The electric vehicle battery pack is the core energy storage unit of a modern electric vehicle, and its performance directly determines driving range, safety, and service life. Lithium-ion batteries are widely used in electric vehicle battery packs because of their high energy density, low self-discharge rate, and long cycle life. However, the optimal operating temperature range of most electric vehicle battery packs is approximately 10 °C to 40 °C. When the ambient temperature deviates from this range, the electric vehicle battery pack suffers from significant capacity loss, increased internal resistance, reduced peak power, and even lithium plating during charging. These problems are especially severe in cold regions, where winter temperatures frequently fall below 0 °C and can reach −30 °C. In such environments, the electric vehicle battery pack cannot deliver its nominal performance, and the user experience differs greatly from that of conventional fuel vehicles. Therefore, fast and uniform low-temperature preheating of the electric vehicle battery pack is essential for extending battery life, improving vehicle performance, increasing energy utilization efficiency, and enhancing overall vehicle safety.
To address the low-temperature degradation of the electric vehicle battery pack, researchers have explored two main routes: material modification and thermal management. Material modification includes replacing graphite anodes with lithium titanate anodes or using low-viscosity electrolytes. Although these methods can suppress lithium plating to some extent, they cannot fully satisfy the requirements of cost, energy density, and safety. Thermal management, especially preheating, is therefore considered a more practical and adaptable solution. Existing preheating strategies for the electric vehicle battery pack can be classified into external heating, internal heating, and composite heating. External heating uses an independent heat source, such as air, liquid, phase change material, or electric heating elements, to transfer heat to the electric vehicle battery pack. Internal heating uses the battery itself as a heat source by applying a current through its internal resistance. Composite heating combines internal and external heat sources to achieve better overall performance. In my research, I focus on a composite preheating strategy that couples electric-drive pulse self-heating with liquid-cooling plate heating for the electric vehicle battery pack.
Low-Temperature Performance Experiments of the Electric Vehicle Battery Pack
I first investigated the structure and operating principle of lithium-ion batteries. A typical cylindrical cell consists of a positive electrode, a negative electrode, a separator, an electrolyte, and auxiliary components such as sealing rings, tabs, a top cap, a safety valve, a shell, and an insulating plate. The positive electrode is usually a lithium-containing compound, and the negative electrode is graphite. During charging, lithium ions are extracted from the positive electrode, migrate through the electrolyte and separator, and intercalate into the negative electrode. During discharging, the reverse process occurs. The electrochemical reactions can be summarized as follows:
$$ \mathrm{Li_aX_aY_c \rightleftharpoons Li_{a-\theta}X_aY_b + \theta Li^+ + \theta e^-} $$
$$ \mathrm{xLi^+ + yC + xe^- \rightleftharpoons Li_xC_y} $$
For my experiments, I used a commercial 18650 cell with a nominal capacity of 2 Ah and a nominal voltage of 3.8 V. The cathode was nickel-cobalt-aluminum oxide, and the anode was graphite. The charge cutoff voltage was 4.2 V, and the discharge cutoff voltage was 2.7 V. The experimental platform included a battery test system, a high-low temperature humidity chamber, an adiabatic foam box, thermocouples, and a host computer. The temperature chamber could operate from −45 °C to 150 °C with a fluctuation of no more than ±0.3 °C and a deviation of no more than ±2 °C.
I designed a series of experiments to characterize the low-temperature behavior of the electric vehicle battery pack. The first was a capacity test at different temperatures: 20 °C, 10 °C, 0 °C, −10 °C, and −20 °C. The cell was first charged to 4.2 V at 2 A in constant-current mode, then charged in constant-voltage mode until the current dropped below 0.2 A. After resting, the cell was discharged at 1/3 C until the voltage reached 2.75 V. The measured discharge capacities are shown in Table 1.
| Temperature (°C) | Discharge capacity (Ah) | Capacity retention relative to 20 °C (%) |
|---|---|---|
| 20 | 2.17 | 100.0 |
| 10 | 1.84 | 84.79 |
| 0 | 1.63 | 75.11 |
| −10 | 1.32 | 60.05 |
| −20 | 1.04 | 47.93 |
The results show that when the temperature drops from 20 °C to −20 °C, the discharge capacity of the electric vehicle battery pack decays by more than 50%. This decay is mainly caused by increased electrolyte viscosity, reduced lithium-ion diffusion rate, and increased solid-electrolyte interphase impedance. The capacity loss directly reduces the driving range of an electric vehicle and weakens the power capability of the electric vehicle battery pack.
