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Experimental Study on the Internal Resistance and Heat Generation Characteristics of Lithium Ion Power Battery with NCM/C Material System.

1. Introduction

At present, lithium-ion batteries are widely used in electric vehicles for their favorable features of high voltage, high energy density and long usage life [1, 2]. In the processes of charging and discharging, Li-ion batteries generate large amount of heat due to the effects of ohmic resistance, Li-ion migration and polarization phenomenon etc. For the lithium-ion cells with large capacities, the heat generation rate will increase with the rising of charge and discharge currents. The heat generated inside the battery will cause the increase of the cell temperature and the nonuniformity of the internal temperature, which results in reduction of the batterie's efficiency, cycle performance, safety and consistency etc.

In recent years, quantitative analysis on the thermal characteristics of lithium-ion battery has been reported in several works. Chen et al. [3] quantitatively analyzed the heat generation characteristics of a 20 Ah soft-coated lithium iron phosphate cell using calorimetry at current rates of 0.25 C~3 C and temperatures between -10~40 [degrees]C. Veth et al. [4] analyzed the thermal characteristics of a 50 Ah pouch lithium-ion cell under high current discharge conditions. Schuster et al. [5] reported the heat generation of a commercial 40 Ah ternary material pouch cell at current rates of 0.0125 C~1 C. Eddahech [6] et al. evaluated the thermal behavior of two high-power Li-ion cells using an ARC. They measured the heat generation during charging and discharging processes at several C-rates. The parts of reversible and joule loss are also compared with each other. In general, it is of great significance to analyze and understand the thermal characteristics of various kinds of lithium-ion cells with the specific materials system. However, works reporting quantitative analysis of heat generation power of lithium-ion cells are yet to be perfected [7, 8, 9, 10].

For the internal resistance, it can be drowned from a widely applied calculation formula of heat generation power, which is called the Bernardi Equation (Equation 1). The first part is irreversible heat due to the ohmic resistance and polarization effect, and the second part is the reversible heat caused by enthalpy change during battery electrochemical reactions. It should be noted that heat generation caused by phase changes and mixing effects is usually minute in quantity and thus neglected. From Equation 1, it is clear that the resistance is one of the key factors influencing the thermal behavior of these lithium ion batteries [10].

q = [I.sup.2][R.sub.t] - IT [[partial derivative]E/[partial derivative]T] (1)

where q is the heat generation power, W; I the current rate, A; [R.sub.t] the total internal resistance of the battery cell, [OMEGA]; T the battery temperature, [degrees]C; [partial derivative]E/[partial derivative]T the entropic coefficient, V/[degrees]C.

Testing methods for the internal resistance mainly include the DC and AC impedance methods, in which the hybrid pulse power characteristic (HPPC) method belonging to the DC type is widely used. This method can be used to study the ohmic resistance, polarization resistance and total internal resistance of a battery cell at different sates of charge (SOCs (State of Charges)) and temperatures. Several previous studies [9, 10, 11] have analyze the variation of DC resistance with SOC and operating temperature using the HPPC method. On the other hand, the AC impedance method tests the ohmic, diffusion and charge transfer resistances of the battery cell at different SOCs and temperatures using the electrochemical impedance spectroscopy (EIS). Evaluations of the battery internal resistance by EIS are reported in the literature [12, 13, 14, 15, 16]. However, comparative study of these two methods has been rarely seen so far.

In this paper, thermal characteristics of the Li-ion cell with NMC/graphite material system are quantitatively analyzed during the charging and discharging processes using the Extended Volume-Accelerating Rate Calorimeter (E[V.sup.+]-ARC) in association with a battery electrochemical test system. In addition, HPPC and EIS methods are applied to analyze the internal resistance of the battery cell under different conditions. Based on the experimental results, the similarities and differences between two kinds of internal resistance test methods are compared. Heat generation characteristics of the lithium ion cell were also analyzed based on the obtained internal resistance. This work is in the hope of providing a better understanding of the heat generation characteristics of lithium ion batteries, which could be helpful for the optimization of power battery cells and the design of thermal management systems.

2. Experimental

2.1. Battery Cell

The pouch type Li-ion power cell has NMC as the cathode material and graphite as the anode material. Specific parameters of the battery cell are shown in Table 1.

2.2. Experimental Equipment

The EIS analysis was carried out using the German Zahner-Zennium electrochemical workstation. During the HPPC test, charge and discharge of the battery cell were performed using the United States Bitroded MCV Series battery test system. Environmental conditions with a constant temperature and humidity were provided by the Giant Force chamber.

