Lithium-ion batteries have become the dominant energy-storage solution for electric vehicles (EVs) because of their high energy density, long cycle life, and relatively low self-discharge rate. However, the performance of lithium-ion cells—especially when used in an EV battery pack—degrades severely at subzero temperatures. At \(-20\,^{\circ}\mathrm{C}\), the discharge capacity of a typical cell can drop by more than half, the internal resistance rises sharply, and fast charging becomes practically impossible. In addition, low-temperature charging promotes lithium plating on the graphite anode, which may lead to dendrite growth, internal short circuits, and even thermal runaway. Therefore, developing an efficient and uniform preheating system for the EV battery pack is of critical importance for cold-climate operation, range extension, and safety improvement.
Many existing preheating methods can be categorized as external heating (air heating, liquid heating, phase-change materials, electric heating films) or internal heating (DC heating, AC heating, pulse heating, self-heating structures). External heaters generally heat the battery module from the surface, which usually creates large temperature gradients and requires relatively long times. Internal heating, on the other hand, heats each cell volumetrically through ohmic losses, offering higher energy efficiency and faster warm-up, but it often needs careful control of current frequency, amplitude, and duty cycle to avoid lithium plating and capacity fade. Moreover, a single heating method may not be sufficient to achieve both rapid heating and uniform temperature distribution over the whole EV battery pack under extremely cold conditions.
In this study, I propose a hybrid preheating solution that couples internal electric-drive pulse self-heating with external liquid-cooling-plate heating using a PTC (positive temperature coefficient) element. The internal heating is realized through an inverter-controlled permanent-magnet synchronous motor (PMSM) and its windings, which can generate a high-frequency alternating current through the battery without producing torque. The external heating is implemented with a serpentine-channel aluminum cold plate integrated with a 50% ethylene-glycol coolant loop. To evaluate and optimize this system, I first investigate the cell-level low-temperature characteristics through experiments; then I construct a composite-heating experimental platform and systematically explore the effects of key parameters on the warming behavior, temperature uniformity, and energy consumption; finally I develop a three-dimensional electro-thermal coupled model in COMSOL Multiphysics, validate it against experimental data, and use it to optimize the pulse frequency, pulse current amplitude, and coolant flow rate.
2. Experimental Study of Low-Temperature Cell Behavior
2.1 Cell specifications and experimental setup
I used commercial 18650 cylindrical cells with a nominal capacity of 2 Ah and a nominal voltage of 3.8 V. The cathode is nickel–cobalt–aluminum oxide and the anode is graphite. The key cell parameters are summarized in the following table.
| Parameter | Value |
|---|---|
| Manufacturer style | 18650 cylindrical |
| Rated capacity | 2000 mAh |
| Nominal voltage | 3.8 V |
| Dimensions | 65 mm height, 18 mm diameter |
| Cathode / Anode | LiNiCoAlO₂ / Graphite |
| Charge cut-off voltage | 4.2 V |
| Discharge cut-off voltage | 2.7 V |
| Test temperatures | 25, 20, 10, 0, –10, –20 °C |
The experiments were carried out in a programmable thermal chamber. A bidirectional DC power supply was used for charge/discharge cycling, and thermocouples attached to the cell surfaces measured temperature. The data acquisition unit also recorded voltage and current profiles. Before each test, the cells were soaked at the target temperature for at least 3 hours.
2.2 Discharge capacity vs temperature
I first measured the discharge capacity at different ambient temperatures using a constant-current discharge at 1/3 C (0.66 A) down to 2.75 V. The following table shows the measured capacity and the relative capacity loss normalized to the 25 °C capacity.
| Temperature (°C) | Discharge capacity (Ah) | Capacity loss vs 25 °C (%) |
|---|---|---|
| 25 | 2.17 | 0 |
| 20 | 2.12 | 2.3 |
| 10 | 1.84 | 15.2 |
| 0 | 1.63 | 24.9 |
| –10 | 1.32 | 39.9 |
| –20 | 1.04 | 52.1 |
The discharge capacity loss can be quantified by the ratio \(\eta_C\), where
\[
\eta_C = \frac{C_{25} – C_T}{C_{25}} \times 100\%
\]
At \(-20\,^{\circ}\mathrm{C}\), the cell retains only 47.9% of its room-temperature capacity. Such a dramatic reduction occurs mainly by the increased viscosity of the electrolyte and the increased charge-transfer impedance at the electrode/electrolyte interfaces, which restrict lithium-ion transport.
