Lithium-ion battery discharge behaviors at low temperatures and cell-to-cell uniformity 锂离子电池低温放电性能及电池间一致性 英文

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1 ISSN CN /U 汽车安全与节能学报, 214 年, 第 5 卷 第 4 期 J Automotive Safety and Energy, 214, Vol. 5 No. 4 13/ Lithium-ion battery discharge behaviors at low temperatures and cell-to-cell uniformity ZHANG Jianbo, HUANG Jun, CHEN Lufan, LI Zhe (State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 184, China) Abstract: The discharge behavior and uniformity of lithium-ion batteries were experimentally investigated at low temperatures. The discharge test and electrochemical impedance spectroscopy (EIS) test were conducted for several commercial 1865 type cells. The cell average capacity decreases by 58.4% with the capacity standard deviation increasing by 6.6 times when the temperature decreases from to -2. The charge transfer resistance (Rct) dramatically increases, dominating other types of resistance. The cell impedance variations, mainly in the Rct, increase significantly at lower temperatures. A linear correlation between the capacity and the over-potential resistance is established by statistics from 15 cells. Therefore, at low temperatures, the cell-to-cell capacity variation increase is attributed to the cell over-potential resistance (mainly the Rct) variation increase. Key words: lithium-ion battery; cell-to-cell uniformity; low temperature discharge behavior; electrochemical impedance spectroscopy; sorting method 锂离子电池低温放电性能及电池间一致性 英文 张剑波 黄 俊 陈璐凡 李 哲 清华大学 汽车安全与节能国家重点实验室 北京 184 中国 摘 要 用实验方法研究了锂离子电池在低温下的放电性能以及电池间一致性 在不同温度下 测量 了多节 1865 型号的锂离子电池的恒流放电与电化学阻抗谱 EIS 当环境温度从 降至 2 时 4 节电池的平均容量降低了 58.4% 而容量的标准方差增大了6 倍 EIS 结果表明 降低环境温度 会明显增大电池的阻抗 特别是电荷转移阻抗 (RCT) 同时 电池间的阻抗差异也被放大 15 节电池 的统计结果表明 电池放电容量与其阻抗之间存在线性关系 因此 低温下电池容量方差的增大是由 于电池阻抗方差的增大引起的 而其中 电荷转移阻抗 (RCT) 起了主要作用 关键词 锂离子电池 电池一致性 低温放电性能 电化学阻抗谱 电池分选方法 中图分类号 TM 911 文献标识码 A DOI: /j.issn 收稿日期 / Received 基金项目 / Supported by 国家自然科学基金资助项目 (51278, ) 第一作者 / First author 张剑波 1967 男 汉 河南 教授 jbzhang@mail.tsinghua.edu.cn 第二作者 / Second author 黄俊 1989 男 汉 湖南 博士研究生 huangjun12@mails.tsinghua.edu.cn.

2 392 J Automotive Safety and Energy 214, Vol. 5 No. 4 Introduction Traction battery pack for automotive application consists of hundreds or even thousands of lithium-ion cells connected in serial or parallel. It is found in electric vehicle demonstration program that the life of the pack is significantly shorter than that of its composing cells [1]. This is caused by the cell-to-cell non-uniformity and its evolution during the usage. In addition, the cell-to-cell non-uniformity is thought to deteriorate in low temperatures. In this study, the discharge behavior and evolution of the cellto-cell variations at low temperatures are investigated. In the literature review section, open literature of low temperature performance and cell to cell non-uniformity are reviewed. In the experimental section, cell specifications and details of experimental design are introduced. In the results and discussion section, the performance decay and the deterioration of cell-to-cell uniformity during the constant current discharge tests at low temperatures are elaborated. Based on the results of the Electrochemical Impedance Spectroscopy (EIS/ 电化学阻抗 ) technique, the performance decay is attributed to the increased over-potential. The deterioration in cell-tocell uniformity is quantitatively explained by correlating the discharge capacity with the over-potential resistance, for which the charge transfer resistance makes a dominating contribution. In addition, the voltage recovery observed during discharge at low temperatures is explained using a thermal-electrochemically coupled model of the battery. The predictions are substantiated with experimental measurement. 1 Literature Review Much efforts have been concentrated on understanding the origins and the development of the cell-to-cell nonuniformity and the ways to suppress it [2-8]. To understand the origins of the cell-to-cell variations in terms of performance, Dubarry et al. conducted a statistical and electrochemical analysis of the performance of 1 Li-ion cells at the room temperature, and then categorized the origins into the thermodynamic and the kinetic aspects [2]. Three critical and independent attributes, namely the amount of active materials, the polarization resistance, and the localized kinetic factors, were derived to address cell-to-cell non-uniformity. In a latter study [3], they took into account the cell-to-cell variations in a battery module model (three Li-ion batteries in series) based on an equivalent electric circuit model. It was reported that an improved