My research is devoted to the thermal management of lithium-ion power packs used in electric vehicles, with a special focus on fast and uniform warm-up at sub-zero temperatures. Vehicle electrification is one of the major technological pathways to reduce greenhouse-gas emissions and petroleum consumption. Among the various storage technologies, the lithium-ion battery is the leading solution because of its high energy density, low self-discharge rate, long cycle life and limited environmental impact. In particular, the high-voltage battery system in modern electric vehicles must satisfy stringent requirements for power capability, driving range and safety. Nevertheless, the high-voltage battery is highly sensitive to temperature. Whereas the optimal operating window of most lithium-ion cells is about 10 °C to 40 °C, the winter environment in northern China can easily fall below −20 °C. When a high-voltage battery is exposed to such low temperatures, its electrolyte viscosity increases, lithium-ion diffusivity in the graphite anode drops, the solid electrolyte interface impedance rises, and the internal resistance can increase by several times compared with room-temperature values.
At temperatures below −10 °C, the available discharge capacity of a typical high-voltage battery may be reduced by more than half, and even moderate charging rates can drive the anode potential below the lithium plating voltage. Lithium plating is a key degradation mechanism: metallic lithium deposits on the graphite surface, consumes cyclable lithium, degrades the solid electrolyte interphase, and may form dendrites that eventually pierce the separator. Such internal short-circuit phenomena create severe safety hazards. From the perspective of the user, the vehicle may not accept a fast charge in winter, regenerative braking may be limited, and the usable range may be reduced dramatically. Therefore, before charging, starting or driving in cold climates, the high-voltage battery should be heated to a suitable temperature as quickly as possible while maintaining satisfactory temperature uniformity.
1. Classification of Existing Battery-Heating Techniques
Many attempts to solve the low-temperature problem of high-voltage batteries can be divided into two broad families: external heating and internal heating. External approaches supply heat from outside the cell. Air heating uses fans and electric resistances; liquid heating circulates heated coolant through jackets, cold plates or immersion systems; phase-change materials release latent heat during solidification; and electric heating films or wires can be attached to the module surface. External heating is relatively easy to implement and does not require a modulation of the cell current. However, because heat must travel from the hot source through interfaces and inactive components into the core of each cell, the path is long, and part of the energy is lost to the surroundings. Consequently, the heating rate is often low and the core-to-surface temperature gradient can be significant.
Internal self-heating applies a current directly through the high-voltage battery cell. The Joule heat produced by the cell internal resistance becomes the heat source, so the heat is generated at the place where it is needed. Various excitation profiles have been considered in the literature. Constant-current heating is simple but may cause severe polarization and current inhomogeneity. Alternating-current heating mitigates polarization, but a dedicated AC source is required. Pulse heating is a more flexible approach: it toggles between discharge and charge modes in a high-frequency sequence, and the pulse parameters can be adjusted independently. In comparison with continuous DC heating, pulsed self-heating can reduce the heating duration, lower the average lithium-ion concentration gradient and minimize the deterioration of cell health.
A third family, composite heating, combines an internal method with an external method. The philosophy is to use the internal heat source to raise the cell temperature rapidly while the external heater provides additional thermal input and improves the temperature uniformity from the boundary. In my work I propose a composite preheating method built around the electric-drive inverter and a liquid-cooled/aluminium cold plate. The internal part is an electric-drive high-frequency zero-torque pulse current, obtained by controlling the d-axis current through a permanent-magnet synchronous machine and an inverter. The external part is a PTC heater, a water/glycol circulation loop and an optimized serpentine-flow cold plate. The two loops are activated simultaneously. I verified the methodology through a low-temperature experimental platform and a COMSOL-based three-dimensional electro-thermal-coupled model. This paper presents the system design, the experimental findings, the model validation and the parameter-optimization results.
| Category of heating | Representative implementation | Main merit | Typical limitation |
|---|---|---|---|
| External | Air circulation with heating wires | Simple structure | Low heating rate, high energy loss |
| External | Liquid heating through cold plate | Uniform boundary temperature | Slow heat penetration, pump consumption |
| External | Phase-change material / heating film | Good peak shaving | Integration complexity |
| Internal | DC or AC current excitation | Fast internal heat generation | Risk of degradation, uneven current |
| Internal | High-frequency pulse current | Fast and controllable | Requires power-electronics modulation |
| Composite | Internal pulse plus external liquid | Fast, uniform and flexible | Two coupled control loops |
2. Low-Temperature Characterization of the High-Voltage Battery Cell
To build a reliable thermal model and to define the heating target, I first characterized the cell at low temperatures. The cell used throughout the study is an 18650 cylindrical lithium-ion cell with a nickel-cobalt-aluminium oxide cathode and a graphite anode. Its main physical parameters are summarized below. The charge cut-off voltage is 4.2 V and the discharge cut-off voltage is 2.75 V. In every low-temperature experiment, the cell was soaked in a temperature chamber for at least 3 h to ensure thermal equilibrium before testing.
