# Sensitivity Analysis on the Parameters of Lithium-Ion Battery DC Pulse Preheating under Low Temperature

Authors: Chengwei Luo; Furong Liu; Pan Chen; Wenguang Luo; Hongtao Ye; Shu Liu; Changjun Xie
Journal: International Journal of Energy Research
 (2023)

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## Abstract

Lithium-ion batteries (LIBs) require to be preheated under cold weather to restore performance, while DC pulse discharging is often considered a promising approach. Applying a larger pulse current can shorten the heating time, but it may lead to battery decay and demand additional cost. To keep the current lower in preheating, it is necessary to explore the effects of pulse current on the cell temperature rise and make full use of the battery’s heat-generating potential. This paper experimentally compared the effects of DC pulse, average (AVG) current, root mean square (RMS) current, pulse frequency, and state of charge (SOC) of the LIBs on its temperature rise rate, respectively. It is found that within the frequency of 1 kHz~10 kHz, the heat generation is affected by all factors above, among which the frequency has less impact while AVG current has the highest impact. During DC pulse discharging, it is shown that there is more entropy heat produced than the Joule heat in some SOC ranges. Therefore, entropy heat cannot be overlooked in the heat generation model. Moreover, as the thermal coefficient of entropy varies greatly with the SOC, the battery temperature rise rate will be inconsistent during the DC pulse discharging, which might cause an inconsistent warm-up time.


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## Body

## 1. Introduction

Renewable energy and electric vehicles have rapidly rolled out worldwide to reduce emissions and achieve carbon neutrality. The lithium-ion battery has become their primary source of energy for its excellent performance in output power, energy density, and cycle life. However, the performance of lithium batteries is significantly reduced by undesirable working temperatures. Under cold conditions, the internal resistance increases, causing the output power to decrease and the available capacity to drop sharply, resulting in a severe decrease in the electric vehicle’s range. Additionally, the limited transport kinetics causes the lithium deposit on the anode surface, causing irreversible battery capacity loss and even battery safety issues [1]. To avoid this, a lower charging rate has to be employed, which leads to a significant increase in the charging time. Many efforts have been made to overcome the low-temperature challenge of LIBs by reformulating electrolytes and adopting different electrode materials. However, the improvements on these aspects cannot be completed in the short term. A more suitable way to address these challenges is to preheat the battery to a friendly operating temperature to eliminate the negative effect of low temperature. LIBs can be preheated internally and externally. External preheating is where the heat is mainly provided by external heating sources (such as PTC or other electrical heating elements) and transferred to LIBs by convection or conduction. This method is currently applied by most commercial vehicles. The pitfalls of this method include long preheating time, high energy consumption, and poor temperature consistency. On the contrary, the internal preheating method can avoid the complex heat transfer path and energy loss by generating heat within the LIBs, generally improving the energy efficiency, heating rate, and temperature consistency. However, due to the immaturity of this technology, the method of internal heating has not yet been fully commercialized.Internal preheating can be classified into embedded heating component preheating [2–4] and charge/discharge preheating. The embedded heating component can preheat the battery efficiently and rapidly, but a modification to the cell structure is required, increasing the cost and complexity. The charge/discharge preheating does not need to alter the battery structure, giving it an edge over the embedded component preheating methods. Based on the current polarity in the preheating, the charge/discharge preheating method can be divided into AC preheating [5–7] and DC pulse discharge preheating [8]. DC discharge preheating can be regarded as a particular case of DC pulse discharge preheating where the pulse frequency is 0 Hz.The comprehensive advantages of DC pulse discharge preheating are low cost, simplicity, high efficiency, and little negative impact on the battery life [1, 9]. Qu et al. [10] experimented with the low-frequency pulsed discharge. The results showed that the heating rate could reach 7°C/min at a discharge rate of 4-4.5°C. This paper also experimented with comparing DC pulse discharge and DC discharge heating, concluding that the heating rate and heating efficiency of DC pulse heating are similar to those of DC heating. The heating rate is not sensitive to the frequency within the range of 1-10 Hz, but the battery life applied pulse is 2.2 times that of the DC heating. Xiong et al. [11] achieved rapid preheating by controlling the intermittent high-current self-discharge of the battery, where they achieved a heating rate of 14.85°C/min. The study analysed the influence of the initial state of charge (SOC), heating frequency, and duty cycle on the heating outcome. Comparing the heating outcome with the frequencies of 2000 Hz and 10 Hz, the researchers found that the difference in the heating rate was small.However, when Shang et al. [12] experimented with a high-frequency triangular pulse discharge current generated by a switching circuit, they found that the temperature rise rate of batteries under the 150 kHz pulse was significantly higher than that of 50 kHz. This observation is similar to the results for AC preheating, but their study only experimented with two particular frequencies. Shang et al. [12, 13] conducted AC preheating experiments to show that the internal heat generation rate is positively correlated with the frequency. Increasing the current frequency can significantly boost the internal heat generation. This observation is rarely reflected in other research, nor commonly seen in battery heat generation models [5]. So [14] specifically modified the battery heat generation model according to this observation for further simulation studies.In the past two years, there has been a tendency for internal preheating, external preheating, DC pulse preheating, and AC preheating to be used in combination. [15, 16] proposed a low-temperature composite self-heating strategy that combines internal DC and external electric heating, improving heating efficiency and shortening the heating time without additional power supply.In summary, the DC pulse preheating method can guarantee a good heating outcome, whereas there are two heat-generating related doubts that exist: (1) whether the internal heat generation model of the pulse discharge currently used is feasible. Usually, the heat generation model in studies only considers the Joule heat inside the battery and ignores the electrochemical heat generation. Although it reduces the algorithm’s complexity, whether the error is negligible or not is still under debate. (2) Whether a positive correlation between the DC pulse discharge frequency and the internal heat generation rate of the battery exists. Unfortunately, there are few experiments on the correlation between DC pulse frequency and heat generation rate in the studies. The studies only concentrated on low frequencies below tens of Hz or ultrahigh frequencies of 50 kHz and 150 kHz. There is a lack of coverage in the easily engineered 1 kHz-10 kHz frequency range. At the same time, the relationship between the current parameter and the battery temperature rise rate under the condition of low-temperature pulse discharge is not clear, which brings confusion to the selection of the battery preheating scheme.To address the two doubts above, this study built a pulse discharge platform, developed experiments to observe the preheating process, revealed the electrical and thermal characteristics of lithium-ion batteries in low temperatures, and explored the relationship of the pulse discharge frequency, the battery SOC, and the current RMS value with the heating rate at low temperature. It is hoped that it can provide a basis for the selection of low-temperature preheating schemes for lithium batteries and its optimization.


