude, the pulse frequency, the duty cycle, the PTC power, and the coolant flow rate. This experimental setup serves as the main tool for studying the multi-parameter coupling behavior of the low-temperature vehicle traction battery heating system.
3. Experimental Study and Parameter Analysis
In this section, I use the experimental platform to investigate the heating behavior of the battery under three heating modes: pulse internal heating only, liquid external heating only, and composite heating. The relevant test parameters are summarized in Table 8.
| Heating scheme | Variable | Value |
|---|---|---|
| Pulse heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Current amplitude | 1 C, 2 C, 3 C | |
| MOSFET frequency | 3000 Hz, 5000 Hz, 8000 Hz | |
| Liquid heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Flow rate | 0.2–0.73 L/min | |
| Composite heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Main heating parameters | 3 C, 3000 Hz, 300 W, 0.56 L/min |
Every temperature-rise result in this thesis is expressed as the average heating rate from the initial battery temperature to 10 °C:
$$ \bar{v}_{T}=\frac{T_{\rm target}-T_{\rm initial}}{\Delta t}. $$
3.1 Influence of pulse frequency
To identify the influence of MOSFET switching frequency on the internal heating effect, I carried out a series of experiments with a duty cycle of 50% and amplitudes of 2 C and 3 C. The switching frequency was set to 3000 Hz, 5000 Hz, or 8000 Hz. Table 9 reports the average heating rates at three ambient temperatures.
| Ambient temperature | Pulse current | Heating rate at 3000 Hz (°C/min) | Heating rate at 5000 Hz (°C/min) | Heating rate at 8000 Hz (°C/min) |
|---|---|---|---|---|
| −10 °C | 2 C | 2.37 | 2.05 | 1.76 |
| −15 °C | 2 C | 2.78 | 2.23 | 2.09 |
| −20 °C | 2 C | 2.54 | 1.78 | 1.61 |
| −10 °C | 3 C | 3.42 | 3.36 | 2.95 |
| −15 °C | 3 C | 4.26 | 3.71 | 3.20 |
| −20 °C | 3 C | 4.36 | 3.83 | 3.56 |
The experimental results demonstrate that raising the pulse frequency does not improve the heating performance of the vehicle traction battery. On the contrary, higher switching frequencies cause more switching loss in the inverter, more driving loss in the gate circuit, and more core loss in the motor windings. These energy losses do not contribute directly to battery heating. As a result, the net heating rate decreases when the switching frequency becomes higher. The best heating effect is obtained at 3000 Hz, which is therefore selected for the subsequent composite tests.
3.2 Influence of duty cycle
Duty cycle is another key parameter in the pulse-heating strategy. It defines the share of the switching period in which the positive current is applied. In the experiments, the duty cycle was set to 25%, 50%, and 75%, while the pulse frequency remained at 3000 Hz. The measured heating rates are given in Table 10.
| Ambient temperature | Pulse current | Heating rate at 25% duty (°C/min) | Heating rate at 50% duty (°C/min) | Heating rate at 75% duty (°C/min) |
|---|---|---|---|---|
| −10 °C | 2 C | 1.95 | 2.25 | 2.54 |
| −15 °C | 2 C | 2.52 | 2.87 | 3.03 |
| −20 °C | 2 C | 2.32 | 2.54 | 2.57 |
| −10 °C | 3 C | 2.93 | 3.32 | 3.92 |
| −15 °C | 3 C | 3.84 | 4.24 | 4.43 |
| −20 °C | 3 C | 4.01 | 4.34 | 5.19 |
It can be seen that the heating rate increases only moderately when the duty cycle is increased from 25% to 75%. The maximum pulse-heating rate is 5.19 °C/min, which is obtained at −20 °C with a pulse current of 3 C and a duty cycle of 75%. In general, a higher duty cycle means that the battery is conducting current for a longer time within each switching period, so more ohmic heat is generated. However, the improvement is not linear, because a longer positive-current duration also leads to a higher average SOC change within each cycle and increases the risk of local lithium concentration at the anode surface.