| Parameter | Value |
|---|---|
| Manufacturer | Commercial 18650 cell |
| Rated capacity | 2 Ah |
| Nominal voltage | 3.8 V |
| Cell dimensions | 65 mm height, 18 mm diameter |
| Cathode material | LiNiCoAlO2 |
| Anode material | Graphite |
| Charge cut-off voltage | 4.2 V |
| Discharge cut-off voltage | 2.75 V |
The electrochemical reactions occurring in the high-voltage battery during discharge and charge can be expressed as follows. At the positive electrode, lithium ions are released when the NCA active material is oxidized:
$$ \mathrm{LiNiCoAlO_2} \rightleftharpoons \mathrm{Li}_{1-x}\mathrm{NiCoAlO_2} + x\mathrm{Li}^+ + x e^- . $$
At the negative electrode, lithium ions intercalate into the graphite structure during charging and de-intercalate during discharging:
$$ x\mathrm{Li}^+ + x e^- + \mathrm{C_6} \rightleftharpoons \mathrm{Li}_x\mathrm{C_6} . $$
During low-temperature operation, the charge-transfer kinetics and the solid-state diffusion are hindered. This phenomenon appears macroscopically as an increase in ohmic resistance, charge-transfer resistance and concentration polarization.
| Component | Role in the high-voltage battery cell |
|---|---|
| Positive electrode | Supplies lithium ions through de-intercalation and receives electrons |
| Negative electrode | Stores lithium ions by intercalation during charging |
| Separator | Prevents direct contact between electrodes while allowing ionic transport |
| Electrolyte | Transports lithium ions between electrodes |
| Current collectors | Collect and transport electrons to the external circuit |
2.1 Capacity Measurement versus Temperature
The capacity test used a full charge at 1 C with a constant-current/constant-voltage protocol followed by a discharge at 1/3 C until the voltage reached 2.75 V. The measured discharge capacities at six temperatures are listed below. At 20 °C, the actual capacity is 2.17 Ah. When the temperature falls to −10 °C, the capacity is reduced to 1.32 Ah, and at −20 °C the cell stores only 1.04 Ah. Compared with the value at 25 °C, the capacity loss reaches approximately 52 % at −20 °C. This large decay is mainly caused by the decrease of ionic conductivity, the slow lithium diffusion in graphite and the increase of SEI resistance.
| Temperature (°C) | Discharge capacity (Ah) | Relative capacity loss (%) |
|---|---|---|
| 20 | 2.17 | 0 |
| 10 | 1.84 | 15.2 |
| 0 | 1.63 | 24.9 |
| −10 | 1.32 | 39.2 |
| −20 | 1.04 | 52.1 |
2.2 HPPC Test and Internal Resistance
I carried out the Hybrid Pulse Power Characterization test at several temperatures and SOC levels to measure the open-circuit voltage and the internal resistance. The cell was fully charged, then each pulse sequence consisted of a 10 s discharge at 1 C, a 40 s rest, a 10 s charge at 1/3 C and a final rest period. Between pulse sequences the cell was discharged by a 1/3 C current for a fixed duration to the next SOC step, followed by a 1 h relaxation. The results show that the open-circuit voltage is affected by both SOC and temperature. In the mid-SOC region the OCV is relatively flat; below 20 % SOC it drops sharply, whereas above 80 % SOC it also rises sharply. The internal resistance, on the contrary, is strongly temperature dependent. At −20 °C the ohmic resistance is several times larger than at room temperature. Because the internal resistance directly determines the heat generation rate during pulse preheating, this measurement also provides important input parameters for the electro-thermal simulation.
| SOC interval (%) | OCV behavior | Internal resistance behavior |
|---|---|---|
| 0–20 | Strongly decreasing with decreasing SOC | Increases significantly at low temperature |
| 20–80 | Almost flat plateau | Weak SOC dependence, strong temperature dependence |
| 80–100 | Rapidly increasing with SOC | Slightly increasing with SOC |
2.3 Entropic Heat Coefficient
The reversible heat produced during charge or discharge is proportional to the entropic heat coefficient
$$ \frac{dE_{\mathrm{OCV}}}{dT} . $$
I measured this coefficient using a potentiometric method: the cell was placed in the temperature chamber, the temperature was changed stepwise between −20 °C and 20 °C while the cell rested at a fixed SOC, and the open-circuit voltage was recorded after thermal equilibrium. The result depends strongly on the SOC. At low SOC values, the entropic heat coefficient is positive; between roughly 20 % and 60 % SOC it becomes negative, meaning that discharge absorbs heat and charge releases heat. Around 60 % SOC, the coefficient is close to zero, which is the turning point of reversible heat. At SOC levels above about 70 %, the coefficient turns positive again. The measured behavior is summarized below. These data are used in the thermal model to separate the reversible heat from the irreversible Joule heat.
| SOC range (%) | Entropic coefficient sign | Thermal consequence |
|---|---|---|
| 0–20 | Positive | Discharge promotes heating |
| 20–60 | Negative | Reversible heat mitigates the temperature rise |
| 60–70 | Approximately zero | Negligible reversible heat |
| 70–100 | Positive | Charge and discharge both increase heat |
A low-temperature experiment therefore reveals a clear picture: a high-voltage battery that is used at −20 °C loses more than half of its energy, becomes hard to charge, suffers from lithium plating and exhibits a large internal resistance. These findings motivate the development of an active preheating strategy.