## 2. Experimental Design

The details of the experiment are shown in Figure1. Experiment appliance BTS-5V6A (manufactured by Neware, with an accuracy of ±0.05%) was used to detect the battery capacity and to calibrate the battery’s SOC in order to study the battery’s capacity loss at low temperatures and after pulse discharge, as well as to calculate the heat generation efficiency of the battery. Constant current discharge is adopted during the capacity test, where it is set to 0.2°C when the battery is stable until a cut-off voltage of 3.0 V is reached. As for the SOC calibration, the battery was first charged to the full SOC with a constant current of 0.2°C and a constant voltage of 4.2 V and then discharged to the desired SOC with a constant current of 0.2°C. Low-temperature pulse discharge is carried out with a customized discharge circuit, as shown in Figure 2.Figure 1
Experimental outline.Figure 2
Equivalent circuit of the pulse preheating experiment.A cylindrical lithium-ion battery was used in the experiments, where its details are listed in Table1.Table 1
Basic battery parameters.
NameParametersElectrode materialLi(NiCoMn)O2/graphiteBattery capacity (Ah)2.9Standard voltages (V)3.7Battery mass (g)47Battery surface area (m2)0.00418The experimental setup for the research is shown in Figure3. The frequency and duty cycle of the pulse current are determined by the MOSFET. Multiple cells with uniform internal resistance were selected to form a battery in series. The battery was placed in a -20°C (253 k) incubator for 4 hours before the experiment. T-type thermocouples were used to record the battery temperatures, where the thermocouples were placed on four points of the two batteries, which were recorded as points A, B, C, and D. In the meantime, the voltage changes of the terminal and the current change of the battery were measured by voltage probe and Hall element, where the data were sent to the computer through a thermometer and a digital oscilloscope. In order to reduce the experimental error, the connection wires in the battery discharge circuit were as short as possible. The thermocouple is closely attached to the battery through a thin tape to effectively track the battery surface temperature. Moreover, in order to reduce the error due to heat conduction between the batteries, the thermocouple was attached to the battery near the middle.Figure 3
Experimental equipment and the circuit diagram.


## 3. Models in the Experiments of Pulse Preheating

### 3.1. Circuit Model

The experimental circuit for pulse preheating is shown in Figure2. Considering the polarization of discharge, the Thevenin equivalent model of the lithium battery is used [16], where OCV is the battery open-circuit voltage, R0 is the equivalent ohmic resistance, Rs is the equivalent polarized resistance, Cs is the equivalent polarized capacitance, and Rd is a resistor in the circuit to limit the battery current. The equivalent circuit does not consider the resistance and inductance of the connecting wires. According to Kirchhoff’s law, when the MOSFET is switched on, there is
(1)UOCV−R0+Rdi=Uc,UcRs+Cs∂Uc∂t=i,where i is the battery current, is is the current flowing through the polarized resistance, and Uc is the voltage across the polarized capacitor. With the initial condition of Uc0=0, when Rd+R0>>Rs, Equation (1) can be simplified as
(2)ist≈UOCVRd+R01−exp−1CsRst.In the meantime, the battery current can be approximated as unchanged, which can further simplify it as(3)it≈UOCVRd+R0.When the MOSFET is switched off,it=0, so the RMS of the battery current in one period is
(4)Irms≈UOCVRd+R0D.And the AVG current value is(5)Iavg≈UOCVRd+R0D,where D is the duty cycle of one period; changing the value of D will change both the RMS and the AVG values of battery current. When D is close to 1, the circuit will approximate the case of DC discharge.