3.3 Influence of pulse current amplitude
The pulse current amplitude determines the Joule heating power inside the vehicle traction battery because the heating power is proportional to the square of the current amplitude. The measured heating rates at different current amplitudes are shown in Table 11.
| Ambient temperature | Frequency | Heating rate at 1 C (°C/min) | Heating rate at 2 C (°C/min) | Heating rate at 3 C (°C/min) |
|---|---|---|---|---|
| −10 °C | 3000 Hz | 0.70 | 2.24 | 3.31 |
| −15 °C | 3000 Hz | 0.80 | 2.63 | 4.24 |
| −20 °C | 3000 Hz | 1.14 | 2.58 | 3.64 |
| −10 °C | 5000 Hz | 0.61 | 1.44 | 3.94 |
| −15 °C | 5000 Hz | 1.13 | 2.23 | 4.97 |
| −20 °C | 5000 Hz | 0.72 | 2.58 | 3.64 |
The data clearly show that doubling the pulse current roughly doubles or even triples the average heating rate in many cases. Increasing the current amplitude is therefore more effective than increasing the pulse frequency. When the current amplitude is increased by 100%, the average heating rate increases approximately by 120%. This result suggests that, from the perspective of fast preheating, the internal pulse heater should be operated with the largest current that is acceptable for the battery lifetime and the inverter capacity.
3.4 Temperature uniformity of pulse heating
Although pulse heating provides a rapid temperature rise, the temperature uniformity inside the pack must also be evaluated. I therefore attached five thermocouples to the surfaces of five cells. The tests were performed at an initial temperature of −10 °C, −15 °C, and −20 °C, respectively, using a frequency of 3000 Hz and a current amplitude of 2 C or 3 C. As the ambient temperature decreases, the maximum temperature difference inside the five-cell module increases considerably. For the pulse-only scheme, the maximum internal temperature difference can exceed 5 °C. The non-uniformity mainly originates from the difference in the internal resistance among the individual cells. In a real vehicle traction battery pack with dozens or hundreds of cells, this non-uniformity can be more severe. External heating, by contrast, helps to reduce the maximum temperature difference because the liquid cooling plate acts as a boundary heat source that homogenizes the edge temperature.
3.5 Influence of coolant flow rate and PTC heating power
In the liquid-heating mode, heat is produced by the PTC heater and transported to the liquid cooling plate by the coolant. The heat-transfer process can be described by the convective heat-transfer equation between the plate surface and the coolant:
$$ q = h_{c}\left(T_{\rm plate}-T_{\rm coolant}\right), $$
where \(h_{c}\) is the convective heat-transfer coefficient, which depends strongly on the flow rate.
The effect of flow rate was investigated at PTC powers of 200 W and 300 W. The flow rate was varied from 0.2 L/min to 0.73 L/min. The results reveal a non-monotonic trend. At flow rates lower than about 0.43 L/min, the heat-transfer coefficient is too small, and the temperature difference between the inlet and outlet is large. The thermal energy delivered by the coolant cannot compensate for the heat loss at the edge of the cold plate. At flow rates above approximately 0.73 L/min, the fluid passes too quickly through the cooling plate, so the heat-exchange time is insufficient. Both extremes lead to a low effective heating rate. The optimum range is observed near 0.56 L/min. At this flow rate, the heated coolant distributes heat evenly across the plate and the battery module reaches the target temperature faster than at other tested rates.