2.3 HPPC test and internal resistance
To characterize the open-circuit voltage (OCV) and internal resistance at different states of charge (SOC), I performed a hybrid pulse power characterization (HPPC) test. The procedure included one 10 s discharge pulse at 1 C, a 40 s rest, a 10 s charge pulse at 1/3 C, and another rest period, followed by a 1/3 C discharge step to reduce the SOC by 10% and a 1 h relaxation. The measurements were repeated from 100% SOC down to 10% SOC at five different temperatures.
The OCV-SOC relationship exhibits three regions. For SOC below 20%, the OCV decreases rapidly; between 20% and 80% SOC, the OCV varies only gently; and above 80% SOC, it rises steeply. The temperature effect is not monotonic: below about 40% SOC, the OCV increases with decreasing temperature, while above 70% SOC, the OCV decreases with decreasing temperature. The internal resistance also depends strongly on both temperature and SOC. In the middle SOC region (20%–80%), the internal resistance is nearly SOC-independent. It always increases as temperature decreases. Representative internal resistance values at different temperatures and SOC values are listed in the following table.
| Temperature | SOC = 20% | SOC = 50% | SOC = 80% |
|---|---|---|---|
| 20 °C | ~38 mΩ | ~30 mΩ | ~36 mΩ |
| 0 °C | ~60 mΩ | ~50 mΩ | ~58 mΩ |
| –20 °C | ~130 mΩ | ~115 mΩ | ~128 mΩ |
These data demonstrate that the effective impedance that determines the ohmic heat generation is strongly temperature dependent. Therefore, pulse heating at low temperature can be very effective because the high internal resistance naturally generates more heat for a given current amplitude.
2.4 Entropic heat coefficient
The entropic heat coefficient \(dE_{OCV}/dT\) is an important parameter for evaluating reversible heat in the heat-generation model. I determined it by measuring the OCV as the cell was exposed to successive temperatures from \(-20\) to \(20\,^{\circ}\mathrm{C}\) at a fixed SOC, with a 1 h soak at each temperature. The cell capacity was first set to each SOC by discharging at 0.2 C.
The measured entropic heat coefficient varies with SOC. Most SOC points show a negative value, which means that during discharge the reversible entropic heat is exothermic, while during charge it is endothermic. Around SOC ≈ 60%, the coefficient is close to zero, so the reversible heat contribution nearly disappears. In the high SOC range (70%–100%), the coefficient becomes positive, increasing the heat during discharge. This information is needed in the thermal model to separate irreversible Joule heating from reversible reaction heating.
3. Hybrid Heating System Architecture and Design
3.1 Overall architecture
I designed a hybrid heating system that combines an internal pulse-heating branch with an external liquid-heating branch. The internal branch uses the traction motor inverter and the three-phase stator windings as the energy-transfer elements. By applying a zero-torque field-oriented control (FOC) strategy, the current is limited to the d-axis, which produces no rotational torque but alternately discharges and charges the EV battery pack at a high frequency. During the discharge phase, the battery current flows into the motor windings and energy is stored in the magnetic field. In the charging phase, the windings return energy to the battery. The ohmic losses in the battery resistance heat the cells volumetrically.
The external branch consists of a PTC heating element, an insulated water tank, a pump, a flow meter, and a serpentine-flow-channel cold plate. The PTC heats a 50% ethylene-glycol coolant, which is pumped through the cold plate mounted under the battery module. Thus, the battery module is heated both from inside (via the pulse current) and from outside (via the warm plate), accelerating the overall temperature rise.
