#
The Degradation Behavior of LiFePO_{4}/C Batteries during Long-Term Calendar Aging

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## Abstract

**:**

_{4)}batteries were subjected to long-term (i.e., 27–43 months) calendar aging under consideration of three stress factors (i.e., time, temperature and state-of-charge (SOC) level) impact. By means of capacity measurements and resistance calculation, the battery’s long-term degradation behaviors were tracked over time. Battery aging models were established by a simple but accurate two-step nonlinear regression approach. Based on the established model, the effect of the aging temperature and SOC level on the long-term capacity fade and internal resistance increase of the battery is analyzed. Furthermore, the storage life of the battery with respect to different stress factors is predicted. The analysis results can hopefully provide suggestions for optimizing the storage condition, thereby prolonging the lifetime of batteries.

## 1. Introduction

_{4}) active material when in the charging and discharging processes of the battery, the amount of active materials and available lithium ions will determine the battery capacity directly. Therefore, according to the research, the degradation modes of the battery can be summarized as the loss of lithium-ion inventory (LII) and loss of anode/cathode active materials (LAM) [4,5,6]. Those degradation modes are caused by some complicated and coupled physical and/or chemical side reactions inside of the battery, such as graphite exfoliation, loss of electrolytes, solid electrolyte interface (SEI) film formation and continuous thickening, lithium plating, etc. [4]. As a result, at the macroscopic level, the aging of the battery is most intuitively manifested in two aspects: capacity fade and power decrease [7]. Due to the difficulty in studying power fade, the internal resistance is usually investigated by many researchers [6,8].

_{4}) battery over at least 27 months. By considering the storage temperature and SOC level as the stress factors, an aging test matrix was designed such that the tested batteries were subjected to the aging test under five different conditions. Based on the aging results, the impact of storage temperature and SOC level on the long-term performance degradation behavior of fifteen LiFePO

_{4}battery cells was analyzed. Next, a two-step nonlinear regression method is proposed for the accurate modeling of the battery cells’ capacity fade and internal resistance behavior. Subsequently, the established performance degradation models can be generalized to predict the performance degradation of a battery subjected to different storage conditions. Finally, the storage lifetime of the battery with respect to the different stress factors is predicted.

## 2. Experimental Setup

#### 2.1. LiFePO_{4}/C under Test

_{4}/C (with LiFePO

_{4}and graphite as positive and negative active materials, respectively) battery cells were used. The main parameters of the cells are summarized in Table 1.

#### 2.2. Calendar Aging Test

_{4}/C battery cells is in the range of years, elevated temperatures were considered in order to reduce the time in which the degradation behavior was obtained. Finally, to obtain statistical relevance and reduce the influence of possible outliers, three LiFePO

_{4}/C battery cells were tested at all five aging conditions presented in Figure 1.

#### 2.3. Reference Measurements

_{4}/C battery cells, the calendar aging tests were stopped after every 30 days and reference measurements were performed at different conditions, as illustrated in Figure 2. During the reference measurements, the capacity, internal resistance and the small-signal AC impedance were measured at 25 °C. The capacity of the cells was measured at 2.5 A (1C-rate) and 10 A (4C-rate) following a constant current procedure during charging and constant current during discharging. The internal resistance of the battery was measured using the current pulse train profile, presented in Figure 3, which was applied at 20%, 50%, and 80% SOC. Furthermore, during the last step of the reference measurements, the cells were charged to the SOC levels mentioned in Figure 1, recording the number of charged Ah. Then, after 30 days of calendar aging, during the first step of the reference measurements, the cells were fully discharged, recording the number of discharged Ah. Thus, the self-discharge of the battery cells at different calendar aging conditions was also analyzed. An exemplification of the current and voltage profiles of the LiFePO

_{4}/C cells during the reference measurements is presented in Figure 4.

## 3. Calendar Aging Modeling

_{4}/C battery cells’ performance are quantified. Generally, the health state of the battery cell could be measured by the capacity fade or the internal resistance increase. Subsequently, lifetime models that could estimate the capacity fade and the internal resistance increases were developed.

