- Email: [email protected]
Accelerated cycle life testing and capacity degradation modeling of LiCoO2-graphite cells
Journal of Power Sources 435 (2019) 226830
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Accelerated cycle life testing and capacity degradation modeling of LiCoO2-graphite cells Weiping Diao *, Saurabh Saxena, Michael Pecht Center for Advanced Life Cycle Engineering (CALCE), University of Maryland, College Park, MD, 20742, USA
H I G H L I G H T S
� Conducted a large design of experiment with 192 LiCoO2-based cells and 24 testing conditions. � Analyzed effects of stress factors including temperature, discharge C-rates and charge cut-off C-rates along with possible degradation mechanisms. � Determined optimal accelerated testing conditions. � Developed an empirical accelerated degradation model that can describe the two-stage capacity fade process. A R T I C L E I N F O
A B S T R A C T
Keywords: Accelerated cycle life testing Capacity degradation model Temperature Discharge C-Rate Charge cut-off C-Rate Knee point
Accelerated cycle life testing of lithium-ion batteries is conducted as a means to assess whether a battery will meet its life cycle requirements. This paper presents a study to identify optimal accelerated cycle testing con ditions for LiCoO2-graphite cells. A full factorial design of experiment with three stress factors—ambient tem perature (10 � C, 25 � C, 45 � C, 60 � C), discharge current rate (C-rate, 0.7C, 1C, 2C), and charge cut-off C-rate (C/5, C/40)—is used to study the effects of these stress factors on battery capacity fade and to obtain the data necessary for decision making. An empirical accelerated degradation model is then developed to capture the characteristics of the two-stage capacity degradation process, along with an accelerated test planning approach.
1. Introduction Commercialization of lithium-ion batteries has enabled applications ranging from portable consumer devices to high-power electric vehicles to become commonplace [1]. However, one of the key concerns asso ciated with lithium-ion battery technology is performance degradation during usage and storage. As a critical performance metric, the capacity retention of lithium-ion batteries is often used to determine if they have reached the end of life (EOL), usually defined as a 20% reduction in the initial or rated capacity [2]. Lithium-ion batteries with unsatisfactory lifetimes can significantly reduce customer satisfaction and make products of little use. In order to characterize the capacity degradation trend, companies test batteries according to the performance requirements and the life expectation for their targeted application. While for most cases the test purpose is to determine the number of cycles to EOL, there are instances where the amount of capacity fade for a particular number of cycles or the full capacity fade profiles of the batteries are required. When batteries with a
lifetime of 1000 cycles are tested continuously under normal conditions (e.g., 25 � C, 0.5C), each cycle takes about 4.5 h and nearly 6 months pass until the test is finished. Accelerated cycle life testing is thus needed to quickly precipitate degradation by increasing levels of stress factors. Historically, accelerated cycle life testing of lithium-ion batteries has been conducted by elevating the ambient temperature [3–6]. High temperature accelerates the kinetics of the solid electrolyte interphase (SEI) layer on the graphite negative anode as a parasitic side electro chemical reaction [7,8]. However, the kinds of battery degradation mechanisms are dependent on the temperature. For example, Waldmann et al. [9] evaluated the effect of different temperatures on the electrode polarizations of lithium-ion cells with graphite anode and found that low temperature (T < 25 � C) accelerates lithium dendrite growth, whereas high temperature (T > 25 � C) advances SEI layer growth. Furthermore, the characteristics of battery components also impose temperature limits on the operation as well as testing. The thermal stability of the typical electrolyte salts (LiPF6), organic solvent (ethylene carbonate, dimethyl carbonate ethyl methyl carbonate, propylene carbonate, etc.)
* Corresponding author. E-mail addresses: [email protected] (W. Diao), [email protected] (S. Saxena), [email protected] (M. Pecht). https://doi.org/10.1016/j.jpowsour.2019.226830 Received 16 April 2019; Received in revised form 11 June 2019; Accepted 28 June 2019 Available online 2 July 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
constrains the upper operating temperature limit, often between 60 � C and 70 � C [10]. At temperatures lower than the liquidus temperature (usually above 20 � C for most electrolyte compositions), solvent pre cipitates and the electrolyte is kinetically unstable [10]. Besides temperature, charge/discharge C-rate [11,12], state of charge (SOC) operation rang [13,14], and combinations of these stress factors with temperature can also be used to accelerate the degradation mechanisms of lithium-ion batteries. Increasing the charge/discharge C-rate reduces the time required to conduct a charge/discharge cycle and affects capacity fade rate over cycles. High C-rate can cause lithium to be crowded in the outer shell of the electrode particle [15]. When the resulting mechanical stress of the particle surpasses the yield stress of the material [16], particle cracking occurs and causes further structural integrity loss including contact loss between active material particles and between active material and current collectors [17,18]. The amount of particle cracking accumulates with cycling. High C-rate also accounts for the excess temperature increase of the cell as compared to the ambient temperature [19,20]. At high charge C-rate or low temperature, lithium dendrite growth is accelerated because the high overpotential across the anode resistance decreases the anode potential to a level below 0.0 V (vs Li/Liþ) where lithium preferentially plates onto the graphite anode rather than intercalating into the graphite [21]. These mechanisms should be considered when determining the ranges of C-rate for accelerated testing. Numerous studies have reported on the effect of mean SOC and ΔSOC on the battery degradation. Ecker et al. [22] found that Li (NiMnCo)O2 based cells cycled with ΔSOC ¼ 10% experienced the most severe degradation cycled at [5–15%] and [90–100%], and cells cycled with mean SOC ¼ 50% had the highest degradation rate at a full SOC operation range (ΔSOC ¼ 100%). On the other hand, Wang et al. [19] did not observe any effect for LiFePO4-based cells. Saxena et al. [23] tested LiCoO2-based cells with different mean SOC and ΔSOC, and concluded that for the first 500 equivalent full cycles mean SOC is found to have a major effect on the capacity fade of cells as compared to ΔSOC, whereas towards the end of the testing (600–800 equivalent cycles) ΔSOC becomes the major factor affecting the capacity loss rate of the cells. Gao et al. [14] tested Li(NiMnCo)O2-based cells at five non-overlapping SOC operation ranges (ΔSOC ¼ 20%) as well as at a full range. They showed that the sum of the capacity degradation in each SOC range was not equal to that gained at a full SOC range. Features from the incremental capacity analysis (ICA) of cells at each SOC operation range were then extracted and mapped to the ICA of cells cycled at full SOC range by developing a model. The SOC operation range is not a directly controllable factor. A predetermined SOC operation range is often obtained by controlling the ratio of the amount of charge drawn from a battery at a certain SOC level to the battery’s capacity [24]. Because the actual available capacity varies with loading conditions, including temperature and C-rate, and decreases over cycles, the same values of SOC operation range at different loading conditions and health states are not essentially equivalent. The charge cut-off voltage and charge cut-off current during the constant voltage part of the charging, which determine the upper limit of SOC operation range, do not have controllability issues and can also be considered as stress factors [25]. Hence, charge cut-off C-rate has been included as a stress variable in this study rather than SOC operation range, and its effects on accelerating the battery cycle life testing have been investigated. With the accelerated cycling test, an accelerated degradation model as a function of cycles and stress factors is needed to extrapolate testing data at higher stress levels to predict the capacity fade under normal operating conditions. In terms of the cycle dependence, numerous empirical models have been developed, in which a power law rela tionship has been extensively used to model the square root dependence of capacity fade on time/cycles/accumulated Ah throughput [19,22,26, 27]. However, a multitude of cells with cathode chemistries such as LiCoO2 [28,29], Li(NiCoAl)O2 [30], and Li(NiMnCo)O2 [31] have
Table 1 Testing procedure in a charge/discharge cycle. Cycle stage
Profile
Charge
1st CCCV ① CC: 1.5C until voltage reaches 4.2 V ② CV: 4.2 V until current drops to 1C 5 min CC: 0.7C to 3.0 V 5 min
Rest Discharge Rest
2nd CCCV ③ CC: 1C until voltage reaches 4.4 V ④ CV: 4.4 V until current drops to C/40
shown two-stage degradation behaviors. Their capacity fade curves usually consist of a slow degradation stage followed by a fast degrada tion stage, with a distinct knee point in between. A double-exponent model has shown good performances in fitting these degradation curves [28,29,32], but none of these studies expanded this model to take into account the dependence of aging on any stress factor. In a two-term logarithm model developed by Yang et al. [31], a hyperparameter must be selected based on experience, and there is a strict limit for coefficients because only positive numbers have real logarithms, making the model impractical. This paper investigates the accelerated cycle life testing conditions for LiCoO2-graphite cells using three different stress factors. A full factorial design of experiment (DOE) has been conducted on 192 cells to statistically investigate the influence of the ambient temperature, discharge C-rate, charge cut-off C-rate, and their interactions on ca pacity fade over cycles. A qualitative analysis has been carried out to determine how these stress factors affect the capacity fade trend and accelerate the cycle life testing. Following this discussion, an empirical accelerated degradation model has been developed to describe the twostage degradation process and the effects of stress factors on capacity fade of lithium-ion batteries. This paper highlights the methodology of accelerated cycle life testing and modeling in exploration of the optimal accelerated testing conditions and acceleration factors. The effect of charge cut-off C-rate, individually or combined with other stress factors, has also not been studied so far by the research community to determine whether it can accelerate capacity fade. The remaining sections of this paper are as follows. Section 2 in troduces cell specifications and the design of experiment (DOE). Sec tions 3, 4, and 5 present the experimental results and discuss the effect of ambient temperature, discharge C-rate, and charge cut-off C-rate, respectively. Section 6 presents the methodology of model development and implementation. Section 7 provides the conclusions. 2. Design of experiment The DOE involved two types of tests: characterization tests and cycling tests. Characterization tests periodically determined the cell electrical parameters that provide a measure for performance degrada tion. Cycling tests exposed the cells to different operating conditions continuously, which can be represented by a cycling test matrix. For the pouch cells tested in the DOE, the major composition of the cathode, anode, and electrolyte was LiCoO2, graphite, and LiPF6-salt mixed with liquid organic solvent, respectively. The electrode layers of the cells were wound. The nominal capacity and operation voltage range were 3.36 Ah and 3.0–4.4 V, respectively. The maximum continuous current of these cells was 2C. The recommended operating temperature ranges for these cells during the charge/discharge process were 20–60 � C, and 0–50 � C, respectively. In the characterization test, the discharge capacity and electrical impedance spectroscopy (EIS) of cells at 100% SOC were measured after every 50 cycles of cycling test. The capacity testing procedure in a charge/discharge cycle is shown in Table 1, where the two constantcurrent/constant-voltage (CCCV) charging stages were recommended 2
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
25 � C, 45 � C, and 60 � C—were selected due to the considerable dendrite growth at temperatures lower than 10 � C even at normal charging Crates and the instability of the electrolyte at temperatures over 60 � C. Increasing the discharge C-rate can shorten the testing time per cycle, regardless of its effect on the capacity degradation. Most lithiumion batteries designed for consumer electronics have low power capa bility as compared to electric vehicle batteries, thus they are not allowed to be operated at high C-rates. With the maximum continuous C-rate of 2C and the rated discharge C-rate of 0.7C given in the battery manu facturer’s specifications, three stress levels of 0.7C, 1C, and 2C were selected. The charge cut-off C-rate determines the upper level of the SOC operation range and is easy to control. Two stress levels of C/5 and C/40 were set, of which C/40 was recommended in the battery manufac turer’s specifications. A charge cut-off C-rate of C/5 can significantly reduce the testing time per cycle. However, C/5 represents a lower stress level and may reduce the capacity degradation rate over cycles. Hence, an optimal charge cut-off C-rate for accelerated testing should provide a trade-off between these two opposite effects and achieve the maximum acceleration.