The influence of PTC power was further examined at a flow rate of 0.43 L/min. Table 12 lists the required heating time and the corresponding average heating rate for three different PTC powers.
| Ambient temperature | Heating duration and rate at 100 W | Heating duration and rate at 200 W | Heating duration and rate at 300 W |
|---|---|---|---|
| −10 °C | 1020 s, 1.18 °C/min | 700 s, 1.69 °C/min | 460 s, 2.67 °C/min |
| −15 °C | 1250 s, 1.20 °C/min | 720 s, 2.08 °C/min | 590 s, 2.54 °C/min |
| −20 °C | 1800 s, 1.00 °C/min | 900 s, 2.00 °C/min | 650 s, 2.58 °C/min |
A higher PTC power always improves the heating rate. At the same PTC power, the required heating time increases by roughly 40% for every 5 °C decrease of the ambient temperature. This observation indicates that liquid heating alone is slow and strongly dependent on the boundary conditions. Therefore, liquid heating should be combined with internal heating when the environment is extremely cold.
4. Comparison of Heating Strategies
After identifying the influence of individual parameters, I compared the three heating strategies under identical conditions. The comparison tests were carried out at −10 °C, −15 °C, and −20 °C. The pulse current was 3 C, the switching frequency was 3000 Hz, the PTC power was 300 W, and the coolant flow rate was 0.56 L/min. The temperature-rise curves and average heating rates are summarized in Table 13.
| Ambient temperature | Heating scheme | Heating time to 10 °C (s) | Average heating rate (°C/min) |
|---|---|---|---|
| −10 °C | Liquid only | 460 | 2.61 |
| Pulse only | 380 | 3.15 | |
| Composite | 180 | 6.67 | |
| −15 °C | Liquid only | 570 | 2.63 |
| Pulse only | 420 | 3.57 | |
| Composite | 210 | 7.14 | |
| −20 °C | Liquid only | 690 | 2.61 |
| Pulse only | 460 | 3.94 | |
| Composite | 230 | 7.83 |
At every ambient temperature, the composite-heating scheme achieves a significantly higher heating rate than any single method. In particular, at −20 °C the composite method heats the vehicle traction battery from −20 °C to 10 °C within 230 s, corresponding to an average heating rate of 7.83 °C/min. This rate is approximately twice as high as the pulse-only method and about three times as high as the liquid-only method. Moreover, the advantage of composite heating becomes more obvious as the initial temperature decreases. This is because the internal pulse current exploits the negative temperature coefficient of the battery resistance: at a lower temperature, the resistance is higher, so the same pulse current raises the local temperature more effectively. Meanwhile, the external liquid heating reduces heat loss through the module surface and simultaneously supplies continuous heat from the bottom boundary.
4.2 Temperature uniformity of composite heating
For a vehicle traction battery, the maximum temperature difference inside the module is an important safety index. During the composite-heating tests, five thermocouples were used to monitor the temperature of each cell. The maximum temperature difference is presented in Table 14.
| Initial temperature | Heating time to 10 °C (s) | Maximum temperature difference |
|---|---|---|
| −10 °C | 180 | Less than 3 °C |
| −15 °C | 210 | Less than 3 °C |
| −20 °C | 230 | Less than 3 °C |
In the composite mode, the maximum temperature difference increases only slightly when the ambient temperature decreases, and the increase is smaller than 0.5 °C per 10 °C reduction of the ambient temperature. In comparison, pulse-only heating produced a maximum temperature difference above 5 °C, which is too large for reliable operation of a large vehicle traction battery pack. The external liquid loop helps to equalize the cell temperature by supplying heat to the bottom of the module. Therefore, composite heating not only accelerates the warm-up process but also improves the thermal uniformity.
