Electric vehicle batteries, particularly lithium-ion batteries, have become the dominant energy storage technology in the automotive industry due to their high energy density, low self-discharge rate, and environmental friendliness. However, low-temperature environments cause severe performance degradation, such as reduced capacity, increased internal resistance, and charging difficulties, which significantly hinder the widespread adoption of electric vehicles in cold regions. To address these challenges, effective thermal management strategies are essential. This work aims to develop a comprehensive low-temperature heating system and control strategy for electric vehicle battery packs, integrating internal pulse self-heating and external liquid cooling plate heating. Through systematic experiments, numerical simulations, and optimization, we propose a hybrid heating approach that achieves rapid, uniform, and energy-efficient preheating, thereby improving battery performance and safety in subzero conditions.
1 Introduction
The global push toward reducing carbon emissions has accelerated the development of electric vehicles. Among various battery technologies, lithium-ion batteries are preferred for their superior characteristics, including high energy density, long cycle life, and low self-discharge. Nevertheless, the performance of lithium-ion batteries is highly temperature-dependent. The optimal operating temperature range is typically between 10°C and 40°C. When the ambient temperature drops below 0°C, the electrolyte viscosity increases, lithium-ion diffusivity decreases, and the solid electrolyte interface (SEI) resistance rises, leading to a significant capacity loss, power fade, and the risk of lithium plating. In particular, at temperatures below −20°C, the battery may lose more than 50% of its usable capacity and become nearly impossible to charge safely.
To mitigate these issues, researchers have developed various preheating techniques. These can be broadly classified into external heating, internal heating, and hybrid heating methods. External heating relies on heat transfer from external sources, such as air, liquid, phase change materials, or electric heating elements. Internal heating generates heat inside the battery by applying electrical currents, utilizing the internal resistance of the battery itself. Hybrid heating combines both internal and external approaches to achieve better performance. The objective of this thesis is to propose and validate a composite preheating method for electric vehicle battery packs that integrates electric-drive pulse internal self-heating with liquid cooling plate external heating. We aim to comprehensively analyze the thermal behavior, evaluate key parameters, and optimize the system through experimental and simulation approaches.
2 Literature Review
2.1 External Heating Techniques
External heating methods transfer heat from an external source to the battery through a medium. Air heating, for example, was studied by Ji and Wang (2013) using a system with a heating wire and a fan, achieving a temperature rise rate of 27.5°C/min from −20°C to 20°C, but resulting in significant internal temperature gradients and added system complexity. Liquid heating systems, which use water, oil, or ethylene glycol mixtures, offer better heat transfer coefficients. Luo et al. (2016) designed an immersion heating system using transformer oil, enabling heating from −30°C to 0°C in 35 minutes with temperature differences below 3°C. Wang et al. (2021) simulated a liquid immersion method and achieved a heating rate of 4.18°C/min. Phase change materials (PCMs) have also been employed; He et al. (2018) combined electric heating sheets with expanded graphite/paraffin PCM, achieving fast preheating and excellent uniformity with a maximum temperature difference of 2.82°C. Electric heating elements, such as heating films or heat pipes, are another alternative. Liu et al. (2018) validated a micro heat pipe–based design, demonstrating that attaching the heating film to the heat pipe’s fin side is a cost-effective and maintainable solution.
2.2 Internal Heating Techniques
Internal heating methods use the battery itself as the heat source, based on ohmic heating from current flow. Wang et al. (2016) introduced a self-heating lithium-ion battery structure with an embedded nickel foil, achieving an extraordinary heating rate of 60°C/min from −30°C to 0°C. Constant current discharge heating was studied by Wu et al. (2017), who found that increasing the discharge rate exponentially reduces heating time and energy consumption. Alternating current (AC) heating, which applies an alternating current to the battery, was investigated by Zhang et al. (2015); they showed that with an amplitude of 7 A (2.25C) and a frequency of 1 Hz, the battery heated from −15°C to 5°C at 2.33°C/min with good internal temperature uniformity. Jiang et al. (2018) proposed an AC-superimposed-DC strategy using a soft-switching resonant circuit, achieving heating from −20.8°C to 2.1°C in 600 seconds with a temperature difference below 1.6°C. Pulse heating, which applies intermittent currents, has been shown to improve uniformity and reduce capacity loss. Ruan et al. (2019) demonstrated a pulse self-heating method that achieved 1.9°C/min while preserving battery life. Qu et al. (2019) used pulse discharge to heat cylindrical batteries, achieving a rate of 6.8°C/min without significant aging.