#### 3.1. The Degradation Behavior of the Capacity

#### 3.1.1. The Capacity Fade

_{4}/C battery cells was measured during the reference measurements for both charging and discharging conditions with 1C-rate and 4C-rate; nevertheless, in this work, for analyzing the degradation behavior of this parameter, only the measurements carried out during discharging with 1C-rate current (2.5 A) were considered. Based on the obtained capacity values after each one-month aging, the decrease of capacity can be calculated as

_{fade}represents the capacity fade of the battery cell and C

_{ini}and C

_{present}represent the capacity value at the beginning of life and after each reference measurement, respectively. The capacity fade behavior of the LiFePO

_{4}cells obtained for all the considered calendar aging conditions is presented in Figure 5a. As previously mentioned, three cells were tested at each of the five idling conditions mentioned in Section 2.2. Thus, the results presented in this section (see Figure 5a) were obtained by choosing the median value of three batteries. The capacity fade standard deviation was used to measure the variability across the capacity fade data between cells, and the standard deviation was expressed using (2). It can be seen from Figure 5b that, for each case, as the aging process advanced, σ tended to increase and eventually became constant. A similar trend was presented for NMC-based Li-ion cells by Baumhöfer et al. in [25]. This behavior was attributed to the inherent tolerances during the manufacturing process; nevertheless, in the case of the tested LiFePO

_{4}battery cells, a maximum standard deviation of 2% was observed, which indicated a good consistency between cells.

#### 3.1.2. Modeling of the Capacity Fade

_{4}/C battery cells, a two-step nonlinear regression method was followed. In the first step, the dependence of the capacity fade on the storage time for each considered test condition was modeled, while in the second step, the dependence of the capacity fade on the storage temperature and SOC level was obtained. Figure 6 shows the structure of nonlinear regression for battery capacity fade modeling. For a set of N battery capacity fade data pairs D

_{N}= {(t

_{i}

**,**y

_{i}), i = 1, 2,…, N}, the vector ω of the parameter can be optimized by the nonlinear least squares method such that the regression function f(t, w) best fits the given data. The goal is to minimize the sum of squared errors between the model and the output as follows:

_{i}and ${\widehat{y}}_{i}$ are the real and the estimated capacity fade values, respectively. When minimizing Equation (3), the weights are optimized by solving the following equations:

^{2}, which is calculated as given in (6), and a R

^{2}value closer to 1 indicates a better fit.

_{res}is the sum of squares of residuals that describes the deviation between the measured points ${y}_{i}$ and fitted curve ${\widehat{y}}_{i}$, SS

_{tot}is the total sum of squares that describes the deviation between the measured points ${y}_{i}$ and their average value ${\overline{y}}_{i}$.

_{4}/C battery cells from these three cases are shown in Figure 8. Table 3 lists the obtained coefficients for each case, and it can be seen that both parameters a

_{T}and b

_{T}change with temperature. During long-term calendar aging, higher storage temperature led to a higher rate of capacity fade. The coefficient b

_{T}less than 1 also accorded with the aging characteristics of the battery, i.e., the rate of capacity fade decreases with time. As mentioned in the Introduction, the degradation of the battery is attributed to LII and LAM [6,28]. The formation and continuous thickening of the SEI film on the surface of the graphite anode is one of the main reasons for the LII. Furthermore, the LAM may be caused by electrolyte decomposition, graphite exfoliation or metal dissolution, etc. The reason for the aforementioned aging trend is that the growth of the SEI film is accelerated by increasing the temperature. However, the thickening of the SEI film will, in turn, prevent side reactions inside the battery, thereby leading to a lower aging rate of the battery.

_{4}/C battery cells stored at 55 °C and three different SOC levels (i.e., 10%, 50% and 90%) are shown in Figure 10. Correspondingly, the coefficients for each case are listed in Table 4. It can be seen that the influence of the SOC level during storage was different at different time ranges. Before the battery cells reached the EOL (i.e., 20% capacity fade), higher SOC was also accompanied by a higher rate of capacity fade. The reason is similar to the effect of temperature. A higher SOC will accelerate the side reaction, causing the decomposition of the electrolyte and the increase of the SEI film. In addition, at higher SOC levels where the graphite anode is lithiated more than 50%, the low anode potential accelerates the loss of lithium ions [6,28]. On the contrary, from the perspective of very long-term aging (i.e., capacity fade higher than 20%), an SOC level in the mid-SOC range (i.e., around 50% SOC) will speed up the degradation rate of the battery. This may be because a SEI film with high stability is formed, which effectively prolongs the battery life stored at 90% SOC level [1].