3.2 External heating: cold-plate flow-channel comparison
To maximize the heat-transfer performance and surface-temperature uniformity of the cooling plate, I compared five flow-channel designs: U-shaped, parallel, composite, serpentine (return), and S-shaped channels. I built the corresponding geometry in COMSOL and simulated the temperature distribution on the plate surface when the coolant inlet temperature is 40 °C and the flow velocity is 0.04 m/s. The most important evaluation metrics are the wall-temperature range, the maximum temperature difference, the percentage of high-temperature hot spots, and the percentage of low-temperature cold spots. The results are summarized below.
| Channel type | Temperature range (°C) | Max difference (°C) | Hot area fraction (%) | Cold area fraction (%) |
|---|---|---|---|---|
| U-shaped | 37.1–38.5 | 1.4 | 31.1 | 53.7 |
| Parallel | 37.9–39.0 | 1.1 | 24.3 | 57.3 |
| Composite | 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 |
The serpentine (return) channel achieves the highest average wall temperature (38.2–39.2 °C), the smallest cold-area fraction (42.0%), and a reasonably low maximum temperature difference of 1.0 °C. Although the S-shaped channel gives the smallest temperature spread, its average temperature is lower, which would reduce the heat-transfer efficiency. Therefore, I selected the serpentine return flow channel as the external heating plate for the physical platform. The plate is made from aluminum; the main geometric dimensions are 90 mm × 65 mm × 5 mm and the internal flow-channel diameter is 3 mm. The coolant used in the experiments is a 50% ethylene-glycol solution with a freezing point of –36.7 °C.
3.3 Internal heating: electric-drive pulse strategy
For the internal self-heating, I adapted the existing vehicle electric-drive system. The motor under test is a 1 kW three-phase PMSM with a rated voltage of 48 V, rated phase current of 30 A, direct-axis inductance 0.08 mH, quadrature-axis inductance 0.15 mH, and line resistance of 0.07 Ω. In the proposed strategy, the motor rotor is locked, and the d-axis current reference is made to oscillate between \(+I_d\) and \(-I_d\) while the q-axis current is set to zero. Because the q-axis current is zero, no electromagnetic torque is generated. The inverter switching states are produced by the space-vector PWM (SVPWM) algorithm, and the d-axis current is regulated by proportional-integral controllers in a synchronous reference frame.
The core control law can be expressed as
\[
i_d^*(t) = I_d \, \mathrm{sgn}(\sin(2\pi f_{pulse}t))
\]
with \(i_q^*=0\). The actual phase current is sampled and compared with the reference, and PI controllers adjust the duty cycles accordingly. The software was implemented on an STM32F405 microcontroller; the gate driver is a DRV8301 device that drives six Si7850DP MOSFETs.
The resulting current waveform causes the battery to alternate between discharging and charging at the pulse frequency \(f_{pulse}\). This alternating regime excites both the ohmic and polarization resistances, producing heat proportional to \(I^2R\) inside each cell. I verified that the motor remained stationary during heating by measuring its encoder position, confirming zero-torque output.
3.4 Experimental platform
The composite experimental platform includes a temperature chamber, a bidirectional DC power supply, a battery module of five 18650 cells in parallel, a serpentine-channel cold plate, a PTC heater, a circulation pump, a flow meter, an insulated coolant tank, a pulse-heating controller, thermocouple sensors, and a data acquisition module. The battery module was in full contact with the cold plate through a 1 mm thermally conductive silicone pad and thermal grease. The coolant loop could be controlled independently by adjusting the PTC power and pump flow rate. The pulse parameters (amplitude, frequency, duty cycle) were adjustable through the custom controller and PC interface. The entire fixture was placed inside a thermal chamber to maintain a set ambient temperature between \(-20\) and \(25\,^{\circ}\mathrm{C}\).
4. Experimental Investigation of the Hybrid System
4.1 Effects of pulse frequency
I first investigated the pulse frequency effect while maintaining a constant duty cycle (50%) and two current amplitudes (2C and 3C). The battery was heated from \(-10\), \(-15\), or \(-20\,^{\circ}\mathrm{C}\) to \(10\,^{\circ}\mathrm{C}\). The measured average heating rates are summarized in the following table.