2.3 Hybrid Heating Methods
Hybrid methods combine internal and external heating to exploit the advantages of both. Xiong et al. (2019) combined wide-line metal film heating with AC heating, achieving a 22% faster heating rate and 23% lower energy consumption compared to AC alone, while also improving temperature consistency. Ruan et al. (2021) proposed a composite self-heating method based on discharge DC internal heating and external contact heating. Their system reached an average temperature rise of 31°C/min from −30°C to 2°C, but with a large internal temperature gradient of 15°C. These studies suggest that while hybrid approaches can significantly improve heating rate and efficiency, careful parameter optimization is required to maintain temperature uniformity and minimize battery aging.
Given the limitations of single heating methods, we propose a composite preheating strategy that combines electric-drive pulse internal self-heating with external liquid cooling plate heating. This approach leverages the high heating efficiency of internal pulse heating and the superior temperature uniformity of liquid cooling, aiming to achieve a balanced performance in heating rate, temperature uniformity, and energy consumption.
3 Experimental Study on Low-Temperature Battery Characteristics
3.1 Experimental Setup and Methodology
To understand the degradation mechanisms of lithium-ion batteries under low temperatures, we conducted a series of controlled experiments. The experimental platform comprised a Neware CT-4004-5V battery tester, a programmable temperature and humidity chamber, a custom insulation enclosure, and K-type thermocouples connected to a data acquisition system. The tested cells were 18650 cylindrical lithium-ion batteries manufactured by Panasonic with a nominal capacity of 2 Ah, a nominal voltage of 3.8 V, and cut-off voltages of 4.2 V (charge) and 2.7 V (discharge). The cell chemistry includes a nickel-cobalt-aluminum (NCA) cathode and a graphite anode.
3.2 Capacity Test Results
We measured the discharge capacity at six temperature points: 25°C, 20°C, 10°C, 0°C, −10°C, and −20°C. The battery was fully charged using a constant-current constant-voltage (CC-CV) protocol (2 A to 4.2 V, then CV until current dropped below 0.2 A). After soaking at each target temperature for 3 hours, the battery was discharged at a constant current of 0.66 A (1/3C) until the voltage reached 2.75 V. The measured capacities are summarized in Table 1.
| Temperature (°C) | Discharge Capacity (Ah) | Capacity Retention vs. 25°C (%) |
|---|---|---|
| 25 | 2.17 | 100 |
| 20 | 2.08 | 95.9 |
| 10 | 1.84 | 84.8 |
| 0 | 1.63 | 75.1 |
| −10 | 1.32 | 60.8 |
| −20 | 1.04 | 47.9 |
As shown in the table, at −20°C the capacity is only 47.9% of that at 25°C, indicating a capacity fade of more than 50%. This dramatic reduction is attributed to increased electrolyte viscosity, reduced lithium-ion diffusivity, and elevated SEI resistance at low temperatures.
3.3 HPPC Test Results
We performed the Hybrid Pulse Power Characterization (HPPC) test to extract the open-circuit voltage (OCV) and internal resistance as functions of state of charge (SOC) and temperature. The test involved a 10 s discharge pulse of 2 C followed by a 40 s rest, a 10 s charge pulse of 1/3 C, and then a 10 s rest, with a 1/3 C discharge to decrement SOC by 0.1. The cell was allowed to rest for one hour to reach equilibrium at each SOC point. Tests were conducted at 25°C, 10°C, 0°C, −10°C, and −20°C.
The OCV–SOC curves reveal three distinct regions: for SOC below 20%, the OCV drops sharply with decreasing SOC; between 20% and 80% SOC, the OCV changes gently; and for SOC above 80%, the OCV rises rapidly with increasing SOC. Temperature also influences the OCV: for SOC below 40%, OCV decreases with increasing temperature, whereas for SOC above 70%, OCV increases with temperature. The internal resistance–SOC curves show that resistance remains nearly constant for SOC between 20% and 80%, decreases at very low SOC, and increases at high SOC. More importantly, the resistance increases significantly as temperature decreases. These results confirm that both OCV and internal resistance depend jointly on temperature and SOC, which must be accounted for in thermal management strategies.