Fig. 1. Voltage profile during the manufacturer-recommended charge process. Table 2 Cycling test matrix. Charge cut-off C-rate C/5 C/40 C/5 C/40 C/5 C/40
Ambient temperature (� C)
Discharge C-rate
10
25
45
60
Test # 1 #2 #3 #4 #5 #6
#7 #8 #9 # 10 # 11 # 12
# # # # # #
# 19 # 20 # 21 # 22 # 23 # 24
13 14 15 16 17 18
3. Effect of ambient temperature
0.7C
Fig. 2 shows the capacity degradation curves at different tempera tures, where Ccut is the charge cut-off C-rate and Cdisch is the discharge Crate. In Fig. 2(a), the capacity degradation curves at 60 � C consist of two stages with a knee point occurring at around 250th cycle. The first stage, where the slopes of these curves decrease over cycles, is characterized by a moderate degradation rate and possibly relates to the steady SEI layer growth that consumes cyclable lithium [17]. SEI layer growth has been found to have an approximate square root dependency on the cycle number or time [11,19,27], which can be used to model this portion of the curve. However, starting from the 250th cycle, the capacity starts to decline rapidly. Mechanical degradation has been reported to primarily account for this behavior [17]. At this fast degradation stage, the loss of electrical contact between electrode particles as well as between particles and current collectors is getting much more severe, thus its effect on capacity loss is expected to far exceed the effect of steady SEI layer growth. A similar phenomenon is observed on the 60 � C degradation curve in Fig. 2(b). The EIS of cells tested under this condition was measured at 100% SOC to investigate the kinetics changes before and after the occurrence of knee points. On the EIS plot in Fig. 3, the intercept on the real axis at the high-frequency range represents the ohmic resistance of cells, the semi-circles at the middle-frequency range indicate the SEI layer characteristics and kinetics during the charge-transfer process, and the short tail at the low-frequency range is related to the kinetics during the mass-transfer process [33]. As shown in Fig. 3(a), the ohmic resis tance increases over cycles, and these semi-circles shift to the right. This
1C 2C
by the battery manufacturer. Fig. 1 shows the voltage profile of a fresh cell during the charge process. The purpose of reducing the charge Crate at the voltage range between 4.2 V and 4.4 V was to avoid lithium plating onto the anode surface. All the cells that underwent cycling tests were characterized at 25 � C using this capacity testing procedure. Data from two charge/discharge cycles were recorded in each characterization test, and the average values were calculated. The cycling test matrix is shown in Table 2. The 3 stress factors and a full factorial design resulted in 24 testing conditions. The numbers 1–24 in this table represent the condition IDs, and 8 cells were tested under each condition. The rationale behind this cycling test matrix was to choose suitable stress factors for acceleration and determine their boundaries in such a way that the major degradation mechanisms do not change. The ambient temperature has been recognized as a useful stress factor for accelerating cell degradation, because the side reactions inside the cell take place more rapidly at higher temperatures. However, as discussed in Section 1, the temperature range needs to be determined carefully since not all degradation mechanisms can be accelerated by elevating the temperature and excessively high temperature may induce new degradation mechanisms. Thus, 4 different temperatures—10 � C,
Fig. 2. Discharge capacity over cycles - effect of ambient temperature. 3
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 3. Electrical impedance spectroscopy of cells under testing condition #20 at 100% SOC.
Fig. 4. Discharge capacity and ohmic resistance over cycles - effect of discharge C-rate.
4
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 5. Discharge capacity over cycles - effect of charge cut-off C-rate.
reaction kinetics degradation will increase the overpotential of cells and accounts partially for the discharge capacity degradation. The amount of shift in EIS trajectories shift is most significant from the 150th cycle to the 200th cycle, which is consistent with the amount of discharge ca pacity change. Both the capacity fade curves in Fig. 2(b) and EIS plots in Fig. 3 show that variations among cells become larger after knee points. As shown in Fig. 3(b), an equivalent circuit model [34] was fitted to the average EIS data of the eight cells, where R1 is the ohmic resistance, R2 is the SEI resistance, R3 is the charge transfer resistance, CPE stands for constant phase element, W is the Warburg impedance related to diffusion process, and L is the inductance. R2 and CPE1 have a smaller time constant and thus will respond to higher frequencies as compared to R3 and CPE2 . The resistances in the equivalent circuit model were identified using “eissa1” EIS Analyser and are plotted in Fig. 3(b). It shows that the charge transfer resistance is the highest as compared to ohmic and SEI resistances, and these resistances increase over cycles. In Fig. 2(a) where the charge cut-off C-rate is C/5, the slopes of the 45 � C curves also decrease at first, then they keep nearly constant. The degradation curves at 25 � C and 10 � C present similar characteristics as the 45 � C curves but with a slower degradation rate, suggesting a consistent degradation mechanism. At the charge cut-off C-rate of C/40 as shown in Fig. 2(b), knee points are observed on the 45 � C degradation curve. It is interesting that an interaction of high temperature of 45 � C and higher charge cut-off current stress of C/40 precipitates knee point before the 600th cycle. The testing conditions at 45 � C and 60 � C act as accelerated ones, it is thus expected that cells will also show knee point behavior at normal operating conditions (25 � C, Cdisch ¼ 0.7C). Williard [28] and He et al. [29] tested LiCoO2-based batteries with different capacities at room temperature and observed that the capacity fade occurred in a near linear fashion followed by a pronounced reduction. At other discharge C-rates (1C, 2C), the degradation curves at different ambient temperatures show similar characteristics and the effect of ambient temperature on battery degradation did not change with the change in the discharge C-rate. Thus, these testing data have not been repeatedly plotted and discussed.
The ambient temperature can effectively accelerate the capacity degradation. At the testing condition of Ccut@C/40 and [email protected] when there is a 10% capacity fade, 100 cycles are needed for 60 � C and 600 cycles are needed for 25 � C, thus an acceleration factor of 6 can be gained at 60 � C. The effect of ambient temperature can be modeled to predict the capacity degradation trend at normal temperatures. 4. Effect of discharge C-rate Fig. 4 displays the capacity degradation curves at different discharge C-rates. As shown in Fig. 4(a)~(c), these curves almost overlap at different discharge C-rates. This result is unexpected since numerous papers have reported the significant effect of the discharge C-rate on capacity degradation rate of LiCoO2- [35] and LiFePO4- [19,36] based cells, although a few observed no effect on capacity degradation of Li (NiMnCo)O2- [13] based cells. In this study, the capacity degradation over cycles is found to be independent of the discharge C-rate in the range of C/7~2C at 10 � C–45 � C. The number of cycles when knee points occur at different discharge C-rates is around 550, as shown in Fig. 4(c) with the testing temperature of 45 � C. One possible explanation for the influence of discharge C-rate is that the batteries have been designed using such small electrode particle size that lithium in the particle maintains nearly a homogeneous distribution at different discharge C-rates and the induced stress does not exceed the yield point of the material. Hence, they can sustain this discharge C-rate range without experiencing par ticle crack [15]. However, at 60 � C, cells cycled at a discharge C-rate of 2C degrade much faster than those cycled at lower discharge C-rates. The C-rate can affect the battery temperature due to ohmic heating [37]. In the elec trolytes used in these cells, the salt LiPF6 will decompose over 70 � C [10], causing the conductivity of the electrolyte to decrease. Meanwhile, the chemical decomposition of electrolyte in SEI layer growth is highly accelerated at this temperature [9]. The gas generated from both ther mal and chemical decomposition can cause delamination of electrode 5
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 6. Discharge capacity over testing time - effect of charge cut-off C-rate.
layers and thus increase the ohmic resistance [38]. Fig. 4(e) plots the evolution of average ohmic resistance of cells in each condition (0.7C, 1C, 2C) up to 100 cycles. It shows that the ohmic resistance of cells cycled at 2C increases much faster than cells cycled at 0.7C and 1C. Considering Joule’s law, we hypothesized that the temperature in creases of cells at the 60 � C, 2C condition could have induced a signifi cant amount of electrolyte thermal decomposition, which is indicated by the large change in the ohmic resistance. At the charge cut-off C-rate of C/5, the capacity fade at each testing temperature is also independent of discharge C-rate, and the cycle numbers when knee points occur at 60 � C are almost the same for different discharge C-rates. Thus, these testing data have not been repeatedly analyzed. Since the discharge C-rate does not affect the capacity degradation over cycles, there is no need to model its effect. However, the testing discharge C-rate can be increased to 2C at 45 � C and 1C at 60 � C to reduce the testing time of each cycle.
degradation model. 6. Accelerated capacity degradation model Sections 4 and 5 showed that the discharge C-rate does not affect the capacity degradation over cycles and increasing the charge cut-off C-rate cannot accelerate the testing process, hence a capacity degradation model has been developed as a function of number of cycles and the stress factor of ambient temperature. The capacity data used for modeling has been normalized with the cells’ initial discharge capacity, and a nonlinear regression technique has been adopted in the modeling work. To start with, a capacity model as a function of number of cycles is needed to simulate the capacity degradation behaviors with knee points. However, the popular empirical model—single power law—as in Eq. (1) is not capable of fitting these degradation curves because it presents either an increasing or decreasing slope (K1 b1 *Nðb1 1Þ ) if b1 is not equal to 1.