_{SOC}and b

_{SOC}varied as an exponential function and a power function of the SOC level, respectively.

#### 3.2. The Increasing Behavior of the Internal Resistance

#### 3.2.1. The Internal Resistance R_{i} Increase

_{i}. The effect of calendar aging on the voltage drop of the LiFePO

_{4}/C battery cells during the R

_{i}measurements at different moments is presented in Figure 13. On the basis of measured voltage and current profiles, the R

_{i}of the LiFePO

_{4}/C battery cells was calculated for the five considered aging cases as

_{0s}is the voltage before applying the current pulse, V

_{18s}represents the voltage at the end of 18s pulse and I is the amplitude of the current. As the increase of R

_{i}is an important parameter to quantify the degradation behavior of LiFePO

_{4}/C battery cells, it is calculated as

_{i_increase}represents the increase of the resistance and R

_{i_ini}and R

_{i_now}represent the resistance of the battery cell at the beginning of life and after each reference measurement, respectively.

_{i}and its aging behavior under the considered accelerated aging conditions, which are summarized in Figure 1. The discharge R

_{i}values during the consecutive reference measurements throughout the accelerated calendar aging test are presented in Figure 14, and the median values are further used to analyze the aging behavior of R

_{i}. As seen in Figure 14a, for Case 4 and Case 5, the consistency between the tested three battery cells was good. However, for the other three cases, the resistance increase between cells showed an obvious inconsistency at some points. In order to reduce the effect of inconsistency between cells on model accuracy, the median value of R

_{i}was obtained for each calendar test condition.

_{4}/C battery cells increased slowly relative to the rate of the capacity fade. Taking Case 4 (i.e., T = 55 °C, SOC = 50%) as an example, the LiFePO

_{4}/C battery cells reached 20% capacity fade after 27 months of aging. At that time, the battery cells were considered to reach their EOL criterion. However, it should be stressed that for the same aging condition, there was only a 40% R

_{i}increase. Moreover, the R

_{i}increase characteristics were similar to the capacity fade. On one hand, the R

_{i}increased steadily during the lifetime of LiFePO

_{4}/C cells, and on the other hand, the rate of the increase tended to slow down as the aging time increased.

#### 3.2.2. Modeling of R_{i} Increase

_{i}increase on the storage time, temperature and SOC level was analyzed for the values measured during the reference measurement at 80% SOC with a 4C-rate discharge pulse. The two-step fitting procedure was used as well for analyzing the aging behaviors of the LiFePO

_{4}/C cells in terms of the R

_{i}increase. Thus, the dependence of the R

_{i}increase on the storage time for each considered test condition was studied in the first step, while in the second step, the dependence on the storage temperature and SOC level was investigated. The power function, defined in (19), was used to fit with high accuracy the measured increase of R

_{i}over the storage time.

_{i}increase were considered separately in the second step. The influence of the storage temperature could be determined based on the aging tests of Case 1, Case 2, and Case 3. For these cases, the storage temperature varied from 55 °C to 40 °C, and the SOC level was fixed to 50%. Then, the fitting function has the form of

_{T}obtained by fitting was very small, in order to reduce the complexity of the model, the same q

_{T}value of 0.75 was selected at different temperatures. Figure 15 presents the measured and the fitted R

_{i}increase characteristics for the LiFePO

_{4}/C battery cells that were aged at 50% SOC and three different temperatures (i.e., 55 °C, 47.5 °C, and 40 °C). The obtained coefficients for each case are listed in Table 5. As can be seen from the results, the lower the storage temperature, the lower the rate of R

_{i}increase during the long-term calendar aging. This was due to the relatively lower rate of SEI formation and continued thickening at low SOC levels [6].

_{T}on the storage temperature. The exponential function given in (18) was found to be accurately correlated (R

^{2}= 0.9999) to the p

_{T}obtained during the first-round fitting and the storage temperature, and the second-round curve fitting result is shown in Figure 16.

_{i}increase during storage at SOC = 50% and various temperatures (mainly, higher than 25 °C) was obtained:

_{i}increase on the SOC level at which the battery cells were stored could be modeled based on a two-step nonlinear regression procedure. First, Case 1, Case 4, and Case 5 were considered, and the objective function had the form of (23).