3.4 Entropic Heat Coefficient Test
The entropic heat coefficient, or \( \frac{dE_{OCV}}{dT} \), determines the reversible heat generation during charge and discharge. We measured this coefficient by placing the cell at different temperatures and recording the OCV at various SOC levels. The cell was charged to 100% SOC, then the temperature was sequentially changed to −20°C, −10°C, 0°C, 10°C, and 20°C, with a 12-hour rest at each step. After measuring the OCV, the cell was discharged by 10% SOC with a 0.2 C rate, and the procedure was repeated. The resulting entropic heat coefficient as a function of SOC is shown in Figure (not included here). We found that for most SOC ranges, the coefficient is negative, meaning that reversible heat tends to suppress temperature rise. Around 60% SOC, the coefficient is nearly zero, acting as a “turning point.” In the high SOC region (70–100%), the coefficient becomes positive, amplifying temperature rise. These findings emphasize the importance of reversible heat in battery thermal management.
4 Design of the Composite Heating System
Based on the low-temperature characteristics, we developed a composite heating system that combines internal electric-drive pulse self-heating and external liquid cooling plate heating. The overall architecture is illustrated in Figure (we place the relevant image here).
The internal heating circuit uses a three-phase permanent-magnet synchronous motor (PMSM) and an inverter controller. By controlling the d-axis current with zero torque output, the battery is alternately discharged and charged, generating heat through internal resistance. The external heating loop uses a PTC heater to warm a coolant (50% ethylene glycol solution), which is then pumped through a liquid cooling plate in thermal contact with the battery module. We designed and fabricated a liquid cooling plate with a serpentine flow channel, which was selected after a comparative thermal analysis of five flow channel configurations.
4.1 External Heating: Liquid Cooling Plate Design
We considered five flow channel designs: U-type, parallel-type, composite-type, serpentine (return) type, and S-type. Using COMSOL simulations, we evaluated the temperature distribution on the plate wall under a constant coolant inflow velocity of 0.04 m/s and inlet temperature of 40°C. The plate dimensions were 90 mm × 65 mm × 5 mm, with a channel diameter of 3 mm. The plate material was aluminum, and the coolant was a 50% ethylene glycol solution (density 1100 kg/m³, specific heat 3300 J/(kg·K), thermal conductivity 0.43 W/(m·K), dynamic viscosity 0.00339 Pa·s). The simulation results are summarized in Table 2.
| Channel Type | Temperature Range (°C) | ΔT (°C) | Max Temp (°C) | High-Temp Area (%) | Low-Temp Area (%) |
|---|---|---|---|---|---|
| U | 37.1–38.5 | 1.4 | 38.5 | 31.05 | 53.66 |
| Parallel | 37.9–39.0 | 1.1 | 39.0 | 24.28 | 57.32 |
| Composite | 37.8–38.9 | 1.1 | 38.9 | 17.21 | 64.21 |
| Serpentine (return) | 38.2–39.2 | 1.0 | 39.2 | 36.78 | 42.03 |
| S | 38.2–38.7 | 0.5 | 38.7 | 22.50 | 56.49 |
The serpentine (return) channel exhibited the smallest temperature difference (1.0°C) and the highest maximum temperature (39.2°C), indicating both good uniformity and strong heating capability. Therefore, we selected the serpentine flow channel for the physical fabrication. The manufactured liquid cooling plate, shown in Figure 3.5 of the original thesis, is integrated into the battery module with a 1 mm thermal silicone pad to enhance heat transfer.
4.2 Internal Heating: Electric-Drive Pulse Self-Heating
The internal heating method utilizes the existing traction motor and inverter hardware. The control strategy is based on field-oriented control (FOC) with space-vector pulse-width modulation (SVPWM). To achieve zero torque output, we set the q-axis current reference to zero. Simultaneously, the d-axis current reference is modulated as a square wave oscillating between +Id_ref and −Id_ref at a specified frequency. When the d-axis current is positive, the battery discharges through the inverter into the motor windings; when negative, the magnetic energy stored in the windings is returned to the battery, effectively charging it. This alternating charge/discharge cycle excites the battery’s internal resistance and generates joule heat.