I then conducted hybrid pulse power characterization (HPPC) experiments to obtain the open-circuit voltage (OCV) and internal resistance as functions of state of charge (SOC) and temperature. The HPPC procedure consisted of a 10 s discharge pulse at 1 C, a 40 s rest, a 10 s charge pulse at 1/3 C, another 40 s rest, and then a 1/3 C discharge for 1075 s to reach the next SOC point. This sequence was repeated from 100% SOC down to 10% SOC. The OCV and internal resistance were measured at 20 °C, 10 °C, 0 °C, −10 °C, and −20 °C. The OCV-SOC curves exhibit three regions: below 20% SOC, the OCV drops sharply; between 20% and 80% SOC, the OCV changes gradually; above 80% SOC, the OCV rises rapidly. The internal resistance also shows three regions: below 20% SOC, the resistance decreases sharply as SOC increases; between 20% and 80% SOC, the resistance is almost constant; above 80% SOC, the resistance increases slowly. Temperature has a strong effect: at any given SOC, the internal resistance increases as temperature decreases. Both the OCV and the internal resistance of the electric vehicle battery pack are jointly determined by temperature and SOC.
I also measured the entropic heat coefficient, which describes the reversible heat effect. The cell was charged to 100% SOC, rested for 12 h, and then the ambient temperature was changed stepwise from −20 °C to 20 °C in 10 °C increments. The OCV and surface temperature were recorded. After each temperature step, the cell was discharged by 10% of its rated capacity. The entropic heat coefficient was calculated as:
$$ \frac{\partial E_{\mathrm{OCV}}}{\partial T} $$
The results show that the entropic heat coefficient is negative for most SOC ranges, meaning that the reversible heat effect suppresses temperature rise. Near 60% SOC, the entropic heat coefficient is close to zero. In the high-SOC range from 70% to 100%, the coefficient becomes positive, so the reversible heat effect enhances temperature rise. These data provide important input for the thermal management of the electric vehicle battery pack.
Composite Heating System Architecture and Design
Based on the low-temperature characteristics, I proposed a composite heating system for the electric vehicle battery pack that combines internal electric-drive pulse self-heating with external liquid-cooling plate heating. The internal heating loop uses a three-phase permanent magnet synchronous motor and an inverter to generate high-frequency pulse currents through the battery. The external heating loop uses a positive temperature coefficient (PTC) heater to heat a coolant, which is circulated by a pump through a liquid-cooling plate attached to the electric vehicle battery pack. By adjusting the pulse amplitude, frequency, PTC power, and pump flow rate, the temperature of the electric vehicle battery pack can be raised efficiently and uniformly.
For the external heating design, I evaluated five different flow channel structures for the liquid-cooling plate: U-shaped, parallel, composite, return-type (serpentine), and S-shaped. The material was aluminum because of its good thermal conductivity, low density, and low cost. The cooling plate dimensions were 90 mm × 65 mm × 5 mm, and the channel diameter was 3 mm. The coolant was a 50% ethylene glycol aqueous solution with a freezing point of −36.7 °C. The physical properties are listed in Table 2.
| Property | Liquid-cooling plate (aluminum) | Coolant (50% ethylene glycol) |
|---|---|---|
| Density (kg/m³) | 2719 | 1100 |
| Specific heat capacity (J/(kg·K)) | 891 | 3300 |
| Thermal conductivity (W/(m·K)) | 202.4 | 0.43 |
| Viscosity (Pa·s) | — | 0.00339 |
| Freezing point (°C) | — | −36.7 |
I performed thermal simulations of the five cold plates with a coolant velocity of 0.04 m/s and an inlet temperature of 40 °C. The wall temperature distributions after 240 s are summarized in Table 3. The return-type cold plate had a maximum temperature of 39.2 °C, a temperature difference of 1.0 °C, and a high-temperature area fraction of 36.78%. Although the S-shaped cold plate had the smallest temperature difference of 0.5 °C, its maximum temperature was only 38.7 °C. The return-type cold plate provided the best combination of heating capability and temperature uniformity. Therefore, I selected the return-type flow channel for the liquid-cooling plate and manufactured it for the experimental platform.
| Cold plate type | Temperature range (°C) | Maximum temperature difference (°C) | High-temperature area fraction (%) | Low-temperature area fraction (%) |
|---|---|---|---|---|
| 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-type | 38.2–39.2 | 1.0 | 36.78 | 42.03 |
| S-shaped | 38.2–38.7 | 0.5 | 22.5 | 56.49 |
For the internal heating design, I used the existing electric-drive system of an electric vehicle. The system consists of a three-phase permanent magnet synchronous motor and an inverter. When the vehicle is stopped, the rotor remains stationary. By controlling the q-axis current to be zero, the motor output torque is zero. At the same time, the d-axis current is oscillated between positive and negative values. When the d-axis current is positive, the electric vehicle battery pack discharges through the inverter to the motor windings. When the d-axis current is negative, the energy stored in the motor windings is fed back to the electric vehicle battery pack. This high-frequency charge-discharge alternation excites the internal resistance of the battery and generates Joule heat inside the electric vehicle battery pack.