accuracy was achieved in the prediction of the module performance by considering the cellto-cell variations. Besides the variation in performance, Paul et al. [4] investigated the variation in ageing in a battery system consisted of 96 lithium-ion cells during a cycle life test. Discrepancies in the ageing state of different cells, such as the capacity and internal resistance, in the battery system were detected and ascribed to the cell-to-cell variations in cell loading as a consequence of temperature and SOC non-uniformity. Furthermore, a simulation approach, based on a thermal-electrical ageing model of the entire battery system and the Monte Carlo method, was introduced to predict the life of the battery system. Santhanagopalan and White [5] presented a quantitative analysis on the impact of material uncertainties on the initial cellto-cell variations using an impedance model. The relative importance of uncertainties in different component materials was compared. In addition, a procedure setting quality control criterions for the various materials in cells was proposed, which is able to reduce the cell-to-cell variations while preventing excessive increase in manufacturing cost to meet the high demands on cell uniformity. It was also reported that if nonuniform cells were left in use without any control, severe decrease of the energy storage capacity would occur quite soon [7]. Therefore, numerous dissipative and nondissipative charge balancing schemes and circuits have been proposed to suppress the evolution of the initial cell-to-cell variations [8]. Electric vehicles are required to function in subzero environment. For example, it should be able to charge at - 3 and survive at - 46 [9]. As shown Table 1, the factors that result in poor low temperature performance have been widely investigated. Both material and operational approaches have been studied to improve the low temperature performance, as shown in Table 2. However, all the previous works focused on the low temperature performance of a single cell, little study has been found to address the effect of the temperature on the cell-to-cell uniformity at low temperatures. Table 1 Limiting Factors of the Low Temperature Performance Location Limiting factor Ref. Electrodes Solid electrolyte interface (SEI) Electrolyte Slow Li diffusion through the bulk of active material particles Sluggish electrokinetics and substantially increased charge-transfer resistance at the electrolyte-electrode interface Huang, et al. (2) [1] Zhang, et al. (22) [11] Ji, et al. (213) [12] Nagasubramanian (21) [13] Zhang, et al. (23) [14] Jow, et al. (27) [15] High resistance of SEI film Wang, et al. (22) [16] Low diffusivity of Li-ion in electrolyte Low ionic conductivity of electrolyte Ji, et al. (213) [17] Shiao, et al. (2) [18] Plichta and Behl. (2) [19]

3 ZHANG Jianbo, et al: Discharge behavior and uniformity of lithium-ion batteries at low temperatures 393 Table 2 Efforts to Improve the Low Temperature Performance Table 4 Experimental Details Test Item Value Aspect Effort Ref. New/modified battery materials Electrode Electrolyte Nanostructure electrodes [19] Surface-coating [2] Composition modification [21-] Constant current discharge tests Temperature /,, 1, 2 Discharge current / A 2. Initial state at Mode Fully charged using CC-CV. Galvanostatically Optimized battery design Preheating strategies 2 Experimental Optimizing the electrode thickness, electrode porosity, electrolyte concentration and particle size [12] Internal heating [27-28] External heating [26] Fifteen 1865 cells were purchased from a commercial battery vendor and the cell specifications are shown in Table 3. Before the tests, all the cells were subjected to five conditioning cycles using the manufacture s recommended Constant Current Constant Voltage (CC-CV) algorithm, that is, during charging, the cells were charged to 4.2 V with a constant current (1 C), then kept at this constant voltage until the current decreased to 1/1 C, during discharge, the cells were discharged to 3. V with a constant current (1 C). A Maccor Series 4 system was used to charge/discharge these cells in the conditioning cycles and subsequent tests, and an environment chamber GDJW-2 (Yashilin, China) was used to provide constant temperature environment. Table 3 Specifications of the Experimental Cells Model Cathode material Capacity Mass Internal resistance Nominal voltage NCM1865 NCM material 2.2 Ah 45 g 6 mω 3.6 V 2.1 Constant Current Discharge Test As shown in Table 4, the constant current discharge tests of four cells were conducted at four different temperatures:,, - 1, - 2, individually. Before the