5. Effect of charge cut-off C-rate
NDC1 ¼ 1
As shown in Fig. 5, the effect of the charge cut-off C-rate varies with the ambient temperature. At 10 � C and 25 � C, the capacity differences of cells using C/5 and C/40 at the 500th cycle are 2.13% and 2.76% of these cells’ average initial capacity, respectively, which suggests that charge cut-off C-rate had a minimal impact on capacity degradation. At 60 � C, the capacity difference at 100 cycles (before knee points occurred) is 1.57%, whereas this difference rises to 10.03% at 150 cycles (after knee points occurred). This result indicates that the charge cut-off C-rate of C/40 (higher ΔSOC) induces more stress at high temperature than it does at low temperature. Deshpande et al. [39,40] found that SEI layer growth is primarily caused by SEI layer fracture during electrode expansion at low charge C-rate where the stress in the graphite particles is trivial as compared to the fracture strength. Under this condition, they
K1 *N b1
(1)
where NDC is the normalized discharge capacity, N is the number of cycles, and K1, b1 are the model coefficients. To model the knee point behavior as shown in Fig. 2(b), one more power term is added to this model where the first term is used to simulate the slow degradation stage with the exponent less than 1, and the second power law term increases significantly after the knee points with the exponent larger than 1: NDC ¼ 1
K1 *N b1
K2 *N b2
(2)
The next step is to investigate how K1, b1 and K2, b2 change with ambient temperature to determine an appropriate accelerated model form and initial values for all coefficients in the accelerated model, and this step is all guided by experimental data. Because these two terms are dominant at different degradation stages and experimental data at 10 � C and 25 � C lack the fast degradation stage, this step is decomposed into two substeps. The first substep is to determine how temperature affects K1 * Nb1 using data from the slow degradation stage (all testing data at 10 � C and 25 � C, testing data in the first 550 cycles at 45 � C and first 100 cycles at 60 � C in Fig. 2(b)), using the model represented by Eq. (3). This model form and its derivatives have been widely used to describe ca pacity fade behaviors with a decreasing degradation rate. The coeffi cient b1 is independent of stress factors, and its initial value can be set to approximately 0.5 [19,20,22,26,27].
noted that the capacity loss is directly proportional to ðΔSOCÞ2 [40], and this proportion has a positive correlation with temperature. It is thus hypothesized that the interaction between temperature and charge cut-off C-rate is due to the greater SEI layer fracture at C/40 than that at C/5 when the temperature is increased to 60 � C. Although increasing the charge cut-off C-rate can reduce the testing time of each cycle, more cycles are needed for cells to have the same amount of capacity loss as lower charge cut-off C-rate especially at high temperature (60 � C). The favorable accelerated temperature testing condition at 60 � C requires 400 cycles for cells tested at C/5 to reach the failure threshold (80% threshold), almost twice the cycles for cells tested at C/40 to reach the failure threshold. Fig. 5(c) and (d) have been replotted as in Fig. 6(a) and (b) to compare the overall testing time using C/5 and C/40. This replotting demonstrates that the testing process cannot be accelerated by increasing the charge cut-off C-rate at 45 � C and 60 � C, thus this factor will not be incorporated into the accelerated
NDC1 ¼ 1
expðA * T þ BÞ*N b1
(3)
Using the curve fitting toolbox in Matlab, model coefficients in Eq. (3) can be determined. These coefficients serve as initial values when fitting all experimental data to the final accelerated model NDC ¼ fðN; 6
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
with the temperature, whereas b2 decreases linearly with the tempera ture. Fig. 7(a) shows that the fitted curves match well with the experi mental data with the R2 value of 0.9774. In Fig. 7(b)(c), the contribution of the first and second power law term is plotted. It shows that the first power law term is dominant at the degradation stage before knee point occurrence, whereas the second power law term increases fast and be comes dominant after knee point occurrence. The model applicability is further examined using the capacity degradation data of another type of lithium-ion cells. These cells had the same specifications as previous cells but contained polymer gel elec trolyte. They were tested at 60 � C, 45 � C, and 25 � C for about a month. Two discharge C-rates of 0.7C and 1.8C were chosen. There were 6 testing conditions with 3 cells in each. Cycling tests and characterization tests followed the same routine as described in Section 2. As shown in Fig. 8(a), at each testing temperature, the overlap of capacity degradation curves of these new batteries (solid lines) at different discharge C-rates indicates that the discharge C-rate also does not affect the capacity degradation rate with respect to cycles. In Fig. 8 (b), new batteries are compared with previous batteries at the same testing condition. The capacity degradation curves at 25 � C of new batteries followed the same trajectories as those of previous batteries, suggesting a great similarity between them. However, the testing data at 60 � C and 45 � C showed remarkably different trajectories without any knee point. Using the developed model form, coefficients have been recalibrated as in Eq. (7). As shown in Fig. 8(c), the fitted curves with an R2 value of 0.997 agree well with the experimental data.
Table 3 Model coefficients at different temperatures. Coefficients
10 � C
25 � C
45 � C
60 � C
K1 K2 b1 b2
0.000725 4.98E-59 0.774 18.14
0.0010 2.68E-44 0.774 13.83
0.0016 1.17E-24 0.774 8.09
0.0023 7.78E-15 0.774 3.78
TÞ. In the second substep, the contribution of the first term was sub tracted from the experimental data at 45 � C and 60 � C in Fig. 2(b), and what was left in the data was used to determine how coefficients in the second term vary with temperature. Experimental data has shown that the higher the temperature, the earlier the knee point occurs. The co efficient K2 is also assumed to vary exponentially with temperature as shown in Eq. (4). It is then found that the coefficient b2 needs to decrease with temperature increase to simulate the capacity fade trend. Thus, a linear model as shown in Eq. (5) is used to capture this correlation. K2 ¼ expðC * T þ DÞ
(4)
b2 ¼ E*T þ F
(5)
The empirical model is thus established as in Eq. (6). NDC ¼ f ðN; TÞ ¼ 1
expðA * T þ BÞ *N b1
expðC * T þ DÞ*N E*TþF
(6)
In the last step, using all the testing data shown in Fig. 2(b), the “fitnlm” function that uses Levenberg-Marquardt nonlinear least squares algorithms is employed to obtain the best-fit values of these 7 model coefficients, given their initial values (A ¼ 0.03638, B ¼ 18.362, b1 ¼ 0.69, C ¼ 2.28, D ¼ 782, E ¼ 0.2771, F ¼ 96.44). The coefficient b1 and the derived K1, K2, and b2 at each temperature are shown in Table 3. The coefficients K1 and K2 increase exponentially
NDC ¼ 1
expð0:05 * T
21:9Þ*N 0:76
expð2:3 * T
773:5Þ*N ð
0:28*Tþ94:3Þ
(7)
This model has shown generalization capability in describing mul tiple degradation behaviors and can be applied to accelerated test
Fig. 7. (a) Curve fitting results; (b) Contribution of the first power law term; (c) Contribution of the second power law term. 7
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 8. (a) The effect of ambient temperature and discharge C-rate on degradation of new batteries; (b) Comparison of the new batteries with previous batteries at same testing conditions; (c) Fitted curves for new batteries using the developed model form.
planning of general lithium-ion cells. The capacity fade or lifetime of cells under normal temperature can be predicted by fitting this model to testing data obtained from normal temperature and accelerated tem peratures, where the entire test lasts only for a short amount of time (e. g., a month). To determine the model coefficients, at least two temper atures are required to test cells. For cells that present knee point be haviors, this model requires two groups of knee point data to correctly predict the knee point at normal temperature. This empirical accelerated degradation model considers one accel erating stress factor—the ambient temperature. However, the basic form of this model (NDC ¼ 1 K1 *Nb1 K2 *Nb2 ) can be used to describe general battery degradation behavior consisting of two stages, as a starting point to incorporate other accelerating stress factors.
fade trend with knee points, and the dependency of ambient tempera ture is further incorporated with detailed explanation. The fitted curves show strong agreement with the experimental data with an R2 value of 0.9774. The generalization capability of this model has been validated using testing data of different LiCoO2-graphite cells without knee point behaviors. Therefore, accelerated cycle life testing can be conducted on general lithium-ion batteries using two accelerated temperatures. The capacity fade trend including occurrence of knee points at normal temperature can be estimated by calibrating model coefficients of the developed model. Author contributions Weiping Diao: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Roles/ Writing - original draft. Saurabh Saxena: Formal analysis, Software, Validation, Writing - review & editing. Michael Pecht: Conceptualiza tion, Methodology, Project administration, Resources, Supervision, Writing - review & editing.