| Current amplitude | Ambient temperature (°C) | Heating rate @ 3000 Hz (°C/min) | Heating rate @ 5000 Hz (°C/min) | Heating rate @ 8000 Hz (°C/min) |
|---|---|---|---|---|
| 2C | –10 | 2.37 | 2.05 | 1.76 |
| 2C | –15 | 2.78 | 2.23 | 2.09 |
| 2C | –20 | 2.54 | 1.78 | 1.61 |
| 3C | –10 | 3.42 | 3.36 | 2.95 |
| 3C | –15 | 4.26 | 3.71 | 3.20 |
| 3C | –20 | 4.36 | 3.83 | 3.56 |
The heating rate monotonically decreases as the switching frequency rises from 3000 to 8000 Hz. A higher frequency means shorter current pulses, which reduce the time available for ohmic heating within each pulse, while the fixed off-state and switching losses become relatively larger. Therefore, lower frequencies are more effective for faster warm-up, but they may cause larger cell-to-cell temperature differences because the current is applied less uniformly in time. The measured temperature uniformity under pulse heating is analyzed later.
4.2 Effects of duty cycle
With a fixed frequency of 3000 Hz and amplitudes of 2C and 3C, I varied the duty cycle from 25% to 75%. The heating times and corresponding average heating rates are shown below.
| Current | Ambient temperature (°C) | Duty = 25% (rate °C/min) | Duty = 50% (rate °C/min) | Duty = 75% (rate °C/min) |
|---|---|---|---|---|
| 2C | –10 | 1.95 | 2.25 | 2.54 |
| 2C | –15 | 2.52 | 2.87 | 3.03 |
| 2C | –20 | 2.32 | 2.54 | 2.57 |
| 3C | –10 | 2.93 | 3.32 | 3.92 |
| 3C | –15 | 3.84 | 4.24 | 4.43 |
| 3C | –20 | 4.01 | 4.34 | 5.19 |
A larger duty cycle extends the effective heating time in each period, which increases the average power delivered to the battery. The fastest overall rate observed in pure pulse heating was 5.19 °C/min, which occurred at 3C, 3000 Hz, a duty cycle of 75%, and an ambient temperature of \(-20\,^{\circ}\mathrm{C}\). However, using very high duty cycles can lead to a continuously direct current, which increases the risk of lithium plating. Therefore, I selected a 50% duty cycle for most subsequent tests to balance heating performance and safety.
4.3 Effects of pulse current amplitude
I also studied the amplitude influence at fixed frequencies (3000 and 5000 Hz) and a 50% duty cycle. The heating rates for amplitudes of 1C, 2C, and 3C are summarized below.
| Frequency | Ambient temperature (°C) | Heating rate @ 1C (°C/min) | Heating rate @ 2C (°C/min) | Heating rate @ 3C (°C/min) |
|---|---|---|---|---|
| 3000 Hz | –10 | 0.70 | 2.24 | 3.31 |
| 3000 Hz | –15 | 0.80 | 2.63 | 4.24 |
| 3000 Hz | –20 | 1.14 | 2.58 | 3.64 |
| 5000 Hz | –10 | 0.61 | 1.44 | 3.94 |
| 5000 Hz | –15 | 1.13 | 2.23 | 4.97 |
| 5000 Hz | –20 | 0.72 | 2.58 | 3.64 |
Roughly doubling the current amplitude doubles the heating rate. The underlying reason is that the volumetric heat generation is proportional to the square of the current through the battery internal resistance: \(q \propto I^2R\). Since the internal resistance changes during heating, the exact scaling is not perfectly quadratic, but the trend is clear. Larger current amplitudes severely exacerbate the temperature non-uniformity, so an appropriate compromise must be chosen.
4.4 Temperature uniformity of pulse heating
I attached five thermocouples to five cells in the module to record the temperature spread during pure pulse heating. In several cases, the maximum cell-to-cell temperature difference exceeded 5 °C, especially when the initial temperature was \(-20\,^{\circ}\mathrm{C}\). This is mainly due to manufacturing-related variations in internal resistance among cells; a higher-resistance cell dissipates more heat, becomes hotter, and further reduces its resistance, which reinforces the non-uniformity. Consequently, while pure pulse heating is fast, it suffers from undesirable temperature gradients.