_{i}increase characteristics for the LiFePO

_{4}/C battery cells stored at 55 °C and three different SOC levels (i.e., 20%, 50% and 90%) are shown in Figure 17. The effect of the storage SOC level on the R

_{i}increase showed a staging behavior before R

_{i}of the LiFePO

_{4}/C cells reached a 100% increase, and the doubled R

_{i}was usually seen as another EOL criterion. In the first stage, when the increase of R

_{i}is less than 30%, a higher storage SOC level made R

_{i}increase faster. Moreover, in the second stage (i.e., the R

_{i}increased by more than 30%), R

_{i}increased more when the battery was stored in the mid-SOC level (i.e., around 50% SOC). As discussed in Section 3.1.2, during the first time range, the increase of the SEI film and the low anode potential will accelerate the loss of lithium ions, thereby increasing the internal resistance. After Ri increases by more than 30%, a stable SEI film is probably formed inside the battery stored at a 90% SOC level. In this case, Ri increased more and more slowly [29].

_{SOC}and q

_{SOC}varied as the exponential functions. It can be seen that the SOC level influenced in a bit different manner the calendar degradation of the internal resistance (both p

_{SOC}and q

_{SOC}showed an exponential dependence) than the capacity (a

_{SOC}showed an exponential dependence and b

_{SOC}showed a polynomial dependence).

_{i}increases during storage at 25 °C and different SOC levels was obtained:

_{i}increases to the storage temperature and to the storage SOC level were fitted separately. By combining all the considered stress factors and taking into account the interactions between them, the model that is able to predict the calendar lifetime in terms of R

_{i}increases is given as

_{i}increase of the LiFePO

_{4}/C battery cells can be extrapolated to storage temperatures close to ones encountered during normal operation. The predicted lifetime based on R

_{i}increase model is shown in Figure 18. It can be seen that the SOC levels at both ends (smaller than 20% SOC or larger than 80% SOC) and cooler temperatures preserved the Li-ion battery when not in use, which followed the analysis results based on the capacity fade model. Compared with the lifetime prediction results shown in Figure 12 and Figure 19, it can be seen that the predicted lifetime based on the R

_{i}increase model was longer than that based on the capacity fade model at a higher temperature (higher than 40 °C). For example, the tested battery cell can withstand approximately 5.0 years in terms of capacity if stored at 50% SOC and 55 °C. However, in terms of resistance, the batteries’ lifetimes only last for 1.1 years if they are stored under the same conditions. On the contrary, the R

_{i}increase model gives a shorter lifetime when the temperature decreases to 25 °C as compared with the capacity fade model. For example, the tested battery cell can withstand approximately 14.9 years in terms of capacity if stored at 50% SOC and 25 °C. However, in terms of resistance, the batteries will have 23.8 years if they are stored under the same conditions. This is because when investigating the influence of the storage temperature, the coefficient q

_{T}in the R

_{i}increase model is a constant 0.75 while the coefficient b

_{T}in the capacity fade model is an amount that varies with temperature. As the temperature decreases, the rate of capacity fate decreases exponentially, resulting in a longer predicted lifetime of the capacity-based model

_{4}/C battery cells in terms of capacity (see (16)) and resistance (see (27)), it might be concluded that the degradation during storage of these two performance parameters is not caused by the same aging mechanisms. Moreover, it has to be stressed that the use of the aforementioned lifetime models for determining the aging behavior at temperatures below 25 °C might return erroneous results; this is because lifetime tests performed at lower temperatures (e.g., 15 °C, 10 °C or lower temperatures, etc.) were not considered when developing the test matrices, being outside of the scope of this paper.

#### 3.3. Comparison with the Semi-Empirical Model

_{a}is the activation energy of a reaction happening at a temperature T, T is the absolute temperature in Kelvin, k

_{ref}is the obtained coefficient corresponding to the temperature T

_{ref}and R

_{g}is the gas constant. It should be noted that during long-term calendar aging, the influence of the SOC level was different during different time ranges. The model established in this paper could describe this behavior well by introducing the variable exponent, as shown in (15) and (26). However, the Arrhenius equation describes the monotonic trend of the coefficient changing with the stress factor (i.e., the temperature). In the case of very long-term aging, the traditional semi-empirical model with the Arrhenius equation is not applicable to analyze the effect of SOC on battery degradation. Therefore, in this section, the proposed model and the traditional semi-empirical model are compared only in terms of temperature dependence.