discharge tests at each temperature, the cells were adjusted to fully-charged state at using the CC-CV profile, then the chamber was tuned to the specified temperature. After a rest stage of 1 h to stabilize the electrochemical and the thermal state of the cells, the cells were discharged to 3. V with a constant current of 2 A. In addition, in order to validate the linear relationship between the capacity and the overpotential resistance in section 3.3.3, 15 cells of the same type were discharged at - 2 with three current rates:.2,.3,.5 C. EIS tests 2.2 EIS Test Frequency range / Hz 1-2 ~1 4 Data points(1 points per decade) 61 Amplitude(.1 C) / ma 2 SOC / % 1, 75, 5,, Temperature /,, 1, 2 EIS tests of four cells were performed on an Autolab PGSTAT32N impedance analyzer (Eco Chemie, Netherland) with the temperature controlled. The EIS of each cell was measured under a sinusoidal excitation of.2 A amplitude over the frequency range of Hz at five SOCs and four temperatures as shown in Table 4. It is worth mentioning that all the SOCs were regulated at with a current of 2 A, and all the EIS tests were conducted after a rest interval of 1 h for stabilization. The collected EIS date was analyzed using ZSimpWin software. 3 Results and Discussion 3.1 Performance Decay and Deterioration of Cellto-Cell Uniformity 1) Effect of temperature on the discharge curve Fig. 1 shows the results of the constant current discharge tests of four cells at four temperatures. Several characteristics of the discharge behaviors under different temperatures are found: Voltage / V θ/ Diacharge current 2 A Capacity / Ah Fig. 1 The Discharge Curves of Four Cells at Four Different Temperatures

4 J Automotive Safety and Energy 2.5 b) The discharge curves become more and more dispersed when the temperature decreases, which indicates a deterioration of the cell-to-cell uniformity at low temperatures; 2. c) The discharge curves at lower temperatures are located at lower voltage region, which implies that the overpotential resistances are larger at lower temperatures; Cav / Ah a) Smaller capacities and poorer performance are found at lower temperatures; Fig. 2 shows the capacities of the four cells at four temperatures. Capacity / Ah ) Effect of temperature on the cell performance and cell-tocell uniformity d) At -2, all the discharge curves exhibit a voltage recovery during the early stage of discharge , Vol. 5 No. 4 σ c / mah θ / Fig. 3 The Change of the Average Capacity and its Standard Deviation with the Temperature temperature decreases, while the Cav decreases severely. Quantitatively, the δc at 2 increases 6.6 times compared to its value at, which reveals that the cell-to-cell uniformity is deteriorated at low temperatures. The underlying causes are discussed below using EIS method. cell 1 cell 2 cell 3 cell Exploring the Causes Using the EIS 1. 1) The SOC and temperature dependency of the EIS and discussions on the origins of the poor performance at low temperatures.5 Typical impedance spectrums in the range of 1 mhz to 1 khz at two SOCs and four temperatures are shown in Fig. 4. Fig θ / The Temperature Dependency of the Cell Capacity At and 1, the Li-ion cells retains, averagely, 77.7% and 57.5% of the capacity measured at, respectively. However, the ratio declines to 41.6% at 2. This observation is similar to those reported previously [11]. The performance decay at low temperatures is associated with the combined effect of the following factors: low electrolyte ionic conductivity, poor kinetics of charge transfer at electrolyteelectrode interface, increased Solid/Electrolyte Interphase (SEI / 固体电解质界面 ) film resistance, and slow Li-ion diffusion process in the electrolyte, through the SEI film and in the bulk of active material particles [12]. A separation and comparison of these rate-limiting effects is presented in the later section 3.2 using EIS method. Another observation from Fig. 2 is the dispersion of the capacities at low temperatures. The difference between the maximum and minimum value of capacity, denoted as Cmax Cmin, at 2 is 6 times larger than that at. The notion of standard deviation was adopted here to describe the cell-to-cell variations in terms of capacity, as shown in Fig. 3, where Cav denotes the average capacity, and δc for the capacity standard deviation. According to Fig. 3, the δc increases significantly when the The overall shape of the Nyquist plots in Fig. 4 is composed of three sections [28]: Section 1: the straight line at very high frequencies, which is ascribed to the inductive behavior caused by inductive reactance of metallic elements in the cell and connecting wires; Section 2: several depressed semicircles at middle frequencies. Generally, the first semicircle is associated with the SEI film. The second semicircle represents the charge transfer process at the electrolyte-electrode interface; Section 3: the oblique lines at very low frequencies, which is related to the diffusion processes in the electrodes. Fig. 4 reveals that the EIS of this cell shrinks in both the real and the imaginary dimensions with the temperature increment. Besides, the EIS results at low temperatures show some interesting structural changes as compared with the ones at higher temperatures. One can see that both at 1 and 2, three semicircles appear in the EIS of % SOC at the middle frequencies, and the oblique lines at very low frequencies are almost diminished. These findings are similar with the results in Ref. [29], in which the authors lowered the temperature to 2 to increase the EIS. According to Ref. [29], the three semicircles from high to low frequency were ascribed to the SEI film, the charge transfer process of the anode, and the charge transfer process of the cathode, respectively. It was reported that the separation of these

5 395 ZHANG Jianbo, et al: Discharge behavior and uniformity of lithium-ion batteries at low temperatures θ / Z /Ω -Z /Ω Z /Ω θ / Z /Ω 2. (a) SOC = % (b) SOC = 1% Fig. 4 Typical Impedance Spectrum at a Series of Temperatures (Results of Only One Cell are Shown, Z and Z Represent the Real and Imaginary Part of Impedance, Respectively) three semicircles was due to the diversification of the time constants of each process when the temperature decreased [29]. In addition, since the characteristic frequency of the diffusion process shifts to lower values outside the preset frequency range, the oblique line corresponding to the diffusion process finally vanishes in the measured spectrum. However, at a SOC of 1%, the semicircles are overlapped and only two of them can be detected at all the test temperatures including 2. Therefore, it can be inferred that a near-empty charged state is more favorable for differentiating the responses of each process than a fully-charged state. This deduction is in consistency with the results in Ref. [29]. Fig. 5 presents the SOC dependency of the EIS at. When the SOC increases from % to 75%, the spectrum shrinks in both dimensions successively. However, as the SOC further rises to 1%, the size of impedance spectrum is enlarged instead as compared with the one of 75% SOC. This phenomenon is also observed at other temperatures and is consistent with Ref. [28]. The causes are discussed below based on the analysis of the SOC dependency of each semicircle. 15 SOC / % 1 -Z / mω θ= Fig. 5 Two equivalent circuits based on the circuits proposed in Ref. [29] and [3] are shown in Fig. 6, with the elements defined in Ref. [29] and [3]. The equivalent circuit (a) was employed to fit the EIS results showing two semicircles, while the other one was applied to fit the EIS results showing three semicircles occurred at extreme situation, for instance, 2 and % SOC. The goodness of the fit is confirmed by comparison between the simulation and measurement both in Nyquist plot and Bode plot. The fitted parameters, including the Ohmic resistance Rs, the SEI film resistance RSEI, and the charge transfer resistance Rct, are plotted in Fig. 7 as a function of temperature and SOC (where L accounts for the inductive loop, Rs, RSEI, Rct are the Ohmic resistance, SEI film resistance and charge transfer resistance, separately. CPE (constant phase element) represents the capacitance, and W is for diffusion effect). -5 in the impedance spectrum between different SOCs is found on the second semicircle, which implies that the charge transfer process is closely correlated to the SOC. To be specific, the charge transfer resistance is larger at lower SOC in the SOC range of % to 75%. Contrarily, it increases when the SOC rises from 75% to 1%. The turning point between 75% and 1% SOC is considered to be correlated with the sharp increase of the charge transfer resistance at the anode. The anode is fully-lithiated when the SOC of the whole cell equals 1%, at this circumstance, its charge transfer resistance will increase remarkably [11]. Since the impedance of the Li-ion cell is the sum of the contributions from cathode and anode electrode, therefore, the impedance of 1% SOC exceeds the one of 75% SOC. 1 2 Z /mω 3 4 The Effect of the SOC on the EIS of Li-Ion Cells The first semicircle shows no significant SOC dependency, that is, the process corresponding to the SEI film is almost irrelevant to the SOC. Nevertheless, a significant discrepancy 1) As shown in Fig. 7a, the Ohmic resistance, Rs at all SOCs increases slightly when the temperature decreases. However, the SOC dependency of the Rs is not a monotonic function. The maximum and minimum value of the Rs are found at % and 1% SOC at most temperatures, respectively. 2) With regard to the SEI film resistance, RSEI, one can see from Fig. 7b that RSEI also increases when the temperature decreases. An approximately linear relationship can be detected between