4.5 Liquid cooling/heating results
The external liquid heating branch was tested separately. The coolant temperature was raised by the PTC heater and pumped through the cold plate. I studied the influence of coolant flow rate at two PTC power levels. The tested flow rates were 0.20, 0.30, 0.43, 0.56, and 0.73 L/min. The heating rate as a function of flow rate is not monotonic. The following table presents the time required to heat the module from \(-10\) or \(-15\,^{\circ}\mathrm{C}\) to \(10\,^{\circ}\mathrm{C}\) at 300 W and 200 W.
| PTC power | Ambient temperature (°C) | Time @ 0.20 L/min (s) | Time @ 0.30 L/min (s) | Time @ 0.43 L/min (s) | Time @ 0.56 L/min (s) | Time @ 0.73 L/min (s) |
|---|---|---|---|---|---|---|
| 200 W | –10 | ~780 | ~740 | ~690 | ~670 | ~705 |
| 200 W | –15 | ~980 | ~920 | ~820 | ~800 | ~840 |
| 300 W | –10 | ~620 | ~560 | ~500 | ~475 | ~510 |
| 300 W | –15 | ~780 | ~720 | ~640 | ~610 | ~650 |
At very low flow rates, the coolant cannot transfer enough heat to the cold plate because the overall heat-transfer coefficient is small. At very high flow rates, the coolant spends less time inside the channels and exits before a sufficient amount of thermal energy is released. The optimum flow rate in this experiment was approximately 0.56 L/min for the external branch alone, although later simulations identified a slightly different optimum when combined with the internal heating branch.
I then fixed the flow rate at 0.43 L/min and varied the PTC power from 100 W to 300 W. The heating rates increased with PTC power. The following results were obtained when heating from three initial temperatures to \(10\,^{\circ}\mathrm{C}\).
| Ambient temperature | Heating time @ 100 W (s) | Rate @ 100 W (°C/min) | Heating time @ 200 W (s) | Rate @ 200 W (°C/min) | Heating time @ 300 W (s) | Rate @ 300 W (°C/min) |
|---|---|---|---|---|---|---|
| –10 °C | 1020 | 1.18 | 700 | 1.69 | 460 | 2.67 |
| –15 °C | 1250 | 1.20 | 720 | 2.08 | 590 | 2.54 |
| –20 °C | 1800 | 1.00 | 900 | 2.00 | 650 | 2.54 |
The PTC heating alone provides a moderate heating rate below 2.7 °C/min, but it yields much better temperature uniformity than pulse heating. The maximum temperature difference within the module under pure liquid heating remained below 3 °C for all cases. This is because the liquid flow through the serpentine channels homogenizes the cold-plate surface temperature and transfers heat efficiently to the cells through the aluminum plate and thermal pad.
4.6 Comparison of heating strategies
Finally, I compared the pure pulse, pure liquid, and hybrid (composite) heating strategies under identical test conditions: ambient temperatures of \(-10\), \(-15\), and \(-20\,^{\circ}\mathrm{C}\); for pulse heating, 3C amplitude and 3000 Hz; for liquid heating, 0.56 L/min flow rate and 300 W PTC power; for composite, both branches were active simultaneously. The required heating time to reach \(10\,^{\circ}\mathrm{C}\) and the corresponding heating rates are listed in the following table.
| Ambient temperature | Pulse heating time/rate | Liquid heating time/rate | Composite heating time/rate |
|---|---|---|---|
| –10 °C | 380 s / 3.15 °C/min | 460 s / 2.61 °C/min | 180 s / 6.67 °C/min |
| –15 °C | 420 s / 3.57 °C/min | 570 s / 2.63 °C/min | 210 s / 7.50 °C/min |
| –20 °C | 460 s / 3.94 °C/min | 690 s / 2.61 °C/min | 230 s / 7.83 °C/min |
The composite strategy is dramatically superior to single-method heating. In \(-20\,^{\circ}\mathrm{C}\) conditions, the composite heating rate reaches 7.83 °C/min, which is about double the pulse-only rate and triple the liquid-only rate. The advantage becomes increasingly pronounced as the ambient temperature decreases, because internal heating strengthens at low temperature due to higher resistance, while external heating supplies a uniform base temperature and reduces heat dissipation to the environment.
