Abstract
The performance of lithium-ion batteries largely depends on the operating temperature of the battery. However, the temperature data usually obtained is measured by thermocouples attached to the surface of the battery, which may not accurately reflect the actual temperature inside the battery, especially in low ambient temperatures and high discharge rates. This article will introduce an innovative method that utilizes differential voltage technology to predict the internal temperature of a 40Ah lithium-ion soft pack battery. The difference between internal and external temperature measurements depends on the discharge rate and ambient temperature. During the continuous discharge process, the difference between the surface and the measured temperature increases in the early stage of discharge, reaches its peak in the middle stage, and then decreases in the late stage of discharge. The results of this study can actively support control strategies in battery management systems (BMS).
1. Introduction
With the increasing attention to environmental issues and the commitment of governments to reduce emissions, electric vehicles (EVs) are increasingly being valued as a potential solution. One of the key factors for their success is the energy storage system (ESS) used. The ideal ESS should have high energy and power density, excellent lifespan, and demonstrate reliability under various operating conditions such as driving cycles, temperature, etc. In commercial battery technology, lithium-ion batteries have become the preferred choice for pure electric vehicles (BEVs) due to their highest volume and weight energy/power density.
BEVs based on lithium-ion batteries will significantly reduce their range and power performance under low temperature and high C-rate conditions. The reasons for performance degradation include decreased electrolyte conductivity, decreased solid-state lithium diffusion, high polarization of graphite anodes, and slow charge transfer kinetics. In the study of 2.2 Ah 18650 lithium-ion batteries, the electrochemical performance of the battery strongly depends on its operating temperature. However, the operating temperature of batteries is usually measured by thermocouples attached to the surface of the battery, which may not accurately reflect the electrochemical processes inside the battery. Differential voltage (DV) measurement is used to infer the stoichiometric alignment of electrodes at or near equilibrium to detect capacity decay. To avoid charge transfer phenomenon, high current should be avoided. DV represents the voltage variation per unit discharge capacity (dV/dQ), which reflects the cumulative impact of operating conditions (ambient temperature, C-rate, SOC, impedance, and self heating) on the battery.
The goal of this article is to use DV technology to predict the "effective resistance" of batteries under different continuous discharge currents at ambient temperatures ranging from -20 to 25 ° C, and then predict their internal temperature. The deviation between the internal and measured battery surface temperatures is directly related to the discharge current and decreases with the decrease of ambient temperature. These predictions may help improve the accuracy of battery temperature estimation and enhance control strategies within battery management systems (BMS).
2. Research methods
A. Experimental details
In order to investigate battery behavior, a lithium-ion soft pack battery weighing 0.97 kilograms with an NMC positive electrode was tested. The battery has a nominal voltage of 3.7 volts and a capacity of 40 ampere hours. A K-type thermocouple is installed at the geometric center of the main surface of the soft pack battery. The battery is placed in the Votsch hot cell and subjected to charge and discharge cycles using a Bitrode battery cycler. The test was conducted at four different ambient temperatures: -20 ° C, -10 ° C, 0 ° C, and 25 ° C. Charging is only carried out at 25 ° C, charging at a rate of 0.5C (20 amps) until the voltage reaches 4.2 volts. The charging current then drops to 0.05C while maintaining a voltage of 4.2 volts. The discharge currents used include 0.1C, 0.2C, 0.5C, 1C, 2C, 5C, and 8C. The directly measured parameters include battery voltage (V), capacity (Ah), power (W), discharge energy (Wh), and battery surface (measured) temperature (° C). The cut-off voltage of this battery is 2.7 volts.
B. In order to calculate the "internal temperature" from measurement parameters using differential voltage technology, we have taken the following steps for internal temperature prediction (see Figure 1):
1. Voltage change calculation: Calculate the voltage change (∆ V) at each time step.
2. Effective resistance calculation: "Effective resistance" R is a linear function of DV, obtained by dividing ∆ V by the discharge current.
Figure 1. Simple heat generation model
3. Heat generation calculation: Calculate the heat generated at each time step Qgen=∆ V ²/R.
4. Heat conduction calculation: The heat conduction calculation from the battery core to the surface is Qbond=(k × A × ∆ T)/(L/2), where k is the planar thermal conductivity of the battery, A is the surface area, and L is the distance between the battery core and the surface.
5. Convective heat transfer calculation: The convective heat transfer calculation on the surface of the battery is Qconv=(h × A × (T-Tamb)), where h is the convective heat transfer coefficient and Tamb is the ambient temperature.
6. Temperature change calculation: Calculate the temperature change ∆ T every second as (QGen Qcond QConv)/(m × C). Here, t is the time step (in seconds), m is 0.97 kilograms, and C is the heat capacity. Assuming Qbond is zero at t=0 seconds, then use Qbond from the previous time step.
7. Internal temperature calculation: Calculate the internal temperature by integrating ∆ T at each time step.
This method provides a new approach for accurately predicting the internal temperature of batteries by comprehensively considering their electrochemical performance and thermal characteristics, which is of great significance for optimizing battery management systems (BMS) and improving battery performance.
