Electric vehicles have developed rapidly because of environmental pressure and energy requirements. A traction battery, particularly a lithium-ion battery, is the most critical component because it determines driving range, safety and lifespan. Nevertheless, the performance of lithium-ion batteries degrades seriously when the environmental temperature drops below zero. Low temperature increases electrolyte viscosity, reduces lithium-ion diffusivity and aggravates the solid-electrolyte interphase resistance, which leads to capacity loss and charging difficulties. In extreme cold conditions, lithium plating may even occur, creating micro-short-circuit risks and severe ageing. Thus, effective preheating of the traction battery before normal operation is not only a comfort problem but also an essential technical requirement for vehicle safety and durability.
Many researchers have proposed various heating methods for traction batteries. In general, these methods can be classified as external heating, internal heating and composite heating. External heating usually uses air, liquid, phase-change material or electric heating elements; heat is transported from an external source to the surface of the battery and finally to the core. Internal heating directly makes the battery itself the heat source by passing current through the cell so that Joule heat is generated by ohmic resistance. Composite heating combines internal energy dissipation with external heat input, seeking a faster and more uniform warm-up. In my work, I focused on a composite strategy that integrates an electric-drive pulse self-heating process with liquid-cold-plate heating driven by a PTC heater. I expected that the high-frequency pulse current can generate heat rapidly inside every cell, while the external liquid loop can suppress edge cooling and reduce the maximum temperature difference of the module. Therefore, I systematically investigated the low-temperature behaviour of a commercial 18650 lithium-ion traction battery, designed the corresponding heating hardware, built a multi-parameter test platform, conducted extensive experiments, and developed a simulation-based optimisation procedure for the proposed system.
1 Low-Temperature Characteristics of the Traction Battery
Before designing the heating strategy, I experimentally characterised the relationship between temperature and several key battery properties, because an accurate thermal management scheme should be based on quantitative knowledge of capacity loss, impedance, open-circuit voltage and entropy coefficient. The tested cell was an 18650 lithium-ion cell with a nickel-cobalt-aluminium cathode and a graphite anode. Its rated capacity is 2 Ah, the nominal voltage is 3.8 V, and the charge/discharge limits are 4.2 V and 2.7 V. I placed the cell inside a programmable temperature chamber and connected it to a Neware battery test system. Thermocouples were adhered to the cell surface to record temperature changes. Table 1 lists the basic characteristics of the tested traction battery cell.
| Parameter | Value |
|---|---|
| Manufacturer | Panasonic |
| Rated capacity | 2 Ah |
| Nominal voltage | 3.8 V |
| Diameter / Height | 18 mm / 65 mm |
| Cathode active material | Nickel-cobalt-aluminium oxide |
| Anode active material | Graphite |
| Charge cut-off voltage | 4.2 V |
| Discharge cut-off voltage | 2.7 V |
I performed capacity tests at \(-20\) °C, \(-10\) °C, 0 °C, 10 °C and 20 °C. Before each test, the cell was held at the target temperature for three hours. The battery was fully charged by a constant-current constant-voltage procedure and then discharged at a 1/3 C rate until the voltage reached 2.75 V. The measured discharge capacities are summarised in Table 2.
| Temperature (°C) | Discharge capacity (Ah) | Decrease relative to 20 °C |
|---|---|---|
| 20 | 2.17 | 0 |
| 10 | 1.84 | 15.2% |
| 0 | 1.63 | 24.9% |
| -10 | 1.32 | 39.2% |
| -20 | 1.04 | 52.1% |
The results clearly show that the capacity of the traction battery at \(-20\) °C is less than half of its capacity at 20 °C. This severe degradation is mainly caused by the higher viscosity of the electrolyte, the lower ionic diffusion coefficient, and the increased charge-transfer resistance at the electrode-electrolyte interface. From the viewpoint of thermal management, these experimental data imply that the traction battery must be warmed above at least 0 °C before a satisfactory discharge capability can be restored.