6 396 J Automotive Safety and Energy 214, Vol. 5 No. 4 CPE 1 CPE 2 CPE 1 CPE 2 CPE 3 L R Ω L R Ω RSEI R ct W R SEI R ct,1 R ct,2 W (a) with two semicircles (b) with three semicircles Fig. 6 Equivalent Circuits Used in This Paper: Circuit for the EIS with 2 and 3 Semicircles. R s / mω SOC / % R SEI / mω SOC / % θ/ θ/ (a) Ohmic resistance (b) SEI film resistance R ct / Ω SOC / % Resistance fraction R ct R S.5.2 R SEI θ/ θ/ 2 3 (c) Charge transfer resistance (d) Corresponding fraction of three resistances Fig. 7 The Resistances and Its Fraction as a Function of the Temperature at Various SOCs R SEI and the temperature, and the correlation is more significant as compared with R s. 3) The charge transfer resistance, R ct follows an exponential relationship with respect to the temperature, which can be interpreted by the rate law [31]. 4) In Fig. 7d, the five lines for certain resistance are corresponding to five SOCs as in Fig.7c, the resistance fraction of the above three resistances, is defined as the ratio between a specified resistance (R s, R SEI or R ct ) and the sum of the three resistances. (The five lines in Fig.6d for certain resistance are corresponding to five SOCs as in Fig.7c.) Fig. 7d captures the most significant feature that the fraction of R ct goes up quickly as the temperature decreases, and approaches.9 at - 2. On the contrary, the fraction of R s and R SEI keep descending with respect to the decreasing temperature. As a result, R ct gradually becomes dominating at lower temperatures, whereas, at, R s holds the largest fraction of 6% among the overall resistance. So far, one can find that the poor performance of the Liion cells at low temperatures mainly originates from the substantial rising of R ct. Generally, a high R ct corresponds to a sluggish kinetics of the charge transfer process. According to Ogumi [31], the charge transfer process can be further separated into several steps: the transport, adsorption, de-solvation of

7 ZHANG Jianbo, et al: Discharge behavior and uniformity of lithium-ion batteries at low temperatures 397 the solvated-li +, followed by the diffusion of the Li + in the SEI film, the Li + + e - Li reaction at the electrolyte-electrode interface, and then the diffusion of Li-ions in the electrode. For the case of low temperature, Zhang et al. [11] contended that the Li-ions diffusion in graphite is the limiting one among the above steps for a Li/graphite cell. Consistently, Dokko et al..8 detected that there exists a close correlation between the R ct and the apparent diffusivity of Li-ions in the particles of electrode [32]. 2) The cell-to-cell variations in terms of the EIS The EIS of four cells at 5% SOC are displayed in Fig. 8 as a function of the temperature. 2 -Z / Ω Z / mω Z / Ω (a) overview Z / mω (b) detail view Fig. 8 The EIS at 5% SOC of Four Cells at Different Temperatures One can see that the EIS becomes more dispersed at lower temperatures, that is, the cell-to-cell uniformity of the EIS is deteriorated at lower temperatures. Specifically, the ohmic resistances, R s, of the four cells, denoted as the intercepts of the EIS curves with the horizontal axis, are approximately identical at each temperature point, and similarly, the SEI film resistances of the four cells are quite close since the first semicircles of each curve are almost overlapped. In contrast, the second semicircles of four cells varies remarkably from each other, especially at lower temperatures. Therefore, the predominant origin of the cell-to-cell variations in terms of the EIS can be ascribed to the R ct, that is, the charge transfer process during the electrochemical reactions. After fitting the EIS result of each cell using the equivalent circuits in Fig. 6, the standard deviation of three fitted resistances, i.e., the R s, R SEI and R ct, are shown in Fig. 9a as a function of the SOC and temperature. The result at 1% SOC and each temperature is plotted in Fig. 9b. It is noticed that the standard deviation of the Rct increases steeply when the temperature decreases, while that of the R s and R SEI almost keep constant with respect to the temperature. Meanwhile, the standard deviation of the R ct has a greater magnitude