The hardware circuit includes a main control module, a motor drive module, a power management module, and a communication interface module. The main controller is an STM32F405RGT6 with an ARM Cortex-M4 core running at up to 168 MHz and 1 MB of flash memory. The gate driver is a DRV8301DCAR, which drives a three-phase full-bridge inverter composed of six MOSFETs. The MOSFETs are Si7850DP-HXY with a drain-source voltage of 60 V, a drain current of 30 A, and an operating temperature range from −55 °C to 150 °C. The power management module uses two low-dropout linear regulators to supply the digital and analog circuits. The communication module uses a CH340K for USB-to-serial conversion and an encoder interface for position feedback. I designed the PCB with two layers and copper pour on both sides to carry high currents. The software was developed with STM32CubeMX and Keil. The control algorithm uses field-oriented control (FOC) and space vector pulse width modulation (SVPWM). The q-axis current reference is set to zero to ensure zero torque, and the d-axis current reference oscillates at a set frequency and amplitude. The control code also includes overcurrent and overtemperature protection. The motor parameters are listed in Table 4.
| Parameter | Value |
|---|---|
| Rated voltage | 48 V |
| Rated output power | 1000 W |
| Rated current | 30 A |
| Quadrature-axis inductance | 0.15 mH |
| Direct-axis inductance | 0.08 mH |
| Rated speed | 3000 rpm |
| Line-to-line resistance | 0.07 Ω |
The composite heating experimental platform integrates the electric vehicle battery pack, the bidirectional DC power supply, the liquid-cooling plate, the electric-drive pulse heating device, the pump, the flow meter, the insulated water tank, thermocouples, and the host computer. The platform allows independent control of pulse amplitude, frequency, duty cycle, PTC power, coolant flow rate, and ambient temperature. The main equipment parameters are listed in Table 5.
| Equipment | Parameter | Value |
|---|---|---|
| High-low temperature chamber | Temperature range | −40 °C to 80 °C |
| Temperature uniformity | ±1.0 °C | |
| Temperature fluctuation | ±0.5 °C | |
| Bidirectional DC power supply | Current range | 0–10 A |
| Voltage range | 0–36 V | |
| Data acquisition unit | Temperature range | −30 °C to 110 °C |
| Temperature accuracy | ±0.1 °C | |
| Battery pack test system | Voltage | 20–1000 V |
| Current | 100–1000 A | |
| Power | 800 kW | |
| Measurement accuracy | ±0.1% of FS |
Experimental Study of the Composite Heating System
I conducted a systematic experimental study of the composite heating system for the electric vehicle battery pack. The experiments compared three heating methods: pulse heating, liquid-cooling heating, and composite heating. The experimental parameters are listed in Table 6.
| Heating method | Parameter | Value |
|---|---|---|
| Pulse heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Current amplitude | 1C, 2C, 3C | |
| MOSFET switching frequency | 3000 Hz, 5000 Hz, 8000 Hz | |
| Duty cycle | 25%, 50%, 75% | |
| Liquid-cooling heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Flow rate | 0.2–0.73 L/min | |
| PTC power | 100 W, 200 W, 300 W | |
| Composite heating | Battery temperature | −10 °C, −15 °C, −20 °C |
| Heating parameters | 3C, 3000 Hz, 300 W, 0.56 L/min |
For pulse heating, I first studied the effect of frequency at different temperatures. The pulse current amplitude was 2C or 3C, the duty cycle was 50%, and the switching frequency was 3000 Hz, 5000 Hz, or 8000 Hz. The battery was heated from −10 °C, −15 °C, or −20 °C to 10 °C. At 2C, when the frequency increased from 3000 Hz to 5000 Hz and 8000 Hz, the heating rate at −10 °C decreased from 2.37 °C/min to 2.05 °C/min and 1.76 °C/min; at −15 °C, it decreased from 2.78 °C/min to 2.23 °C/min and 2.09 °C/min; at −20 °C, it decreased from 2.54 °C/min to 1.78 °C/min and 1.61 °C/min. At 3C, the heating rate at −10 °C decreased from 3.42 °C/min to 3.36 °C/min and 2.95 °C/min; at −15 °C, it decreased from 4.26 °C/min to 3.71 °C/min and 3.20 °C/min; at −20 °C, it decreased from 4.36 °C/min to 3.83 °C/min and 3.56 °C/min. These results show that higher switching frequency reduces the heating rate. The reason is that although the number of pulses increases, the switching losses, driving losses, and magnetic core losses also increase, which reduces the overall heating efficiency of the electric vehicle battery pack.