### 3.2. Analysis of Battery Resistance to Pulse Discharges

The battery’s terminal voltage will decrease due to three factors [17]: first, the ohmic resistance of the battery will cause the voltage drop, which occurs at the instant of the current pulse start. Second, the voltage drop caused by charge transfer starts to take effect over time until it stabilizes; finally, insufficient diffusion of lithium ions in the active material causes the voltage to drop continuously until the end of the pulse discharge. For high-frequency pulse discharge, the pulse time is short, and the voltage loss caused by the diffusion effect of lithium ions in the electrode particles is negligible. In this case, the voltage drop is mainly caused by the charge transfer resistance and ohmic resistance, which together appears as an internal resistance when observed from the external circuit [10]. The internal resistance of the battery during the discharge can be calculated as follows:
(6)Rd=ΔuΔi,where Rd is the internal resistance, Δu is the pulse voltage drop, and Δi is the pulse current peak value. Figure 4 shows the calculation of the DC internal resistance in the experiment.Figure 4
Experimental pulse discharge waveform.


### 3.3. Thermal Model for the Lithium Battery

The thermal model of lithium batteries is usually represented by a simplified Bernardi model, which is based on the energy conservation equation [17]:
(7)mc∂T∂t=QN+QY−QS.Each term in the model represents the thermal power in watts (w), whereT is the battery temperature, m is the battery mass, and c is the heat capacity of the battery. QN represents the irreversible heat generated by the internal resistance of the battery. According to the circuit analysis in Section 3.1, we have
(8)QN=Irms2R0+Is2Rs≈Irms2Rd.The two terms to the left of the approximate equal sign are the theoretical Joule heat obtained from the battery model. On the right is the actual Joule heat measured externally, where the error between them only depends on the precision of the measuring instrument.The second part,QY, represents the reversible heat that depends on the entropy change of the battery. This part of the heat is produced by the chemical reaction within the battery:
(9)QY=−TΔSNFIavg,where ΔS is the entropy change, which is correlated with the battery SOC. It can be determined by the rate of change of battery open-circuit voltage with temperature ∂UOCV/∂T, that is, the entropy heat coefficient:
(10)ΔS=NF∂UOCV∂T,where F is the Faraday constant. In lithium-ion batteries, N=1.The third part,QS, represents the heat transfer between the battery and the ambient.
(11)QS=−hSTb−T0,where h is the thermal conductivity, S is the surface area of the battery, Tb is the surface temperature of the battery, and T0 is the ambient temperature.Irreversible heat production is always positive no matter the battery is discharged or charged, resulting in an increase in the temperature of the battery. Reversible heat can be either positive or negative based on the SOC of the battery. The conduction heat is based on the difference between the battery surface temperature and the ambient temperature. The greater the temperature difference is, the more conduction heat will be produced. Du et al. [18] found that under the condition of low-rate current discharge of 18650 lithium battery, the temperature gradient of the battery is very small and can be ignored. Therefore, this article uses the average temperature to reflect the actual temperature of the battery. Based on the analysis above, the corresponding battery temperature rise model can be represented as below:
(12)mc∂T∂t=Irms2Rd+−T∂UOCV∂TIavg−hSTb−T0,where T is the battery temperature, m is the battery mass, and c is the specific heat capacity of the battery.According to Equation (6) in Section 3.2 and Equation (7) in Section 3.3, adjusting the voltage UOCV and the duty cycle D at the same time can change DUOCV while keeping DUOCV constant, which in turn changes the current RMS value Irms. Similarly, DUOCV may be kept unchanged while changing DUOCV, and the current AVG value Iavg will be changed accordingly. Equation (12) shows that these two adjustments will change the Joule heat and the reversible heat generated by the battery, respectively.


## 3.1. Circuit Model

The experimental circuit for pulse preheating is shown in Figure2. Considering the polarization of discharge, the Thevenin equivalent model of the lithium battery is used [16], where OCV is the battery open-circuit voltage, R0 is the equivalent ohmic resistance, Rs is the equivalent polarized resistance, Cs is the equivalent polarized capacitance, and Rd is a resistor in the circuit to limit the battery current. The equivalent circuit does not consider the resistance and inductance of the connecting wires. According to Kirchhoff’s law, when the MOSFET is switched on, there is
(1)UOCV−R0+Rdi=Uc,UcRs+Cs∂Uc∂t=i,where i is the battery current, is is the current flowing through the polarized resistance, and Uc is the voltage across the polarized capacitor. With the initial condition of Uc0=0, when Rd+R0>>Rs, Equation (1) can be simplified as
(2)ist≈UOCVRd+R01−exp−1CsRst.In the meantime, the battery current can be approximated as unchanged, which can further simplify it as(3)it≈UOCVRd+R0.When the MOSFET is switched off,it=0, so the RMS of the battery current in one period is
(4)Irms≈UOCVRd+R0D.And the AVG current value is(5)Iavg≈UOCVRd+R0D,where D is the duty cycle of one period; changing the value of D will change both the RMS and the AVG values of battery current. When D is close to 1, the circuit will approximate the case of DC discharge.