4.3 Energy-consumption comparison
Energy consumption is another key criterion when evaluating heating strategies for a vehicle traction battery, because the heating process consumes energy from the same battery that is being warmed. The energy consumed by the pulse-current source was calculated by
$$ Q_{\rm pulse}=\int_{0}^{t_f} U_{\rm pack}(t) I_{\rm pack}(t)\, dt, $$
and the energy consumed by the PTC heater was calculated from
$$ Q_{\rm PTC}=\frac{P_{\rm PTC}\, \Delta t_{\rm heat}}{\eta_{\rm PTC}}, $$
where \(P_{\rm PTC}\) is the PTC power, \(\Delta t_{\rm heat}\) is the heating duration, and \(\eta_{\rm PTC}\) is the electro-thermal conversion efficiency, which was assumed to be 95%. The energy consumption results are given in Table 15.
| Heating scheme | Energy at −10 °C (J) | Energy at −15 °C (J) | Energy at −20 °C (J) |
|---|---|---|---|
| Pulse only | 42180 | 46620 | 51060 |
| Composite | 76822 | 85358 | 98161 |
| Liquid only | 145263 | 180000 | 217894 |
Pulse heating always consumes the least amount of energy because it generates heat directly inside the battery. In contrast, liquid heating consumes the largest amount of energy because the PTC heater, the water tank, and the connecting pipes all dissipate heat to the ambient air. Composite heating consumes intermediate energy, but it provides a much higher heating rate than pulse-only heating and a much lower heating time than liquid-only heating. As the ambient temperature decreases from −10 °C to −20 °C, the pulse energy increases by 21%, the composite energy increases by 28%, and the liquid-heating energy increases by 51%. Therefore, composite heating is a good compromise between heating speed, warm-up energy loss, and system simplicity.
4.4 Capacity fade after repeated heating cycles
Since the vehicle traction battery is repeatedly subjected to pulsed currents at low temperature, possible lifetime degradation must be assessed. I performed cyclic experiments in which the battery module was first cooled to −20 °C and then heated to 10 °C. The heating cycle was repeated 600 times. Three groups were tested: group A used 1 C pulse current and 100 W PTC power; group B used 2 C pulse current and 200 W PTC power; group C used 3 C pulse current and 300 W PTC power. The capacity fade results are summarized in Table 16.
| Group | Heating condition | Capacity fade after 300 cycles (%) | Capacity fade after 600 cycles (%) |
|---|---|---|---|
| A | 1 C + 100 W | 0.73 | 1.7 |
| B | 2 C + 200 W | 1.7 | 3.0 |
| C | 3 C + 300 W | 2.9 | 4.3 |
The highest current condition leads to the largest capacity fade, but even after 600 cycles the total capacity loss remains lower than 5%. This result demonstrates that the composite-heating method does not cause severe aging of the vehicle traction battery when the pulse parameters are selected within the tested range. The 5% capacity-fade threshold is often used as the end-of-life criterion in traction-battery applications; after 600 operating cycles at −20 °C, the battery is still well above that threshold.
5. Electro-Thermal Coupled Simulation and Optimization
Although experimental tests provide reliable data, they cannot easily cover a wide range of operating conditions and design parameters. In order to broaden the study and explore the optimal heating conditions of the vehicle traction battery, I established a three-dimensional electro-thermal coupled simulation model using COMSOL Multiphysics.
5.1 Governing equations of the electro-thermal model
The energy conservation inside the battery cell can be written as
$$ \rho_{k} C_{p,k}\frac{\partial T}{\partial t}=\nabla \cdot \left(\lambda_{k}\nabla T\right)+q_{\rm gen}, $$
where \(\rho_{k}\) is the cell density, \(C_{p,k}\) is the specific heat capacity, \(T\) is the local temperature, \(t\) is time, \(\lambda_{k}\) is the thermal conductivity of the battery, and \(q_{\rm gen}\) is the volumetric heat-generation rate.
In the simulation model, the heat-generation rate of the lithium-ion battery is calculated using the simplified Bernardi expression
$$ q_{\rm gen}=\frac{1}{V}\left[ I^{2}R – I T \frac{\partial U_{\rm OCV}}{\partial T}\right], $$
where \(V\) is the battery volume, \(I\) is the operating current, \(R\) is the total equivalent internal resistance, \(U_{\rm OCV}\) is the open-circuit voltage, and \(\partial U_{\rm OCV}/\partial T\) is the measured entropic heat coefficient. The first term on the right side represents the irreversible Joule heat, while the second term represents the reversible heat. During the pulse-heating process, the reversible heat alternates between positive and negative values because the current direction changes rapidly; consequently, the reversible contribution is nearly cancelled and can be omitted when interpreting the total heat generation of the vehicle traction battery.