I conducted a hybrid pulse power characterisation (HPPC) test to obtain the open-circuit voltage (OCV) and internal resistance as functions of state-of-charge and temperature. The HPPC sequence was designed at SOC levels from 100% to 10% at intervals of 10%. At each SOC point, a 10-second discharge pulse, a 40-second rest, a 10-second charge pulse, and another 40-second rest were applied. Then the battery was discharged with 1/3 C for a certain period to the next SOC level and allowed to rest for one hour before the next pulse test. The open-circuit voltage and the internal resistance of the cell at different temperatures are shown in Figure 1 of the original dataset; the general tendency is that the OCV-versus-SOC curve has three regimes. For SOC below 20%, OCV drops sharply; between 20% and 80%, the OCV changes mildly; above 80%, the OCV increases rapidly. Regarding internal resistance, when SOC is lower than 20%, resistance rises steeply as SOC decreases; in the middle SOC range, resistance is nearly unchanged; when SOC is above 80%, resistance slowly increases with SOC. At all SOC points, lower environmental temperature results in higher internal resistance. Therefore, the OCV and resistance of a traction battery are jointly governed by temperature and SOC, which should be included in any electrothermal model of the preheating process.
Another important property is the entropic heat coefficient \(\mathrm{d}U_\mathrm{OCV}/\mathrm{d}T\), which determines the reversible heat generated during charge and discharge. I tested the cell at SOC points between 10% and 100% by changing the chamber temperature in steps of 10 °C from \(-20\) °C to 20 °C. The measured entropy coefficient is negative in most SOC ranges, meaning that the reversible heat tends to cool the cell during charging and heat it during discharging, but there is a turning point near 60% SOC where the reversible heat is almost zero. In the SOC window of 70% to 100%, the entropy coefficient becomes positive, so the reversible reaction heat aggravates the temperature rise. These data help estimate the heat generation of the traction battery during pulse heating and provide the basis for the three-dimensional thermal model.
2 Design of the Composite Traction Battery Heating System
The proposed composite heating system consists of two subsystems. The first is an internal heating loop based on the electric-drive power electronics of an electric vehicle. In the conventional vehicle drive configuration, a traction battery feeds a three-phase permanent-magnet synchronous motor through a voltage-source inverter. When the vehicle is stationary, the rotor can be kept motionless while the inverter produces a high-frequency oscillating current in the motor windings. By using field-oriented control, I set the q-axis current reference to zero, so that the motor produces zero torque. At the same time, the d-axis current reference was controlled to alternate between positive and negative values at a prescribed frequency. During the positive half period, the traction battery discharges through the inverter and the motor inductances; during the negative half period, the magnetising energy stored in the stator windings is returned to the traction battery. This charge-discharge alternation creates a periodic pulse current through the cells, and the internal ohmic resistance of the battery generates Joule heat. The physical principle is analogous to AC self-heating but the electrical topology is integrated with the original vehicle motor controller. Figure 2 illustrates the electrical and control architecture used in my experimental setup; the main modules are an STM32F405RGT6 microcontroller, a DRV8301 gate-driver chip, a compact three-phase full-bridge inverter with six MOSFETs, and a three-phase permanent-magnet synchronous motor.
| Component / Parameter | Configuration / Value |
|---|---|
| Microcontroller | STM32F405RGT6, ARM Cortex-M4, 168 MHz |
| Gate driver | DRV8301 |
| Power MOSFET | Si7850DP, 60 V, 30 A |
| Motor rated voltage | 48 V |
| Motor rated power | 1000 W |
| Motor rated current | 30 A |
| d-axis inductance | 0.08 mH |
| q-axis inductance | 0.15 mH |
| Line resistance | 0.07 Ω |
The external subsystem is a liquid-cold-plate heater. A bidirectional DC power supply controls a PTC heater which warms a 50% ethylene glycol-water coolant stored in an insulated water tank. A pump pushes the heated coolant through a flowmeter, pipes and a cold plate under the battery module. The cold plate is made of aluminium, has dimensions of 90 mm × 65 mm × 5 mm, and the internal channels have a diameter of 3 mm. A thermally conductive silicone pad of 1 mm thickness and a small amount of silicone grease were placed between the battery module and the cold plate to reduce the interface thermal resistance. The flow loop is sealed with silicone rubber hoses and polypropylene connectors. The coolant has a freezing point below \(-36\) °C to guarantee operation in low-temperature tests.