The E[V.sup.+]-ARC produced by Thermal Hazard Technology was used for the measuring of specific heat capacity and heat generation of the battery. During the test of the battery thermal behavior, Arbin battery test system was coupled with the E[V.sup.+]-ARC in utilization during various charging and discharging processes, as shown in Figure 1.

2.3. Experimental Methods and Procedures

2.3.1. HPPC Test HPPC test determines the cell charging and discharging resistances by measuring the cell voltage correspondence when the battery is applied with pulse currents. Referring to the method proposed in literature [17], the test procedures are as follow. Firstly the cell is fully charged, then with a DOD (Depth of discharge) step of 10%, the battery is adjusted to certain DOD. Then the cell was charged and discharged with a pulse current of 10 seconds at each DOD. The charging and discharging pulse current rates are 2.5 C and 3 C, respectively. The rest times before the pulse charge and discharge are all set as 1 hour. Figure 2 shows the current and battery voltage in variation with time during the HPPC test.

DC internal resistance of the lithium ion battery consists of two parts, i.e., ohmic resistance and polarized resistance. As shown in Figure 2(b), when the battery is applied with a charging pulse current, the battery's close circuit voltage jumps immediately due to the ohm internal resistance, and rises gradually due to the polarization resistance. The differences between the initial potential with that at 0.1 s and 10s are considered to be the ohmic internal resistance (also called as the 0.1 s resistance) and the total internal resistance (also called as the 10s resistance), which can be calculated using the Equations 2 and 3.

[R.sub.0] = [[[DELTA]U.sub.0]/I] = [|[U.sub.1]-[U.sub.0]|/I] (2)

[R.sub.t] = [[[DELTA]U.sub.t]/t] = [|[U.sub.t]-[U.sub.0]|/I] (3)

where [R.sub.0] and [R.sub.T] are the ohmic internal resistance and the total internal resistance, respectively, [OMEGA]; [U.sub.0] the open-circuit voltage before the pulse current, V; [U.sub.1] and [U.sub.t] are the battery voltage as the pulse time at 0.1 s and 10s, respectively, V; I is the pulse current, A.

2.3.2. EIS Test By measuring the cell open-circuit voltage over time when applied with current excitation, EIS test can differentiate the ohmic internal resistance, charge transfer resistance, diffusion internal resistance, and other parts of the impedance of a Li-ion cell. The one-way scanning frequency of the small-amplitude sine wave was from 10 kHz to 100 mHz in this work. After the Nyquist curve was obtained by the EIS test, different parts of the resistance can be achieved by performing fitting of the Nyquist curves.

2.3.3. Electrochemical-Thermal Analysis of the Battery The heat generation behavior and specific heat capacity of the battery cell were characterized using the E[V.sup.+]-ARC. After placed inside the ARC's chamber, the battery's temperature was measured by a N-type thermocouples located at the center of the cell surface. Through controlling the chamber temperature precisely in synchronization with the cell temperature, an adiabatic environment was thus created. Charging and discharging of the battery was performed using the battery test system. Considering that the heat generated inside the cell was used to heat itself only, heat generation quantity and instantaneous heat generation power can be calculated using Equations 4 and 5, respectively.

Q = m[C.sub.p] [DELTA]T (4)

q = m[C.sub.p][dT/dt] (5)

where Q is the battery heat generation in J, m is cell mass in g, [C.sub.p] is the cell specific heat capacity in J/(g K), AT is cell temperature rise in K, q is battery instantaneous heat generation power in W, and dT/dt is temperature rise rate in K/s.

The initial temperature of the battery cell and ARC chamber is set at 25 [+ or -] 2 [degrees]C. To comprehensively evaluate its thermal performance under adiabatic conditions, the battery was charged and discharged at current rates of 0.33 C, 0.5 C, 1 C, 2 C and 2.5 C. Charge of the Li-ion battery was performed in the constant current-constant voltage (CC-CV) mode and discharge was performed in the constant current mode in a 25 [+ or -] 2 [degrees]C environment.

3. Results and Discussion

3.1. DC Resistance

The measured 0.1 s internal resistance and 10s total internal resistance by HPPC method were shown in Figure 3. It can be observed that the 0.1 s internal resistance is much larger than the polarization resistance, except for SOC = 10%. The charging 0.1 s internal resistances are basically same with the discharging ones both in magnitude and variation trend. Specifically, in the SOC window from 10% to 90%, the charging and discharging 0.1 s internal resistances firstly decrease and then increase. The minimum values were observed at SOC = 70%. For the polarization internal resistance, the charging ones are close to the discharging ones during SOC window of 40%~90%. However, when SOC is less than 40%, the discharging polarization insistence will increase much more quickly with the decrease of SOC, and become two time of the charging one at SOC = 10%. In addition, different with the 0.1 s internal resistance, the polarization resistance reaches the minimum value at SOC = 40%.