7. Conclusions This paper developed an approach to determine the optimized accelerating conditions to reduce overall cycle testing time, by con ducting a full factorial design of experiment in consideration of cell chemistries, degradation mechanisms, and controllability of stress fac tors. It has been found that for these cells, only the ambient temperature can be effectively used to accelerate the battery degradation. The ca pacity degradation over cycles was independent of the discharge C-rate. The effect of the charge cut-off C-rate was coupled with the ambient temperature because the discrepancy between the two capacity fade curves at C/5 and C/40 increases with temperature. As a result, the total testing time at 60 � C and 45 � C was not reduced by increasing the charge cut-off C-rate to C/5. Therefore, the accelerated testing condition with an ambient temperature of 60 � C, a discharge C-rate of 1C, and a charge cut-off C-rate of C/40 is recommended for these cells. Testing data under this condition then present the entire life cycle profile under normal operating conditions (over 1000 cycles) on a much shorter timescale of 200 cycles (nearly a month), with an acceleration factor of 6. The developed empirical model characterizes the two-stage capacity
Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of interest Declarations of interest: none. Acknowledgements The authors would like to thank the more than 150 companies and organizations that support research activities at the Center for Advanced Life Cycle Engineering at the University of Maryland annually. 8
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
References
[21] L. Somerville, J. Bare~ no, S. Trask, P. Jennings, A. McGordon, C. Lyness, I. Bloom, The effect of charging rate on the graphite electrode of commercial lithium-ion cells: a post-mortem study, J. Power Sources 335 (2016) 189–196. [22] M. Ecker, N. Nieto, S. K€ abitz, J. Schmalstieg, H. Blanke, A. Warnecke, D.U. Sauer, Calendar and cycle life study of Li (NiMnCo)O2-based 18650 lithium-ion batteries, J. Power Sources 248 (2014) 839–851. [23] S. Saxena, C. Hendricks, M. Pecht, Cycle life testing and modeling of graphite/ LiCoO2 cells under different state of charge ranges, J. Power Sources 327 (2016) 394–400. [24] L. Serrao, Z. Chehab, Y. Guezennee, G. Rizzoni, An aging model of Ni-MH batteries for hybrid electric vehicles, in: Vehicle Power and Propulsion, 2005 IEEE Conference, IEEE, 2005, September, p. 8. [25] Y. Gao, J. Jiang, C. Zhang, W. Zhang, Z. Ma, Y. Jiang, Lithium-ion battery aging mechanisms and life model under different charging stresses, J. Power Sources 356 (2017) 103–114. � [26] D.I. Stroe, M. Swierczy� nski, A.I. Stan, R. Teodorescu, S.J. Andreasen, Accelerated lifetime testing methodology for lifetime estimation of lithium-ion batteries used in augmented wind power plants, IEEE Trans. Ind. Appl. 50 (6) (2014) 4006–4017. [27] M. Ecker, J.B. Gerschler, J. Vogel, S. K€ abitz, F. Hust, P. Dechent, D.U. Sauer, Development of a lifetime prediction model for lithium-ion batteries based on extended accelerated aging test data, J. Power Sources 215 (2012) 248–257. [28] N.D. Williard, Degradation Analysis and Health Monitoring of Lithium Ion Batteries, Doctoral dissertation, University of Maryland-College Park), 2011. [29] W. He, N. Williard, M. Osterman, M. Pecht, Prognostics of lithium-ion batteries based on Dempster–Shafer theory and the Bayesian Monte Carlo method, J. Power Sources 196 (23) (2011) 10314–10321. [30] K. Smith, J. Neubauer, E. Wood, M. Jun, A. Pesaran, Models for Battery Reliability and Lifetime: Applications in Design and Health Management (Presentation) (No. NREL/PR-5400-58550), National Renewable Energy Lab.(NREL), Golden, CO (United States), 2013. [31] F. Yang, D. Wang, Y. Xing, K.L. Tsui, Prognostics of Li(NiMnCo)O2-based lithiumion batteries using a novel battery degradation model, Microelectron. Reliab. 70 (2017) 70–78. [32] E. Cripps, M. Pecht, A Bayesian nonlinear random effects model for identification of defective batteries from lot samples, J. Power Sources 342 (2017) 342–350. [33] A. Barai, K. Uddin, W.D. Widanage, A. McGordon, P. Jennings, A study of the influence of measurement timescale on internal resistance characterisation methodologies for lithium-ion cells, Sci. Rep. 8 (1) (2018) 21. [34] S.S. Zhang, K. Xu, T.R. Jow, EIS study on the formation of solid electrolyte interface in Li-ion battery, Electrochim. Acta 51 (8–9) (2006) 1636–1640. [35] G. Ning, B. Haran, B.N. Popov, Capacity fade study of lithium-ion batteries cycled at high discharge rates, J. Power Sources 117 (1–2) (2003) 160–169. [36] N. Omar, M.A. Monem, Y. Firouz, J. Salminen, J. Smekens, O. Hegazy, J. Van Mierlo, Lithium iron phosphate based battery–assessment of the aging parameters and development of cycle life model, Appl. Energy 113 (2014) 1575–1585. [37] T.M. Bandhauer, S. Garimella, T.F. Fuller, A critical review of thermal issues in lithium-ion batteries, J. Electrochem. Soc. 158 (3) (2011) R1–R25. [38] P.L. Moss, G. Au, E.J. Plichta, J.P. Zheng, An electrical circuit for modeling the dynamic response of Li-ion polymer batteries, J. Electrochem. Soc. 155 (12) (2008) A986–A994. [39] R. Deshpande, M. Verbrugge, Y.T. Cheng, J. Wang, P. Liu, Battery cycle life prediction with coupled chemical degradation and fatigue mechanics, J. Electrochem. Soc. 159 (10) (2012) A1730–A1738. [40] R.D. Deshpande, D.M. Bernardi, Modeling solid-electrolyte interphase (SEI) fracture: coupled mechanical/chemical degradation of the Lithium ion Battery, J. Electrochem. Soc. 164 (2) (2017) A461–A474.
[1] Y. Jiang, J. Jiang, C. Zhang, W. Zhang, Y. Gao, Q. Guo, Recognition of battery aging variations for LiFePO4 batteries in 2nd use applications combining incremental capacity analysis and statistical approaches, J. Power Sources 360 (2017) 180–188. [2] M. Broussely, Battery requirements for HEVs, PHEVs, and EVs: an overview. Electr. Hybrid Veh. Sources, Model. Infrastruct. Mark, 2010, pp. 305–347. [3] I. Bloom, B.W. Cole, J.J. Sohn, S.A. Jones, E.G. Polzin, V.S. Battaglia, D. Ingersoll, An accelerated calendar and cycle life study of Li-ion cells, J. Power Sources 101 (2) (2001) 238–247. [4] Y. Zhang, C.Y. Wang, X. Tang, Cycling degradation of an automotive LiFePO4 lithium-ion battery, J. Power Sources 196 (3) (2011) 1513–1520. [5] K. Jalkanen, J. Karppinen, L. Skogstr€ om, T. Laurila, M. Nisula, K. Vuorilehto, Cycle aging of commercial NMC/graphite pouch cells at different temperatures, Appl. Energy 154 (2015) 160–172. [6] W. Diao, Y. Xing, S. Saxena, M. Pecht, Evaluation of present accelerated temperature Testing and modeling of batteries, Appl. Sci. 8 (10) (2018) 1786. [7] C. Hendricks, N. Williard, S. Mathew, M. Pecht, A failure modes, mechanisms, and effects analysis (FMMEA) of lithium-ion batteries, J. Power Sources 297 (2015) 113–120. [8] A. Barr� e, B. Deguilhem, S. Grolleau, M. G�erard, F. Suard, D. Riu, A review on lithium-ion battery ageing mechanisms and estimations for automotive applications, J. Power Sources 241 (2013) 680–689. [9] T. Waldmann, M. Wilka, M. Kasper, M. Fleischhammer, M. Wohlfahrt-Mehrens, Temperature dependent ageing mechanisms in Lithium-ion batteries–A PostMortem study, J. Power Sources 262 (2014) 129–135. [10] K. Xu, Nonaqueous liquid electrolytes for lithium-based rechargeable batteries, Chem. Rev. 104 (10) (2004) 4303–4418. [11] S. Saxena, Y. Xing, D. Kwon, M. Pecht, Accelerated degradation model for C-rate loading of lithium-ion batteries, Int. J. Electr. Power Energy Syst. 107 (2019) 438–445. [12] R. Spotnitz, Simulation of capacity fade in lithium-ion batteries, J. Power Sources 113 (1) (2003) 72–80. [13] J. De Hoog, J.M. Timmermans, D. Ioan-Stroe, M. Swierczynski, J. Jaguemont, S. Goutam, P. Van Den Bossche, Combined cycling and calendar capacity fade modeling of a Nickel-Manganese-Cobalt Oxide Cell with real-life profile validation, Appl. Energy 200 (2017) 47–61. [14] Y. Gao, J. Jiang, C. Zhang, W. Zhang, Y. Jiang, Aging mechanisms under different state-of-charge ranges and the multi-indicators system of state-of-health for lithium-ion battery with Li(NiMnCo)O2 cathode, J. Power Sources 400 (2018) 641–651. [15] K. Zhao, M. Pharr, J.J. Vlassak, Z. Suo, Fracture of electrodes in lithium-ion batteries caused by fast charging, J. Appl. Phys. 108 (7) (2010), 073517. [16] J. Christensen, J. Newman, Stress generation and fracture in lithium insertion materials, J. Solid State Electrochem. 10 (5) (2006) 293–319. [17] A.A. Tahmasbi, M.H. Eikerling, Statistical physics-based model of mechanical degradation in lithium ion batteries, Electrochim. Acta 283 (2018) 75–87. [18] J. Vetter, P. Nov� ak, M.R. Wagner, C. Veit, K.C. M€ oller, J.O. Besenhard, A. Hammouche, Ageing mechanisms in lithium-ion batteries, J. Power Sources 147 (1–2) (2005) 269–281. [19] J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, P. Finamore, Cycle-life model for graphite-LiFePO4 cells, J. Power Sources 196 (8) (2011) 3942–3948. [20] S. Sun, T. Guan, X. Cheng, P. Zuo, Y. Gao, C. Du, G. Yin, Accelerated aging and degradation mechanism of LiFePO4/graphite batteries cycled at high discharge rates, RSC Adv. 8 (45) (2018) 25695–25703.