I then studied the effect of duty cycle. At 2C and 3C, with a frequency of 3000 Hz, the duty cycle was set to 25%, 50%, and 75%. At 2C, when the duty cycle increased from 25% to 50% and 75%, the heating rate at −10 °C increased from 1.95 °C/min to 2.25 °C/min and 2.54 °C/min; at −15 °C, it increased from 2.52 °C/min to 2.87 °C/min and 3.03 °C/min; at −20 °C, it increased from 2.32 °C/min to 2.54 °C/min and 2.57 °C/min. At 3C, the heating rate at −10 °C increased from 2.93 °C/min to 3.32 °C/min and 3.92 °C/min; at −15 °C, it increased from 3.84 °C/min to 4.24 °C/min and 4.43 °C/min; at −20 °C, it increased from 4.01 °C/min to 4.34 °C/min and 5.19 °C/min. The highest heating rate of 5.19 °C/min was achieved at −20 °C. For the same duty cycle, each 5 °C decrease in ambient temperature increased the heating time by about 16% on average.
Next, I studied the effect of pulse current amplitude. At 3000 Hz and 5000 Hz, with a duty cycle of 50%, the pulse current amplitude was 1C, 2C, or 3C. At 3000 Hz, when the amplitude increased from 1C to 2C and 3C, the heating rate at −10 °C increased from 0.70 °C/min to 2.24 °C/min and 3.31 °C/min; at −15 °C, it increased from 0.80 °C/min to 2.63 °C/min and 4.24 °C/min; at −20 °C, it increased from 1.14 °C/min to 2.58 °C/min and 3.64 °C/min. At 5000 Hz, the heating rate at −10 °C increased from 0.61 °C/min to 1.44 °C/min and 3.94 °C/min; at −15 °C, it increased from 1.13 °C/min to 2.23 °C/min and 4.97 °C/min; at −20 °C, it increased from 0.72 °C/min to 2.58 °C/min and 3.64 °C/min. These results indicate that doubling the pulse current amplitude increases the average heating rate by about 120%. Increasing the pulse current amplitude is more effective than increasing the switching frequency. Under safe operating conditions, a high-current pulse heating strategy should be preferred for the electric vehicle battery pack.
I also analyzed temperature consistency during pulse heating. Five thermocouples were placed on five cells. At 3000 Hz and 2C or 3C, the battery was heated from −10 °C, −15 °C, or −20 °C to 10 °C. The maximum temperature difference within the electric vehicle battery pack exceeded 5 °C at low temperatures. This non-uniformity is mainly caused by differences in internal resistance among individual cells, which lead to uneven heat generation. The temperature consistency results are summarized in Table 7.
| Pulse current | Ambient temperature (°C) | Heating time to 10 °C (s) | Maximum temperature difference (°C) |
|---|---|---|---|
| 2C | −10 | 500 | >5 |
| 2C | −15 | 650 | >5 |
| 2C | −20 | 700 | >5 |
| 3C | −10 | 350 | >5 |
| 3C | −15 | 350 | >5 |
| 3C | −20 | 400 | >5 |
For liquid-cooling heating, I studied the effect of coolant flow rate and PTC power. The coolant flow rate was set to 0.2, 0.3, 0.43, 0.56, and 0.73 L/min. At −10 °C and −15 °C, the heating performance was best at 0.56 L/min. Flow rates below 0.43 L/min or above 0.73 L/min did not improve the preheating effect significantly. When the flow rate is too low, the heat transfer rate is insufficient, and heat loss at the edge of the cold plate exceeds the input heat. When the flow rate is too high, the heat exchange is incomplete. Therefore, an optimal flow rate threshold exists for the electric vehicle battery pack.
I then studied the effect of PTC power. At a constant flow rate of 0.43 L/min, the PTC power was 100 W, 200 W, or 300 W. At −10 °C, the heating time to 10 °C was 1020 s at 100 W, 700 s at 200 W, and 460 s at 300 W. The corresponding heating rates were 1.18 °C/min, 1.69 °C/min, and 2.67 °C/min. At −15 °C, the heating time was 1250 s, 720 s, and 590 s, with heating rates of 1.20 °C/min, 2.08 °C/min, and 2.54 °C/min. At −20 °C, the heating time was 1800 s, 900 s, and 650 s, with heating rates of 1.00 °C/min, 2.00 °C/min, and 2.54 °C/min. The PTC power is positively correlated with the heating rate. At 300 W, the average heating rate reached 2.58 °C/min. For the same power, each 5 °C decrease in ambient temperature increased the heating time by about 40% on average. The PTC heater must be operated continuously or started in advance to achieve the best heating performance.