## 3.2. Analysis of Battery Resistance to Pulse Discharges

The battery’s terminal voltage will decrease due to three factors [17]: first, the ohmic resistance of the battery will cause the voltage drop, which occurs at the instant of the current pulse start. Second, the voltage drop caused by charge transfer starts to take effect over time until it stabilizes; finally, insufficient diffusion of lithium ions in the active material causes the voltage to drop continuously until the end of the pulse discharge. For high-frequency pulse discharge, the pulse time is short, and the voltage loss caused by the diffusion effect of lithium ions in the electrode particles is negligible. In this case, the voltage drop is mainly caused by the charge transfer resistance and ohmic resistance, which together appears as an internal resistance when observed from the external circuit [10]. The internal resistance of the battery during the discharge can be calculated as follows:
(6)Rd=ΔuΔi,where Rd is the internal resistance, Δu is the pulse voltage drop, and Δi is the pulse current peak value. Figure 4 shows the calculation of the DC internal resistance in the experiment.Figure 4
Experimental pulse discharge waveform.


## 3.3. Thermal Model for the Lithium Battery

The thermal model of lithium batteries is usually represented by a simplified Bernardi model, which is based on the energy conservation equation [17]:
(7)mc∂T∂t=QN+QY−QS.Each term in the model represents the thermal power in watts (w), whereT is the battery temperature, m is the battery mass, and c is the heat capacity of the battery. QN represents the irreversible heat generated by the internal resistance of the battery. According to the circuit analysis in Section 3.1, we have
(8)QN=Irms2R0+Is2Rs≈Irms2Rd.The two terms to the left of the approximate equal sign are the theoretical Joule heat obtained from the battery model. On the right is the actual Joule heat measured externally, where the error between them only depends on the precision of the measuring instrument.The second part,QY, represents the reversible heat that depends on the entropy change of the battery. This part of the heat is produced by the chemical reaction within the battery:
(9)QY=−TΔSNFIavg,where ΔS is the entropy change, which is correlated with the battery SOC. It can be determined by the rate of change of battery open-circuit voltage with temperature ∂UOCV/∂T, that is, the entropy heat coefficient:
(10)ΔS=NF∂UOCV∂T,where F is the Faraday constant. In lithium-ion batteries, N=1.The third part,QS, represents the heat transfer between the battery and the ambient.
(11)QS=−hSTb−T0,where h is the thermal conductivity, S is the surface area of the battery, Tb is the surface temperature of the battery, and T0 is the ambient temperature.Irreversible heat production is always positive no matter the battery is discharged or charged, resulting in an increase in the temperature of the battery. Reversible heat can be either positive or negative based on the SOC of the battery. The conduction heat is based on the difference between the battery surface temperature and the ambient temperature. The greater the temperature difference is, the more conduction heat will be produced. Du et al. [18] found that under the condition of low-rate current discharge of 18650 lithium battery, the temperature gradient of the battery is very small and can be ignored. Therefore, this article uses the average temperature to reflect the actual temperature of the battery. Based on the analysis above, the corresponding battery temperature rise model can be represented as below:
(12)mc∂T∂t=Irms2Rd+−T∂UOCV∂TIavg−hSTb−T0,where T is the battery temperature, m is the battery mass, and c is the specific heat capacity of the battery.According to Equation (6) in Section 3.2 and Equation (7) in Section 3.3, adjusting the voltage UOCV and the duty cycle D at the same time can change DUOCV while keeping DUOCV constant, which in turn changes the current RMS value Irms. Similarly, DUOCV may be kept unchanged while changing DUOCV, and the current AVG value Iavg will be changed accordingly. Equation (12) shows that these two adjustments will change the Joule heat and the reversible heat generated by the battery, respectively.


## 4. Experimental Results and Analysis

In the experiment, the frequency of the pulse discharge is 1 kHz, 2 kHz, 4 kHz, 5 kHz, 7 kHz, and 10 kHz, respectively. The duty cycle changes according to the value of the current. The ambient temperature was set to -20 or -8°C, and the experiment was terminated when the battery surface temperature reached 5°C or the discharge time reached 25 min.