The hardware system is built around an STM32F405RGT6 microcontroller, which implements the FOC algorithm and generates PWM signals. A DRV8301 gate driver board drives a three-phase full-bridge inverter composed of six MOSFETs (Si7850DP). The system includes current sensors, overcurrent protection, and a temperature monitoring interface. We designed the PCB layout using EDA software and fabricated the control board. The software was developed in C using STM32CubeMX and Keil, implementing the current closed-loop control. A code snippet from the implementation is shown in the original thesis, which sets the q-axis current to zero and generates a d-axis current oscillation with a configurable frequency and amplitude.
4.3 Experimental Platform Construction
The complete composite heating test platform comprises the battery module (five 18650 cells connected in series), the liquid cooling plate with a 50% ethylene glycol loop, a PTC heater, a circulation pump, a flow meter, an insulated water tank, a bidirectional DC power supply, a high-low temperature chamber, thermocouple sensors, and a data acquisition unit. The internal heating circuit connects the battery pack to the PMSM and the inverter board. The external heating circuit uses the PTC heater to warm the coolant, which is pumped through the plate. The system allows independent control of pulse amplitude, frequency, duty cycle, coolant flow rate, PTC power, and ambient temperature, enabling comprehensive parametric studies.
5 Experimental Results and Discussion
5.1 Pulse Heating Performance
We first investigated the effects of pulse parameters (frequency, duty cycle, and current amplitude) on battery temperature rise. All experiments were conducted inside the temperature chamber with initial battery temperatures of −10°C, −15°C, and −20°C, and the target final temperature was 10°C. The temperature was recorded every second using five thermocouples attached to the surfaces of the five cells.
5.1.1 Influence of Pulse Frequency
We fixed the pulse current amplitude at 2 C and 3 C, and the duty cycle at 50%, while varying the MOSFET switching frequency among 3000 Hz, 5000 Hz, and 8000 Hz. The measured heating rates are summarized in Table 3.
| Current (C) | Ambient Temp (°C) | 3000 Hz | 5000 Hz | 8000 Hz |
|---|---|---|---|---|
| 2 | −10 | 2.37 | 2.05 | 1.76 |
| −15 | 2.78 | 2.23 | 2.09 | |
| −20 | 2.54 | 1.78 | 1.61 | |
| 3 | −10 | 3.42 | 3.36 | 2.95 |
| −15 | 4.26 | 3.71 | 3.20 | |
| −20 | 4.36 | 3.83 | 3.56 |
The results show that increasing the switching frequency reduces the heating rate nonlinearly. This is because higher frequency leads to a shorter on-time per cycle, limiting the time available for heat accumulation through internal resistance. Moreover, high-frequency switching introduces additional switching and driver losses, which further degrade the effective heating efficiency. Thus, 3000 Hz appears to be a favourable frequency for achieving a relatively high heating rate.
5.1.2 Influence of Duty Cycle
We fixed the frequency at 3000 Hz and varied the duty cycle (25%, 50%, 75%) for pulse amplitudes of 2 C and 3 C. The heating rates are shown in Table 4.
| Current (C) | Ambient Temp (°C) | Duty 25% | Duty 50% | Duty 75% |
|---|---|---|---|---|
| 2 | −10 | 1.95 | 2.25 | 2.54 |
| −15 | 2.52 | 2.87 | 3.03 | |
| −20 | 2.32 | 2.54 | 2.57 | |
| 3 | −10 | 2.93 | 3.32 | 3.92 |
| −15 | 3.84 | 4.24 | 4.43 | |
| −20 | 4.01 | 4.34 | 5.19 |
Increasing the duty cycle increases the effective heating time and thus improves the heating rate. For example, at −20°C and 3 C, a duty cycle of 75% yields a heating rate of 5.19°C/min, which is significantly higher than the 4.01°C/min at 25%. We also observed that for a fixed duty cycle, the heating time increases by about 16% for every 5°C drop in ambient temperature, reflecting the higher internal resistance and increased heat losses at lower temperatures.