I also analyzed temperature consistency during liquid-cooling heating. At a constant flow rate of 0.43 L/min and PTC power of 200 W or 300 W, the maximum temperature difference within the electric vehicle battery pack was less than 3 °C. This is better than pulse heating but worse than the heating rate of pulse heating. The results are summarized in Table 8.
| PTC power | Ambient temperature (°C) | Heating time to 10 °C (s) | Heating rate (°C/min) | Maximum temperature difference (°C) |
|---|---|---|---|---|
| 200 W | −10 | 700 | 1.69 | <3 |
| 200 W | −15 | 720 | 2.08 | <3 |
| 200 W | −20 | 900 | 2.00 | <3 |
| 300 W | −10 | 460 | 2.67 | <3 |
| 300 W | −15 | 590 | 2.54 | <3 |
| 300 W | −20 | 650 | 2.54 | <3 |
For composite heating, I combined pulse heating and liquid-cooling heating. The parameters were 3C, 3000 Hz, 50% duty cycle, 0.56 L/min, and 300 W. The battery was heated from −10 °C, −15 °C, and −20 °C to 10 °C. The comparison of the three heating methods is shown in Table 9. At −10 °C, liquid-cooling heating took 460 s (2.61 °C/min), pulse heating took 380 s (3.15 °C/min), and composite heating took 180 s (6.67 °C/min). At −15 °C, liquid-cooling heating took 570 s (2.63 °C/min), pulse heating took 420 s (3.57 °C/min), and composite heating took 210 s (7.14 °C/min). At −20 °C, liquid-cooling heating took 690 s (2.61 °C/min), pulse heating took 460 s (3.94 °C/min), and composite heating took 230 s (7.83 °C/min). The composite heating method achieved the highest heating rate at all temperatures. The lower the ambient temperature, the greater the relative advantage of composite heating.
| Ambient temperature (°C) | Liquid-cooling heating time (s) | Liquid-cooling heating rate (°C/min) | Pulse heating time (s) | Pulse heating rate (°C/min) | Composite heating time (s) | Composite heating rate (°C/min) |
|---|---|---|---|---|---|---|
| −10 | 460 | 2.61 | 380 | 3.15 | 180 | 6.67 |
| −15 | 570 | 2.63 | 420 | 3.57 | 210 | 7.14 |
| −20 | 690 | 2.61 | 460 | 3.94 | 230 | 7.83 |
I analyzed the temperature consistency of composite heating. At a flow rate of 0.43 L/min, PTC power of 300 W, pulse current of 3C, frequency of 3000 Hz, and duty cycle of 50%, the maximum temperature difference was less than 3 °C in all three low-temperature conditions. As the ambient temperature decreased, the temperature difference increased slightly, but the increase was less than 0.5 °C per 10 °C. The composite heating method provides good temperature uniformity for the electric vehicle battery pack.
I also compared the energy consumption of the three heating methods. The energy consumption of pulse heating and PTC heating can be calculated as:
$$ Q_{\mathrm{Pulsating}} = \int U I \, dt $$
$$ Q_{\mathrm{PTC}} = \frac{P_{\mathrm{PTC}} \Delta t}{\eta} $$
where \( U \) is the total voltage of the electric vehicle battery pack, \( I \) is the total current, \( t \) is the heating time, \( P_{\mathrm{PTC}} \) is the PTC power, \( \Delta t \) is the heating time, and \( \eta \) is the PTC electrothermal conversion efficiency, which was taken as 95%. The energy consumption results are listed in Table 10. At −10 °C, the energy consumption was 42180 J for pulse heating, 76822 J for composite heating, and 145263 J for liquid-cooling heating. At −15 °C, the values were 46620 J, 85358 J, and 180000 J. At −20 °C, the values were 51060 J, 98161 J, and 217894 J. Pulse heating had the lowest energy consumption, but composite heating provided the best balance among heating rate, temperature uniformity, and energy consumption. At −20 °C, the energy consumption of pulse heating was only 23.4% of that of liquid-cooling heating. As the temperature decreased from −10 °C to −20 °C, the energy consumption of pulse heating increased by only 21%, showing the best stability and low-temperature adaptability.
| Ambient temperature (°C) | Pulse heating energy (J) | Composite heating energy (J) | Liquid-cooling heating energy (J) |
|---|---|---|---|
| −10 | 42180 | 76822 | 145263 |
| −15 | 46620 | 85358 | 180000 |
| −20 | 51060 | 98161 | 217894 |
I evaluated the capacity degradation of the electric vehicle battery pack after repeated composite heating cycles. The test was conducted at −20 °C with 600 complete heating cycles from −20 °C to 10 °C. Three groups were tested: group a used 1C pulse + 100 W PTC, group b used 2C pulse + 200 W PTC, and group c used 3C pulse + 300 W PTC. After 300 cycles, the capacity loss was 0.73% for group a, 1.7% for group b, and 2.9% for group c. After 600 cycles, the capacity loss was 1.7% for group a, 3.0% for group b, and 4.3% for group c. All groups had an absolute capacity loss of less than 5%, which is acceptable for engineering applications. The composite heating method does not cause significant negative effects on the long-term cycle life of the electric vehicle battery pack.