## 4. Conclusions

_{4}/C batteries in terms of capacity fade and internal resistance increase during long-term calendar aging. Considering the storage temperature and SOC level as stress factors that characterized the storage condition, their effect on the rate of calendar degradations was also studied.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zubi, G.; Dufo-López, R.; Carvalho, M.; Pasaoglu, G. The lithium-ion battery: State of the art and future perspectives. Sust. Energy Rev.
**2018**, 89, 292–308. [Google Scholar] [CrossRef] - Chen, T.; Jin, Y.; Lv, H.; Yang, A.; Liu, M.; Chen, B.; Xie, Y.; Chen, Q. Applications of lithium-ion batteries in grid-scale energy storage systems. Trans. Tianjin Univ.
**2020**, 26, 208–217. [Google Scholar] [CrossRef] [Green Version] - Stroe, D.I.; Knap, V.; Swierczynski, M.; Stroe, A.I.; Teodorescu, R. Operation of a grid-connected lithium-ion battery energy storage system for primary frequency regulation: A battery lifetime perspective. IEEE Trans. Ind. Appl.
**2017**, 53, 430–438. [Google Scholar] [CrossRef] - Dubarry, M.; Truchot, C.; Liaw, B.Y. Cell degradation in commercial LiFePO
_{4}cells with high-power and high-energy designs. J. Power Sources**2014**, 258, 408–419. [Google Scholar] [CrossRef] - Sarasketa-Zabala, E.; Aguesse, F.; Villarreal, I.; Rodriguez-Martinez, L.M.; López, C.M.; Kubiak, P. Understanding lithium inventory loss and sudden performance fade in cylindrical cells during cycling with deep-discharge steps. J. Phys. Chem. C
**2015**, 119, 896–906. [Google Scholar] [CrossRef] - Han, X.; Lu, L.; Zheng, Y.; Feng, X.; Li, Z.; Li, J.; Ouyang, M. A review on the key issues of the lithium ion battery degradation among the whole life cycle. ETransportation
**2019**, 1, 100005. [Google Scholar] [CrossRef] - Broussely, M.; Biensan, P.; Bonhomme, F.; Blanchard, P.; Herreyre, S.; Nechev, K.; Staniewicz, R.J. Main aging mechanisms in Li ion batteries. J. Power Sources
**2005**, 146, 90–96. [Google Scholar] [CrossRef] - Belt, J.; Utgikar, V.; Bloom, I. Calendar and PHEV cycle life aging of high-energy, lithium-ion cells containing blended spinel and layered-oxide cathodes. J. Power Sources
**2011**, 196, 10213–10221. [Google Scholar] [CrossRef] - Vetter, J.; Novák, P.; Wagner, M.R.; Veit, C.; Möller, K.C.; Besenhard, J.O.; Winter, M.; Wohlfahrt-Mehrens, M.; Vogler, C.; Hammouche, A. Ageing mechanisms in lithium-ion batteries. J. Power Sources
**2005**, 147, 269–281. [Google Scholar] [CrossRef] - Dubarry, M.; Qin, N.; Brooker, P. Calendar aging of commercial Li-ion cells of different chemistries–A review. Curr. Opin. Electrochem.
**2018**, 9, 106–113. [Google Scholar] [CrossRef] - Käbitz, S.; Gerschler, J.B.; Ecker, M.; Yurdagel, Y.; Emmermacher, B.; André, D.; Mitsch, T.; Sauer, D.U. Cycle and calendar life study of a graphite| LiNi1/3Mn1/3Co1/3O2 Li-ion high energy system. Part A: Full cell characterization. J. Power Sources
**2013**, 239, 572–583. [Google Scholar] [CrossRef] - Badey, Q.; Cherouvrier, G.; Reynier, Y.; Duffault, J.M.; Franger, S. Ageing forecast of lithium-ion batteries for electric and hybrid vehicles. Curr. Top. Electrochem.
**2011**, 16, 65–79. [Google Scholar] - Reniers, J.M.; Mulder, G.; Ober-Blöbaum, S.; Howey, D.A. Improving optimal control of grid-connected lithium-ion batteries through more accurate battery and degradation modelling. J. Power Sources
**2018**, 379, 91–102. [Google Scholar] [CrossRef] [Green Version] - Bindner, H.; Cronin, T.; Lundsager, P.; Manwell, J.F.; Abdulwahid, U.; Baring-Gould, I. Lifetime Modelling of Lead Acid Batteries; Risø Nat. Lab.: Roskilde, Denmark, 2005. [Google Scholar]
- Ashwin, T.R.; Barai, A.; Uddin, K.; Somerville, L.; McGordon, A.; Marco, J. Prediction of battery storage ageing and solid electrolyte interphase property estimation using an electrochemical model. J. Power Sources