### 4.1. Uniformity of the Battery Temperature

To ensure the accuracy of the battery temperature data, the temperature rise of four points, ABCD, was recorded in the experiment (refer to Figure3 in Section 1 for details). Figure 5 shows the comparison of four points’ temperature during the 1 kHz pulse discharge.Figure 5
Comparison of temperature rise at the measured spots.From Figure5, it can be observed that the temperature distribution on the battery surface is uniform during the self-discharge process. The temperature difference between the two temperature points of the same battery never exceeds 0.4°C, and the relative error does not exceed 1.6%. Between different battery temperature points, the temperature difference does not exceed 0.6°C, and the relative error does not exceed 2.4%. This difference is slightly larger than that of the same battery. The results show that the battery maintains good temperature consistency under pulse discharge, and the experimental temperature measurement data is accurate.


### 4.2. The Effect of Frequency on Battery Heat Generation

Figure6 shows the temperature rise results of the battery under pulse discharge with different switching frequencies at -20°C. Table 2 summarizes the comparison between the experimental results under different parameters.Figure 6
Temperature rise under different switching frequencies.Table 2
Comparison of different switching frequencies.
Frequency,f (kHz)1245710Discharge time,tdis (min)13.3313.9215.2516.0017.5820.17Temperature rise rate,T/t (°C/min)1.8751.7961.6391.5631.4221.240Capacity loss,Closs (mA∗h)303316324335375430Energy consumption,Econ (%)10.4510.8911.1711.5512.9314.83From Figure6 and Table 2, it can be concluded that during the heating process, the overall trend of the temperature rising is continuously decreasing. This change is determined by the change of the battery’s internal resistance and the discharge current. As the pulse discharge frequency increases, the average temperature rise rate of the lithium batteries gradually decreases. For example, the temperature rise rate of 1 kHz frequency is 1.875°C/min, and it takes 13.33 minutes and 10.45% consumption on the energy to increase the battery temperature from -20°C to 5°C. In contrast, when the frequency is increased to 10 kHz, the temperature rise rate decreases to only 1.24°C/min and only 66% of that of 1 kHz, while the discharge time and energy consumption increase to 20.17 minutes and 14.83%, respectively. Higher discharge frequency leads to longer discharge time, which in turn causes higher capacity loss and greater energy consumption. Under the same conditions of heat dissipation, by analysing Equation (12) of heat generation, it can be determined that the increase in frequency will cause the heat generation of the lithium battery to decrease gradually.Figure7 shows the measured current value and the DC internal resistance as a function of temperature during 1 kHz pulse discharge.Figure 7
1 kHz discharge current and DC internal resistance against temperature.From Figure7, the lower the temperature, the greater the battery’s internal resistance, and the greater the rate of increase as the temperature decreases. When the battery pulse discharge is performed in the temperature range of -20°C to -8°C, the change rate of the internal resistance and current of the battery is relatively large [8]. While in the range of -8°C to 5°C, the change has to be gentle. Figure 6 also shows that the temperature difference between different is small when the pulse discharge is conducted in the low temperature range. As the temperature rises, the temperature differences begin to increase. Considering the controllability and accuracy of the experiment, in order to accurately explore the relationship between the heat production and the discharge frequency, the experiment was repeated at an ambient temperature of -8°C.Figure8 shows the temperature rising curve of different discharge frequencies in the temperature range of -8°C to 5°C. Figure 9 shows the discharge current value of different frequency changes along with the temperature within this range. Figure 10 shows the internal resistance of the battery at different frequency changes along with the temperature within this range.Figure 8
Temperature rise of different discharge frequencies within range.Figure 9
Discharge current against temperature within range.Figure 10
Internal resistance against temperature within range.It can be observed from Figures9 and 10 that, within the temperature range of -8°C to 5°C, the RMS and the AVG values of the current have the same changing pattern for different discharge frequencies. The current value is basically the same, and the maximum differences between each other do not exceed 1.5%. At the same time, the internal resistance under different frequencies also has the same pattern and amplitude, and the maximum differences do not exceed 3%. This shows a high consistency between the different cells used in the study. Comparing the data from Figures 6 and 8, a similar temperature rise result can be observed. Therefore, it can be preliminarily derived that the battery’s heat generation gradually decreases as the discharge frequency increases. To better analyse the impact of the discharge parameters on the temperature rise accurately, all experiments in the following will select -8°C as the ambient temperature.


