Chemical rate phenomenon approach applied to lithium battery capacity fade estimation

MR-12081; No of Pages 6 Microelectronics Reliability xxx (2016) xxx–xxx

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Chemical rate phenomenon approach applied to lithium battery capacity fade estimation I. Baghdadi a,b,⁎, O. Briat a, J.Y. Delétage a, P. Gyan b, J.M. Vinassa a a b

Univ. Bordeaux, CNRS, Bordeaux INP, IMS UMR 5218, F-33400 Talence, France Technocentre Guyancourt, 1 Avenue du Golf, 78288 Guyancourt, France

a r t i c l e

i n f o

Article history: Received 29 June 2016 Accepted 8 July 2016 Available online xxxx

a b s t r a c t This paper deals about a lithium battery capacity aging model based on Dakin's degradation approach. A 15 Ah commercial lithium-ion battery based on graphite/iron-phosphate technology was used for this purpose and aged at nine different conditions. In fact, the effect on aging of temperature (30, 45, and 60 °C) and battery state of charge (30, 65, and 100%) is studied. The Dakin's degradation approach based on chemical kinetics is used to establish the battery aging law. The aging rate expression is then deduced and found equivalent to Eyring's law. The aging rate increases exponentially with rising temperature and SOC. Model simulation is compared with experiment, literature and results are discussed. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Lithium batteries are key solution as power storage systems for several applications including portable devices, space, and electrified vehicles. Their success is principally due to their high power and energy density [1]. Therefore, several researchers are attempting to develop more powerful [2], smaller [3], and more secure batteries [1]. Lithium batteries performance decays over time. The main aging processes are related to solid electrolyte interphase (SEI) growth, active material loss, and lithium plating [4–6]. These chemical phenomena consume available lithium and alter active material properties leading to a decrease in battery capacity and an increase in internal resistance [7]. Power and energy capabilities are then reduced. A major concern of electrified vehicles manufacturers is to ensure the steadiness of vehicle performances through their usage. Thus, the knowledge of an accurate battery aging law is required to optimize the durability, design, and vehicle warranty cost. Several models have been developed for (but not limited to) this purpose including semi-empirical, fatigue approach and electrochemical aging models [8–10]. A principal difference between these different approaches lies in the robustness and computational cost ratio [11]. Electrochemical models based on porous electrode theory are interesting to study in more details and separately the aging rate of the cathode and the anode [10]. However, tens of parameters must be determined, and most among them could not be measured or verified. On the other hand, fatigue approach and semi-empirical models could offer sufficient accuracy with a lower computing time and complexity [8,9]. ⁎ Corresponding author at: Univ. Bordeaux, CNRS, Bordeaux INP, IMS UMR 5218, F33400 Talence, France. E-mail address: [email protected] (I. Baghdadi).

Generally, vehicles spend most of their time (90%) unused or parked at a random battery state of charge (SOC) and exposed to a variable surrounding temperature. Temperature and SOC are thus the principal aging factors in calendar aging which highly contributes to the total performance fade [8,12]. Thus, this aging mode is studied and modeled in this work. The Dakin's degradation approach, inspired from chemical kinetics, is widely used in the literature to study the thermo-oxidative aging of polymer composites and electrical insulations function of the voltage and the temperature [13–15]. On the other hand, the lithium battery separator is generally made by Polyvinylidene fluoride (PVDF) for its high dielectric properties. In fact, the dielectric strength of PVDF is about 1.7 V.μm−1 and a separator in lithium batteries is approximately 25 μm thick. However, the separator is made highly porous to enable electrolyte diffusion which reduces its insulation strength. Thus, a lithium battery voltage window ranging from 2 to 4.2 V is sufficiently high to damage the polymer structure overtime, increasing leakage current and accelerating parasitic reactions. Dakin's degradation approach is then particularly interesting to study battery aging phenomena including SEI growth, active material loss and separator failure.

2. Experimental A 15 Ah commercial lithium-ion battery based on graphite/ironphosphate was aged for this purpose. Its basic characteristics are summarized in Table 1. The characterization tests were performed using VMP multipotentiostats from Biologic with 20 V/ 20 A boosters.

http://dx.doi.org/10.1016/j.microrel.2016.07.058 0026-2714/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: I. Baghdadi, et al., Chemical rate phenomenon approach applied to lithium battery capacity fade estimation, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.058

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α are constants, the solution of the degradation Eq. (1) is described in (2).