**2018**, 385, 141–147. [Google Scholar] [CrossRef] - Swierczynski, M.; Stroe, D.I.; Stan, A.I.; Teodorescu, R.; Kær, S.K. Lifetime estimation of the nanophosphate LiFePO
_{4}/C battery chemistry used in fully electric vehicles. IEEE Trans. Ind. Appl.**2015**, 51, 3453–3461. [Google Scholar] [CrossRef] - Redondo-Iglesias, E.; Venet, P.; Pelissier, S. Modelling lithium-ion battery ageing in electric vehicle applications—calendar and cycling ageing combination effects. Batteries
**2020**, 6, 14. [Google Scholar] [CrossRef] [Green Version] - Schmalstieg, J.; Käbitz, S.; Ecker, M.; Sauer, D.U. A holistic aging model for Li(NiMnCo)O2 based 18650 lithium-ion batteries. J. Power Sources
**2014**, 257, 325–334. [Google Scholar] [CrossRef] - Redondo-Iglesias, E.; Venet, P.; Pelissier, S. Eyring acceleration model for predicting calendar ageing of lithium-ion batteries. J. Energy Storage
**2017**, 13, 176–183. [Google Scholar] [CrossRef] [Green Version] - Hahn, S.L.; Storch, M.; Swaminathan, R.; Obry, B.; Bandlow, J.; Birke, K.P. Quantitative validation of calendar aging models for lithium-ion batteries. J. Power Sources
**2018**, 400, 402–414. [Google Scholar] [CrossRef] - Stroe, D.I.; Świerczyński, M.; Stan, A.I.; Teodorescu, R.; Andreasen, S.J. Accelerated lifetime testing methodology for lifetime estimation of lithium-ion batteries used in augmented wind power plants. IEEE Trans. Ind. Appl.
**2014**, 50, 4006–4017. [Google Scholar] [CrossRef] - Sui, X.; He, S.; Meng, J.; Teodorescu, R.; Stroe, D.I. Fuzzy Entropy-based State of Health Estimation for Li-Ion Batteries. IEEE Trans. Emerg. Sel. Topics Power Electron.
**2020**. early access. [Google Scholar] [CrossRef] - Liu, K.; Li, Y.; Hu, X.; Lucu, M.; Widanage, W.D. Gaussian process regression with automatic relevance determination kernel for calendar aging prediction of lithium-ion batteries. IEEE Trans. Ind. Inform.
**2019**, 16, 3767–3777. [Google Scholar] [CrossRef] [Green Version] - Ecker, M.; Nieto, N.; Käbitz, S.; Schmalstieg, J.; Blanke, H.; Warnecke, A.; Sauer, D.U. Calendar and cycle life study of Li (NiMnCo)O2-based 18650 lithium-ion batteries. J. Power Sources
**2014**, 248, 839–851. [Google Scholar] [CrossRef] - Baumhöfer, T.; Brühl, M.; Rothgang, S.; Sauer, D.U. Production caused variation in capacity aging trend and correlation to initial cell performance. J. Power Sources
**2014**, 247, 332–338. [Google Scholar] [CrossRef] - Schuster, S.F.; Bach, T.; Fleder, E.; Müller, J.; Brand, M.; Sextl, G.; Jossen, A. Nonlinear aging characteristics of lithium-ion cells under different operational conditions. J. Energy Storage
**2015**, 1, 44–53. [Google Scholar] [CrossRef] - Sui, X.; Stroe, D.I.; He, S.; Huang, X.; Meng, J.; Teodorescu, R. The effect of voltage dataset selection on the accuracy of entropy-based capacity estimation methods for lithium-ion batteries. Appl. Sci.
**2019**, 9, 4170. [Google Scholar] [CrossRef] [Green Version] - Schimpe, M.; von Kuepach, M.E.; Naumann, M.; Hesse, H.C.; Smith, K.; Jossen, A. Comprehensive modeling of temperature-dependent degradation mechanisms in Lithium iron phosphate batteries. J. Electrochem. Soc.
**2018**, 165, A181. [Google Scholar] [CrossRef] [Green Version] - Agubra, V.A.; Fergus, J.W. The formation and stability of the solid electrolyte interface on the graphite anode. J. Power Sources
**2014**, 268, 153–162. [Google Scholar] [CrossRef]