than the other two, especially at lower temperatures. Then, it is concluded that the discrepancy in R ct is not only the most temperature-sensitive one among the discrepancies in the three resistances, but it also contributes the most to the cell-to-cell variations in terms of the EIS. Another important implication from Fig. 9 is a more-effective sorting technique for the cells in lithium-ion battery packs. The EIS has been recognized as a powerful technique to sort the lithium-ion cells while revealing the origins of cell variations [4]. It has been proven in this study that the cell-to-cell variations 5 Standart deviration / Ω SOC 1-2 R CT R SEI R S 2 θ/ Standard deviration / mω θ/ R CT R SEI R S (a) overview at different SOCs (b) detail view at 1% SOC Fig. 9 The Standard Deviation of Resistances at Different Temperatures and SOCs

8 398 J Automotive Safety and Energy 214, Vol. 5 No. 4 in terms of EIS will be magnified at low temperatures and low SOCs. Therefore, it is recommended to conduct the EIS measurements at such conditions to provide a higher resolution for the cell sorting. a) The correlation between the capacity and the overpotential resistance. In above sections, we have revealed the deterioration of the cell-to-cell uniformity in capacity at low temperatures using discharge tests, and analyzed the underlying factors of this uniformity deterioration using the EIS results. Here, we try to correlate the capacity with the overpotential resistance quantitatively based on a simple deduction using the overpotential resistance and the measured SOC-OCV curve. In the constant current discharge of Li-ion cells, the discharge process will be terminated at the moment when the terminal voltage reaches the preset lower limit (3. V in this study). The voltage at this moment can be expressed as follows:, (1) here V min is the lower voltage limit, OCV the open-circuit voltage, R the overpotential resistance and I the discharge current. The OCV curve of the Li-ion cell used in this study at - 2 can be measured at the end of a 2 h rest period after a discharge process with a current of 1 A. This method was proposed in Ref. [33]. The obtained OCV curve is shown in Fig. 1. OCV / V SOC Fig. 1 The OCV Curve of the Li-Ion Cell at -2 An approximately linear relationship between the OCV and the SOC is established, that is:, (2) here c 1 and c 2 are two fitting coefficients and the SOC is defined in terms of capacity as follows:, (3) here C d denotes the charge discharged from the cell and C n is the nominal capacity at -2. Combining the Eq. (1)-(3), we can deduce the following equation which correlates the discharge capacity with the overpotential resistance:. (4) In Eq. (4), only the C d and R differ from cell to cell, while the other variables keep constant among different cells of the same chemistry. To validate the linear correlation between C d and R shown in Eq. (4), constant current discharge tests with three current levels, i.e.,.44 A,.66 A and 1.1 A, were conducted on 15 commercial 1865 Li-ion cells at - 2. The discharge capacity of each cell at each current level was measured, and the overpotential resistance of each cell was calculated during the rest period using Eq. (5):. (5) here V(t c ) - V min denotes the voltage change during the rest period of t c after the discharge process. The overpotential resistance is consisted of Ohmic resistance, the SEI film resistance, the charge transfer resistance, and diffusion resistance. The first three kinds of resistance can be obtained from the EIS results, and the diffusion resistance depends on the t c. As a result, a series of t c in the range of 5 s to 1 s were applied in the study. As shown in Fig. 11, a linear correlation between the discharge capacity C d and the overpotential resistance R is proven, and this correlation holds for all the evaluated discharge currents and t c. The correlation expressed in Eq.(4) is applicable to the battery systems with a linear SOC-OCV curve, or more generally, to those batteries whose SOC-OCV curve can be locally linearized in the final stage of discharge. Overpotential resistance / Ω A.66 A.44 A t c / s Capacity / Ah Fig. 11 The Correlation between the Discharge Capacity and the Overpotential Resistance Based on Eq. (4), the relationship between the cell-to-cell variations of capacity and that of the overpotential resistance is further deduced as:. (6) Eq. (6) indicates that the cell-to-cell variation of capacity is linearly correlated with that of the overpotential resistance. As 1 s