Table 1 Battery basic characteristics. Battery

Capacity

Cutoff voltages

Charging protocol

LiFebatt

15 Ah

3.65/2.3 V

I = 15 A until 3.65 V and CV I = 0.75 A

The cell charging protocol consists on a constant current charge followed by a constant voltage phase (CC-CV). In fact, the battery is charged at 15 A until reaching 3.65 V. Then, the voltage is held constant until the current reaches 0.75 A. 2.1. Cells initial condition The cells were initially virgin and stored at low temperature (b10 °C) and at a medium SOC. Before aging, the cells were preconditioned by performing 6 full cycles to identify suspicious elements. For each cycle, the cells are discharged at 15 A until reaching minimal voltage under current, followed by 15 min of rest. Then, the cells are fully charged with CCCV protocol (Table 1) and discharged again until reaching 2.3 V. The initial battery capacity was approximately 14.8 Ah with a standard deviation of 0.3 Ah.

C ðt Þ ¼ C 0 exp−ðkt Þ

α

ð2Þ

where C0 and C are the battery initial capacity and the capacity at a given time, respectively. Assuming that Eqs. (1) and (2) are adequate to describe the battery aging, the time dependent factors are thus deduced from the slopes of the straight lines after a transformation of capacity fade evolution over time using (3).

 C ðt Þ α ln − ln ¼ α ln t þ ln k C0

ð3Þ

Therefore, the degradation rates are determined using (4) after deducing the time dependent factors. ln

C ðt Þ α ¼ −ðktÞ C0

ð4Þ

2.2. Aging tests 4. Model calibration A total of nine different aging tests were performed, including 3 different temperatures (30, 45, 60 °C) at 3 different SOCs (30, 65, 100%), Table 2. For each aging condition, 3 cells were tested to ensure reproducibility and for post-mortem analysis [16]. The aging battery SOCs were set from a fully charged state by ampere hours counting at 25 °C. In fact, the cells are charged using CC-CV protocol. Then, discharged at 15 A for a certain time = 1 h × (100 − SOC)/100. Therefore, cells were set at the corresponding aging temperature in climatic chambers (Climats) without maintaining the voltage. 2.3. Performance checkup Each two months capacity checkups were performed. This period was shortened or extended for extreme aging conditions. The battery capacity (C) was measured by ampere hours counting at 1C (15 A) and 25 °C. In fact, the cells are fully charged using the CC-CV protocol followed by 30 min of rest. Then, the cells are discharged until reaching 2.3 V under current. This operation is performed twice and the capacity of a cell is averaged. 3. Model and equations The experimental results are analyzed using the generalized Dakin degradation equation, described in (1) [13,17,18]. dC α ¼ −k C n dt α

4.1. Identification of time dependent factors The time dependent factors are identified using (3). The identification results are shown in Fig. 1. Fig. 1 shows that the double logarithms of battery capacity decay evolve linearly over time logarithm. In fact, the regression coefficients R2 are close to 1 (Fig. 1). However, low R2 = 0.923 is noted for T60 °C SOC30%. The decreasing R2 at 60 °C with SOC could suggest a different aging mechanism enabled at high temperature and low SOC. The time dependent factors, α, are identified from the slopes of the solid lines (Fig. 1) and summarized in Table 3. α is clearly more sensitive to the temperature than to the SOC. In fact, averaged α with the SOC are 0.94, 0.95, 0.64 with a high standard deviations, 26, 31, 21% for SOC 30, 65 and 100%, respectively. However, averaged α with the temperature are 1.07, 0.88, 0.58 with lower standard deviations, 30, 6, 11% for 30, 45, 60 °C, respectively. A high standard deviation value for 30 °C is noted and is a consequence of the low α value (0.62) for SOC 100% (Table 3). In fact, at a high state of charge the major part of cycleable lithium is inserted in the graphite anode, site of SEI growth reaction. This reaction rate is sensitive to the lithium proportion within the graphite electrode as a principal reagent. According to the literature, SEI growth evolves overtime according to time square root [4]. Low α (~0.5) value at 100% of SOC is thus expected. For greater ease and as a first approach α were averaged in this work with temperature. The results are shown in Fig. 2.

ð1Þ

where t the aging time (days), k the degradation rate (days−1), α (number) the time dependent factor, and n (number) is an exponent which determines the order of the chemical reaction. This study is restricted to the case where the reaction order n = 1. Thus, when k and Table 2 Aging test matrix. SOC(%)/T(°C) 30 65 100

30

45

60

Fig. 1. Time dependent factor identification results.

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4.2. Identification of degradation rates

Table 3 Identified time dependent factors. Time dependent factors, α (number) SOC(%)/T(°C) 30 65 100

30 1.23 1.36 0.62

45 0.97 0.86 0.83

60 0.62 0.64 0.49

Fig. 2 shows that average time dependent factor, α, decreases linearly with the increasing temperature. The same data were analyzed by Grolleau et al. within the SIMCAL project [12]. Grolleau et al. model is presented in (5) and adapted for comparison with Dakin model.
α dC C0 ¼ −kC 0 dt 2C 0 −C

ð5Þ

The solution of (5), considering k and α constants, is shown in (6).   1 C ðt Þ ¼ C 0 2−ððα þ 1Þkt þ 1Þ1þα

ð6Þ

Eq. (6) is similar to square root models widely studied and validated in the literature when α = 1 [19,20]. However, a physical inconsistency of (6) is that C(t) tend to infinity with increasing time. Grolleau et al. have found that the 15 Ah LiFebatt battery aging could not be described as a strict evolution over time0.5 as α is sensitive to temperature. In fact, α were identified using non-linear regression fitting and found greater for 60 °C (α ~ 7) than for 45 °C (α ~ 3). For 30 °C the optimization routine by Grolleau et al. was unable to find a good fitting [12]. Thus, α was set manually equal to 3. For comparison between both models, (2) is approximated using Taylor expansion truncated to the first order in (7).