3. Architecture of the Composite Heating System
I designed the composite heating architecture as two independent but synchronously managed loops. The first loop is a hydraulic external-heating loop composed of a water/glycol reservoir, a PTC heater, a circulation pump, a flowmeter and an aluminium liquid cold plate. The second loop is an internal electrical pulse-heating loop built around the permanent-magnet synchronous machine, the three-phase inverter and the battery pack itself.
The general experimental architecture of the proposed high-voltage-battery preheating system is shown below. The high-voltage battery module is assembled with the cold plates, while the electric machine and the inverter are electrically connected to the pack. The PTC heater heats the coolant in the insulated tank; the pump sends the warm coolant through the cold plate; and the heat is transferred into the battery cells through a thermally conductive silicone pad. The bidirectional DC power source controls the pump and the PTC heater, while the control board and the upper-computer software regulate the pulse amplitude, the pulse frequency and the operating mode of the electric machine.
3.1 External Heating Design and Cold Plate Selection
For the external heating loop, I focused on the liquid cold plate, which is the component that delivers heat to the cells. The cold plate should have high thermal conductivity, low weight and reasonable cost; I therefore selected aluminium. The plate length is 90 mm, width is 65 mm and thickness is 5 mm. The hydraulic channel has a diameter of 3 mm. The coolant is an aqueous solution containing 50 % ethylene glycol by volume; its freezing point is about −36.7 °C, which prevents freezing in the cold environment. A thermally conductive silicone pad of 1 mm thickness is placed between the cells and the plate, while thermal grease is used to fill residual gaps.
The geometry of the internal flow channel has a major influence on the temperature distribution of the cold plate and therefore of the high-voltage battery module. I compared five channel designs:
U-shape, parallel-shape, compound-shape, serpentine-shape and S-shape.
For each configuration, I performed a three-dimensional steady-state thermal simulation in COMSOL with a coolant velocity of 0.04 m/s and an inlet coolant temperature of 40 °C. The maximal plate wall temperatures and temperature differences are reported in the following table. Although the S-shape channel gives the smallest temperature difference, its highest temperature is also lower than that of the serpentine cold plate. A lower plate wall temperature reduces the external heating capacity. A higher plate wall temperature is beneficial for heating the cells. The serpentine channel provides a balance between a high plate temperature and a low in-plane temperature difference, while also covering the plate with a wide high-temperature zone. Therefore, I chose the serpentine coolant-channel design for the high-voltage-battery preheating system.
| Flow-channel type | Temperature range (°C) | Max difference (°C) | Highest temperature (°C) | High-temperature area fraction (%) | Low-temperature area fraction (%) |
|---|---|---|---|---|---|
| U-shape | 37.1–38.5 | 1.4 | 38.5 | 31.05 | 53.66 |
| Parallel-shape | 37.9–39.0 | 1.1 | 39.0 | 24.28 | 57.32 |
| Compound-shape | 37.8–38.9 | 1.1 | 38.9 | 17.21 | 64.21 |
| Serpentine-shape | 38.2–39.2 | 1.0 | 39.2 | 36.78 | 42.03 |
| S-shape | 38.2–38.7 | 0.5 | 38.7 | 22.50 | 56.49 |
The numerical results confirm that the serpentine flow channel leaves only 42 % of the plate in the low-temperature region and produces the largest effective high-temperature fraction. Consequently, its ability to transfer heat into the high-voltage battery is stronger than the other four designs. After the numerical comparison, I manufactured a real serpentine cold plate with an inlet at one corner and an outlet at the opposite corner.
| Property | Aluminium plate | Coolant |
|---|---|---|
| Density (kg/m³) | 2719 | 1100 |
| Specific heat capacity (J/(kg·K)) | 891 | 3300 |
| Thermal conductivity (W/(m·K)) | 202.4 | 0.43 |
| Dynamic viscosity (Pa·s) | — | 0.00339 |
| Freezing point (°C) | — | −36.7 |
3.2 Internal Pulse-Heating Design through the Electric Drive
The internal self-heating concept is based on an important observation: a vehicle is equipped with a three-phase inverter and a permanent-magnet synchronous machine. The stator windings behave as inductors and the inverter switches can shape the battery current with high bandwidth. When the vehicle is stationary, the rotor can be kept at standstill and the q-axis current can be set to zero. The electromagnetic torque of a permanent-magnet synchronous machine is given by
$$ T_e = \frac{3}{2} p \left[\psi_f i_q + (L_d – L_q) i_d i_q\right] . $$
If the q-axis reference is maintained at zero, the torque is zero regardless of the d-axis current, because all terms in the equation contain iq. Therefore, an alternating d-axis current can be applied without producing rotation. This current flows through the motor windings and creates an alternating power flow between the high-voltage battery and the motor-coil inductor. During the positive half-cycle, the battery discharges; during the negative half-cycle, the energy stored in the inductor returns to the battery. The alternating current forces lithium ions to move back and forth inside the cells and produces heat mainly by ohmic and polarization losses.