9
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Accelerated cycle life testing and capacity degradation modeling of LiCoO2-graphite cells Weiping Diao *, Saurabh Saxena, Michael Pecht Center for Advanced Life Cycle Engineering (CALCE), University of Maryland, College Park, MD, 20742, USA
H I G H L I G H T S
� Conducted a large design of experiment with 192 LiCoO2-based cells and 24 testing conditions. � Analyzed effects of stress factors including temperature, discharge C-rates and charge cut-off C-rates along with possible degradation mechanisms. � Determined optimal accelerated testing conditions. � Developed an empirical accelerated degradation model that can describe the two-stage capacity fade process. A R T I C L E I N F O
A B S T R A C T
Keywords: Accelerated cycle life testing Capacity degradation model Temperature Discharge C-Rate Charge cut-off C-Rate Knee point
Accelerated cycle life testing of lithium-ion batteries is conducted as a means to assess whether a battery will meet its life cycle requirements. This paper presents a study to identify optimal accelerated cycle testing con ditions for LiCoO2-graphite cells. A full factorial design of experiment with three stress factors—ambient tem perature (10 � C, 25 � C, 45 � C, 60 � C), discharge current rate (C-rate, 0.7C, 1C, 2C), and charge cut-off C-rate (C/5, C/40)—is used to study the effects of these stress factors on battery capacity fade and to obtain the data necessary for decision making. An empirical accelerated degradation model is then developed to capture the characteristics of the two-stage capacity degradation process, along with an accelerated test planning approach.
1. Introduction Commercialization of lithium-ion batteries has enabled applications ranging from portable consumer devices to high-power electric vehicles to become commonplace [1]. However, one of the key concerns asso ciated with lithium-ion battery technology is performance degradation during usage and storage. As a critical performance metric, the capacity retention of lithium-ion batteries is often used to determine if they have reached the end of life (EOL), usually defined as a 20% reduction in the initial or rated capacity [2]. Lithium-ion batteries with unsatisfactory lifetimes can significantly reduce customer satisfaction and make products of little use. In order to characterize the capacity degradation trend, companies test batteries according to the performance requirements and the life expectation for their targeted application. While for most cases the test purpose is to determine the number of cycles to EOL, there are instances where the amount of capacity fade for a particular number of cycles or the full capacity fade profiles of the batteries are required. When batteries with a
lifetime of 1000 cycles are tested continuously under normal conditions (e.g., 25 � C, 0.5C), each cycle takes about 4.5 h and nearly 6 months pass until the test is finished. Accelerated cycle life testing is thus needed to quickly precipitate degradation by increasing levels of stress factors. Historically, accelerated cycle life testing of lithium-ion batteries has been conducted by elevating the ambient temperature [3–6]. High temperature accelerates the kinetics of the solid electrolyte interphase (SEI) layer on the graphite negative anode as a parasitic side electro chemical reaction [7,8]. However, the kinds of battery degradation mechanisms are dependent on the temperature. For example, Waldmann et al. [9] evaluated the effect of different temperatures on the electrode polarizations of lithium-ion cells with graphite anode and found that low temperature (T < 25 � C) accelerates lithium dendrite growth, whereas high temperature (T > 25 � C) advances SEI layer growth. Furthermore, the characteristics of battery components also impose temperature limits on the operation as well as testing. The thermal stability of the typical electrolyte salts (LiPF6), organic solvent (ethylene carbonate, dimethyl carbonate ethyl methyl carbonate, propylene carbonate, etc.)
* Corresponding author. E-mail addresses: [email protected] (W. Diao), [email protected] (S. Saxena), [email protected] (M. Pecht). https://doi.org/10.1016/j.jpowsour.2019.226830 Received 16 April 2019; Received in revised form 11 June 2019; Accepted 28 June 2019 Available online 2 July 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
constrains the upper operating temperature limit, often between 60 � C and 70 � C [10]. At temperatures lower than the liquidus temperature (usually above 20 � C for most electrolyte compositions), solvent pre cipitates and the electrolyte is kinetically unstable [10]. Besides temperature, charge/discharge C-rate [11,12], state of charge (SOC) operation rang [13,14], and combinations of these stress factors with temperature can also be used to accelerate the degradation mechanisms of lithium-ion batteries. Increasing the charge/discharge C-rate reduces the time required to conduct a charge/discharge cycle and affects capacity fade rate over cycles. High C-rate can cause lithium to be crowded in the outer shell of the electrode particle [15]. When the resulting mechanical stress of the particle surpasses the yield stress of the material [16], particle cracking occurs and causes further structural integrity loss including contact loss between active material particles and between active material and current collectors [17,18]. The amount of particle cracking accumulates with cycling. High C-rate also accounts for the excess temperature increase of the cell as compared to the ambient temperature [19,20]. At high charge C-rate or low temperature, lithium dendrite growth is accelerated because the high overpotential across the anode resistance decreases the anode potential to a level below 0.0 V (vs Li/Liþ) where lithium preferentially plates onto the graphite anode rather than intercalating into the graphite [21]. These mechanisms should be considered when determining the ranges of C-rate for accelerated testing. Numerous studies have reported on the effect of mean SOC and ΔSOC on the battery degradation. Ecker et al. [22] found that Li (NiMnCo)O2 based cells cycled with ΔSOC ¼ 10% experienced the most severe degradation cycled at [5–15%] and [90–100%], and cells cycled with mean SOC ¼ 50% had the highest degradation rate at a full SOC operation range (ΔSOC ¼ 100%). On the other hand, Wang et al. [19] did not observe any effect for LiFePO4-based cells. Saxena et al. [23] tested LiCoO2-based cells with different mean SOC and ΔSOC, and concluded that for the first 500 equivalent full cycles mean SOC is found to have a major effect on the capacity fade of cells as compared to ΔSOC, whereas towards the end of the testing (600–800 equivalent cycles) ΔSOC becomes the major factor affecting the capacity loss rate of the cells. Gao et al. [14] tested Li(NiMnCo)O2-based cells at five non-overlapping SOC operation ranges (ΔSOC ¼ 20%) as well as at a full range. They showed that the sum of the capacity degradation in each SOC range was not equal to that gained at a full SOC range. Features from the incremental capacity analysis (ICA) of cells at each SOC operation range were then extracted and mapped to the ICA of cells cycled at full SOC range by developing a model. The SOC operation range is not a directly controllable factor. A predetermined SOC operation range is often obtained by controlling the ratio of the amount of charge drawn from a battery at a certain SOC level to the battery’s capacity [24]. Because the actual available capacity varies with loading conditions, including temperature and C-rate, and decreases over cycles, the same values of SOC operation range at different loading conditions and health states are not essentially equivalent. The charge cut-off voltage and charge cut-off current during the constant voltage part of the charging, which determine the upper limit of SOC operation range, do not have controllability issues and can also be considered as stress factors [25]. Hence, charge cut-off C-rate has been included as a stress variable in this study rather than SOC operation range, and its effects on accelerating the battery cycle life testing have been investigated. With the accelerated cycling test, an accelerated degradation model as a function of cycles and stress factors is needed to extrapolate testing data at higher stress levels to predict the capacity fade under normal operating conditions. In terms of the cycle dependence, numerous empirical models have been developed, in which a power law rela tionship has been extensively used to model the square root dependence of capacity fade on time/cycles/accumulated Ah throughput [19,22,26, 27]. However, a multitude of cells with cathode chemistries such as LiCoO2 [28,29], Li(NiCoAl)O2 [30], and Li(NiMnCo)O2 [31] have
Table 1 Testing procedure in a charge/discharge cycle. Cycle stage
Profile
Charge
1st CCCV ① CC: 1.5C until voltage reaches 4.2 V ② CV: 4.2 V until current drops to 1C 5 min CC: 0.7C to 3.0 V 5 min
Rest Discharge Rest
2nd CCCV ③ CC: 1C until voltage reaches 4.4 V ④ CV: 4.4 V until current drops to C/40
shown two-stage degradation behaviors. Their capacity fade curves usually consist of a slow degradation stage followed by a fast degrada tion stage, with a distinct knee point in between. A double-exponent model has shown good performances in fitting these degradation curves [28,29,32], but none of these studies expanded this model to take into account the dependence of aging on any stress factor. In a two-term logarithm model developed by Yang et al. [31], a hyperparameter must be selected based on experience, and there is a strict limit for coefficients because only positive numbers have real logarithms, making the model impractical. This paper investigates the accelerated cycle life testing conditions for LiCoO2-graphite cells using three different stress factors. A full factorial design of experiment (DOE) has been conducted on 192 cells to statistically investigate the influence of the ambient temperature, discharge C-rate, charge cut-off C-rate, and their interactions on ca pacity fade over cycles. A qualitative analysis has been carried out to determine how these stress factors affect the capacity fade trend and accelerate the cycle life testing. Following this discussion, an empirical accelerated degradation model has been developed to describe the twostage degradation process and the effects of stress factors on capacity fade of lithium-ion batteries. This paper highlights the methodology of accelerated cycle life testing and modeling in exploration of the optimal accelerated testing conditions and acceleration factors. The effect of charge cut-off C-rate, individually or combined with other stress factors, has also not been studied so far by the research community to determine whether it can accelerate capacity fade. The remaining sections of this paper are as follows. Section 2 in troduces cell specifications and the design of experiment (DOE). Sec tions 3, 4, and 5 present the experimental results and discuss the effect of ambient temperature, discharge C-rate, and charge cut-off C-rate, respectively. Section 6 presents the methodology of model development and implementation. Section 7 provides the conclusions. 2. Design of experiment The DOE involved two types of tests: characterization tests and cycling tests. Characterization tests periodically determined the cell electrical parameters that provide a measure for performance degrada tion. Cycling tests exposed the cells to different operating conditions continuously, which can be represented by a cycling test matrix. For the pouch cells tested in the DOE, the major composition of the cathode, anode, and electrolyte was LiCoO2, graphite, and LiPF6-salt mixed with liquid organic solvent, respectively. The electrode layers of the cells were wound. The nominal capacity and operation voltage range were 3.36 Ah and 3.0–4.4 V, respectively. The maximum continuous current of these cells was 2C. The recommended operating temperature ranges for these cells during the charge/discharge process were 20–60 � C, and 0–50 � C, respectively. In the characterization test, the discharge capacity and electrical impedance spectroscopy (EIS) of cells at 100% SOC were measured after every 50 cycles of cycling test. The capacity testing procedure in a charge/discharge cycle is shown in Table 1, where the two constantcurrent/constant-voltage (CCCV) charging stages were recommended 2
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
25 � C, 45 � C, and 60 � C—were selected due to the considerable dendrite growth at temperatures lower than 10 � C even at normal charging Crates and the instability of the electrolyte at temperatures over 60 � C. Increasing the discharge C-rate can shorten the testing time per cycle, regardless of its effect on the capacity degradation. Most lithiumion batteries designed for consumer electronics have low power capa bility as compared to electric vehicle batteries, thus they are not allowed to be operated at high C-rates. With the maximum continuous C-rate of 2C and the rated discharge C-rate of 0.7C given in the battery manu facturer’s specifications, three stress levels of 0.7C, 1C, and 2C were selected. The charge cut-off C-rate determines the upper level of the SOC operation range and is easy to control. Two stress levels of C/5 and C/40 were set, of which C/40 was recommended in the battery manufac turer’s specifications. A charge cut-off C-rate of C/5 can significantly reduce the testing time per cycle. However, C/5 represents a lower stress level and may reduce the capacity degradation rate over cycles. Hence, an optimal charge cut-off C-rate for accelerated testing should provide a trade-off between these two opposite effects and achieve the maximum acceleration.