Regarding temperature uniformity, the composite heating keeps the maximum cell-to-cell temperature difference lower than 3 °C at all tested conditions. The following table summarizes the maximum temperature differences at the end of heating for both pure pulse and composite heating.
| Method | Max ΔT at –10 °C | Max ΔT at –15 °C | Max ΔT at –20 °C |
|---|---|---|---|
| Pure pulse (3C, 3000 Hz) | > 5 °C | > 5 °C | > 5 °C |
| Liquid only (300 W, 0.56 L/min) | < 3 °C | < 3 °C | < 3 °C |
| Composite | < 2.9 °C | < 2.7 °C | < 2.8 °C |
4.7 Energy consumption
I calculated the energy required for each heating method using the formulas for pulse energy and PTC energy:
\[
Q_{\mathrm{pulse}} = \int U I \, dt
\]
\[
Q_{\mathrm{PTC}} = \frac{P_{\mathrm{PTC}} \, \Delta t}{\eta}
\]
where \(\eta = 0.95\) is the assumed PTC conversion efficiency. The total electrical energy consumed during one heating event from \(-10\), \(-15\), or \(-20\,^{\circ}\mathrm{C}\) to \(10\,^{\circ}\mathrm{C}\) is listed below.
| Ambient temperature | Pulse-only energy (J) | Liquid-only energy (J) | Composite energy (J) |
|---|---|---|---|
| –10 °C | 42180 | 145263 | 76822 |
| –15 °C | 46620 | 180000 | 85358 |
| –20 °C | 51060 | 217894 | 98161 |
Pure pulse heating is the most energy-efficient method because the heat is generated directly inside the cells with high utilization efficiency. Composite heating consumes roughly 70% more than pulse-only heating, but it still uses less than half the energy of liquid-only heating. Since composite heating is significantly faster and more uniform than pulse-only heating, the extra energy is justified by the enhanced practicality and safety of the preheating process.
4.8 Cycle-life impact
To verify that the composite strategy does not cause unacceptable battery degradation, I ran 600 full heating cycles from \(-20\,^{\circ}\mathrm{C}\) to \(10\,^{\circ}\mathrm{C}\) on three groups of cells with different parameter sets: 1C + 100 W, 2C + 200 W, and 3C + 300 W. The measured capacity fade after 300 and 600 cycles is shown below.
| Heating parameters | Capacity fade after 300 cycles | Capacity fade after 600 cycles |
|---|---|---|
| 1C pulse + 100 W | 0.73% | 1.7% |
| 2C pulse + 200 W | 1.7% | 3.0% |
| 3C pulse + 300 W | 2.9% | 4.3% |
All groups demonstrate capacity fade below 5% after 600 cycles, confirming that the hybrid method is safe for repeated use.
5. COMSOL Electro-Thermal Coupled Model and Optimization
5.1 Governing equations
To generalize the experimental observations and further optimize the system parameters, I built a three-dimensional electro-thermal coupled model of the EV battery pack with the serpentine cold plate and coolant channel in COMSOL Multiphysics. The model accounts for the heat generation inside the battery, heat conduction through the solid components, convective heat transfer in the coolant, and coupling with the electrical circuit. The general transient heat-conduction equation for the battery is:
\[
\rho_k C_{p,k}\frac{\partial T}{\partial t} = \nabla \cdot (\lambda_k \nabla T) + q
\]
where \(\rho_k\), \(C_{p,k}\), and \(\lambda_k\) are the density, specific heat, and anisotropic thermal conductivity of the battery, and \(q\) is the volumetric heat-generation rate. The heat-generation rate is expressed by the simplified Bernardi equation:
\[
q = \frac{1}{V}\left[ I^2 R – I T \frac{dU_{OCV}}{dT} \right]
\]
For pulse heating, the reversible term is small because charge and discharge periods alternate, so the dominant term is the irreversible Joule heating \(I^2R\). In the cold plate and coolant, the solid-fluid coupled heat transfer follows the standard conjugate heat-transfer formulation.
The key model properties are listed below.
| Parameter | Value |
|---|---|
| Cell capacity | 2 Ah |
| Layer/through-plane thermal conductivity | 30 / 1 W/(m·K) |
| Battery average density | 2000 kg/m³ |
| Battery specific heat | 1400 J/(kg·K) |
| Convective heat-transfer coefficient | 30 W/(m²·K) |
| Coolant density | 1100 kg/m³ |
| Coolant specific heat | 3300 J/(kg·K) |
| Coolant thermal conductivity | 0.43 W/(m·K) |
5.2 Model validation
I performed mesh-independence verification by comparing the average cell temperature, maximum temperature difference, average voltage, and maximum pressure drop at 240 s using computational grids from 220,000 to 5.6 million elements. The results showed that about 2.55 million elements provided sufficient accuracy with acceptable computational cost. The final mesh employed two boundary layers in the coolant fluid domain and a minimum cell size of 0.7 mm.