One important design task was selection of the internal flow-channel pattern of the cold plate. I compared five representative configurations: U-shaped, parallel-shaped, composite-shaped, loop-shaped and S-shaped. I modelled these geometries in COMSOL with an inlet velocity condition of 0.04 m/s and a constant inlet coolant temperature of 40 °C. After 240 s of transient simulation, I evaluated the wall-temperature distribution, the maximum temperature difference, the high-temperature area share and the low-temperature area share. The obtained results are summarised in Table 3.
| Channel type | Temperature range (°C) | Max. difference (°C) | High-temp. range (°C) | High-temp. area share | Low-temp. range (°C) | Low-temp. area share |
|---|---|---|---|---|---|---|
| U-shaped | 37.1–38.5 | 1.4 | 37.8–38.5 | 31.05% | 37.1–37.6 | 53.66% |
| Parallel | 37.9–39.0 | 1.1 | 38.4–39.0 | 24.28% | 37.9–38.2 | 57.32% |
| Composite | 37.8–38.9 | 1.1 | 38.4–38.9 | 17.21% | 37.8–38.2 | 64.21% |
| Loop-shaped | 38.2–39.2 | 1.0 | 38.7–39.2 | 36.78% | 38.2–38.6 | 42.03% |
| S-shaped | 38.2–38.7 | 0.5 | 38.5–38.7 | 22.50% | 38.2–38.4 | 56.49% |
The loop-shaped channel provided the highest wall temperature and simultaneously a relatively small temperature difference. Although the S-shaped channel gave the smallest temperature difference of 0.5 °C, its heating capability measured by surface temperature was lower. Since the primary purpose of the cold plate in this system is to supply heat to the traction battery at a sufficiently high rate, I selected the loop-shaped flow channel. The manufactured cold plate was fabricated from aluminium and integrated into the composite test bench.
The control software of the internal heater was implemented on the STM32 platform. The system clock is generated by an external 25 MHz crystal and multiplied to 168 MHz by a phase-locked loop. The advanced timer TIM1 is configured in centre-aligned PWM mode to produce six complementary PWM signals with a dead time of 100 clock cycles. Timer TIM2 provides a 10 kHz interrupt as the fundamental control cycle of the field-oriented control algorithm. An incremental encoder is read by TIM3 to obtain the rotor position and rotational speed. The analogue-to-digital converter ADC1 samples the phase currents and the DC-link voltage synchronously on the trigger of TIM1. Digital communication includes SPI for the DRV8301 configuration, UART for host-PC communication, CAN for possible vehicle integration and I²C for EEPROM parameter storage. The main control loop executes Clarke and Park transformations, two proportional-integral controllers for the d-axis and q-axis currents, and the inverse Park transformation to generate the stator voltage vector. Space-vector pulse-width modulation is then used to synthesise the desired output voltage. In the current-loop code, I set the q-axis current reference to zero, while the d-axis current reference is changed from \(+I_d\) to \(-I_d\) according to the desired pulse frequency. A safety interrupt monitors over-current and over-temperature conditions and immediately disables the gate-driver signal when a fault occurs.
3 Experimental Platform and Parameter Effects
After manufacturing all hardware components, I built a complete low-temperature composite-heating platform. The platform consists of five main parts: the battery module, the internal pulse-heating motor drive, the external liquid heating loop, the temperature-control chamber, and the measurement/control PC. The battery module contains five 18650 cells arranged in a row; the arrangement enables simultaneous measurement of cell-to-cell temperature uniformity. A high-low temperature chamber provides stable ambient temperatures of \(-10\) °C, \(-15\) °C and \(-20\) °C during experiments. The bidirectional DC power source supplies the PTC heater and the coolant pump. A data-acquisition unit collects the signals from thermocouples placed on each battery surface. In the experiments, I used a target final temperature of 10 °C because this value is within the recommended operating range of the traction battery. The heating rate, the maximum temperature difference of the module and the electrical energy consumption were computed as quantitative performance metrics.