### 4.3. Influence of Current Value on Battery Heat Generation

It can be seen from Equations (6) and (7) that adjusting the duty cycle during the discharge or changing the battery’s terminal voltage can alter the amplitude of the discharge current. Since the amplitude of the discharge current varies with the temperature, the study took the current of the battery at a temperature of 5°C as the sample. Figure 11 shows the temperature rise rates under the same AVG current and different RMS current when the discharge frequency is set as 1 kHz and 5 kHz. Figure 12, on the other hand, shows the temperature rise rates under different AVG current and the same RMS current. Tables 3 and 4 summarize the comparison of the discharge parameters and the results.Figure 11
Temperature rise under different RMS currents.Figure 12
Temperature rise under different AVG currents.Table 3
Comparison under different RMS currents.
Frequency,f (kHz)15Current AVG,Iavg (A)1.46Current RMS,Irms (A)2.472.121.762.472.121.76Discharge time,tdis (min)6.627.5810.257.289.6710.83Average temperature rise rate,T/t (°C/min)1.9651.7141.2681.7851.3451.200Table 4
Comparison under different AVG currents.
Frequency,f (kHz)15Current RMS,Irms (A)2.12Current AVG,Iavg (A)1.721.461.271.721.461.27Discharge time,tdis (min)5.927.5810.426.919.6712.33Temperature rise rate,T/t (°C/min)2.1971.7141.2481.8801.3451.054By analysing the results above, it can be found that the battery temperature rise rate can be increased significantly by either increasing the RMS value or the AVG value of the current. Under the same AVG value, when the RMS current is 1.76 A, the average temperature rise rate is only 1.268°C/min, and when the RMS current rises to 2.47 A, the temperature rise rate can be increased to 1.965°C/min. The temperature rise rate can be increased by 54% when the RMS current is increased by 40%.As for under the same RMS current, when the AVG current is 1.27 A, the average temperature rise rate is only 1.248°C/min, and when the AVG current rises to 1.72 A, the temperature rise rate can be increased to 2.197°C/min. The temperature rise rate can be increased by 78% when the AVG current is increased by 35%. The results show that, instead of increasing the RMS current, increasing the AVG current is more effective in increasing the battery temperature rise rate. Of course, in the experiment, one can increase the RMS and AVG value of the current at the same time by increasing the duty cycle during the discharge. This will greatly increase the heating rate of the battery.


### 4.4. The Effect of Battery SOC on Heat Generation

Entropy heat is one of the major sources of heat generation by pulse discharge of lithium-ion batteries. It is related to the entropy heat coefficient, and the entropy heat coefficient varies with the SOC [19]. Therefore, the heat generation of the battery pulse discharge under different SOC is not the same. The entropy heat coefficient can be estimated by collecting the change rate of the terminal voltage with the temperature. Figure 13 shows the entropic heat coefficients obtained using the method proposed by [15].Figure 13
Temperature rise comparison under different SOC.From Figure14, it can be seen that the entropy heat coefficient will change along with the battery SOC, being either positive or negative. The current is defined as positive during the discharge process. Thus, when the entropy heat coefficient is positive, the process will behave endothermically. When the entropy heat coefficient is negative, the process is exothermic. The more negative it is, the more entropy heat is released.Figure 14
Entropy thermal coefficient at different temperature ranges.To study the impact of lithium battery SOC on heat generation, four different SOCs were selected for the pulse discharge experiments. The experimental ambient temperature was set to -8°C, and the pulse frequency was set to 1 kHz. Figure13 and Table 5 show the experimental results and temperature rise rate comparisons corresponding to different SOCs.Table 5
Comparison under different SOC.
SOC30%50%80%100%Average temperature rise rate,T/t (°C/min)2.4952.3121.8152.015From Figure13 and Table 5, the temperature rise rate in the case of low SOC (30% SOC, 50% SOC) is significantly higher than that at high SOC (80% SOC, 100% SOC). The average temperature rise rate at 30% SOC is 37.5% higher than that at 80% SOC and 23% higher than that at 100% SOC. The increase is equivalent to that of a 17% increase in the RMS current. This indicates that the effect of battery SOC on the temperature rise rate cannot be ignored in the pulse discharge preheating scheme. From Figure 14, the absolute value of the entropy heat coefficient at 30% and 50% SOC is greater than that at 80% and 100% SOC. Therefore, the entropy heat of battery discharge at low SOCs is greater than that at high SOC conditions and so is the battery temperature rise rate at low SOCs. However, low SOC batteries have less available capacity. Therefore, the low SOC situations are only for reference and are not conducive to commercial applications.


## 4.1. Uniformity of the Battery Temperature

To ensure the accuracy of the battery temperature data, the temperature rise of four points, ABCD, was recorded in the experiment (refer to Figure3 in Section 1 for details). Figure 5 shows the comparison of four points’ temperature during the 1 kHz pulse discharge.Figure 5
Comparison of temperature rise at the measured spots.From Figure5, it can be observed that the temperature distribution on the battery surface is uniform during the self-discharge process. The temperature difference between the two temperature points of the same battery never exceeds 0.4°C, and the relative error does not exceed 1.6%. Between different battery temperature points, the temperature difference does not exceed 0.6°C, and the relative error does not exceed 2.4%. This difference is slightly larger than that of the same battery. The results show that the battery maintains good temperature consistency under pulse discharge, and the experimental temperature measurement data is accurate.