5.1.3 Influence of Pulse Current Amplitude
We carried out experiments at 3000 Hz and 5000 Hz with duty cycle 50%, varying the pulse current amplitude from 1 C to 2 C and 3 C. The heating rates are presented in Table 5.
| Frequency (Hz) | Ambient Temp (°C) | 1 C | 2 C | 3 C |
|---|---|---|---|---|
| 3000 | −10 | 0.70 | 2.24 | 3.31 |
| −15 | 0.80 | 2.63 | 4.24 | |
| −20 | 1.14 | 2.58 | 3.64 | |
| 5000 | −10 | 0.61 | 1.44 | 3.94 |
| −15 | 1.13 | 2.23 | 4.97 | |
| −20 | 0.72 | 2.58 | 3.64 |
The heating rate increases by approximately 120% when the current amplitude is doubled. This highlights that increasing the pulse current is a much more effective way to accelerate heating compared to increasing the frequency. However, higher currents may also increase polarization and the risk of lithium plating, especially at very low temperatures. Therefore, a moderate amplitude such as 3 C is chosen as a practical trade-off in subsequent composite heating tests.
5.1.4 Temperature Uniformity under Pulse Heating
We examined the temperature consistency among the five cells during pulse heating. For a pulse current of 2 C, the maximum temperature difference between any two cells under −10°C, −15°C, and −20°C was recorded. In all cases, the maximum difference exceeded 5°C, indicating poor uniformity. The primary cause is the inherent variation in internal resistance between individual cells, which causes differences in internal heat generation. This non-uniform temperature distribution is a known drawback of pure internal heating and motivates the need for an external heating component to improve temperature homogenization.
5.2 Liquid Cooling Heating Performance
We evaluated the external liquid cooling heating method by adjusting the coolant flow rate and the PTC heating power. The coolant was pumped through the liquid cooling plate from an insulated reservoir heated by a PTC heater.
5.2.1 Influence of Coolant Flow Rate
We tested five flow rates: 0.2, 0.3, 0.43, 0.56, and 0.73 L/min under ambient temperatures of −10°C and −15°C, with PTC powers of 200 W and 300 W. The heating time to reach 10°C was recorded. The results indicated that a flow rate of 0.56 L/min yielded the shortest heating time and the best heating performance. Flow rates below 0.43 L/min caused insufficient heat transfer, leading to excessive heat loss at the edges of the plate. Flow rates above 0.73 L/min reduced the residence time of the coolant, lowering the heat exchange efficiency. Thus, an optimal flow rate exists near 0.56 L/min for this system, allowing a balance between thermal transport and energy consumption.
5.2.2 Influence of PTC Power
We fixed the coolant flow rate at 0.43 L/min and tested PTC powers of 100 W, 200 W, and 300 W at ambient temperatures of −10°C, −15°C, and −20°C. The measured heating rates are listed in Table 6.
| Ambient Temp (°C) | 100 W | 200 W | 300 W |
|---|---|---|---|
| −10 | 1.18 | 1.69 | 2.67 |
| −15 | 1.20 | 2.08 | 2.54 |
| −20 | 1.00 | 2.00 | 2.54 |
Increasing PTC power significantly improves the heating rate. At 300 W, the average heating rate across all temperatures is approximately 2.58°C/min. We also noticed that the heating effect is negligible during the first two minutes because the coolant and the plate need time to reach a sufficient temperature difference with the battery. Therefore, the PTC heater should be started in advance or operated continuously to maximize its benefit.
5.2.3 Temperature Uniformity under Liquid Heating
Unlike pulse heating, the liquid cooling plate provides more uniform temperature distribution. The maximum temperature difference among the five cells was always below 3°C for both 200 W and 300 W PTC powers. The uniformity slightly deteriorates as the ambient temperature drops, but remains within acceptable limits. Thus, the external liquid heating is superior to pulse heating in terms of temperature consistency, although its heating rate is lower.
5.3 Composite Heating Performance
We then combined the internal pulse heating (3 C, 3000 Hz, 50% duty cycle) with the external liquid cooling heating (0.56 L/min flow rate, 300 W PTC) to form the composite heating strategy. We evaluated its performance under ambient temperatures of −10°C, −15°C, and −20°C, and compared it with the individual methods. The key results are summarized in Table 7.
| Ambient Temp (°C) | Method | Heating Time (s) | Heating Rate (°C/min) |
|---|---|---|---|
| −10 | Liquid | 460 | 2.61 |
| Pulse | 380 | 3.15 | |
| Composite | 180 | 6.67 | |
| −15 | Liquid | 570 | 2.63 |
| Pulse | 420 | 3.57 | |
| Composite | 210 | 7.14 | |
| −20 | Liquid | 690 | 2.61 |
| Pulse | 460 | 3.94 | |
| Composite | 230 | 7.83 |
The composite heating significantly outperforms both individual methods. At −20°C, the composite heating rate of 7.83°C/min is about 200% higher than that of liquid heating and 99% higher than that of pulse heating. The advantage becomes more pronounced at lower temperatures, which is highly desirable for extreme cold climates.