The control in the rotating d-q frame is based on the standard field-oriented-control method. After measuring two phase currents and the rotor angle, I applied the Clarke transformation and the Park transformation to obtain id and iq:
$$ \begin{bmatrix} i_d \\ i_q \end{bmatrix} = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} 1 & 0 \\ -1/\sqrt{3} & 2/\sqrt{3} \end{bmatrix} \begin{bmatrix} i_a \\ i_b \end{bmatrix} . $$
Two proportional-integral controllers regulate the d-axis and q-axis currents. The output voltages are transformed back and saturated before the space-vector PWM generator creates the six gate signals. In this way, the pulse current amplitude, frequency and duty cycle applied to the high-voltage battery can be adjusted in a flexible manner. The control code was implemented on an STM32F405RGT6 microcontroller clocked at 168 MHz. A DRV8301 gate-driver integrated circuit amplifies the PWM signals and supplies the three-phase full bridge built with six MOSFETs. A low-value shunt resistor on the low-side transistors provides feedback for overcurrent protection.
| Item | Specification |
|---|---|
| Microcontroller | STM32F405RGT6, Cortex-M4, 168 MHz |
| Flash memory | 1 Mbyte |
| Gate driver | DRV8301 |
| MOSFET | Si7850DP, 60 V, 30 A |
| Motor type | Permanent-magnet synchronous machine |
| Rated motor voltage | 48 V |
| Rated motor power | 1000 W |
| Rated motor current | 30 A |
| Line resistance | 0.07 Ω |
| d-axis inductance | 0.08 mH |
| q-axis inductance | 0.15 mH |
3.3 Integrated Experimental Platform
The assembled experimental platform comprises a high-voltage-battery module with five cells, two aluminium liquid cold plates, a PTC heater, a circulation pump, a flowmeter, a thermal insulated tank, a high-low temperature chamber, thermocouple sensors, a data acquisition instrument, a bidirectional DC power supply and the self-developed electric-drive pulse-heating board. The five cells are pressed between the cold plates with the silicone pad and thermal grease; thermocouples are placed at the same location on each cell surface so that the average temperature and the maximum temperature difference can be identified.
To verify the heat-generation model and to optimize the system, the platform must allow independent changes of:
- the amplitude of the pulse current,
- the MOSFET switching frequency,
- the duty cycle of the pulse,
- the coolant flow rate,
- the PTC heater power,
- the ambient temperature set inside the climate chamber.
During an experiment, the upper computer records the cell voltages, the phase voltages, the battery current, the coolant flow rate and every thermocouple channel. The bidirectional DC supply determines whether the PTC heater is operated at 100 W, 200 W or 300 W. The high-voltage-battery module is maintained at the target initial temperature for at least 3 h before the heating starts, and the heating target is set to 10 °C.
4. Experimental Investigation of the Composite Heating Strategy
In the experimental section, I analyzed the pulse-heating parameters first, then the liquid-heating parameters, and finally the combined operation. The measurements quantify the heating rate, the maximum module temperature difference and the electric energy consumption. The heating rate is defined as the difference between the final temperature and the initial temperature divided by the heating time. The energy consumption of the pulse operation comes from the measured battery terminal voltage and current:
$$ E_{\mathrm{pulse}} = \int U_{\mathrm{bat}} \, I_{\mathrm{bat}} \, dt . $$
The energy supplied by the PTC heater is estimated from its rated power and the operation time:
$$ E_{\mathrm{PTC}} = \frac{P_{\mathrm{PTC}} \, \Delta t}{\eta_{\mathrm{PTC}}} , $$
where ηPTC is the electrical-to-thermal conversion efficiency of the PTC unit, assumed equal to 95 %.
4.1 Electric-Drive Pulse-Heating Results
In the pulse-heating experiments, the initial temperature was −10 °C, −15 °C or −20 °C and the target temperature was 10 °C. The MOSFET switching frequency was changed from 3000 Hz to 5000 Hz and then to 8000 Hz, the duty cycle from 25 % to 75 %, and the pulse current amplitude from 1 C to 2 C and 3 C. The results show that frequency has a pronounced influence. The following table summarizes the measured heating rates for a pulse amplitude of 3 C and a duty cycle of 50 %.
| Ambient temperature (°C) | 3000 Hz (°C/min) | 5000 Hz (°C/min) | 8000 Hz (°C/min) |
|---|---|---|---|
| −10 | 3.42 | 3.36 | 2.95 |
| −15 | 4.26 | 3.71 | 3.20 |
| −20 | 4.36 | 3.83 | 3.56 |
At every initial temperature, the heating rate decreases nonlinearly when the switching frequency increases. A higher switching frequency increases the number of switching events but also increases switching losses and shortens the duration of each current pulse. Because the inductive time constant of the motor is finite, a too-short current pulse cannot establish the full desired current within the cell. The net result is that frequencies above 3000 Hz reduce the effective amount of charge exchanged and thus reduce the Joule heat produced by the high-voltage battery.
I also varied the duty cycle from 25 % to 75 % at a pulse current of 3 C and a frequency of 3000 Hz. The heating times and heating rates are shown below.
| Ambient temperature (°C) | Heating rate at 25 % duty (°C/min) | Heating rate at 50 % duty (°C/min) | Heating rate at 75 % duty (°C/min) |
|---|---|---|---|
| −10 | 2.93 | 3.32 | 3.92 |
| −15 | 3.84 | 4.24 | 4.43 |
| −20 | 4.01 | 4.34 | 5.19 |
The duty cycle is another effective lever. Increasing the duty cycle means that the positive current portion occupies more time in each switching period, so the battery supplies a larger net discharge energy and the heat production increases. Under the most severe condition of −20 °C, the maximum internal pulse-heating rate reaches 5.19 °C/min at a duty cycle of 75 %.