For an approximate energy analysis, the total pulse energy released by the traction battery during heating can be expressed as
$$Q_\text{pulse}=\int_0^{t_f} U(t)\,I(t)\,dt,$$
where \(U\) and \(I\) are the instantaneous voltage and current of the battery pack, and \(t_f\) is the total heating time. The energy supplied to the liquid loop is written as
$$Q_\text{PTC}=\frac{P_\text{PTC}\,\Delta t}{\eta_\text{PTC}},$$
with \(P_\text{PTC}\) the PTC heater power, \(\Delta t\) the duration and \(\eta_\text{PTC}\) the conversion efficiency (fixed to 95% in my tests).
3.1 Effects of pulse frequency, duty cycle and amplitude
I first investigated the influence of MOSFET switching frequency. The pulse amplitude was chosen as 2C or 3C, duty cycle was 50%, and frequencies were 3000, 5000 and 8000 Hz. At all tested ambient temperatures the heating rate decreased as the frequency increased. For example, with a 3C pulse at \(-20\) °C, the heating rate fell from 4.36 °C/min at 3000 Hz to 3.83 °C/min at 5000 Hz and further to 3.56 °C/min at 8000 Hz. A higher switching frequency does not always improve the heating effectiveness because the switching losses and high-frequency current ripples inside the motor windings reduce the energy that can be deposited into the battery. Therefore, a moderate frequency is favourable.
Next, I changed the duty cycle from 25% to 50% and 75% while keeping the frequency at 3000 Hz. Increasing the duty cycle makes the pulse-on time longer on average and therefore increases the RMS current. At \(-20\) °C with a pulse amplitude of 3C, the heating rate increased from 4.01 °C/min at 25% duty to 5.19 °C/min at 75% duty. In general, a larger duty cycle leads to a faster warm-up but may also approach the condition of a continuous DC pulse; the final choice must consider safety and lithium-plating risk.
The pulse amplitude had the strongest influence. At a fixed frequency of 3000 Hz and a 50% duty cycle, I applied 1C, 2C and 3C pulses. In every environment, doubling the current amplitude almost doubled the average heating rate. This result confirms that the internal heating power, which is proportional to the square of the RMS current, is dominated by the current amplitude. Table 4 summarises the pulse-heating trends observed at different temperatures.
| Independent variable | Direction of change | Observed influence on heating rate | Best range or value used |
|---|---|---|---|
| MOSFET frequency | Increase from 1 kHz to 8 kHz | Heating rate decreases | 3000 Hz chosen |
| Duty cycle | Increase from 25% to 75% | Heating rate increases | 50% as compromise |
| Pulse amplitude | Increase from 1C to 3C | Heating rate nearly doubles per C increment | 3C selected |
Temperature uniformity during pure pulse heating was not satisfactory. When five cells were heated from \(-20\) °C to 10 °C, the maximum cell-to-cell temperature difference exceeded 5 °C. The difference originated mainly from the internal-resistance dispersion among the individual cells; the cells with higher resistance generate more heat and become warmer, which in turn lowers their resistance and increases the imbalance. Therefore, internal pulse heating alone is fast but not sufficiently uniform for a large traction battery module.
3.2 Effects of coolant flow rate and PTC power
In the external liquid heating tests, the coolant flow rate was adjusted through the pump and measured with a flow meter. I tested five nominal flow rates: 0.20, 0.30, 0.43, 0.56 and 0.73 L/min at PTC powers of 200 W and 300 W. The experimental results indicated a non-monotonic dependence. When the flow rate was too low, the coolant could not transport sufficient heat to the cells, so the outer cells remained cold and the heating time was long. When the flow rate was too high, the residence time of the fluid in the cold plate was too short for efficient heat exchange, so the average coolant temperature at the outlet increased less and the heating performance per unit of pump power deteriorated. The best heating rate appeared at a flow rate close to 0.56 L/min in the composite experimental platform. This threshold range is important for the pump control strategy.