5.3.1 Temperature Uniformity of Composite Heating
During composite heating, we monitored the five cell temperatures. The maximum temperature difference was always below 3°C for all three ambient temperatures. As the ambient temperature decreased, the temperature difference increased only slightly (less than 0.5°C per 10°C drop). This indicates that the external liquid heating effectively mitigates the non-uniformity caused by internal pulse heating, resulting in excellent overall temperature uniformity. Thus, the composite approach achieves both high heating rate and acceptable temperature distribution.
5.3.2 Energy Consumption Analysis
We calculated the energy consumption for each heating method using the following equations. For pulse heating, the energy consumed from the battery is:
$$Q_{\text{pulsating}} = \int U I \, dt $$
where \(U\) is the terminal voltage, \(I\) is the current, and \(t\) is the time. For the PTC heater, the electrical energy consumed is:
$$Q_{\text{PTC}} = \frac{P_{\text{PTC}} \Delta t}{\eta} $$
where \(P_{\text{PTC}}\) is the PTC power, \(\Delta t\) is the heating time, and \(\eta\) is the electrothermal conversion efficiency (assumed 95%). The results are compared in Table 8.
| Ambient Temp (°C) | Pulse Heating | Composite Heating | Liquid Heating |
|---|---|---|---|
| −10 | 42,180 | 76,822 | 145,263 |
| −15 | 46,620 | 85,358 | 180,000 |
| −20 | 51,060 | 98,161 | 217,894 |
Pulse heating consumes the least energy because it directly converts battery energy into internal heat without going through an intermediate heat transfer medium. Liquid heating consumes the most, mainly because the PTC heater must first heat the coolant and the system incurs significant thermal losses during transfer. Composite heating lies in between and offers a reasonable balance: the pulse component rapidly raises the core temperature, while the liquid component improves uniformity without excessive additional energy. Therefore, the composite strategy is more energy-efficient than pure external heating while providing much better temperature uniformity than pure internal heating.
5.4 Capacity Fade after Repeated Heating Cycles
We assessed the long-term impact of the composite heating strategy on battery health by performing 600 complete heating cycles from −20°C to 10°C. Three groups of cells were tested: Group A (1 C pulse + 100 W PTC), Group B (2 C pulse + 200 W PTC), and Group C (3 C pulse + 300 W PTC). The capacity retention after 300 and 600 cycles is shown in Table 9.
| Group | Capacity loss after 300 cycles (%) | Capacity loss after 600 cycles (%) |
|---|---|---|
| A (1C+100W) | 0.73 | 1.70 |
| B (2C+200W) | 1.70 | 3.00 |
| C (3C+300W) | 2.90 | 4.30 |
All groups showed capacity losses below 5% after 600 cycles, confirming that the composite heating method causes acceptable degradation to the battery. The capacity loss increases with higher pulse current and PTC power, but remains within a safe engineering limit. This demonstrates the practical feasibility and long-term durability of the proposed approach.
6 Simulation Modeling and Optimization
To further improve the heating performance and expand the parameter space beyond the physical experiments, we developed a three-dimensional electro-thermal coupled model using COMSOL Multiphysics. The model integrates the battery cell electrochemical heat generation, heat conduction in the solid domains, convective heat transfer in the coolant, and the flow field in the liquid cooling plate.
6.1 Mathematical Model
The battery heat generation is calculated based on the Bernardi equation:
$$q = \frac{1}{V} \left( I^2 R – I T \frac{\partial U_{ocv}}{\partial T} \right)$$
where \(V\) is the cell volume, \(I\) is the current, \(R\) is the total resistance, \(T\) is the temperature, and \(\frac{\partial U_{ocv}}{\partial T}\) is the entropic heat coefficient. For pulse heating, the reversible term (the second part) is negligible because charge and discharge occur alternately, so the heat generation is dominated by the irreversible ohmic and polarization heat.