Fig. 1. Voltage profile during the manufacturer-recommended charge process. Table 2 Cycling test matrix. Charge cut-off C-rate C/5 C/40 C/5 C/40 C/5 C/40
Ambient temperature (� C)
Discharge C-rate
10
25
45
60
Test # 1 #2 #3 #4 #5 #6
#7 #8 #9 # 10 # 11 # 12
# # # # # #
# 19 # 20 # 21 # 22 # 23 # 24
13 14 15 16 17 18
3. Effect of ambient temperature
0.7C
Fig. 2 shows the capacity degradation curves at different tempera tures, where Ccut is the charge cut-off C-rate and Cdisch is the discharge Crate. In Fig. 2(a), the capacity degradation curves at 60 � C consist of two stages with a knee point occurring at around 250th cycle. The first stage, where the slopes of these curves decrease over cycles, is characterized by a moderate degradation rate and possibly relates to the steady SEI layer growth that consumes cyclable lithium [17]. SEI layer growth has been found to have an approximate square root dependency on the cycle number or time [11,19,27], which can be used to model this portion of the curve. However, starting from the 250th cycle, the capacity starts to decline rapidly. Mechanical degradation has been reported to primarily account for this behavior [17]. At this fast degradation stage, the loss of electrical contact between electrode particles as well as between particles and current collectors is getting much more severe, thus its effect on capacity loss is expected to far exceed the effect of steady SEI layer growth. A similar phenomenon is observed on the 60 � C degradation curve in Fig. 2(b). The EIS of cells tested under this condition was measured at 100% SOC to investigate the kinetics changes before and after the occurrence of knee points. On the EIS plot in Fig. 3, the intercept on the real axis at the high-frequency range represents the ohmic resistance of cells, the semi-circles at the middle-frequency range indicate the SEI layer characteristics and kinetics during the charge-transfer process, and the short tail at the low-frequency range is related to the kinetics during the mass-transfer process [33]. As shown in Fig. 3(a), the ohmic resis tance increases over cycles, and these semi-circles shift to the right. This
1C 2C
by the battery manufacturer. Fig. 1 shows the voltage profile of a fresh cell during the charge process. The purpose of reducing the charge Crate at the voltage range between 4.2 V and 4.4 V was to avoid lithium plating onto the anode surface. All the cells that underwent cycling tests were characterized at 25 � C using this capacity testing procedure. Data from two charge/discharge cycles were recorded in each characterization test, and the average values were calculated. The cycling test matrix is shown in Table 2. The 3 stress factors and a full factorial design resulted in 24 testing conditions. The numbers 1–24 in this table represent the condition IDs, and 8 cells were tested under each condition. The rationale behind this cycling test matrix was to choose suitable stress factors for acceleration and determine their boundaries in such a way that the major degradation mechanisms do not change. The ambient temperature has been recognized as a useful stress factor for accelerating cell degradation, because the side reactions inside the cell take place more rapidly at higher temperatures. However, as discussed in Section 1, the temperature range needs to be determined carefully since not all degradation mechanisms can be accelerated by elevating the temperature and excessively high temperature may induce new degradation mechanisms. Thus, 4 different temperatures—10 � C,
Fig. 2. Discharge capacity over cycles - effect of ambient temperature. 3
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 3. Electrical impedance spectroscopy of cells under testing condition #20 at 100% SOC.
Fig. 4. Discharge capacity and ohmic resistance over cycles - effect of discharge C-rate.
4
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 5. Discharge capacity over cycles - effect of charge cut-off C-rate.
reaction kinetics degradation will increase the overpotential of cells and accounts partially for the discharge capacity degradation. The amount of shift in EIS trajectories shift is most significant from the 150th cycle to the 200th cycle, which is consistent with the amount of discharge ca pacity change. Both the capacity fade curves in Fig. 2(b) and EIS plots in Fig. 3 show that variations among cells become larger after knee points. As shown in Fig. 3(b), an equivalent circuit model [34] was fitted to the average EIS data of the eight cells, where R1 is the ohmic resistance, R2 is the SEI resistance, R3 is the charge transfer resistance, CPE stands for constant phase element, W is the Warburg impedance related to diffusion process, and L is the inductance. R2 and CPE1 have a smaller time constant and thus will respond to higher frequencies as compared to R3 and CPE2 . The resistances in the equivalent circuit model were identified using “eissa1” EIS Analyser and are plotted in Fig. 3(b). It shows that the charge transfer resistance is the highest as compared to ohmic and SEI resistances, and these resistances increase over cycles. In Fig. 2(a) where the charge cut-off C-rate is C/5, the slopes of the 45 � C curves also decrease at first, then they keep nearly constant. The degradation curves at 25 � C and 10 � C present similar characteristics as the 45 � C curves but with a slower degradation rate, suggesting a consistent degradation mechanism. At the charge cut-off C-rate of C/40 as shown in Fig. 2(b), knee points are observed on the 45 � C degradation curve. It is interesting that an interaction of high temperature of 45 � C and higher charge cut-off current stress of C/40 precipitates knee point before the 600th cycle. The testing conditions at 45 � C and 60 � C act as accelerated ones, it is thus expected that cells will also show knee point behavior at normal operating conditions (25 � C, Cdisch ¼ 0.7C). Williard [28] and He et al. [29] tested LiCoO2-based batteries with different capacities at room temperature and observed that the capacity fade occurred in a near linear fashion followed by a pronounced reduction. At other discharge C-rates (1C, 2C), the degradation curves at different ambient temperatures show similar characteristics and the effect of ambient temperature on battery degradation did not change with the change in the discharge C-rate. Thus, these testing data have not been repeatedly plotted and discussed.
The ambient temperature can effectively accelerate the capacity degradation. At the testing condition of Ccut@C/40 and [email protected] when there is a 10% capacity fade, 100 cycles are needed for 60 � C and 600 cycles are needed for 25 � C, thus an acceleration factor of 6 can be gained at 60 � C. The effect of ambient temperature can be modeled to predict the capacity degradation trend at normal temperatures. 4. Effect of discharge C-rate Fig. 4 displays the capacity degradation curves at different discharge C-rates. As shown in Fig. 4(a)~(c), these curves almost overlap at different discharge C-rates. This result is unexpected since numerous papers have reported the significant effect of the discharge C-rate on capacity degradation rate of LiCoO2- [35] and LiFePO4- [19,36] based cells, although a few observed no effect on capacity degradation of Li (NiMnCo)O2- [13] based cells. In this study, the capacity degradation over cycles is found to be independent of the discharge C-rate in the range of C/7~2C at 10 � C–45 � C. The number of cycles when knee points occur at different discharge C-rates is around 550, as shown in Fig. 4(c) with the testing temperature of 45 � C. One possible explanation for the influence of discharge C-rate is that the batteries have been designed using such small electrode particle size that lithium in the particle maintains nearly a homogeneous distribution at different discharge C-rates and the induced stress does not exceed the yield point of the material. Hence, they can sustain this discharge C-rate range without experiencing par ticle crack [15]. However, at 60 � C, cells cycled at a discharge C-rate of 2C degrade much faster than those cycled at lower discharge C-rates. The C-rate can affect the battery temperature due to ohmic heating [37]. In the elec trolytes used in these cells, the salt LiPF6 will decompose over 70 � C [10], causing the conductivity of the electrolyte to decrease. Meanwhile, the chemical decomposition of electrolyte in SEI layer growth is highly accelerated at this temperature [9]. The gas generated from both ther mal and chemical decomposition can cause delamination of electrode 5
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 6. Discharge capacity over testing time - effect of charge cut-off C-rate.
layers and thus increase the ohmic resistance [38]. Fig. 4(e) plots the evolution of average ohmic resistance of cells in each condition (0.7C, 1C, 2C) up to 100 cycles. It shows that the ohmic resistance of cells cycled at 2C increases much faster than cells cycled at 0.7C and 1C. Considering Joule’s law, we hypothesized that the temperature in creases of cells at the 60 � C, 2C condition could have induced a signifi cant amount of electrolyte thermal decomposition, which is indicated by the large change in the ohmic resistance. At the charge cut-off C-rate of C/5, the capacity fade at each testing temperature is also independent of discharge C-rate, and the cycle numbers when knee points occur at 60 � C are almost the same for different discharge C-rates. Thus, these testing data have not been repeatedly analyzed. Since the discharge C-rate does not affect the capacity degradation over cycles, there is no need to model its effect. However, the testing discharge C-rate can be increased to 2C at 45 � C and 1C at 60 � C to reduce the testing time of each cycle.
degradation model. 6. Accelerated capacity degradation model Sections 4 and 5 showed that the discharge C-rate does not affect the capacity degradation over cycles and increasing the charge cut-off C-rate cannot accelerate the testing process, hence a capacity degradation model has been developed as a function of number of cycles and the stress factor of ambient temperature. The capacity data used for modeling has been normalized with the cells’ initial discharge capacity, and a nonlinear regression technique has been adopted in the modeling work. To start with, a capacity model as a function of number of cycles is needed to simulate the capacity degradation behaviors with knee points. However, the popular empirical model—single power law—as in Eq. (1) is not capable of fitting these degradation curves because it presents either an increasing or decreasing slope (K1 b1 *Nðb1 1Þ ) if b1 is not equal to 1.