3.2. EIS Test Results

The Nyquist curve of the investigated cell obtained by the EIS test are depicted in Figure 4. It is generally considered that the ohm internal resistance [R.sub.b] appeared at the point of intersection between the curve and the real axis in the high frequency region. [R.sub.b] includes resistances of internal components such as the electrolyte, separator and current collector. The semicircle of the intermediate frequency region is related to the charge transfer process of the Li-ion cell, and the value of semicircle's diameter is regarded as the charge transfer resistance [R.sub.ct]. What's more, the linear part of the high-frequency region corresponding to the diffusion impedance [R.sub.diff].

Performing fitting of the Nyquist curves in Figure 4, the ohmic resistance, charge transfer internal resistance and diffusion resistance of the cell at different SOC were obtained, as shown in Figure 5. It can be seen that the diffusion resistance accounts for a smaller proportion of the AC impedance (between 5.5%~11.7%, wherein the minimum and maximum proportion appeared at SOC = 0.7 and 0.4, respectively). The charge transfer resistance is approximately twice times that of the ohmic internal resistance. And the fluctuation of charge transfer resistance with SOC is obviously higher than that of ohmic resistance.

Comparison between these two kinds of internal resistance test methods were qualitatively analyzed, as shown in Figure 6. The ohmic resistance measured by the HPPC method can be interpreted as the ohmic impedance and SEI membrane impedance measured by the EIS method. And the polarization resistance measured by the HPPC method can be understood as the charge transfer impedance and diffusion impedance measured by the EIS method. However as shown in Figure 6, the total internal resistance measured by EIS test was approaching to the ohmic internal resistance obtained by the HPPC method. The difference was attributed to the pulse current rate and experimental equipment limitation in HPPC test. In other words, the results of EIS test were not affected by the rate of current, while the HPPC tested results were affected. In addition, there is also polarization effect unavoidably happens to some extent during the 0.1 s process, which are considered to be the voltage drop due to the ohmic resistance.

3.3. Electrochemical-Calorimetric Analysis of the NCM/C Battery Cell

3.3.1. Specific Heat Capacity The specific heat capacity is essential to calculate thermal characteristics of the battery cell. Same as the measuring procedures in [10], the specific heat capacity of the Li-ion battery was measured using the E[V.sup.+]-ARC. The temperature data and heating power were recorded in the test. The specific heat capacity of the Li-ion cell could be obtained by fitting the slope of battery's temperature-time curve, and calculated to be 1.5864 J*[kg.sup.-1]*[k.sup.-1].

3.3.2. Thermal Characteristics of the Battery Cell (1) Charging Process. The total heat generation and average heat generation power of the Li-ion battery cell during the charging processes as a function of current rates were shown in Figure 7. It can be observed that the heat generation power during 0.33 C and 0.5 C-rate charging processes were considerably very low in magnitude and could be ignored. When the current is higher than 0.5 C, the temperature rise increases as the charging current rate rising. The temperature rises of the Li-ion cell were 14.52, 20.25 and 20.10 [degrees]C, and the average temperature rise rates were 0.194, 0.445 and 0.504 [degrees]C/min at the rate of 1 C, 2 C and 2.5 C, respectively. As a result, the average heat production power showed the tend of increasing linearly as the current rate rising from 0.5 C to 2.5 C.

The heat generation power and current changing as a function of time during charging processes at different current rates are shown in Figure 8. It can be seen that the heat generation power of the battery increases obviously when the charge current rate rises, and the fluctuation degree of the heat generation power at higher current rate is also much higher. When the current rate is high, the ohmic internal resistance and the polarization resistance of the Li-ion cell are comparatively large during the initial stage (as shown in Figure 3). Therefore, it is quite high for the instantaneous heat generation power at low SOCs as presented in Figure 8. After that, the heat generation power decreases gradually with the charging in progress. In the final period of constant current charging, the heat generation power increases again significantly in a short period of time. During the constant voltage charging stage, heat generation power gradually reduced as current gradually dropping to 0.6 A.

(2) Discharging Process. The total heat generation and the average heat generation power of the battery cell during discharging processes as a function of current rate are shown in Figure 9. It can be observed that, same as the charging process, the heat generation power during 0.33 C and 0.5 C-rate discharging processes were considerably low. While during 1 C, 2 C and 2.5 C-rate discharging tests, the temperature rises of the Li-ion cell were 8.84, 16.98 and 21.39 [degrees]C. That is, the average heating generation power of the cell during discharging process increases significantly with current rate rising.