## 4.2. The Effect of Frequency on Battery Heat Generation

Figure6 shows the temperature rise results of the battery under pulse discharge with different switching frequencies at -20°C. Table 2 summarizes the comparison between the experimental results under different parameters.Figure 6
Temperature rise under different switching frequencies.Table 2
Comparison of different switching frequencies.
Frequency,f (kHz)1245710Discharge time,tdis (min)13.3313.9215.2516.0017.5820.17Temperature rise rate,T/t (°C/min)1.8751.7961.6391.5631.4221.240Capacity loss,Closs (mA∗h)303316324335375430Energy consumption,Econ (%)10.4510.8911.1711.5512.9314.83From Figure6 and Table 2, it can be concluded that during the heating process, the overall trend of the temperature rising is continuously decreasing. This change is determined by the change of the battery’s internal resistance and the discharge current. As the pulse discharge frequency increases, the average temperature rise rate of the lithium batteries gradually decreases. For example, the temperature rise rate of 1 kHz frequency is 1.875°C/min, and it takes 13.33 minutes and 10.45% consumption on the energy to increase the battery temperature from -20°C to 5°C. In contrast, when the frequency is increased to 10 kHz, the temperature rise rate decreases to only 1.24°C/min and only 66% of that of 1 kHz, while the discharge time and energy consumption increase to 20.17 minutes and 14.83%, respectively. Higher discharge frequency leads to longer discharge time, which in turn causes higher capacity loss and greater energy consumption. Under the same conditions of heat dissipation, by analysing Equation (12) of heat generation, it can be determined that the increase in frequency will cause the heat generation of the lithium battery to decrease gradually.Figure7 shows the measured current value and the DC internal resistance as a function of temperature during 1 kHz pulse discharge.Figure 7
1 kHz discharge current and DC internal resistance against temperature.From Figure7, the lower the temperature, the greater the battery’s internal resistance, and the greater the rate of increase as the temperature decreases. When the battery pulse discharge is performed in the temperature range of -20°C to -8°C, the change rate of the internal resistance and current of the battery is relatively large [8]. While in the range of -8°C to 5°C, the change has to be gentle. Figure 6 also shows that the temperature difference between different is small when the pulse discharge is conducted in the low temperature range. As the temperature rises, the temperature differences begin to increase. Considering the controllability and accuracy of the experiment, in order to accurately explore the relationship between the heat production and the discharge frequency, the experiment was repeated at an ambient temperature of -8°C.Figure8 shows the temperature rising curve of different discharge frequencies in the temperature range of -8°C to 5°C. Figure 9 shows the discharge current value of different frequency changes along with the temperature within this range. Figure 10 shows the internal resistance of the battery at different frequency changes along with the temperature within this range.Figure 8
Temperature rise of different discharge frequencies within range.Figure 9
Discharge current against temperature within range.Figure 10
Internal resistance against temperature within range.It can be observed from Figures9 and 10 that, within the temperature range of -8°C to 5°C, the RMS and the AVG values of the current have the same changing pattern for different discharge frequencies. The current value is basically the same, and the maximum differences between each other do not exceed 1.5%. At the same time, the internal resistance under different frequencies also has the same pattern and amplitude, and the maximum differences do not exceed 3%. This shows a high consistency between the different cells used in the study. Comparing the data from Figures 6 and 8, a similar temperature rise result can be observed. Therefore, it can be preliminarily derived that the battery’s heat generation gradually decreases as the discharge frequency increases. To better analyse the impact of the discharge parameters on the temperature rise accurately, all experiments in the following will select -8°C as the ambient temperature.


## 4.3. Influence of Current Value on Battery Heat Generation

It can be seen from Equations (6) and (7) that adjusting the duty cycle during the discharge or changing the battery’s terminal voltage can alter the amplitude of the discharge current. Since the amplitude of the discharge current varies with the temperature, the study took the current of the battery at a temperature of 5°C as the sample. Figure 11 shows the temperature rise rates under the same AVG current and different RMS current when the discharge frequency is set as 1 kHz and 5 kHz. Figure 12, on the other hand, shows the temperature rise rates under different AVG current and the same RMS current. Tables 3 and 4 summarize the comparison of the discharge parameters and the results.Figure 11
Temperature rise under different RMS currents.Figure 12
Temperature rise under different AVG currents.Table 3
Comparison under different RMS currents.
Frequency,f (kHz)15Current AVG,Iavg (A)1.46Current RMS,Irms (A)2.472.121.762.472.121.76Discharge time,tdis (min)6.627.5810.257.289.6710.83Average temperature rise rate,T/t (°C/min)1.9651.7141.2681.7851.3451.200Table 4
Comparison under different AVG currents.
Frequency,f (kHz)15Current RMS,Irms (A)2.12Current AVG,Iavg (A)1.721.461.271.721.461.27Discharge time,tdis (min)5.927.5810.426.919.6712.33Temperature rise rate,T/t (°C/min)2.1971.7141.2481.8801.3451.054By analysing the results above, it can be found that the battery temperature rise rate can be increased significantly by either increasing the RMS value or the AVG value of the current. Under the same AVG value, when the RMS current is 1.76 A, the average temperature rise rate is only 1.268°C/min, and when the RMS current rises to 2.47 A, the temperature rise rate can be increased to 1.965°C/min. The temperature rise rate can be increased by 54% when the RMS current is increased by 40%.As for under the same RMS current, when the AVG current is 1.27 A, the average temperature rise rate is only 1.248°C/min, and when the AVG current rises to 1.72 A, the temperature rise rate can be increased to 2.197°C/min. The temperature rise rate can be increased by 78% when the AVG current is increased by 35%. The results show that, instead of increasing the RMS current, increasing the AVG current is more effective in increasing the battery temperature rise rate. Of course, in the experiment, one can increase the RMS and AVG value of the current at the same time by increasing the duty cycle during the discharge. This will greatly increase the heating rate of the battery.