| Group | Heating parameters | Capacity loss after 300 cycles (%) | Capacity loss after 600 cycles (%) |
|---|---|---|---|
| a | 1C pulse + 100 W PTC | 0.73 | 1.7 |
| b | 2C pulse + 200 W PTC | 1.7 | 3.0 |
| c | 3C pulse + 300 W PTC | 2.9 | 4.3 |
COMSOL Electrothermal Coupled Model and Optimization
To further optimize the composite heating system and extend the range of operating conditions, I built a three-dimensional electrothermal coupled simulation model of the electric vehicle battery pack preheating system using COMSOL Multiphysics. The model couples electrochemical reactions, fluid flow in the liquid-cooling plate, and heat transfer between the battery, the cold plate, and the environment. The battery heat generation model is based on the Bernardi equation:
$$ q = \frac{1}{V} \left[ I^2 R – I T \frac{\partial U_{\mathrm{OCV}}}{\partial T} \right] $$
where \( q \) is the volumetric heat generation rate, \( V \) is the battery volume, \( I \) is the current, \( R \) is the equivalent internal resistance, \( T \) is the battery temperature, and \( \partial U_{\mathrm{OCV}}/\partial T \) is the entropic heat coefficient. The irreversible heat is \( I^2 R \), and the reversible heat is \( I T \partial U_{\mathrm{OCV}}/\partial T \). The three-dimensional heat conduction equation for the electric vehicle battery pack is:
$$ \rho C_p \frac{\partial T}{\partial t} = \lambda_x \frac{\partial^2 T}{\partial x^2} + \lambda_y \frac{\partial^2 T}{\partial y^2} + \lambda_z \frac{\partial^2 T}{\partial z^2} + q $$
where \( \rho \) is the density, \( C_p \) is the specific heat capacity, \( \lambda_x \), \( \lambda_y \), and \( \lambda_z \) are the thermal conductivities in the three directions, and \( q \) is the heat generation rate. The heat transfer model also includes conduction, convection, and radiation. The governing equations for conduction and convection are:
$$ q = -\lambda_n \frac{\partial T}{\partial n} $$
$$ q = h (T_1 – T_2) $$
where \( q \) is the heat flux, \( \lambda_n \) is the thermal conductivity in the normal direction, \( h \) is the convective heat transfer coefficient, \( T_1 \) is the solid surface temperature, and \( T_2 \) is the fluid temperature. Radiation was neglected because of the compact arrangement of the electric vehicle battery pack. The simulation parameters are listed in Table 11.
| Symbol | Parameter | Value |
|---|---|---|
| Q_cell | Battery capacity | 2 Ah |
| J0_0 | Reference exchange current density | 0.85 |
| eta_1C | Reference overpotential | 4.5 mV |
| Ea_J0 | Activation energy of exchange current density | −59 kJ/mol |
| Ea_Tau | Activation energy of relaxation time | 24 kJ/mol |
| tau_0 | Reference relaxation time | 1000 s |
| kT_batt_il | In-layer thermal conductivity | 30 W/(m·K) |
| kT_batt_tl | Through-layer thermal conductivity | 1 W/(m·K) |
| rho_batt | Average battery density | 2000 kg/m³ |
| Cp_batt | Battery specific heat capacity | 1400 J/(kg·K) |
| Ht | Convective heat transfer coefficient | 30 W/(m²·K) |
I performed a grid independence study to ensure the accuracy and efficiency of the simulation. The average temperature, maximum temperature difference, average voltage, and maximum voltage difference at 240 s were used as evaluation parameters. The results are shown in Table 12. When the mesh number was 2.55 million, the maximum temperature difference and maximum voltage difference reached their minimum values. Therefore, I selected a mesh size of approximately 2.55 million elements. The fluid laminar boundary layer was set to two layers, the fluid region mesh size was 0.4 mm, and the minimum mesh size in other regions was 0.7 mm.
| Mesh number | Average temperature (°C) | Maximum temperature difference (°C) | Average voltage (V) | Maximum voltage difference (V) |
|---|---|---|---|---|
| 220451 | 11.291 | 3.31 | 4.09039 | 0.0133 |
| 336178 | 9.911 | 2.32 | 3.97042 | 0.0096 |
| 548178 | 6.937 | 2.43 | 3.96368 | 0.0104 |
| 1108303 | 5.186 | 1.55 | 3.8712 | 0.0206 |
| 2552359 | 5.012 | 1.28 | 3.8512 | 0.0053 |
| 5616842 | 4.952 | 1.39 | 3.8216 | 0.0093 |
I validated the simulation model against experimental data. The comparison was conducted at −10 °C, −15 °C, and −20 °C with a coolant flow rate of 0.56 L/min, pulse current of 3C, and frequency of 3000 Hz. The average temperature differences between simulation and experiment for liquid-cooling heating, pulse heating, and composite heating are summarized in Table 13. The average relative errors were within 9% for all cases. For single-cell temperature prediction, liquid-cooling heating and composite heating had relatively high accuracy, with average relative errors below 5% and 12%, respectively. Pulse heating had larger errors, ranging from 14.5% to 15.7%, which indicates that the model needs further refinement for pulse heating. Overall, the model is reliable and suitable for engineering applications.