PTC power directly determines the available external heat input. I performed tests at PTC powers of 100, 200 and 300 W, with a constant cell flow rate of 0.43 L/min. The heating rates at \(-20\) °C were approximately 1.0 °C/min, 2.0 °C/min and 2.54 °C/min for 100 W, 200 W and 300 W respectively. Similar monotonic improvements were seen at \(-10\) °C and \(-15\) °C. A higher PTC power shortens the heating time, but it also raises the electrical load and may create a greater temperature difference from the inlet side to the outlet side. A ramp-up control of the PTC heater is recommended to avoid a sudden high temperature difference at the beginning of the heating process.
3.3 Comparison of pulse heating, liquid heating and composite heating
After the independent parameter sweeps, I compared the three heating strategies under identical ambient conditions. The pulse strategy used a 3C amplitude at a frequency of 3000 Hz and a duty cycle of 50%. The liquid strategy used a coolant flow rate of 0.56 L/min and a PTC power of 300 W. The composite strategy used both the pulse and the liquid loops simultaneously. The batteries started from \(-10\) °C, \(-15\) °C or \(-20\) °C and were heated to 10 °C. Table 5 compares the required time and average heating rate.
| Ambient temperature (°C) | Heating strategy | Heating time (s) | Average rate (°C/min) |
|---|---|---|---|
| -10 | Liquid only | 460 | 2.61 |
| -10 | Pulse only | 380 | 3.15 |
| -10 | Composite | 180 | 6.67 |
| -15 | Liquid only | 570 | 2.63 |
| -15 | Pulse only | 420 | 3.57 |
| -15 | Composite | 210 | 7.14 |
| -20 | Liquid only | 690 | 2.61 |
| -20 | Pulse only | 460 | 3.94 |
| -20 | Composite | 230 | 7.83 |
The composite strategy clearly out-performed each individual heating method. At \(-20\) °C, composite heating was roughly twice as fast as internal pulse-only heating and three times as fast as liquid-only heating. Moreover, the advantage of the composite strategy increased as the ambient temperature decreased, because the internal heat generation rate is larger when the cell resistance is higher at lower temperatures, while the external liquid loop compensates for the edge heat loss and reduces the thermal gradient.
Uniformity is another key criterion for a traction battery preheating system. During the composite heating experiments, I recorded the individual cell temperatures. The maximum difference across the five cells was always smaller than 3 °C. At \(-20\) °C the maximum difference was about 2.7 °C, while at \(-10\) °C it was below 2 °C. The use of the liquid loop partially equalises the temperature because the cold plate contacts all cells from the bottom and removes local hot spots. The pure pulse scheme had maximum differences above 5 °C, whereas the pure liquid scheme had a lower maximum difference but a very low heating rate. Thus, the composite arrangement offers a compromise that simultaneously achieves a rapid warm-up and an acceptable thermal uniformity for the traction battery module.
I also compared the electrical energy consumption of the three strategies. The energy calculation includes the pulse energy delivered from or to the battery pack and the PTC electrical energy divided by the conversion efficiency. The results are listed in Table 6.
| Strategy | -10 °C (J) | -15 °C (J) | -20 °C (J) |
|---|---|---|---|
| Pulse heating | 42,180 | 46,620 | 51,060 |
| Composite heating | 76,822 | 85,358 | 98,161 |
| Liquid heating | 145,263 | 180,000 | 217,894 |
The pulse-only method has the lowest energy consumption because almost all energy is directly dissipated inside the battery; however, this high efficiency is achieved at the expense of temperature uniformity. The liquid-only method consumes the largest amount of energy because the coolant loop introduces thermal resistance and ambient heat loss. The composite method consumes a moderate amount of energy but shortens the total heating time so strongly that the total PTC energy remains moderate. Considering heating time, energy consumption and uniformity together, the composite method is the most promising low-temperature preheating solution for traction batteries.