The transient heat conduction in the battery and plate is governed by:
$$\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + q$$
where \(\rho\) is the density, \(C_p\) the specific heat, and \(\lambda\) the thermal conductivity (with anisotropic values for the battery). The fluid flow is modeled using the incompressible Navier–Stokes equations, and the heat transfer between the coolant and the plate is handled by the conjugate heat transfer module.
6.2 Model Setup and Mesh Independence
The three-dimensional geometry consists of five 18650 cells arranged in a module, with the liquid cooling plate attached on one side through a 1 mm thermal silicone pad. The coolant flows through the serpentine channels. We set the ambient temperature to −20°C, the pulse current to 2 C (4 A), the frequency to 3000 Hz, and the coolant inlet temperature ramps to 40°C over 120 seconds. Six mesh sizes were tested, ranging from 220,000 to 5.6 million elements. The average temperature and maximum temperature difference at 240 seconds were recorded. As shown in Table 10, beyond 2.55 million elements, the average temperature and voltage change only slightly. Therefore, we selected a mesh with approximately 2.55 million elements for subsequent simulations, balancing accuracy and computational efficiency.
| Number of Elements | Avg Temp (°C) | Max ΔT (°C) | Avg Voltage (V) | Max ΔV (V) |
|---|---|---|---|---|
| 220,451 | 11.291 | 3.31 | 4.09039 | 0.0133 |
| 336,178 | 9.911 | 2.32 | 3.97042 | 0.0096 |
| 548,178 | 6.937 | 2.43 | 3.96368 | 0.0104 |
| 1,108,303 | 5.186 | 1.55 | 3.87120 | 0.0206 |
| 2,552,359 | 5.012 | 1.28 | 3.85120 | 0.0053 |
| 5,616,842 | 4.952 | 1.39 | 3.82160 | 0.0093 |
6.3 Model Validation
We validated the simulation model by comparing the predicted average battery temperature with experimental data for all three heating methods (liquid, pulse, and composite) at ambient temperatures of −10°C, −15°C, and −20°C. The maximum average relative error was below 9%, and most data points had errors below 5%. For individual cells, the liquid heating and composite heating models showed good accuracy (average relative errors below 5% and 12%, respectively), while the pulse heating model exhibited larger deviations, likely due to the simplified assumption of uniform heat generation and the neglect of contact resistances between cells. Overall, the model is sufficiently accurate for parameter optimization and trend prediction.
6.4 Parameter Optimization
Using the validated model, we performed a series of simulations to explore the influence of key parameters beyond the physical test range.
6.4.1 Influence of Pulse Frequency
We simulated pulse heating with a 3 C current and 50% duty cycle at frequencies of 1000, 3000, 5000, and 8000 Hz. The average temperature rise after 500 seconds and the maximum temperature difference in the battery pack are shown in Table 11.
| Frequency (Hz) | Temperature Rise (°C) | Max ΔT (°C) |
|---|---|---|
| 1000 | 30.7 | 6.6 |
| 3000 | 27.2 | 5.3 |
| 5000 | 24.4 | 4.5 |
| 8000 | 20.3 | 3.6 |
The results confirm the experimental trend: lower frequencies yield higher temperature rise but also larger temperature gradients. A frequency of 3000 Hz offers a good compromise, providing a high heating rate while maintaining a moderate temperature spread.
6.4.2 Influence of Pulse Current Amplitude
We simulated currents from 1 C to 5 C at a fixed frequency of 3000 Hz and 50% duty cycle. The results after 500 seconds are presented in Table 12.
| Current (C) | Temperature Rise (°C) | Max ΔT (°C) |
|---|---|---|
| 1 | 16.1 | 2.3 |
| 2 | 22.9 | 3.6 |
| 3 | 27.2 | 5.3 |
| 4 | 34.3 | 7.2 |
| 5 | 39.9 | 9.3 |
Although higher currents produce faster heating, they markedly increase the temperature non-uniformity. A current of 3 C is identified as the optimal choice because it achieves a good heating rate with acceptable unevenness, balancing heat generation and internal thermal gradients.