The three-dimensional heat-conduction equation used for the solid regions of the cooling plate is expressed as
$$ \rho C_{p}\frac{\partial T}{\partial t}=\lambda_{x}\frac{\partial^{2}T}{\partial x^{2}}+\lambda_{y}\frac{\partial^{2}T}{\partial y^{2}}+\lambda_{z}\frac{\partial^{2}T}{\partial z^{2}}+q_{\rm gen}. $$
For the coolant domain, both the continuity equation and the incompressible Navier–Stokes equation are used to describe the flow field:
$$ \nabla \cdot \mathbf{u}=0, $$
$$ \rho_{f}\left(\mathbf{u}\cdot\nabla\right)\mathbf{u}=-\nabla p+\mu\nabla^{2}\mathbf{u}, $$
where \(\mathbf{u}\) is the coolant velocity, \(p\) is the pressure, \(\rho_{f}\) is the coolant density, and \(\mu\) is the dynamic viscosity. The conjugate heat transfer between the flow channel and the solid plate is handled by solving the energy equation in both domains.
5.2 Material parameters and mesh independence
The main simulation parameters of the battery model are listed in Table 17.
| Symbol | Parameter | Value |
|---|---|---|
| Qcell | Cell capacity | 2 Ah |
| J0,0 | Reference exchange current density | 0.85 A/m² |
| Ea,J0 | Activation energy of exchange current density | −59 kJ/mol |
| kT,batt,il | In-plane thermal conductivity | 30 W/(m·K) |
| kT,batt,tl | Through-plane thermal conductivity | 1 W/(m·K) |
| ρbatt | Average density | 2000 kg/m³ |
| Cp,batt | Specific heat capacity | 1400 J/(kg·K) |
| h | Convective heat-transfer coefficient | 30 W/(m²·K) |
Before running the full parametric analysis, a mesh-independence study was performed. The battery module model was discretized with different numbers of elements, from roughly 220,000 up to 5.6 million elements. At an ambient temperature of −20 °C, with a pulse current of 2 C and a frequency of 3000 Hz, the average temperature, maximum temperature difference, average voltage, and maximum voltage difference at 240 s were compared. When the mesh count is approximately 2.55 million, the target quantities converge and the maximum temperature difference reaches a stable value. Therefore, a mesh size of about 2.55 million elements is selected for the simulations. The model includes two boundary layers in the fluid domain, a minimum mesh size of 0.4 mm in the fluid region, and a minimum size of 0.7 mm in the remaining regions.
5.3 Model validation
To verify the accuracy of the three-dimensional simulation model, I compared the simulated average temperature of the battery module with the experimental data. The tests were carried out at −10 °C, −15 °C, and −20 °C. The three heating schemes were reproduced in the simulation by applying the same boundary conditions and the same pulse parameters. The comparison results are listed in Table 18.
| Ambient temperature | Heating scheme | Mean temperature deviation | Mean relative error | Maximum absolute deviation |
|---|---|---|---|---|
| −10 °C | Liquid only | 0.33 °C | 4.32% | 0.88 °C |
| Pulse only | −0.14 °C | 2.83% | 0.56 °C | |
| Composite | −0.29 °C | 5.74% | 0.56 °C | |
| −15 °C | Liquid only | 0.91 °C | 6.82% | 1.48 °C |
| Pulse only | −0.10 °C | 1.52% | 0.70 °C | |
| Composite | −0.36 °C | 5.21% | 1.45 °C | |
| −20 °C | Liquid only | −0.08 °C | 6.67% | 0.80 °C |
| Pulse only | 0.77 °C | 7.82% | 1.40 °C | |
| Composite | −0.77 °C | 8.92% | 1.70 °C |
For all three heating modes, the mean relative error between the simulation and the experiment is less than 9%. The average-level deviation is satisfactory, confirming that the model is appropriate for the subsequent parameter study. At the single-cell level, the liquid-heating mode and the composite-heating mode maintain mean relative errors below 5% and 12%, respectively, while the pulse-only mode shows a somewhat larger error because of the difficulty in reproducing the local current distribution among parallel cells. This limitation does not prevent the model from being used to optimize the system-level heating parameters of the vehicle traction battery.