The amplitude of the pulse current has the strongest influence on the warming speed. When the amplitude is increased from 1 C to 3 C, the heat generation is proportional to the square of the current if the internal resistance remains constant. In reality, the resistance also depends weakly on temperature and frequency, but the square-law trend remains clearly visible. The table below collects the average heating rates observed at a frequency of 3000 Hz and a duty cycle of 50 %.
| Ambient temperature (°C) | Heating rate at 1 C (°C/min) | Heating rate at 2 C (°C/min) | Heating rate at 3 C (°C/min) |
|---|---|---|---|
| −10 | 0.70 | 2.24 | 3.31 |
| −15 | 0.80 | 2.63 | 4.24 |
| −20 | 1.14 | 2.58 | 4.36 |
Doubling the pulse current amplitude almost doubles or more than doubles the heating rate in most cases. This observation suggests that, whenever the cell polarization and safety limits can tolerate a larger peak current, increasing the pulse amplitude is a more powerful strategy than increasing the switching frequency. Nevertheless, an excessively high current is not desirable because it may exaggerate the current distribution and overheating at the tabs.
Temperature uniformity during pulse self-heating is a critical concern. Because the cells in a module are connected in series, the same current flows through all of them, but small differences between cell internal resistances produce different heat generation rates. I placed thermocouples on five cell surfaces and measured the maximum temperature difference during heating. The result reveals that the pure pulse-heating scheme, although fast, produces a maximum temperature difference larger than 5 °C at low initial temperatures. The non-uniformity becomes more pronounced when the initial temperature is lower, because the internal-resistance spread is amplified at sub-zero temperatures.
| Initial temperature (°C) | Pulse amplitude (C) | Duration to 10 °C (s) | Max temperature difference (°C) |
|---|---|---|---|
| −10 | 2 | 500 | 5.6 |
| −15 | 2 | 650 | 6.2 |
| −20 | 2 | 700 | 7.1 |
| −20 | 3 | 400 | 7.8 |
4.2 Liquid-Heating Results
In the liquid-heating tests, the high-voltage-battery module is heated only by the warm coolant flowing through the cold plate. The coolant flow rate and the PTC power are the two key input parameters. I tested five flow rates: 0.20, 0.30, 0.43, 0.56 and 0.73 L/min. The figure below-like results show that neither a too-small flow rate nor a too-large flow rate gives the fastest heating. A low flow rate limits the convective heat delivery and allows excessive cooling of the coolant at the plate edge; a very high flow rate means that the coolant passes through the exchanger too quickly to release its heat effectively. An optimum is found around 0.56 L/min under the tested conditions.
The PTC power directly sets the coolant temperature rise in the heating tank. Three power levels, 100 W, 200 W and 300 W, were tested at a constant flow rate of 0.43 L/min. Increasing the PTC power from 100 W to 300 W significantly shortens the heating time. For example, at −20 °C, the heating times are about 1800 s at 100 W, 900 s at 200 W and 650 s at 300 W. Thus, the 300-W heater achieved an average heating rate of approximately 2.58 °C/min over a 30 °C temperature rise.
| Ambient temperature (°C) | PTC power (W) | Heating time to 10 °C (s) | Average heating rate (°C/min) |
|---|---|---|---|
| −10 | 100 | 1020 | 1.18 |
| −10 | 200 | 700 | 1.69 |
| −10 | 300 | 460 | 2.61 |
| −15 | 300 | 570 | 2.63 |
| −20 | 300 | 650 | 2.58 |
The liquid cold plate produces a very uniform temperature distribution on the outer surfaces of the cells. At all tested temperatures, the maximum temperature difference remains below 3 °C, and often around 2 °C. This is an advantage compared with pure pulse heating. The reason is that the liquid acts as a distributed heat source and continuously averages the temperature along the coolant channels. However, the pure liquid heating method is slower than the internal pulse method, because the heat must penetrate the passive layers and the inactive cell components before reaching the electrode core.
4.3 Composite Heating Performance
After separate characterization of the internal and external methods, I combined them as the composite preheating strategy. The test parameters were chosen as follows: pulse current = 3 C, switching frequency = 3000 Hz, duty cycle = 50 %, PTC heater power = 300 W and coolant flow rate = 0.56 L/min. All three initial temperatures were considered. The following table compares the three strategies.
| Initial temperature (°C) | Strategy | Heating time (s) | Average rate (°C/min) | Rate improvement vs liquid (%) |
|---|---|---|---|---|
| −10 | Liquid heating | 460 | 2.61 | — |
| −10 | Pulse heating | 380 | 3.15 | +21 |
| −10 | Composite heating | 180 | 6.67 | +156 |
| −15 | Liquid heating | 570 | 2.63 | — |
| −15 | Pulse heating | 420 | 3.57 | +36 |
| −15 | Composite heating | 210 | 7.14 | +172 |
| −20 | Liquid heating | 690 | 2.61 | — |
| −20 | Pulse heating | 460 | 3.94 | +51 |
| −20 | Composite heating | 230 | 7.83 | +200 |
At −10 °C the composite heating strategy reaches 6.67 °C/min, which is 156 % faster than the liquid-only scheme and 112 % faster than the pulse-only scheme in the same condition. At −20 °C, the composite scheme reaches 7.83 °C/min, about twice as fast as liquid heating. The advantage of the composite strategy actually becomes larger when the ambient temperature is lower, because the internal resistance of the high-voltage battery is larger in a colder environment; therefore the same pulse current produces more Joule heat, and the external liquid loop supplies additional boundary heat that partially counterbalances the heat lost to the cold environment.