5. Effect of charge cut-off C-rate
NDC1 ¼ 1
As shown in Fig. 5, the effect of the charge cut-off C-rate varies with the ambient temperature. At 10 � C and 25 � C, the capacity differences of cells using C/5 and C/40 at the 500th cycle are 2.13% and 2.76% of these cells’ average initial capacity, respectively, which suggests that charge cut-off C-rate had a minimal impact on capacity degradation. At 60 � C, the capacity difference at 100 cycles (before knee points occurred) is 1.57%, whereas this difference rises to 10.03% at 150 cycles (after knee points occurred). This result indicates that the charge cut-off C-rate of C/40 (higher ΔSOC) induces more stress at high temperature than it does at low temperature. Deshpande et al. [39,40] found that SEI layer growth is primarily caused by SEI layer fracture during electrode expansion at low charge C-rate where the stress in the graphite particles is trivial as compared to the fracture strength. Under this condition, they
K1 *N b1
(1)
where NDC is the normalized discharge capacity, N is the number of cycles, and K1, b1 are the model coefficients. To model the knee point behavior as shown in Fig. 2(b), one more power term is added to this model where the first term is used to simulate the slow degradation stage with the exponent less than 1, and the second power law term increases significantly after the knee points with the exponent larger than 1: NDC ¼ 1
K1 *N b1
K2 *N b2
(2)
The next step is to investigate how K1, b1 and K2, b2 change with ambient temperature to determine an appropriate accelerated model form and initial values for all coefficients in the accelerated model, and this step is all guided by experimental data. Because these two terms are dominant at different degradation stages and experimental data at 10 � C and 25 � C lack the fast degradation stage, this step is decomposed into two substeps. The first substep is to determine how temperature affects K1 * Nb1 using data from the slow degradation stage (all testing data at 10 � C and 25 � C, testing data in the first 550 cycles at 45 � C and first 100 cycles at 60 � C in Fig. 2(b)), using the model represented by Eq. (3). This model form and its derivatives have been widely used to describe ca pacity fade behaviors with a decreasing degradation rate. The coeffi cient b1 is independent of stress factors, and its initial value can be set to approximately 0.5 [19,20,22,26,27].
noted that the capacity loss is directly proportional to ðΔSOCÞ2 [40], and this proportion has a positive correlation with temperature. It is thus hypothesized that the interaction between temperature and charge cut-off C-rate is due to the greater SEI layer fracture at C/40 than that at C/5 when the temperature is increased to 60 � C. Although increasing the charge cut-off C-rate can reduce the testing time of each cycle, more cycles are needed for cells to have the same amount of capacity loss as lower charge cut-off C-rate especially at high temperature (60 � C). The favorable accelerated temperature testing condition at 60 � C requires 400 cycles for cells tested at C/5 to reach the failure threshold (80% threshold), almost twice the cycles for cells tested at C/40 to reach the failure threshold. Fig. 5(c) and (d) have been replotted as in Fig. 6(a) and (b) to compare the overall testing time using C/5 and C/40. This replotting demonstrates that the testing process cannot be accelerated by increasing the charge cut-off C-rate at 45 � C and 60 � C, thus this factor will not be incorporated into the accelerated
NDC1 ¼ 1
expðA * T þ BÞ*N b1
(3)
Using the curve fitting toolbox in Matlab, model coefficients in Eq. (3) can be determined. These coefficients serve as initial values when fitting all experimental data to the final accelerated model NDC ¼ fðN; 6
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
with the temperature, whereas b2 decreases linearly with the tempera ture. Fig. 7(a) shows that the fitted curves match well with the experi mental data with the R2 value of 0.9774. In Fig. 7(b)(c), the contribution of the first and second power law term is plotted. It shows that the first power law term is dominant at the degradation stage before knee point occurrence, whereas the second power law term increases fast and be comes dominant after knee point occurrence. The model applicability is further examined using the capacity degradation data of another type of lithium-ion cells. These cells had the same specifications as previous cells but contained polymer gel elec trolyte. They were tested at 60 � C, 45 � C, and 25 � C for about a month. Two discharge C-rates of 0.7C and 1.8C were chosen. There were 6 testing conditions with 3 cells in each. Cycling tests and characterization tests followed the same routine as described in Section 2. As shown in Fig. 8(a), at each testing temperature, the overlap of capacity degradation curves of these new batteries (solid lines) at different discharge C-rates indicates that the discharge C-rate also does not affect the capacity degradation rate with respect to cycles. In Fig. 8 (b), new batteries are compared with previous batteries at the same testing condition. The capacity degradation curves at 25 � C of new batteries followed the same trajectories as those of previous batteries, suggesting a great similarity between them. However, the testing data at 60 � C and 45 � C showed remarkably different trajectories without any knee point. Using the developed model form, coefficients have been recalibrated as in Eq. (7). As shown in Fig. 8(c), the fitted curves with an R2 value of 0.997 agree well with the experimental data.
Table 3 Model coefficients at different temperatures. Coefficients
10 � C
25 � C
45 � C
60 � C
K1 K2 b1 b2
0.000725 4.98E-59 0.774 18.14
0.0010 2.68E-44 0.774 13.83
0.0016 1.17E-24 0.774 8.09
0.0023 7.78E-15 0.774 3.78
TÞ. In the second substep, the contribution of the first term was sub tracted from the experimental data at 45 � C and 60 � C in Fig. 2(b), and what was left in the data was used to determine how coefficients in the second term vary with temperature. Experimental data has shown that the higher the temperature, the earlier the knee point occurs. The co efficient K2 is also assumed to vary exponentially with temperature as shown in Eq. (4). It is then found that the coefficient b2 needs to decrease with temperature increase to simulate the capacity fade trend. Thus, a linear model as shown in Eq. (5) is used to capture this correlation. K2 ¼ expðC * T þ DÞ
(4)
b2 ¼ E*T þ F
(5)
The empirical model is thus established as in Eq. (6). NDC ¼ f ðN; TÞ ¼ 1
expðA * T þ BÞ *N b1
expðC * T þ DÞ*N E*TþF
(6)
In the last step, using all the testing data shown in Fig. 2(b), the “fitnlm” function that uses Levenberg-Marquardt nonlinear least squares algorithms is employed to obtain the best-fit values of these 7 model coefficients, given their initial values (A ¼ 0.03638, B ¼ 18.362, b1 ¼ 0.69, C ¼ 2.28, D ¼ 782, E ¼ 0.2771, F ¼ 96.44). The coefficient b1 and the derived K1, K2, and b2 at each temperature are shown in Table 3. The coefficients K1 and K2 increase exponentially
NDC ¼ 1
expð0:05 * T
21:9Þ*N 0:76
expð2:3 * T
773:5Þ*N ð
0:28*Tþ94:3Þ
(7)
This model has shown generalization capability in describing mul tiple degradation behaviors and can be applied to accelerated test
Fig. 7. (a) Curve fitting results; (b) Contribution of the first power law term; (c) Contribution of the second power law term. 7
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
Fig. 8. (a) The effect of ambient temperature and discharge C-rate on degradation of new batteries; (b) Comparison of the new batteries with previous batteries at same testing conditions; (c) Fitted curves for new batteries using the developed model form.
planning of general lithium-ion cells. The capacity fade or lifetime of cells under normal temperature can be predicted by fitting this model to testing data obtained from normal temperature and accelerated tem peratures, where the entire test lasts only for a short amount of time (e. g., a month). To determine the model coefficients, at least two temper atures are required to test cells. For cells that present knee point be haviors, this model requires two groups of knee point data to correctly predict the knee point at normal temperature. This empirical accelerated degradation model considers one accel erating stress factor—the ambient temperature. However, the basic form of this model (NDC ¼ 1 K1 *Nb1 K2 *Nb2 ) can be used to describe general battery degradation behavior consisting of two stages, as a starting point to incorporate other accelerating stress factors.
fade trend with knee points, and the dependency of ambient tempera ture is further incorporated with detailed explanation. The fitted curves show strong agreement with the experimental data with an R2 value of 0.9774. The generalization capability of this model has been validated using testing data of different LiCoO2-graphite cells without knee point behaviors. Therefore, accelerated cycle life testing can be conducted on general lithium-ion batteries using two accelerated temperatures. The capacity fade trend including occurrence of knee points at normal temperature can be estimated by calibrating model coefficients of the developed model. Author contributions Weiping Diao: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Roles/ Writing - original draft. Saurabh Saxena: Formal analysis, Software, Validation, Writing - review & editing. Michael Pecht: Conceptualiza tion, Methodology, Project administration, Resources, Supervision, Writing - review & editing.