3.4 Capacity-fading validation
To ensure that the proposed composite heating method does not seriously degrade the health of the traction battery, I carried out a long-term cycling experiment. Three groups of cells were heated from \(-20\) °C to 10 °C for 600 complete heating cycles. 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. The cell capacity was measured after every 300 cycles. The capacity losses are shown in Table 7.
| Group | Pulse current | PTC power | Loss after 300 cycles | Loss after 600 cycles |
|---|---|---|---|---|
| A | 1C | 100 W | 0.73% | 1.7% |
| B | 2C | 200 W | 1.7% | 3.0% |
| C | 3C | 300 W | 2.9% | 4.3% |
In all three groups, the absolute capacity loss after 600 cycles was below 5%, which indicates that the composite heating method does not induce severe battery wear. The loss increases with the current and PTC power, as expected, but remains within a tolerable region for the targeted fast preheating application.
4 Electrothermal Model and Simulation Optimisation
Although experiments provide essential knowledge, an accurate multi-physics model enables a much broader parameter study without the limitations of hardware safety and time. I built a three-dimensional electrothermal model of the battery preheating system using the COMSOL Multiphysics software. The model couples the battery electrical sub-model, the thermal sub-model, and the laminar flow of the coolant through the cold plate.
The general energy conservation equation of a battery cell is:
$$\rho_\text{cell} C_{p,\text{cell}} \frac{\partial T}{\partial t} = \nabla \cdot \left( \lambda_\text{cell} \nabla T \right) + q_\text{gen},$$
where \(\rho_\text{cell}\) is the density, \(C_{p,\text{cell}}\) the heat capacity, \(\lambda_\text{cell}\) the temperature-dependent thermal conductivity tensor and \(q_\text{gen}\) the volumetric heat-generation rate. In the simulation, the total heat generation rate can be approximated by the Bernardi equation:
$$q_\text{gen} = \frac{1}{V_\text{cell}} \left[ I^2 R_\text{total} – I T \frac{\mathrm{d} U_\text{ocv}}{\mathrm{d}T} \right],$$
where \(V_\text{cell}\) is the cell volume, \(I\) is the current, \(R_\text{total}\) is the total internal resistance, \(T\) is the temperature and \(\mathrm{d}U_\text{ocv}/\mathrm{d}T\) is the entropic heat coefficient measured in Section 1. For the pulse-heating process, both positive and negative currents alternate, so the reversible term is treated with appropriate sign when needed. In the simplified heating model during very fast pulses, the reversible contribution can be practically considered symmetric and smaller than the irreversible Joule term, but I included it in the full electrothermal model for completeness.
The heat-conduction equation inside the solid domains is separated into three directions:
$$\rho C \frac{\partial T}{\partial t} = \lambda_x \frac{\partial^2 T}{\partial x^2} + \lambda_y \frac{\partial^2 T}{\partial y^2} + \lambda_z \frac{\partial^2 T}{\partial z^2} + q_\text{gen}.$$
For the liquid domain, the velocity and pressure fields are obtained by solving the incompressible Navier-Stokes equations under laminar conditions, while the energy equation of the fluid accounts for convection:
$$\rho_f C_{p,f} \left( \frac{\partial T_f}{\partial t} + \mathbf{u} \cdot \nabla T_f \right) = \nabla \cdot \left( k_f \nabla T_f \right),$$
where \(\mathbf{u}\) is the fluid velocity vector, \(T_f\) is the fluid temperature and \(k_f\) is the thermal conductivity of the coolant.
I carefully selected the computational mesh. To assess grid independence, I compared the average temperature, the maximum temperature difference, the average voltage and the maximum pressure difference after 240 s of simulated heating with seven mesh resolutions. The results are shown in Table 8.
| Mesh count | Avg. temperature (°C) | Max. temperature difference (°C) | Avg. voltage (V) | Max. pressure difference (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 |
When the mesh count was around 2.55 million, the average temperature and temperature difference became almost stable; the maximum pressure difference reached its lowest value. Therefore, I used roughly 2.55 million mesh elements for all following simulations. The fluid boundary layer was resolved with two prism layers and the minimum mesh size in the fluid region was set to 0.4 mm.