## 4.4. The Effect of Battery SOC on Heat Generation

Entropy heat is one of the major sources of heat generation by pulse discharge of lithium-ion batteries. It is related to the entropy heat coefficient, and the entropy heat coefficient varies with the SOC [19]. Therefore, the heat generation of the battery pulse discharge under different SOC is not the same. The entropy heat coefficient can be estimated by collecting the change rate of the terminal voltage with the temperature. Figure 13 shows the entropic heat coefficients obtained using the method proposed by [15].Figure 13
Temperature rise comparison under different SOC.From Figure14, it can be seen that the entropy heat coefficient will change along with the battery SOC, being either positive or negative. The current is defined as positive during the discharge process. Thus, when the entropy heat coefficient is positive, the process will behave endothermically. When the entropy heat coefficient is negative, the process is exothermic. The more negative it is, the more entropy heat is released.Figure 14
Entropy thermal coefficient at different temperature ranges.To study the impact of lithium battery SOC on heat generation, four different SOCs were selected for the pulse discharge experiments. The experimental ambient temperature was set to -8°C, and the pulse frequency was set to 1 kHz. Figure13 and Table 5 show the experimental results and temperature rise rate comparisons corresponding to different SOCs.Table 5
Comparison under different SOC.
SOC30%50%80%100%Average temperature rise rate,T/t (°C/min)2.4952.3121.8152.015From Figure13 and Table 5, the temperature rise rate in the case of low SOC (30% SOC, 50% SOC) is significantly higher than that at high SOC (80% SOC, 100% SOC). The average temperature rise rate at 30% SOC is 37.5% higher than that at 80% SOC and 23% higher than that at 100% SOC. The increase is equivalent to that of a 17% increase in the RMS current. This indicates that the effect of battery SOC on the temperature rise rate cannot be ignored in the pulse discharge preheating scheme. From Figure 14, the absolute value of the entropy heat coefficient at 30% and 50% SOC is greater than that at 80% and 100% SOC. Therefore, the entropy heat of battery discharge at low SOCs is greater than that at high SOC conditions and so is the battery temperature rise rate at low SOCs. However, low SOC batteries have less available capacity. Therefore, the low SOC situations are only for reference and are not conducive to commercial applications.


## 5. Conclusions

In this research, a 18650 ternary (Li(NiCoMn)O2/graphite) lithium-ion battery was used to carry out an experimental study on the LIB preheating while DC pulse discharge is employed. The effect of AVG current, RMS current, pulse frequency, and SOC of the LIBs on its temperature rise rate, respectively, were analysed, and the following conclusions were drawn from the experimental results:(1)
The temperature rise rate of the lithium battery is positively correlated with the AVG value and RMS value of the pulse discharge current. Increasing the AVG value and the RMS value can both significantly increase the temperature rise rate(2)
During the low-temperature preheating process of pulse discharge, the entropy heat generated by the electrochemical reaction is one of the main contributors to the temperature rise. It is affected by the AVG value of the pulse discharge current and the entropy heat coefficient. As far as this study is concerned, it is shown that entropic heat has a greater effect on battery temperature rise than Joule heat in some SOC ranges(3)
Because the entropy heat coefficient varies significantly with the SOCs, which can be either positive or negative, so does the entropy heat generated, which may lead to inconsistent temperature rise rates during the application of low-temperature preheating of pulse discharge(4)
The frequency of DC pulse affects the temperature rise rate of the battery during the preheating. In the frequency range of 1 kHz-10 kHz, it is observed that increasing the frequency of DC pulse will result in lower temperature rise rate. It is recommended to adopt lower frequencies while DC discharge pulse between 1 kHz and 10 kHz is applied for LIB preheating(5)
Experiments show that the thermal characteristic of LIBs under DC discharge pulse between 1 kHz and 10 kHz is not similar to those of AC triangle current, in which the heat generation rate is positively correlated with its frequency. The heat generation rate of the DC pulse between 1 kHz and 10 kHz can be correctly reflected by the simplified Bernardi modelFuture studies will explore the effect of higher discharge frequency on battery heating, conduct more in-depth research on the impact of pulse discharge on battery health and energy utilization efficiency, and study the discharge scheme with controllable discharge current, aiming to provide supports for the low-temperature preheating design of lithium batteries.



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*Source: 5706355-2023-02-04.xml*