7. Conclusions This paper developed an approach to determine the optimized accelerating conditions to reduce overall cycle testing time, by con ducting a full factorial design of experiment in consideration of cell chemistries, degradation mechanisms, and controllability of stress fac tors. It has been found that for these cells, only the ambient temperature can be effectively used to accelerate the battery degradation. The ca pacity degradation over cycles was independent of the discharge C-rate. The effect of the charge cut-off C-rate was coupled with the ambient temperature because the discrepancy between the two capacity fade curves at C/5 and C/40 increases with temperature. As a result, the total testing time at 60 � C and 45 � C was not reduced by increasing the charge cut-off C-rate to C/5. Therefore, the accelerated testing condition with an ambient temperature of 60 � C, a discharge C-rate of 1C, and a charge cut-off C-rate of C/40 is recommended for these cells. Testing data under this condition then present the entire life cycle profile under normal operating conditions (over 1000 cycles) on a much shorter timescale of 200 cycles (nearly a month), with an acceleration factor of 6. The developed empirical model characterizes the two-stage capacity
Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of interest Declarations of interest: none. Acknowledgements The authors would like to thank the more than 150 companies and organizations that support research activities at the Center for Advanced Life Cycle Engineering at the University of Maryland annually. 8
W. Diao et al.
Journal of Power Sources 435 (2019) 226830
References
[21] L. Somerville, J. Bare~ no, S. Trask, P. Jennings, A. McGordon, C. Lyness, I. Bloom, The effect of charging rate on the graphite electrode of commercial lithium-ion cells: a post-mortem study, J. Power Sources 335 (2016) 189–196. [22] M. Ecker, N. Nieto, S. K€ abitz, J. Schmalstieg, H. Blanke, A. Warnecke, D.U. Sauer, Calendar and cycle life study of Li (NiMnCo)O2-based 18650 lithium-ion batteries, J. Power Sources 248 (2014) 839–851. [23] S. Saxena, C. Hendricks, M. Pecht, Cycle life testing and modeling of graphite/ LiCoO2 cells under different state of charge ranges, J. Power Sources 327 (2016) 394–400. [24] L. Serrao, Z. Chehab, Y. Guezennee, G. Rizzoni, An aging model of Ni-MH batteries for hybrid electric vehicles, in: Vehicle Power and Propulsion, 2005 IEEE Conference, IEEE, 2005, September, p. 8. [25] Y. Gao, J. Jiang, C. Zhang, W. Zhang, Z. Ma, Y. Jiang, Lithium-ion battery aging mechanisms and life model under different charging stresses, J. Power Sources 356 (2017) 103–114. � [26] D.I. Stroe, M. Swierczy� nski, A.I. Stan, R. Teodorescu, S.J. Andreasen, Accelerated lifetime testing methodology for lifetime estimation of lithium-ion batteries used in augmented wind power plants, IEEE Trans. Ind. Appl. 50 (6) (2014) 4006–4017. [27] M. Ecker, J.B. Gerschler, J. Vogel, S. K€ abitz, F. Hust, P. Dechent, D.U. Sauer, Development of a lifetime prediction model for lithium-ion batteries based on extended accelerated aging test data, J. Power Sources 215 (2012) 248–257. [28] N.D. Williard, Degradation Analysis and Health Monitoring of Lithium Ion Batteries, Doctoral dissertation, University of Maryland-College Park), 2011. [29] W. He, N. Williard, M. Osterman, M. Pecht, Prognostics of lithium-ion batteries based on Dempster–Shafer theory and the Bayesian Monte Carlo method, J. Power Sources 196 (23) (2011) 10314–10321. [30] K. Smith, J. Neubauer, E. Wood, M. Jun, A. Pesaran, Models for Battery Reliability and Lifetime: Applications in Design and Health Management (Presentation) (No. NREL/PR-5400-58550), National Renewable Energy Lab.(NREL), Golden, CO (United States), 2013. [31] F. Yang, D. Wang, Y. Xing, K.L. Tsui, Prognostics of Li(NiMnCo)O2-based lithiumion batteries using a novel battery degradation model, Microelectron. Reliab. 70 (2017) 70–78. [32] E. Cripps, M. Pecht, A Bayesian nonlinear random effects model for identification of defective batteries from lot samples, J. Power Sources 342 (2017) 342–350. [33] A. Barai, K. Uddin, W.D. Widanage, A. McGordon, P. Jennings, A study of the influence of measurement timescale on internal resistance characterisation methodologies for lithium-ion cells, Sci. Rep. 8 (1) (2018) 21. [34] S.S. Zhang, K. Xu, T.R. Jow, EIS study on the formation of solid electrolyte interface in Li-ion battery, Electrochim. Acta 51 (8–9) (2006) 1636–1640. [35] G. Ning, B. Haran, B.N. Popov, Capacity fade study of lithium-ion batteries cycled at high discharge rates, J. Power Sources 117 (1–2) (2003) 160–169. [36] N. Omar, M.A. Monem, Y. Firouz, J. Salminen, J. Smekens, O. Hegazy, J. Van Mierlo, Lithium iron phosphate based battery–assessment of the aging parameters and development of cycle life model, Appl. Energy 113 (2014) 1575–1585. [37] T.M. Bandhauer, S. Garimella, T.F. Fuller, A critical review of thermal issues in lithium-ion batteries, J. Electrochem. Soc. 158 (3) (2011) R1–R25. [38] P.L. Moss, G. Au, E.J. Plichta, J.P. Zheng, An electrical circuit for modeling the dynamic response of Li-ion polymer batteries, J. Electrochem. Soc. 155 (12) (2008) A986–A994. [39] R. Deshpande, M. Verbrugge, Y.T. Cheng, J. Wang, P. Liu, Battery cycle life prediction with coupled chemical degradation and fatigue mechanics, J. Electrochem. Soc. 159 (10) (2012) A1730–A1738. [40] R.D. Deshpande, D.M. Bernardi, Modeling solid-electrolyte interphase (SEI) fracture: coupled mechanical/chemical degradation of the Lithium ion Battery, J. Electrochem. Soc. 164 (2) (2017) A461–A474.
[1] Y. Jiang, J. Jiang, C. Zhang, W. Zhang, Y. Gao, Q. Guo, Recognition of battery aging variations for LiFePO4 batteries in 2nd use applications combining incremental capacity analysis and statistical approaches, J. Power Sources 360 (2017) 180–188. [2] M. Broussely, Battery requirements for HEVs, PHEVs, and EVs: an overview. Electr. Hybrid Veh. Sources, Model. Infrastruct. Mark, 2010, pp. 305–347. [3] I. Bloom, B.W. Cole, J.J. Sohn, S.A. Jones, E.G. Polzin, V.S. Battaglia, D. Ingersoll, An accelerated calendar and cycle life study of Li-ion cells, J. Power Sources 101 (2) (2001) 238–247. [4] Y. Zhang, C.Y. Wang, X. Tang, Cycling degradation of an automotive LiFePO4 lithium-ion battery, J. Power Sources 196 (3) (2011) 1513–1520. [5] K. Jalkanen, J. Karppinen, L. Skogstr€ om, T. Laurila, M. Nisula, K. Vuorilehto, Cycle aging of commercial NMC/graphite pouch cells at different temperatures, Appl. Energy 154 (2015) 160–172. [6] W. Diao, Y. Xing, S. Saxena, M. Pecht, Evaluation of present accelerated temperature Testing and modeling of batteries, Appl. Sci. 8 (10) (2018) 1786. [7] C. Hendricks, N. Williard, S. Mathew, M. Pecht, A failure modes, mechanisms, and effects analysis (FMMEA) of lithium-ion batteries, J. Power Sources 297 (2015) 113–120. [8] A. Barr� e, B. Deguilhem, S. Grolleau, M. G�erard, F. Suard, D. Riu, A review on lithium-ion battery ageing mechanisms and estimations for automotive applications, J. Power Sources 241 (2013) 680–689. [9] T. Waldmann, M. Wilka, M. Kasper, M. Fleischhammer, M. Wohlfahrt-Mehrens, Temperature dependent ageing mechanisms in Lithium-ion batteries–A PostMortem study, J. Power Sources 262 (2014) 129–135. [10] K. Xu, Nonaqueous liquid electrolytes for lithium-based rechargeable batteries, Chem. Rev. 104 (10) (2004) 4303–4418. [11] S. Saxena, Y. Xing, D. Kwon, M. Pecht, Accelerated degradation model for C-rate loading of lithium-ion batteries, Int. J. Electr. Power Energy Syst. 107 (2019) 438–445. [12] R. Spotnitz, Simulation of capacity fade in lithium-ion batteries, J. Power Sources 113 (1) (2003) 72–80. [13] J. De Hoog, J.M. Timmermans, D. Ioan-Stroe, M. Swierczynski, J. Jaguemont, S. Goutam, P. Van Den Bossche, Combined cycling and calendar capacity fade modeling of a Nickel-Manganese-Cobalt Oxide Cell with real-life profile validation, Appl. Energy 200 (2017) 47–61. [14] Y. Gao, J. Jiang, C. Zhang, W. Zhang, Y. Jiang, Aging mechanisms under different state-of-charge ranges and the multi-indicators system of state-of-health for lithium-ion battery with Li(NiMnCo)O2 cathode, J. Power Sources 400 (2018) 641–651. [15] K. Zhao, M. Pharr, J.J. Vlassak, Z. Suo, Fracture of electrodes in lithium-ion batteries caused by fast charging, J. Appl. Phys. 108 (7) (2010), 073517. [16] J. Christensen, J. Newman, Stress generation and fracture in lithium insertion materials, J. Solid State Electrochem. 10 (5) (2006) 293–319. [17] A.A. Tahmasbi, M.H. Eikerling, Statistical physics-based model of mechanical degradation in lithium ion batteries, Electrochim. Acta 283 (2018) 75–87. [18] J. Vetter, P. Nov� ak, M.R. Wagner, C. Veit, K.C. M€ oller, J.O. Besenhard, A. Hammouche, Ageing mechanisms in lithium-ion batteries, J. Power Sources 147 (1–2) (2005) 269–281. [19] J. Wang, P. Liu, J. Hicks-Garner, E. Sherman, S. Soukiazian, M. Verbrugge, P. Finamore, Cycle-life model for graphite-LiFePO4 cells, J. Power Sources 196 (8) (2011) 3942–3948. [20] S. Sun, T. Guan, X. Cheng, P. Zuo, Y. Gao, C. Du, G. Yin, Accelerated aging and degradation mechanism of LiFePO4/graphite batteries cycled at high discharge rates, RSC Adv. 8 (45) (2018) 25695–25703.
9