| Ambient temperature (°C) | Heating method | Average temperature difference (°C) | Average relative error (%) | Maximum absolute difference (°C) |
|---|---|---|---|---|
| −10 | Liquid-cooling | 0.33 | 4.32 | 0.88 |
| −10 | Pulse | −0.14 | 2.83 | 0.56 |
| −10 | Composite | −0.29 | 5.74 | −0.56 |
| −15 | Liquid-cooling | 0.91 | 6.82 | 1.48 |
| −15 | Pulse | −0.10 | 1.52 | 0.70 |
| −15 | Composite | −0.36 | 5.21 | 1.45 |
| −20 | Liquid-cooling | −0.08 | 6.67 | 0.80 |
| −20 | Pulse | 0.77 | 7.82 | 1.40 |
| −20 | Composite | −0.77 | 8.92 | −1.70 |
Using the validated model, I analyzed the effect of pulse frequency on the preheating performance. The simulation was conducted at −20 °C for 500 s with a pulse amplitude of 3C and a duty cycle of 50%. The switching frequency was varied from 1000 Hz to 8000 Hz. The results are shown in Table 14. At 1000 Hz, the temperature rise was 30.7 °C and the maximum temperature difference was 6.6 °C. At 3000 Hz, the temperature rise was 27.2 °C and the maximum temperature difference was 5.3 °C. At 5000 Hz, the temperature rise was 24.4 °C and the maximum temperature difference was 4.5 °C. At 8000 Hz, the temperature rise was 20.3 °C and the maximum temperature difference was 3.6 °C. Lower frequency increases the heating rate but also increases the temperature difference. Considering both heating rate and temperature uniformity, I selected 3000 Hz as the optimal frequency for the electric vehicle battery pack.
| 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 |
I also analyzed the effect of pulse current amplitude. The simulation was conducted at −20 °C with a frequency of 3000 Hz and a duty cycle of 50%. The pulse current amplitude was varied from 1C to 5C. The results are shown in Table 15. At 1C, the temperature rise was 16.1 °C and the maximum temperature difference was 2.3 °C. At 2C, the temperature rise was 22.9 °C and the maximum temperature difference was 3.6 °C. At 3C, the temperature rise was 27.2 °C and the maximum temperature difference was 5.3 °C. At 4C, the temperature rise was 34.3 °C and the maximum temperature difference was 7.2 °C. At 5C, the temperature rise was 39.9 °C and the maximum temperature difference was 9.3 °C. Higher current increases the heating rate but also increases the temperature difference. The 3C condition provided the best balance between heating rate and temperature consistency for the electric vehicle battery pack.
| Current amplitude | Temperature rise after 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 |
I further analyzed the effect of coolant flow rate. Nine flow rates were selected: 0.2, 0.25, 0.3, 0.365, 0.43, 0.495, 0.56, 0.645, and 0.73 L/min. The simulation was conducted at −20 °C for 500 s. The results are shown in Table 16. The heating effect increased with flow rate from 0.2 L/min to 0.43 L/min, but decreased when the flow rate exceeded 0.56 L/min. The maximum temperature rise was achieved at 0.495 L/min. The maximum temperature difference was also the smallest at 0.495 L/min, with a value of 1.5 °C. Therefore, I selected 0.495 L/min as the optimal coolant flow rate for the electric vehicle battery pack.
| Flow rate (L/min) | Temperature rise after 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 0.2 | — | 2.4 |
| 0.25 | — | 2.3 |
| 0.3 | — | 2.2 |
| 0.365 | — | 2.0 |
| 0.43 | — | 1.8 |
| 0.495 | Maximum | 1.5 |
| 0.56 | — | 1.8 |
| 0.645 | — | 2.3 |
| 0.73 | — | 2.8 |
Based on the above analyses, I proposed an optimal coupled preheating scheme for the electric vehicle battery pack: pulse current of 3C, frequency of 3000 Hz, duty cycle of 50%, and coolant flow rate of 0.495 L/min. The optimized scheme was validated at −10 °C, −15 °C, and −20 °C. The results are shown in Table 17. At −10 °C, the heating time was reduced from 180 s to 140 s, and the average heating rate increased from 6.67 °C/min to 9.69 °C/min. At −15 °C, the heating time was reduced from 210 s to 160 s, and the average heating rate increased from 7.14 °C/min to 10.29 °C/min. At −20 °C, the heating time was reduced from 230 s to 180 s, and the average heating rate increased from 7.83 °C/min to 10.84 °C/min. The average heating rate improved by approximately 45% to 50%. The maximum temperature difference was reduced to less than 1 °C in all three conditions. The optimized scheme achieved simultaneous improvement in heating efficiency and temperature uniformity for the electric vehicle battery pack.