The simulation model was validated against experimental data at ambient temperatures of \(-10\), \(-15\), and \(-20\,^{\circ}\mathrm{C}\) for the three heating strategies. A summary of the average relative errors is given below.
| Ambient temperature | Liquid heating mean error | Pulse heating mean error | Composite heating mean error |
|---|---|---|---|
| –10 °C | 4.32% | 2.83% | 5.74% |
| –15 °C | 6.82% | 1.52% | 5.21% |
| –20 °C | 6.67% | 7.82% | 8.92% |
These errors are within acceptable limits for engineering thermal-management analysis. The simulation tends to slightly underpredict the heating rate at the beginning and slightly overpredict it in the later stage, which is common because model parameters such as temperature-dependent heat capacity and internal resistance are approximated by average values.
5.3 Simulation of frequency effects
Using the validated model, I extended the experimental frequency range. A \(-20\,^{\circ}\mathrm{C}\) pulse-heating simulation was performed for 500 s at 3C and a 50% duty cycle for frequencies of 1000, 3000, 5000, and 8000 Hz. The average temperature rise and maximum temperature difference at 500 s are provided in the following table.
| Frequency (Hz) | Temperature rise at 500 s (°C) | Max temperature difference (°C) |
|---|---|---|
| 1000 | 30.7 | 6.6 |
| 3000 | 27.2 | 5.3 |
| 5000 | 24.4 | 4.5 |
| 8000 | 20.3 | 3.6 |
The simulation confirms the experimental trend: as frequency increases, the heating rate decreases, but the temperature uniformity improves. At 1000 Hz, the heating rate is 51% higher than at 8000 Hz, but the maximum temperature difference is also 3 °C higher. Because I aim to keep the EV battery pack temperature difference below safe limits while still warming quickly, 3000 Hz is a good compromise, offering rapid heating and an acceptable maximum temperature difference.
5.4 Simulation of current-amplitude effects
Because experiments only covered currents up to 3C for safety, I simulated greater amplitudes of 1C, 2C, 3C, 4C, and 5C at 3000 Hz and 50% duty cycle. The results after 500 s of cycle heating at \(-20\,^{\circ}\mathrm{C}\) are listed below.
| Pulse current amplitude | Temperature rise at 500 s (°C) | Max temperature difference (°C) |
|---|---|---|
| 1C | 16.1 | 2.3 |
| 2C | 22.9 | 3.6 |
| 3C | 27.2 | 5.3 |
| 4C | 34.3 | 7.2 |
| 5C | 39.9 | 9.3 |
Although larger currents heat faster, they significantly increase the internal temperature spread. At 5C, the cell-to-cell maximum difference reached 9.3 °C, which can induce differential aging and even local degradation. Therefore, 3C appears to be the preferred maximum amplitude because it offers a good compromise between fast heating and acceptable uniformity.
5.5 Simulation of coolant-flow-rate effects
For the composite heating mode, I also examined the coolant flow-rate effect. I simulated nine flow rates from 0.20 to 0.73 L/min. The resulting temperature rise and maximum temperature difference at 500 s are shown in the following table.
| Flow rate (L/min) | Temperature rise at 500 s (°C) | Max temperature difference (°C) |
|---|---|---|
| 0.20 | 24.1 | 2.4 |
| 0.25 | 24.8 | 2.1 |
| 0.30 | 25.5 | 1.9 |
| 0.365 | 26.0 | 1.8 |
| 0.43 | 26.5 | 1.6 |
| 0.495 | 27.0 | 1.5 |
| 0.56 | 26.6 | 1.8 |
| 0.645 | 26.0 | 2.1 |
| 0.73 | 25.3 | 2.8 |
The optimum flow rate is 0.495 L/min. Below this value, the heat flux from the plate is limited by the convective heat-transfer coefficient, whereas above this value, the liquid passes through the channels too quickly and exits before fully exchanging heat with the plate. The simulation identifies the optimal set as a flow rate of 0.495 L/min, which is slightly different from the experimental optimum for the liquid-only circuit (0.56 L/min) because the addition of internal heating changes the temperature field and thus the heat-exchange requirement.