The temperature uniformity of the composite heating is also satisfactory. I monitored the five cell-surface temperatures continuously. The maximum differences for the composite scheme are about 1.9 °C at −10 °C, 2.9 °C at −15 °C and 2.7 °C at −20 °C in the repeated tests. Although the internal pulse current generates heat at the individual cell level, the liquid cold plate simultaneously removes or supplies heat at the module boundary, and thus it compensates for cell-to-cell resistance differences. The result always remains below 3 °C, which is acceptable for a vehicle high-voltage battery in a preheating operation.
4.4 Energy Consumption Comparison
Energy consumption is as important as heating speed, because the energy used for preheating is taken from the high-voltage battery or from the grid before a trip. I calculated the energy for the three methods using the integral equations presented above. The results are summarized in the following table.
| Initial temperature (°C) | Pulse heating energy (J) | Composite heating energy (J) | Liquid heating energy (J) |
|---|---|---|---|
| −10 | 42180 | 76822 | 145263 |
| −15 | 46620 | 85358 | 180000 |
| −20 | 51060 | 98161 | 217894 |
The pulse-heating strategy consumes the least external energy because it uses the internal ohmic heat of the cells themselves. The liquid heating strategy consumes the most energy because the PTC heater has to warm the entire coolant mass and a large portion of the heat is lost through the hoses and the tank. The composite scheme is more energy-demanding than pure pulse heating because the PTC and pump run for the whole heating process, but the total energy remains far below that of the pure liquid scheme. For a given heating time, the composite energy penalty is justified by the significant reduction of heating time and the improved uniformity.
4.5 Capacity Retention after Repeated Preheating
To verify that the proposed heating method does not severely degrade the high-voltage battery, I conducted 600 complete warming cycles from −20 °C to 10 °C. Three groups of cells were subjected to increasingly aggressive composite conditions:
- Group A: 1 C pulse plus 100 W PTC;
- Group B: 2 C pulse plus 200 W PTC;
- Group C: 3 C pulse plus 300 W PTC.
The capacity measured after 300 and 600 cycles is compared with the fresh capacity. The capacity fade values are reported below.
| Group | Capacity fade after 300 cycles (%) | Capacity fade after 600 cycles (%) |
|---|---|---|
| A (1 C + 100 W) | 0.73 | 1.70 |
| B (2 C + 200 W) | 1.70 | 3.00 |
| C (3 C + 300 W) | 2.90 | 4.30 |
All three groups retain more than 95 % of the initial capacity after 600 complete low-temperature preheating cycles. The capacity fade is slightly larger in Group C because a higher pulse current and a higher PTC power impose a larger electrical and thermal stress on the cells. Nevertheless, the absolute remaining capacity is within the usual engineering acceptance limit, and the composite heating strategy therefore appears to be compatible with the cycle life requirement of an electric-vehicle high-voltage battery.
5. Electro-Thermal Coupled Simulation and Parameter Optimization
To expand the parameter space beyond the experimentally tested conditions and to optimize the system globally, I built a three-dimensional electro-thermal-coupled simulation model of the complete high-voltage-battery preheating system in the COMSOL Multiphysics environment. The model couples the electric-double-layer dynamics with heat transfer and laminar flow in the coolant channels.
5.1 Model formulation
The heat generation in each cell is calculated with the Bernardi equation, which decomposes the heat into an irreversible Joule term and a reversible entropic term:
$$ \dot{q} = \frac{1}{V_{\mathrm{cell}}} \left( I^2 R_{\mathrm{cell}} – I T \frac{\partial E_{\mathrm{OCV}}}{\partial T} \right) . $$
For pulse current during the preheating process, the charge and discharge periods alternate quickly; the reversible term partially cancels over one complete switching cycle. The irreversible Joule heat remains dominant:
$$ \dot{q}_{\mathrm{irr}} = \frac{I^2 R_{\mathrm{cell}}}{V_{\mathrm{cell}}} . $$
The transient temperature distribution within the cells, the cold plates, the electric machine housing and the coolant is described by the energy balance equation:
$$ \rho C_p \frac{\partial T}{\partial t} = \nabla\cdot\left( k \nabla T \right) + \dot{q} . $$
Since the cell is a layered structure, the thermal conductivity is different in the through-plane direction from the in-plane direction. The model accounts for these anisotropic thermo-physical properties. The battery used in the simulation is described by the parameters listed below. The values were partly obtained from the experimental measurements in Chapter 2 and partly from the material database.