| Ambient temperature (°C) | Optimized heating time (s) | Optimized heating rate (°C/min) | Original heating time (s) | Original heating rate (°C/min) | Optimized maximum temperature difference (°C) |
|---|---|---|---|---|---|
| −10 | 140 | 9.69 | 180 | 6.67 | 0.6 |
| −15 | 160 | 10.29 | 210 | 7.14 | 0.7 |
| −20 | 180 | 10.84 | 230 | 7.83 | 0.8 |
The temperature consistency of the optimized scheme was also analyzed. Before optimization, the maximum temperature difference was 1.9 °C at −10 °C, 2.9 °C at −15 °C, and 2.7 °C at −20 °C. After optimization, the maximum temperature difference was 0.6 °C, 0.7 °C, and 0.8 °C, respectively. The optimized scheme maintained a low temperature difference even at lower ambient temperatures, indicating high thermal uniformity and good low-temperature robustness. The matching optimization of current, frequency, duty cycle, and flow rate effectively coordinated pulse heat generation and liquid-cooling heat transfer, suppressed local hot spots, and improved the temperature synchronization of the entire electric vehicle battery pack.
Summary and Future Work
In this research, I systematically studied the low-temperature performance of an electric vehicle battery pack, designed and implemented a composite heating system, experimentally investigated the effects of key parameters, and optimized the system using a validated electrothermal coupled simulation model. The main conclusions are as follows.
First, I revealed the low-temperature degradation characteristics of the electric vehicle battery pack. When the temperature dropped from 25 °C to −20 °C, the discharge capacity decayed by more than 50%, the internal resistance increased significantly, and both the open-circuit voltage and internal resistance were jointly affected by temperature and state of charge. The entropic heat coefficient showed different reversible heat effects in different SOC ranges, which provides a basis for thermal management strategy formulation.
Second, I proposed and implemented a composite preheating method that combines electric-drive pulse internal self-heating and liquid-cooling plate external heating. For external heating, I compared five flow channel structures and selected the return-type flow channel for the liquid-cooling plate. For internal heating, I designed a zero-torque high-frequency pulse self-heating strategy based on the vehicle electric-drive system and developed a main control system with an STM32 microcontroller to achieve precise current closed-loop control. I successfully built a composite heating experimental platform with multi-parameter control capability.
Third, I experimentally analyzed the effects of key parameters on preheating performance. Under −20 °C conditions, the heating rates of pulse heating and liquid-cooling heating were 5.19 °C/min and 2.58 °C/min, respectively. The composite heating scheme achieved heating rates of 6.67 °C/min, 7.5 °C/min, and 7.83 °C/min at −10 °C, −15 °C, and −20 °C, respectively. The lower the temperature, the more significant the advantage of composite heating over single heating methods. The maximum temperature difference within the electric vehicle battery pack remained below 3 °C. The energy consumption values were 42180 J, 46620 J, and 51060 J for pulse heating at the three temperatures. After 600 complete low-temperature preheating cycles, the capacity decay rate of the electric vehicle battery pack using the composite heating strategy was less than 5%. The composite heating method achieved the best balance among heating rate, temperature uniformity, and energy consumption.
Fourth, I built a three-dimensional electrothermal coupled simulation model of the electric vehicle battery pack preheating system using COMSOL and validated its accuracy. Using this model, I optimized the pulse frequency, current amplitude, and coolant flow rate. The optimal coupled scheme was determined to be a pulse current of 3C, a frequency of 3000 Hz, a duty cycle of 50%, and a coolant flow rate of 0.495 L/min. The simulation results showed that the optimized scheme increased the average heating rate by approximately 45% to 50% and controlled the maximum temperature difference within 1 °C, achieving simultaneous improvement in efficiency and uniformity for the electric vehicle battery pack.
For future work, several directions can be pursued. First, the composite heating strategy should be tested under real vehicle conditions to further verify model accuracy, module temperature consistency, and matching with power loads. Second, real-time dynamic control based on massive experimental data should be developed to implement a precise regulation mechanism for different ambient temperatures, enabling scientific energy management and improved thermal conversion efficiency. Third, the current PTC liquid-cooling preheating technology has limitations such as low energy conversion efficiency and strong dependence on an external power supply. Future research should focus on developing more energy-efficient preheating schemes to further improve the performance of the electric vehicle battery pack.
In conclusion, the composite heating method proposed in this research provides a promising solution for fast, safe, and reliable low-temperature preheating of the electric vehicle battery pack. The combination of internal pulse heating and external liquid-cooling heating effectively addresses the limitations of single heating methods and offers significant engineering application potential for electric vehicles operating in cold environments.