5.4 Simulation study of the pulse frequency
In order to broaden the experimental conclusions, I used the validated model to analyze the effect of pulse frequency over a wider range. The simulations were performed at −20 °C for a duration of 500 s. The pulse current amplitude was fixed at 3 C with a duty cycle of 50%, and the MOSFET switching frequency was set to 1000 Hz, 3000 Hz, 5000 Hz, and 8000 Hz, respectively. The simulation data are summarized in Table 19.
| Switching frequency (Hz) | Temperature rise after 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 model predicts that lower switching frequencies produce a larger total temperature rise because the current remains in the same direction for a longer time in every pulse cycle. At the same time, the maximum temperature difference also increases. In practical applications, the designer must balance the desire for fast heating against the requirement for uniform temperature distribution. Since a switching frequency of 3000 Hz gives a satisfactory temperature rise while limiting the temperature difference, this value is retained as the optimal frequency for the following composite-heating optimization.
5.5 Simulation study of the pulse current amplitude
The pulse current amplitude was further studied in simulation because the available experimental currents were limited to 1 C, 2 C, and 3 C for safety reasons. In the simulation, the battery was heated at −20 °C for 500 s with pulse currents from 1 C to 5 C. The resulting temperature-rise values and maximum temperature differences are listed in Table 20.
| Pulse current amplitude | Temperature rise after 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 1 C | 16.1 | 2.3 |
| 2 C | 22.9 | 3.6 |
| 3 C | 27.2 | 5.3 |
| 4 C | 34.3 | 7.2 |
| 5 C | 39.9 | 9.3 |
Although the temperature rise increases almost linearly with the current amplitude, the temperature difference also grows rapidly. A larger current amplifies the difference in ohmic heating between cells with slightly different internal resistance, and the local hot spots appear near the tabs or around the points where the current density is highest. The maximum temperature difference at 5 C is 9.3 °C, which is too high for a safe vehicle traction battery operation. The value of 3 C achieves the best compromise between heating speed and temperature stability; therefore, 3 C is chosen for the optimum composite-heating scheme.
5.6 Simulation study of the coolant flow rate
In the external liquid loop, the coolant flow rate is coupled with the heat-transfer capacity of the liquid cooling plate. Experiments have shown that an optimal flow-rate window exists. Simulation results further reveal that the optimal flow rate is close to 0.495 L/min. At this flow rate, the average temperature rise of the battery module is maximized after 500 s of heating, while the maximum temperature difference is minimized. When the flow rate is either increased or decreased away from this value, the heating performance deteriorates. The simulated maximum temperature difference at 0.495 L/min is approximately 1.5 °C, which is much smaller than the temperature difference at the other tested flow-rate values. This result confirms that the external liquid circuit and the internal pulse circuit must be operated in a coordinated way; an arbitrary flow-rate setting degrades the final thermal state of the vehicle traction battery.