| Parameter | Symbol | Value |
|---|---|---|
| Cell capacity | Q_cell | 2 Ah |
| Reference exchange current density | j0 | 0.85 A/m² |
| Activation energy of exchange current | Ea,j0 | −59 kJ/mol |
| Activation energy of relaxation time | Ea,tau | 24 kJ/mol |
| Reference relaxation time | τ0 | 1000 s |
| In-plane conductivity | kparallel | 30 W/(m·K) |
| Through-plane conductivity | kperp | 1 W/(m·K) |
| Battery density | ρcell | 2000 kg/m³ |
| Battery heat capacity | Cp,cell | 1400 J/(kg·K) |
| Convective heat-transfer coefficient | h | 30 W/(m²·K) |
5.2 Model validation and mesh independence
I first selected a mesh size that yields accurate results without excessive computational time. The selection is based on the average cell temperature and the maximum temperature difference at 240 s. The grid independence test shows that once the mesh exceeds roughly 2.55 million elements, the calculated temperature changes only marginally; therefore all subsequent simulations use a mesh with about 2.55 million cells. Boundary-layer meshes are used in the coolant region and a finer mesh is applied to the battery electrode foils and to the cold-plate walls.
| Number of elements | Average temperature (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 220,000 | 11.29 | 3.31 |
| 336,000 | 9.91 | 2.32 |
| 1,108,000 | 5.19 | 1.55 |
| 2,550,000 | 5.01 | 1.28 |
| 5,620,000 | 4.95 | 1.39 |
To verify the accuracy of the model, I compared the simulated average temperature of the high-voltage-battery module with the experimental temperature curves for the liquid heating, pulse heating and composite heating modes. The validation is performed at −10 °C, −15 °C and −20 °C. The tables below give the average relative error and the maximum absolute error.
| Heating strategy | Temperature condition (°C) | Average relative error (%) | Maximum absolute error (°C) |
|---|---|---|---|
| Liquid heating | −10 | 4.32 | 0.88 |
| Liquid heating | −15 | 6.82 | 1.48 |
| Liquid heating | −20 | 6.67 | 0.80 |
| Pulse heating | −10 | 2.83 | 0.56 |
| Pulse heating | −15 | 1.52 | 0.70 |
| Pulse heating | −20 | 7.82 | 1.40 |
| Composite heating | −10 | 5.74 | 0.56 |
| Composite heating | −15 | 5.21 | 1.45 |
| Composite heating | −20 | 8.92 | 1.70 |
For the liquid-heating and composite-heating modes, the predicted temperature matches the experimental values closely, with an average relative error well below 9 %. The pulse-heating mode has a larger deviation at −20 °C, mainly due to the difficulty of capturing the frequency-dependent resistance at very low temperature. Nevertheless, the model satisfies the engineering accuracy requirement and is suitable for parameter optimization.
5.3 Effect of Pulse Frequency in Simulation
Using the validated model, I extended the pulse-frequency study to 1000 Hz, 3000 Hz, 5000 Hz and 8000 Hz at an amplitude of 3 C and a duty cycle of 50 %. The temperature rise after 500 s and the maximum temperature difference of the high-voltage-battery pack are reported below.
| Switching frequency (Hz) | Temperature rise in 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 1000 | 30.7 | 6.6 |
| 3000 | 27.2 | 5.3 |
| 5000 | 24.4 | 4.5 |
| 8000 | 20.3 | 3.6 |
The simulation confirms the experimental trend: as the frequency increases, the temperature rise becomes smaller. At 1000 Hz the highest temperature is obtained because each pulse has a longer on-time and more charge is transferred inside each cycle. At 8000 Hz the heating rate is the lowest because the switching losses dominate and the current barely reaches the desired plateau. However, the maximum temperature difference also decreases with increasing frequency. Therefore, there is a trade-off between heating speed and uniformity. A compromise at 3000 Hz is reasonable for a vehicle high-voltage battery heater because it still produces a sufficiently high heating rate while limiting the thermal gradient.
5.4 Effect of Pulse Current Amplitude in Simulation
Because high currents above 3 C are difficult to realize safely on the experimental bench, I used the simulation model to study pulse amplitudes from 1 C to 5 C at 3000 Hz and a 50 % duty cycle. The simulated results after a 500-s preheating period are given below.
| Pulse current amplitude | Temperature rise in 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 1 C | 16.1 | 2.3 |
| 2 C | 22.9 | 3.6 |
| 3 C | 27.2 | 5.3 |
| 4 C | 34.3 | 7.2 |
| 5 C | 39.9 | 9.3 |
The temperature rise increases strongly between 1 C and 5 C; at the same time the temperature non-uniformity also grows from 2.3 °C to 9.3 °C. The 3 C value appears to be a good compromise: it provides a temperature rise of 27.2 °C in 500 s and keeps the maximum temperature difference slightly above 5 °C. Currents above 3 C would heat the high-voltage battery faster, but the spread between the core and the surface, as well as the spread between different cells, approaches a level that may increase degradation and even locally induce lithium plating. Therefore, the optimum pulse amplitude is 3 C for this module.