9 399 ZHANG Jianbo, et al: Discharge behavior and uniformity of lithium-ion batteries at low temperatures stated previously, the Rct dominates the overpotential resistance at low temperatures. Finally, it can be concluded that the deterioration of the cell-to-cell uniformity in terms of capacity is mainly ascribed to the enlarged variation of Rct from cell to cell at low temperatures. b) Voltage recovery during discharge at low temperatures The simulated Vt captures the voltage recovery at the early stage of discharge. In a word, the voltage recovery can be ascribed to the more-rapid temperature rising in the early discharge stage at 2. However, it must be admitted that a more sophisticated electrochemical-thermal coupled model is needed to simulate the experimental results with higher precision [12]. In closing, the interesting voltage recovery phenomenon during the early stage of discharge at low temperatures is explained in more details. This phenomenon was also detected by Ji et al. recently [12]. A simple voltage model considering the interactions between temperature and voltage is applied in this study to interpret the voltage recovery phenomenon. Overpotential resistance / Ω.4 Similar to Eq. (1), the terminal voltage of the Li-ion cell during discharge is expressed as:. (7) According to Eq. (7), the Vt is a function of the SOC and temperature T. To explore the causes of voltage fluctuation, the temperature history during the whole discharge process has been investigated in a discharge test at a current of 2 A at 2. Two temperatures on the cell surface were monitored, and the temperatures at three different locations in the environment chamber were also measured as the baseline. As shown in Fig. 12, the cell temperatures increases rapidly at the early stage of discharge, and then the rising trend slows down when the DOD approaches around.3. A total rise of 8 is observed when the discharge test is terminated. As shown in Fig.7, all the three kinds of impedance follow a negative correlation with the T. Therefore, the temperature rising will lead to a decrease of R, and further induces the voltage recovery phenomenon shortly after the discharge is started. 5 1 Duration of discharge / s Figure The Interpolated Overpotential Resistance during Discharge at Voltage / V 4. Simulation Experimental 5 1 Duration of discharge / s 15 cell temp.1-1 θ / cell temp Fig. 12 Figure 14 The Comparison between Simulated and Experimental Terminal Voltage of the Cell during Discharging at 2 with a Current of 2 A. ambient temp Depth of discharge.8 1 The Cell Temperature and Ambient Temperature Measured during Discharge at 2 Based on the EIS tests and the measured T during discharge, the R was linearly interpolated and shown in Fig. 13. Combining the OCV curve and the R, the Vt during discharge was simulated based on Eq. (7), the simulated results were compared with the experimental results, as shown in Fig. 14. Conclusion In this study, the discharge behavior and cell-to-cell variation were examined in terms of capacity and impedance at low temperatures. Analysis of the discharge tests showed that: (1) the cell capacity was reduced severely when the temperature decreased; (2) the standard deviation of the capacity of 4 cells, σc, increased steeply; (3) a voltage recovery in the early stage of discharge was observed and attributed to the self-heating due to the large internal resistance at low temperatures. From the EIS tests, it is found that the Rs, RSEI and especially Rct increased when lowering the temperature. The standard deviation of the Rct increased steeply when the temperature decreased, however, that of the Rs and RSEI was less sensitive to the temperature change. Consequently, it is concluded that

10 4 J Automotive Safety and Energy 214, Vol. 5 No. 4 the variation of R ct dominated the cell-to-cell nonuniformity at low temperatures. Furthermore, a linear correlation between the discharge capacity and the overpotential resistance was established by varying the discharge current rate and the rest time. This correlation quantitatively disclosed that the deterioration of the cell-to-cell capacity uniformity at low temperatures was a consequence of the enlarged variation of the overpotential resistance, which was mainly the charge transfer resistance R ct. As a potential application of the result in this study, performing the EIS tests at low temperatures and low SOCs is recommended as a powerful sorting method for the lithium-ion cells due to its superiority of amplifying the nonuniformity of cells. REFERNCES / ( 参考文献 ) [1] Burke A F. cycle life considerations for batteries in electric and hybrid vehicles [R]. SAE Tech Paper, , [2] Dubarry M, Vuillaume N, Liaw B Y. 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