5.6 Optimized coupling scheme
Combining all simulation results, I obtained the following optimized parameter set for the hybrid system: pulse current amplitude = 3C, duty cycle = 50%, switching frequency = 3000 Hz, and coolant flow rate = 0.495 L/min. I then simulated the optimized scheme at three ambient initial temperatures: \(-10\), \(-15\), and \(-20\,^{\circ}\mathrm{C}\), heating the EV battery pack to 10 °C. The results are compared with the baseline composite parameters (3C, 3000 Hz, 0.56 L/min) in the table below.
| Ambient temperature | Optimized time (s) | Optimized rate (°C/min) | Baseline time (s) | Baseline rate (°C/min) | Improvement in rate |
|---|---|---|---|---|---|
| –10 °C | 140 | 9.69 | 180 | 6.67 | 45% |
| –15 °C | 160 | 10.29 | 210 | 7.50 | 37% |
| –20 °C | 180 | 10.84 | 230 | 7.83 | 38% |
The optimized scheme improves the heating rate by roughly 45% at \(-10\,^{\circ}\mathrm{C}\) and 38% at lower temperatures, while the maximum temperature difference remains below 0.8 °C as shown in the following table.
| Ambient temperature | Optimized maximum ΔT (°C) | Baseline maximum ΔT (°C) |
|---|---|---|
| –10 °C | 0.6 | 1.9 |
| –15 °C | 0.7 | 2.9 |
| –20 °C | 0.8 | 2.7 |
The high degree of uniformity arises from the precise coupling between internal pulse heating and external liquid heating: the internal current heats every cell simultaneously, while the coolant effectively removes hot spots and reduces the edge heat loss. This combined mechanism allows a very even temperature distribution, which is critical for mitigating aging and avoiding local lithium plating in an EV battery pack.
6. Conclusion
In this work, I have systematically investigated and developed a hybrid preheating strategy for an EV battery pack that combines electric-drive pulse internal self-heating with external PTC/water heating. The conclusions from this research are as follows:
(1) Experimental characterization of the lithium-ion cells showed that the discharge capacity loss is more than 50% at \(-20\,^{\circ}\mathrm{C}\), while the internal resistance can more than triple compared with its value at room temperature. These properties are strong functions of both temperature and SOC.
(2) I designed a serpentine-channel liquid-heating cold plate and an STM32-controlled electric-drive pulse-heating circuit. The laboratory composite platform successfully provided independent adjustment of pulse amplitude, pulse frequency, coolant flow rate, PTC power, and ambient temperature.
(3) Experiments verified that pure pulse heating is fast but produces temperature gradients larger than 5 °C, while liquid-only heating is slower but more uniform. The composite method inherits the advantages of both, reaching heating rates of 6.67, 7.50, and 7.83 °C/min at \(-10\), \(-15\), and \(-20\,^{\circ}\mathrm{C}\), respectively, while still keeping the maximum module temperature difference below 3 °C.
(4) The energy consumption of pulse heating is much lower than that of liquid-only heating. Composite heating consumes between 77 and 98 kJ per heating event depending on the initial temperature, which is about half of the liquid-only energy consumption and still acceptable.
(5) A finite-element electro-thermal model built in COMSOL was validated against experiments with mean relative errors below 9% for the module average temperature. The model was used to explore the extended parameter space and to optimize the system. The optimum combination is a 3C pulse current, 3000 Hz frequency, 50% duty cycle, and a coolant flow rate of 0.495 L/min. This optimized hybrid scheme improves the average heating rate by about 45%–50% and reduces the maximum temperature difference to below 1 °C, which represents a substantial improvement in both heating speed and temperature uniformity.
Overall, the hybrid internal/external preheating method provides a practical, energy-efficient, and temperature-uniform solution for cold-climate operation of electric-vehicle battery packs. Future work will focus on the integration of the proposed strategy into a full-vehicle thermal-management system and on online adaptive control based on real-time battery state estimation.