5.5 Effect of Coolant Flow Rate in Simulation
The coolant flow rate in the external liquid loop influences both the average heating rate and the temperature uniformity. In the experimental campaign I tested only five flow rates; in simulation I explored nine values between 0.20 L/min and 0.73 L/min. After a 500-s transient calculation with an inlet temperature that rises linearly to 40 °C, the maximum average temperature is obtained at 0.495 L/min. The maximum temperature difference is also the lowest at this same flow rate. The results show that a coolant flow that is too low cannot transport enough heat from the PTC reservoir to the plate, while a coolant flow that is too high reduces the residence time and prevents the heat from being released into the cold plate. This non-monotonic behavior supports the existence of an optimum in the range of 0.43–0.56 L/min, with a refined optimum at roughly 0.495 L/min.
| Coolant flow rate (L/min) | Temperature rise in 500 s (°C) | Maximum temperature difference (°C) |
|---|---|---|
| 0.20 | 24.1 | 2.4 |
| 0.30 | 25.0 | 2.8 |
| 0.43 | 26.3 | 2.0 |
| 0.495 | 27.8 | 1.5 |
| 0.56 | 27.2 | 2.2 |
| 0.73 | 25.6 | 2.8 |
5.6 Optimized Coupled Parameters
Based on the experimental and simulation findings, I selected the following optimized combination for the composite preheating system:
- pulse current amplitude = 3 C;
- switching frequency = 3000 Hz;
- pulse duty cycle = 50 %;
- coolant flow rate = 0.495 L/min.
I then compared the optimized composite system with the pre-optimized composite conditions used in the experimental campaign. The heating time from −10 °C, −15 °C and −20 °C to 10 °C is simulated with the same external parameters. The results are summarized below.
| Initial temperature (°C) | Heating time before optimization (s) | Heating rate before optimization (°C/min) | Heating time after optimization (s) | Heating rate after optimization (°C/min) | Improvement of heating rate (%) |
|---|---|---|---|---|---|
| −10 | 180 | 6.67 | 140 | 9.69 | 45 |
| −15 | 210 | 7.14 | 160 | 10.29 | 44 |
| −20 | 230 | 7.83 | 180 | 10.84 | 38 |
At −10 °C the optimized heating rate rises from 6.67 °C/min to 9.69 °C/min, and at −20 °C it rises from 7.83 °C/min to 10.84 °C/min, an improvement of roughly 38 % to 45 %. At the same time, the maximum temperature difference is reduced below 1 °C in the optimized system. This result is particularly important for a high-voltage battery because a small internal temperature spread not only extends the cycle life but also helps the BMS estimate the battery state more accurately.
The optimized composite heating scheme therefore successfully improves both objectives simultaneously: the average heating rate increases by about 38 % to 45 % compared with the original composite setting, and the module temperature uniformity is kept well within the desired range. The heat generated by the internal pulse is synchronized with the external heat supplied by the PTC-liquid loop. In this way, the total heat flux inside the high-voltage battery can be shaped so that the core temperature follows the boundary temperature closely, avoiding large thermal gradients.
6. Conclusions and Future Outlook
In this work I designed, built and validated a composite low-temperature heating system for an electric-vehicle high-voltage battery. The system combines internal pulse self-heating through the electric-drive machine with external liquid heating through a serpentine-flow aluminium cold plate and a PTC heater. I first characterized the high-voltage battery under low-temperature conditions. The capacity at −20 °C was less than half of its room-temperature value; the internal resistance increased significantly and the open-circuit voltage depended on both temperature and SOC. These experimental results supplied the required parameters for the electro-thermal model. I then manufactured a serpentine-flow liquid cold plate, developed an STM32-based pulse-heating controller and integrated the complete hardware platform.
Experiments showed that a higher switching frequency reduces the heating rate while improving the temperature uniformity; a higher duty cycle increases the heating speed; and the pulse current amplitude is the most powerful control knob but should remain bounded in order to control the temperature spread. The liquid flow has an optimum speed near 0.495–0.56 L/min. The composite heating strategy reached an average heating rate of 7.83 °C/min at −20 °C, while maintaining a maximum module temperature difference below 3 °C. Over 600 full warming cycles, the capacity fade of the composite-heated high-voltage battery remained below 5 %, demonstrating good compatibility with the long service life required by vehicle applications.
Using a three-dimensional COMSOL model with a mesh of about 2.55 million elements, I reproduced the experimental temperature curves within a reasonable error. The validated model allowed me to study currents up to 5 C, frequencies down to 1000 Hz and nine different flow rates. The optimized parameter set, 3 C, 3000 Hz, 50 % duty cycle and a flow rate of 0.495 L/min, increases the heating rate by roughly 38 %–45 % relative to the original composite configuration and keeps the maximum temperature difference below 1 °C. This optimized electro-thermal coupling scheme provides a practical solution for the cold-start problem of electric vehicles.
In future work, I plan to verify the composite heating strategy on a full electric-vehicle powertrain under real driving conditions. The control strategy can also be improved by introducing model-predictive thermal control so that the optimal pulse and PTC parameters are adapted in real time to the actual battery SOC, temperature and ageing state. Another important direction is the synergy with the thermal management system during fast charging: the same hardware can be used to precondition the high-voltage battery optimally before a highway charging stop. The liquid-circuit part can additionally reject heat during hot summer operation or during high-power fast charging, enabling a bidirectional thermal management architecture. Finally, the energy conversion efficiency of the PTC heating unit may be further improved by exploring heat-pump-assisted liquid heating or by recovering residual heat from the power electronics and the motor. In this way, the composite preheating strategy can evolve from a laboratory prototype into a robust and energy-efficient thermal-management solution for next-generation electric vehicles.