**Figure 1.**The test matrix for determining the calendar lifetime of the LiFePO

_{4}/C battery cells (possible interaction between stress factors is not considered.

**Figure 3.**Current pulse train profile applied to measure the internal resistance of the LiFePO

_{4}/C battery cells at 20%, 50% and 80% state of charge (SOC).

**Figure 5.**Capacity fade curves of calendar-aged cells under different conditions. (

**a**) Boxplot of the capacity fade, (

**b**) Standard deviation of the capacity fade.

**Figure 7.**Fitting results between the capacity fade and storage time using different target functions. (Illustrated by the calendar aging test of Case 1).

**Figure 8.**Effect of storage time and temperature on the decrease of the capacity (at 50% SOC level).

**Figure 9.**The relationship between the curve fitting coefficients and the corresponding storage temperature. (

**a**) Exponential relationship between a

_{T}and T, (

**b**) Power relationship between b

_{T}and T.

**Figure 11.**The relationship between the curve fitting coefficients and the corresponding storage SOC level. (

**a**) Exponential relationship between a

_{SOC}and SOC, (

**b**) Power relationship between b

_{SOC}and SOC.

**Figure 12.**Lifetime prediction results using the established capacity fade model (when 20% capacity fade EOL criterion has been reached).

**Figure 13.**The pulse voltage responses applied to measure the internal resistance of the LiFePO

_{4}/C battery cell.

**Figure 14.**Resistance increase curves of calendar-aged cells (R

_{i}was calculated from 4C-rate discharging pulse at 80% SOC). (

**a**) Boxplot of the resistance increase, (

**b**) Standard deviation of the resistance increase.

**Figure 15.**Effects of storage time and temperature on the increase of the resistance (at 50% SOC level).

**Figure 16.**The exponential relationship between the curve fitting coefficients p

_{T}and the corresponding storage temperature T.

**Figure 18.**The relationship between the curve fitting coefficients and the corresponding storage temperature. (

**a**) Exponential relationship between a

_{SOC}and SOC, (

**b**) Exponential relationship between b

_{SOC}and SOC.

**Figure 19.**Lifetime prediction results using the established resistance increase model (when 100% resistance increase EOL criterion has been reached).

**Figure 20.**Arrhenius equation for determining the temperature dependence of capacity fade (at 50% SOC level).

**Figure 21.**Comparison of modeling results for temperature dependence of capacity fade (at 50% SOC level).

**Figure 22.**Arrhenius equation for determining the temperature dependence of resistance increase (at 50% SOC level).

**Figure 23.**Comparison of modeling results for temperature dependence of resistance increase (at 50% SOC level).

Item | Value |
---|---|

Type | cylindrical |

Dimensions | Ø 26 × 65 mm |

Weight | 76 g |

Nominal capacity | 2.5 Ah |

Nominal voltage | 3.3 V |

Maximum voltage | 3.6 V |

Minimum voltage | 2.0 V |

Maximum-continuous charge current | 10 A (4C) |

Maximum-continuous discharge current | 50 A (20C) |

Operating temperature | −30 °C to 55 °C |

Storage temperature | −40 °C to 60 °C |

**Table 2.**The curve fitting coefficients of the capacity fade model considering temperature variation (SOC level is fixed to 50%).

Fitting Function Type | Number of Parameters | R^{2} | |
---|---|---|---|

Logarithmic function | ${C}_{fade}(t)=a\times \mathrm{ln}(b\times t)$ | 2 | 0.9748 |

Polynomial function | ${C}_{fade}(t)=a\times t+b$ | 2 | 0.9876 |

Power function with a variable constant term | ${C}_{fade}(t)=a\times {t}^{b}+c$ | 3 | 0.9980 |

Power function with a fixed constant term | ${C}_{fade}(t)=a\times {t}^{b}+0.7$ | 2 | 0.9974 |

**Table 3.**The curve fitting coefficients of the capacity fade model considering the temperature variation (SOC level is fixed to 50%).