I validated the model by comparing simulation predictions with the experimental temperature-rise curves for the three heating strategies. At ambient temperatures of \(-10\) °C, \(-15\) °C and \(-20\) °C, the simulated average cell temperatures of the battery module are close to the measured values. The average relative error of the module-average temperature was below 9% for all tested conditions, and most data points had relative errors below 5%. For the individual-cell predictions, the liquid-heating model had the smallest average relative error, below 5%, while the composite-heating model gave errors below 12%. The pulse-only model was less accurate at the cell level because the internal-resistance dispersion among cells is not perfectly represented in a deterministic simulation, but the global trend and the system-level accuracy were still satisfactory. Thus, the simulation model can be used as a reliable tool for optimisation.
4.1 Frequency effect in simulation
After the model validation, I enlarged the parameter range beyond the experimental envelope. For instance, the model was exposed to a \(-20\) °C environment and a 3C pulse with 50% duty cycle at switching frequencies of 1000, 3000, 5000 and 8000 Hz. After 500 s, the temperature rise and the maximum module temperature difference were computed. The simulation results are summarised in Table 9.
| Frequency (Hz) | Temperature rise after 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 trends confirm that lower frequencies deliver a larger average temperature rise but create a larger temperature spread. Considering both criteria, 3000 Hz remains an optimal compromise for the traction-battery module used in this study.
4.2 Pulse amplitude effect in simulation
Because experiments were limited to 3C due to safety, I used the simulation to explore amplitudes from 1C to 5C. The remaining conditions were a frequency of 3000 Hz and a duty cycle of 50% at an ambient temperature of \(-20\) °C. Table 10 lists the temperature rise after 500 s and the maximum temperature difference.
| Pulse amplitude | Temperature rise after 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 |
The simulation indicates that very large amplitudes expose the outer cells to higher local temperatures and undesirable thermal gradients. Continuous use of a 5C pulse would require advanced individual-cell uniformization. Therefore, a current amplitude of 3C balances the heating rate and uniformity and also limits the lithium-plating risk. The volumetric heat generation density is related to the RMS current by:
$$q_\mathrm{gen} \approx \frac{I_\mathrm{RMS}^2 R_\mathrm{total}}{V_\mathrm{cell}}.$$
Because \(q_\mathrm{gen}\) grows with the square of the RMS current, an increase from 3C to 5C would raise the heat source by a factor of \((5/3)^2 \approx 2.78\), which is why the outer cells become overheated more easily. Hence, a safety-based upper limit must be enforced in the control strategy of a traction battery preconditioning system.
4.3 Coolant flow rate effect in simulation
I also extended the liquid-flow experimental points by including intermediate values: 0.20, 0.25, 0.30, 0.365, 0.43, 0.495, 0.56, 0.645 and 0.73 L/min. The simulation was run for 500 s with a PTC inlet temperature according to the calibrated curve. The average temperature rise of the module is affected by the flow rate in a non-monotonic way. The highest average temperature rise occurred at 0.495 L/min. At 0.495 L/min, the maximum temperature difference after 500 s was also the lowest among all the studied points, approximately 1.5 °C. When the flow rate was below 0.43 L/min, insufficient heat convection slowed down the temperature rise. When the flow rate exceeded 0.56 L/min, the average temperature rise decreased and the maximum temperature difference increased because the coolant passes too quickly and the heat-exchange time becomes too short. Therefore, the optimum coolant flow rate for this external heater is close to 0.495 L/min.