5.7 Optimization of the composite-heating parameters
Based on the complete simulation analysis, I propose an optimally matched set of heating parameters for the low-temperature vehicle traction battery preheating system:
- Pulse current amplitude: 3 C (6 A)
- MOSFET switching frequency: 3000 Hz
- Duty cycle: 50%
- Coolant flow rate: 0.495 L/min
The optimized composite-heating scheme was then simulated in the three ambient-temperature scenarios. With this configuration, the simulated average heating rate from −10 °C, −15 °C, and −20 °C to 10 °C is approximately 9.7 °C/min, 10.3 °C/min, and 10.8 °C/min, respectively. Compared with the experimentally tested unoptimized composite configuration, the optimized configuration raises the average heating rate by about 45%–50%. The maximum temperature difference inside the battery module is reduced to less than 1 °C at all three ambient temperatures. This result is explained by the highly coordinated effect between the internal pulse heat source and the external liquid heat source. The optimized current amplitude ensures rapid internal heat generation, while the optimized flow rate removes the local hot spots by delivering the heated coolant uniformly to the plate surface. The optimized duty cycle and pulse frequency prevent excessive concentration polarization and limit the variation in cell temperature among the different cells of the vehicle traction battery.
The thermal field obtained in the optimum configuration shows that a certain amount of heat accumulates in the contact area between the battery and the liquid cooling plate. In practice, the contact thermal resistance is larger than in the ideal simulated contact, and the heat flux is able to spread more uniformly across the cooling plate surface. Therefore, the actual thermal stress in the module is expected to be even lower than the simulated value.
6. Conclusions and Further Work
This thesis provides a comprehensive study of a low-temperature composite heating system for the vehicle traction battery. The main conclusions are summarized below.
First, experimental characterization at low temperature confirms that the lithium-ion battery loses more than 50% of its room-temperature discharge capacity at −20 °C. The internal resistance increases dramatically as the temperature drops, and the open-circuit voltage is not only a function of SOC but also a function of temperature. These results highlight the fact that thermal pre-conditioning is essential for a reliable vehicle traction battery in cold regions.
Second, a composite preheating method combining electric-drive pulse internal heating and liquid-cooling-plate external heating was designed and experimentally validated. Among several flow-channel configurations, the serpentine-return channel was selected because it simultaneously provides high wall temperature and a small temperature gradient. The electric-drive pulse-heating strategy was realized by controlling the d-axis current of a permanent-magnet synchronous motor under zero torque. A hardware control system based on STM32 was implemented, and the whole platform enables independent adjustment of the pulse current, frequency, duty cycle, PTC power, and coolant flow rate.
Third, the parametric experimental study reveals that the heating rate of the vehicle traction battery is far more sensitive to the current amplitude than to the switching frequency. Increasing the duty cycle improves the heating rate, but the gain is limited. The liquid-heating mode requires an optimal coolant flow rate, which was experimentally found to be close to 0.56 L/min. In the composite mode, the average heating rate reaches 6.67 °C/min at −10 °C, 7.14 °C/min at −15 °C, and 7.83 °C/min at −20 °C, while the maximum temperature difference within the module remains lower than 3 °C. More importantly, after 600 complete cold-start heating cycles, the capacity fade of the composite-heated cell is below 5%, which is fully acceptable for vehicle traction battery applications.
Fourth, a fully coupled three-dimensional electro-thermal simulation model was built and validated. The model was then used to expand the parametric study and derive an optimized operating point. The optimum pulse current is 3 C, the switching frequency is 3000 Hz, the duty cycle is 50%, and the coolant flow rate is 0.495 L/min. The optimized lithium-ion battery heating system for the vehicle traction battery improves the average heating rate by approximately 45–50% and simultaneously reduces the maximum temperature difference below 1 °C. This demonstrates that internal–external composite heating with well-matched control parameters is an effective solution for low-temperature vehicle traction battery preheating.
In future work, the optimized composite heating strategy should be tested directly on a real electric vehicle under different cold ambient conditions in order to further validate the scalability and control robustness. Additional attention should be paid to the degradation mechanism at different pulse current magnitudes and to the relationship between duty cycle and lithium plating. Finally, a model-based online controller that dynamically adjusts the duty cycle, pulse frequency, and PTC power in response to the real-time battery temperature could bring the proposed technology closer to series production.