The instantaneous heat generation power as a function of time and DOD during discharging processes at different current rates are shown in Figure 10. It can be seen that the heat generation powers are small during the majority of discharging time when the current rate was low. In the final stage of the discharge, heat generation power was increasing significantly due to the high internal resistance. Also, it can be observed that the heat generation power of the cell increases obviously both in magnitude and fluctuation as the discharge current rate rises. In addition, the heat generation powers of the cell are relatively higher during the initial and final periods, and relatively lower during the middle stage. The reasons for the high heat generation power of the cell during the initial discharging stage are still to be further studied.

To further investigate the relationship between the internal resistance and the heat generation, heat generation powers calculated by the Ohm's law using the internal resistance measured by the HPPC test are compared with the ones measured by the ARC test in Figure 11.

As shown in Figure 11, the fitting is much better as low and high DODs and relatively high during the middle DOD area. The absolute errors between the measured and calculated data at certain DODs are between 0.009~0.115 W. Generally, it can be concluded that the heat generation powers obtained from these two methods were well fitted. On the one hand, the 10s internal resistances obtained by the HPPC method are more correlated with the heat generation power of the battery cell. On the other hand, the heat of the cell discharging is mainly based on the irreversible ohmic heat, and the reversible reaction heat and the side reaction heat are basically negligible.

4. Conclusion

In this paper, quantitative analysis of internal resistance by the HPPC, EIS methods and the heat generation behavior of the NCM/C battery during both charging and discharging processes are conducted. It is founded that the charging ohmic resistances of Li-ion cell are basically consistent with the discharging ones both in magnitude and variation trend for the HPPC method. In general, the ohmic internal resistance is much larger than the polarization resistance. For the two different internal resistance measuring methods, the total internal resistance measured by EIS is only approximate to the ohmic internal resistance obtained by the HPPC method. During charging discharging process at 0.33 C and 0.5 C-rates, heat generation powers are considerably very low. And the heat generation power curve presents a U-shaped characteristic that displays some symmetry during discharging processes at high current rates. What's more, the heat generation power calculated by the HPPC measured internal resistances are close to the ARC test results, that is the HPPC method can provide much more reasonable results for the estimation of the battery heat generation power compared with the EIS method. From the above discussion, it can be inferred that the battery heat generation during the discharging process are mainly made up of the irreversible ohmic heat ([I.sup.2]R), and the proportion of reversible reaction heat and side reactions heat are relatively low in magnitude.

It should also be further noted that the battery heat generation data measured in this work can provide reliable boundary condition for the design of thermal management system. Meanwhile, direct current internal resistance can be used to develop the temperature prediction model for the battery cell, where the heat generation data can be used to validate this model. Thus, this work could be helpful for both the optimization of power batteries and the design of their thermal management systems.


This work was financially supported by the National Research and Development Program of China for New Energy Vehicle (2016YFB0100400) and the Special fund of Beijing Co-construction Project.


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Jing Wang, Beijing Institute of Technology

Shiqiang Liu, Chunjing Lin, and Fang Wang, China Automotive Technology and Research Center Co., Ltd.

Chuncheng Liu, Yuefeng Su, Shi Chen, and Feng Wu, Beijing Institute of Technology


Received: 11 Oct 2017

Revised: 10 Jan 2018

Accepted: 11 Mar 2018

e-Available: 18 Apr 2018



Lithium ion battery, HPPC, EIS, Internal resistance, Heat generation characteristic


Wang, J., Liu, S., Lin, C., Wang, F. et al., "Experimental Study on the Internal Resistance and Heat Generation Characteristics of Lithium Ion Power Battery with NCM/C Material System," SAE Int. J. Passeng. Cars--Electron. Electr. Syst. 11(2):2018, doi:10.4271/07-11-02-0012
TABLE 1 Parameters of the lithium ion battery sample.

Type          Parameter

Cathode       NCM
Anode         Graphite
Capacity/Ah    3
Charging       4.35
Discharging    2.75
Size/mm        3.0*100*126
Mass/g        66
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Author:Wang, Jing; Liu, Shiqiang; Lin, Chunjing; Wang, Fang; Liu, Chuncheng; Su, Yuefeng; Chen, Shi; Wu, Fe
Publication:SAE International Journal of Passenger Cars - Electronic and Electrical Systems
Article Type:Technical report
Date:Apr 1, 2018
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