Test Condition | Temperature (°C) | a_{T} | b_{T} | R^{2} |
---|---|---|---|---|

Case 1 | 55 °C | 2.428 | 0.812 | 0.9974 |

Case 2 | 47.5 °C | 1.08 | 0.897 | 0.9943 |

Case 3 | 40 °C | 0.452 | 0.932 | 0.9862 |

**Table 4.**The curve fitting coefficients of the capacity fade model considering the SOC level variation (temperature is fixed to 55 °C).

Test Condition | SOC (%) | a_{SOC} | b_{SOC} | R^{2} |
---|---|---|---|---|

Case 4 | 10% | 1.387 | 0.823 | 0.9973 |

Case 1 | 50% | 2.428 | 0.812 | 0.9974 |

Case 5 | 90% | 4.999 | 0.541 | 0.9990 |

**Table 5.**The curve fitting coefficients of the resistance increase model considering temperature variation (SOC level is fixed to 50%).

Test Condition | Temperature (°C) | p_{T} | q_{T} | R^{2} |
---|---|---|---|---|

Case 1 | 55 °C | 4.63 | 0.75 | 0.999 |

Case 2 | 47.5 °C | 3.575 | 0.75 | 0.998 |

Case 3 | 40 °C | 2.859 | 0.75 | 0.908 |

**Table 6.**The curve fitting coefficients of the resistance increase model considering SOC level variation (temperature is fixed to 55 °C).

Test Condition | SOC (%) | p_{SOC} | q_{SOC} | R^{2} |
---|---|---|---|---|

Case 4 | 10% | 2.518 | 0.845 | 0.975 |

Case 1 | 50% | 4.630 | 0.750 | 0.999 |

Case 5 | 90% | 7.213 | 0.583 | 0.985 |

**Table 7.**Comparison of the lifetime prediction results between the proposed capacity fade model and the semi-empirical model (Only the effects of storage time and temperature are considered; when 20% capacity fade EOL criterion has been reached, SOC level is fixed to 50%).

Temperature (°C) | Predicted Lifetime Using the Proposed Model (Month) | Predicted Lifetime Using Semi-Empirical Model (Month) | Measured Lifetime (Month) |
---|---|---|---|

55 °C | 12.5 | 12 | 13 |

47.5 °C | 25 | 27.5 | 26 |

40 °C | 53.5 | 64.5 | / ^{1} |

25 °C | 285.5 | 400.5 | / |

^{1}The value is not available because the test did not reach the EOL.

**Table 8.**Comparison of the lifetime prediction results between the proposed resistance increase model and the semi-empirical model (Only the effect of storage time and temperature is considered; when 20% capacity fade EOL criterion has been reached, SOC level is fixed to 50%).

Temperature (°C) | Predicted Lifetime Using the Proposed Model (Month) | Predicted Lifetime Using Semi-Empirical Model (Month) | Measured Lifetime (Month) |
---|---|---|---|

55 °C | 60 | 60 | / ^{1} |

47.5 °C | 82 | 84 | / |

40 °C | 114 | 114 | / |

25 °C | 232 | 179 | / |

^{1}The value is not available because the test did not reach the EOL.

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**MDPI and ACS Style**

Sui, X.; Świerczyński, M.; Teodorescu, R.; Stroe, D.-I.
The Degradation Behavior of LiFePO_{4}/C Batteries during Long-Term Calendar Aging. *Energies* **2021**, *14*, 1732.
https://doi.org/10.3390/en14061732

**AMA Style**

Sui X, Świerczyński M, Teodorescu R, Stroe D-I.
The Degradation Behavior of LiFePO_{4}/C Batteries during Long-Term Calendar Aging. *Energies*. 2021; 14(6):1732.
https://doi.org/10.3390/en14061732

**Chicago/Turabian Style**

Sui, Xin, Maciej Świerczyński, Remus Teodorescu, and Daniel-Ioan Stroe.
2021. "The Degradation Behavior of LiFePO_{4}/C Batteries during Long-Term Calendar Aging" *Energies* 14, no. 6: 1732.
https://doi.org/10.3390/en14061732