Table 1. Battery parameters of lithium-ion pouch batteries
| Parameter | Value |
| Thermal conductivity, k | 0.48 W/m/°C |
| Surface Area, A | 0.10125 m² |
| Cell Thickness, L | 0.0009 m |
| Heat Capacity, C | 1243 J/°C/kg |
| Convective Coefficient, h | 10W/m²/°C |
3. Results and Discussion
A. The influence of C-rate and ambient temperature on discharge capacity and discharge energy
The experimental results show that the energy released by the battery decreases with the increase of C-rate and the decrease of ambient temperature. This is because the increase of battery impedance leads to a faster decrease in battery voltage, including a decrease in ion conductivity, an increase in electrolyte resistance, higher anodic polarization, slower charge transfer, and insufficient lithium solid-phase diffusion.
Figure 2. Voltage evolution with discharge energy at different environmental temperatures and c rates
When discharging at 5C at -10 ° C, the voltage will rise for a considerable period of time during the discharge cycle. This is because self heating causes the battery temperature to increase, resulting in a decrease in electrolyte resistance due to an increase in ion conductivity and salt diffusion rate, thereby making the discharge energy higher than during isothermal discharge. At -10 ° C, the discharge capacity of 5C is 3.6% higher than 1C, but the discharge energy is 2.9% lower; At 0 ° C, the discharge capacity of 5C is 1% higher than 1C, and the discharge energy is 5.3% lower, indicating that the capacity benefits brought by self heating may be overestimated, and most of the increased capacity is used for battery heating.
Figure 3. Voltage evolution of batteries with discharge capacity at different ambient temperatures and c rates
B. The influence of C-rate and ambient temperature on predicting internal temperature using differential voltage
Figure 4. Effective resistance and discharge energy at different environmental temperatures and C rates
The effective resistance generally increases with decreasing ambient temperature and increasing C-rate, which means that at some point in the discharge cycle, the voltage changes more significantly with the release of energy. At lower ambient temperatures, especially at high C-rates, the effective resistance is higher due to low ion conductivity, slow charge transfer, high electrolyte resistance, and slow solid-state diffusion. This is consistent with previous studies showing that DC resistance increases with decreasing ambient temperature and increasing C-rates, and the effective resistance increases at the end of discharge. Although the self heating degree of 5C discharge is high at -10 ° C, its effective resistance is still the highest, possibly due to the short discharge time.
Figure 5. Comparison of internal (I) and measured (M) temperatures at different C rates at an ambient temperature of 25 ℃
Figure 6. Comparison of internal (I) and measured (M) temperatures at different C rates at 0 ℃ ambient temperature
During discharge, both the measured temperature and internal temperature increase, with higher temperature rise and greater increase in internal temperature at high C-rate and low ambient temperature. Consistent with other studies, the maximum difference between internal and measured temperatures during the discharge cycle (∆ T) is proportional to the corresponding C-rate, and the difference increases as the ambient temperature decreases. The ∆ T under different operating conditions in this article is slightly higher than the study that only investigates surface temperature gradients, but is more consistent with the study that compares internal and surface temperatures, indicating that the estimated internal temperature in this article represents the average overall temperature of the battery, and the measured temperature comes from surface sensor/thermocouple readings. The difference between the internal temperature of the battery and the measured temperature generally increases with discharge, reaches a peak in the middle of discharge, and then decreases. The magnitude of the difference increases with the increase of C-rate and ambient temperature.
Figure 7. Comparison of internal (I) and measured (M) temperatures at different C rates at an ambient temperature of 25 ℃.
Figure 8. Evolution of internal temperature and measured battery temperature difference every 30 Wh discharge
4. Summary
At lower ambient temperatures, the capacity benefits of self heating may be overestimated and may not translate into an increase in available energy for the battery.
Limitations of self heating effect: In low-temperature environments, although the self heating effect of batteries may increase discharge capacity, it does not always mean that the energy released by the battery will increase. This is because the increased capacity may mainly be used for heating the battery, rather than for doing work or providing more electrical energy.
The effective resistance of a battery is greater at higher discharge currents and lower ambient temperatures.
The relationship between effective resistance and operating conditions: Effective resistance is an important parameter of a battery under specific operating conditions, which increases with the increase of discharge current and the decrease of ambient temperature. This indicates that ion conduction and charge transfer inside the battery are more hindered under high current discharge and low temperature conditions.
The difference between the internal temperature of the battery and the measured surface temperature of the battery increases with the increase of discharge current and the decrease of ambient temperature.
The relationship between temperature difference and operating conditions: The difference between internal and surface temperature (∆ T) is directly related to discharge current and ambient temperature. This means that in high current discharge and low temperature environments, the temperature inside the battery may be much higher than the surface temperature, which is crucial for thermal management and performance optimization of the battery.
During the discharge cycle, the difference between the internal temperature of the battery and the measured surface temperature of the battery increases in the early stages of discharge, reaches its peak in the middle stages, and then decreases in the late stages of discharge.
Dynamic changes in temperature differences: The trend of temperature differences between the internal and surface of a battery during discharge reflects the complexity of the internal thermal dynamics of the battery. This difference increases in the early stages of discharge, possibly due to the rapid increase in heat generated internally when the battery begins to discharge. Peaking during mid discharge may be due to the highest internal temperature of the battery, while decreasing towards the end of discharge may be due to a decrease in heat generated within the battery and the onset of cooling.
These observations are crucial for the design and optimization of battery management systems (BMS), as they provide valuable information about the behavior of batteries under different operating conditions. By understanding and predicting these phenomena, it is possible to more effectively manage the temperature of the battery, thereby improving its performance and lifespan.