4.4 Coupled optimisation and final performance
Based on the experimental and simulation results, I selected the following operating point as the optimal coupling condition:
| Parameter | Optimised value |
|---|---|
| Pulse current amplitude | 3C (6 A) |
| Duty cycle | 50% |
| Switching frequency | 3000 Hz |
| Coolant flow rate | 0.495 L/min |
With this optimal set, I simulated the composite heating process at ambient temperatures of \(-10\) °C, \(-15\) °C and \(-20\) °C until the average battery temperature reached 10 °C. Table 11 compares the original experimental composite strategy with the optimised one.
| Strategy | Starting temperature (°C) | Heating time (s) | Heating rate (°C/min) |
|---|---|---|---|
| Original (0.56 L/min) | -10 | 180 | 6.67 |
| Optimised (0.495 L/min) | -10 | 140 | 9.69 |
| Original (0.56 L/min) | -15 | 210 | 7.14 |
| Optimised (0.495 L/min) | -15 | 160 | 10.29 |
| Original (0.56 L/min) | -20 | 230 | 7.83 |
| Optimised (0.495 L/min) | -20 | 180 | 10.84 |
The optimised composite system improved the average heating rate by approximately 45% to 50% with respect to the original composite system. Importantly, the maximum temperature difference of the module during the optimised preheating process was always below 1 °C: approximately 0.6 °C at \(-10\) °C, 0.7 °C at \(-15\) °C and 0.8 °C at \(-20\) °C. This very even temperature distribution is a direct benefit of the impedance matching between the internal pulse-current generation and the external coolant circulation. In contrast, the original un-optimised composite strategy produced maximum module temperature differences between 1.9 °C and 2.9 °C. Thus, the flow-rate refinement alone significantly improves the thermal homogeneity of the traction battery at no additional hardware cost.
From the thermal-cloud results of the optimised system, the temperature distribution over the module is much more consistent than in the individual-liquid or pulse-only systems. The local hot zone near the battery-coolant contact surface in the numerical cloud is mainly caused by the ideal pressure-free contact assumed in the simulation. In the real prototype, a soft silicone pad and a small gap introduce contact resistances that smooth the local heat flux. Thus, the actual thermal safety in a practical traction-battery pack will be even more favourable than the predicted conservative simulation.
5 Conclusion and Outlook
In this work, I built and tested a low-temperature composite heating system for a lithium-ion traction battery. The system has two complementary sources: an internal pulse current generated by an electric-drive motor inverter and an external liquid coolant heated by a PTC heater and circulated through an aluminium cold plate. Experimental results show that the capacity of the traction battery fell by more than 50% when the temperature was reduced from 20 °C to \(-20\) °C, while the internal resistance increased sharply. The entropy-coefficient measurement further demonstrated the importance of SOC-dependent reversible heat in thermal management. The proposed external/internal composite heating strategy achieved a significantly faster warm-up than either individual method alone. At \(-20\) °C, the composite method reached a heating rate of 7.83 °C/min with a maximum module temperature difference below 3 °C, and its total energy consumption was considerably lower than that of the liquid-only method. After 600 cycles of composite heating, the capacity loss of the battery was less than 5%, which proves the practical feasibility of the method.
A multi-physics electrothermal model was developed in COMSOL Multiphysics and validated against a comprehensive set of experiments. The validated model was used to optimise the pulse frequency, pulse amplitude and coolant flow rate. The optimum parameters are a pulse amplitude of 3C, a switching frequency of 3000 Hz, a duty cycle of 50%, and a coolant flow rate of 0.495 L/min. The simulated optimum configuration increased the average heating speed by roughly 45–50% while keeping the system maximum temperature difference within 1 °C. The combination of fast internal heating and carefully matched external fluid heating therefore proves to be a robust and efficient solution for preconditioning the traction battery of an electric vehicle in very cold climates.
Future work should focus on transferring the proposed control strategy from the laboratory to a real vehicle environment. The integration of the pulse-generation algorithm with the existing motor inverter controller requires no extra high-power components, which makes the solution attractive for mass production. I also plan to use machine-learning models to predict the optimum duty cycle and current amplitude on the fly in response to the state-of-charge and ambient-temperature changes. This may allow a “one-temperature-one-strategy” control law that further reduces energy consumption and extends the life of the traction battery. In parallel, more efficient PTC heating elements and phase-change materials could be introduced into the external loop to shorten the remaining cold-start delay and reduce the electric load on vehicles that are not connected to a charging pile.