6.4.3 Influence of Coolant Flow Rate
In addition to the experimental flow rates (0.2, 0.3, 0.43, 0.56, 0.73 L/min), we simulated intermediate values: 0.25, 0.365, 0.495, and 0.645 L/min. The average temperature rise and maximum ΔT after 500 seconds are shown in Table 13.
| Flow Rate (L/min) | Temperature Rise (°C) | Max ΔT (°C) |
|---|---|---|
| 0.20 | 14.2 | 2.4 |
| 0.25 | 15.1 | 2.2 |
| 0.30 | 16.3 | 2.0 |
| 0.365 | 17.8 | 1.8 |
| 0.43 | 19.2 | 1.7 |
| 0.495 | 20.6 | 1.5 |
| 0.56 | 19.8 | 1.9 |
| 0.645 | 18.9 | 2.3 |
| 0.73 | 17.5 | 2.8 |
The optimal flow rate is approximately 0.495 L/min, which gives the highest temperature rise and the lowest maximum temperature difference (1.5°C). This flow rate ensures sufficient coolant circulation without excessively reducing the heat exchange residence time, thereby enhancing both heating efficiency and thermal uniformity.
6.5 Optimized Composite Heating Scheme
Based on the combined experimental and simulation findings, we determined an optimized coupling parameter set: a pulse current of 3 C, a pulse frequency of 3000 Hz, a duty cycle of 50%, and a coolant flow rate of 0.495 L/min. We then simulated the composite heating with these parameters at ambient temperatures of −10°C, −15°C, and −20°C, and compared the results with the original (pre-optimization) composite scheme (which used 3 C, 3000 Hz, 50% duty, and 0.56 L/min). The comparative performance is shown in Table 14.
| Ambient Temp (°C) | Scheme | Heating Time to 10°C (s) | Avg Heating Rate (°C/min) | Max ΔT (°C) |
|---|---|---|---|---|
| −10 | Original | 180 | 6.67 | 1.9 |
| Optimized | 140 | 9.69 | 0.6 | |
| −15 | Original | 210 | 7.14 | 2.9 |
| Optimized | 160 | 10.29 | 0.7 | |
| −20 | Original | 230 | 7.83 | 2.7 |
| Optimized | 180 | 10.84 | 0.8 |
The optimized scheme improves the average heating rate by approximately 45–50% while simultaneously reducing the maximum temperature difference to below 1°C. This demonstrates that proper coordination of the pulse current, frequency, duty cycle, and coolant flow rate can significantly enhance both heating efficiency and uniformity, offering a compelling solution for electric vehicle battery thermal management in cold climates.
7 Conclusion and Future Work
In this work, we systematically investigated a low-temperature heating system and control strategy for electric vehicle battery packs. We first experimentally characterized the low-temperature behavior of lithium-ion batteries, quantifying the severe capacity fade, resistance increase, and the dependence of OCV and entropic heat coefficient on temperature and SOC. Then, we proposed and constructed a composite heating system that integrates internal electric-drive pulse self-heating with external liquid cooling plate heating. The system was fully realized with a custom-designed serpentine-flow liquid cooling plate, a STM32-based controller, and a complete experimental platform.
Through extensive experiments, we analyzed the effects of pulse current amplitude, frequency, duty cycle, coolant flow rate, and PTC power on heating performance. The composite heating approach was found to significantly outperform both individual methods in terms of heating rate while maintaining excellent temperature uniformity (maximum temperature difference below 3°C) and acceptable energy consumption. Repeated heating cycles of up to 600 times resulted in capacity fade below 5%, confirming the long-term durability of the proposed strategy.
We further developed a three-dimensional electro-thermal coupled simulation model in COMSOL and validated it against experimental data. Using this model, we performed a comprehensive parameter optimization and identified an optimal coupling scheme: pulse current 3 C, frequency 3000 Hz, duty cycle 50%, and coolant flow rate 0.495 L/min. The optimized scheme increases the average heating rate by 45–50% and reduces the maximum temperature difference to below 1°C, achieving a remarkable simultaneous improvement in heating efficiency and thermal uniformity.
Future research will focus on translating this composite heating strategy to real vehicle conditions, integrating it with vehicle-level thermal management systems, and implementing adaptive control algorithms to optimize the heating process based on real-time battery state and ambient conditions. In addition, we will investigate alternative high-efficiency heat sources, such as heat pumps, to further reduce energy consumption and enhance the overall sustainability of electric vehicles.