C0

3

  Xþ∞ −ðkt Þα n  α ≅C0 1−ðktÞ n¼0 n!

ð7Þ

Using (4) and the identified averaged α (Fig. 2), the logarithm of capacity fade is plotted function of timeα(T) and results are shown in Fig. 3. The battery capacity aging rates are then identified using (8). 1 kðSOC; T Þ ¼ a =αðT Þ

ð8Þ

where a represent the straight lines slopes in Fig. 3 and α(T) from Fig. 2. The logarithm of capacity fade function of timeα(T) are linear as the regression coefficients are close to 1, except for T60 °C SOC30% (0.931) and T30 °C SOC100% (0.922). In fact, the identified α for T30 °C SOC100% is lower than the average at the same temperature and this has worsened the fitting results (0.62 b 1.07, Table 3 and Fig. 2). The battery capacity aging rates are summarized in Table 4. The aging rate increases when temperature and SOC increase. However, k is more sensitive to the temperature than to the SOC. The average k is 10 times greater when temperature doubles. However, it is only 2 times greater when the SOC is twice higher. k logarithm is plotted function of 1/T and SOC to check Arrhenius law at each SOC (Fig. 4). Aging rates logarithm could be represented by a flat surface that matches experimental rates (red diamonds). Thus, k logarithm expression follows a flat surface equation described in (9) 1 a  lnk þ b  −c  SOC−d ¼ 0 T

ð9Þ

where a, b, c, and d represent the flat surface parameters. In the identification process, a (J.K−1.mol−1) is set manually equal to the gas constant. Then, b, c, d are identified using least square method by fitting the experimental results. The average error of the identification process is approximately 4% and flat surface parameters are summarized in Table 5. b represents the Arrhenius activation energy, c the activation energy related to the SOC and d a pre-exponential factor. k expression is then deduced from (9), described in (10) and plotted in Fig. 5.

The expansion of Dakin model could be truncated to the first order as (kt)α ≪ 1. In fact, the first order represents the major part, and the superior orders tend to zero. This approximation is equivalent to aging models based on the square root of time when α = 0.5 [17]. From (6) and (7), the time dependent factor of Dakin's degradation approach is equivalent to 1/(1 + α) in the model developed by Grolleau et al. Thus, 1/(1 + α) is also decreasing as they found α increasing with temperature. However, 1/(1 + α) are lower (0.25 for 30 °C and 45 °C and 0.125 for 60 °C) than those identified using Dakin's approach (Fig. 2).

The aging rate increases exponentially with increasing temperature and SOC. The model is globally in agreement with experimental results (red diamonds) with an average error of 14%. In fact, the average error (4%), result of the identification process of flat surface parameters, is amplified when passing from logarithmic to exponential scale (from (9) to (10)).

Fig. 2. Averaged α function of temperature.

Fig. 3. Aging rates identification results.

cSOC a

kðT; SOC Þ ¼ exp

 expa  expð aT Þ d

−b

ð10Þ

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Table 4 Battery capacity degradation rates.

Table 5 Flat surface parameters identification.

Degradation rate, k (10−5 days−1) SOC(%)/T(°C) 30 65 100

30 6.11 9.83 11.6

45 21 30.55 35.45

60 36.41 100.92 118.36

a

b

c

d

(J.K−1.mol−1)

(kJ.mol−1)

(J.K−1.mol−1)

(J.K−1.mol−1)

8.314

60.82

0.0964

116.87

4.3. Model simulation results The established battery aging expression is similar to Eyring's law described in (11) [21] when γ = 0. γ −b d kEyring ðV; T Þ ¼ expðβþT Þ f ðV Þ  expa  expð aT Þ

ð11Þ

In fact, the battery SOC of a lithium battery is correlated to its OCV through a bijective function [1]. Batteries with lithium iron phosphate (LFP) cathode technology have a flat open circuit voltage (OCV) slightly sensitive to the SOC (~3.3 V). In fact, lithium intercalation (de-intercalation) proceeds through a two-phase reaction between compositions very close to LiFePO4 and FePO4 [22]. Thus, the cells aged under different SOCs have almost the same voltage as an aging factor. The increase in aging rate with increasing SOC is thus governed by SEI growth. At elevated SOC, the cycleable lithium as a principal reagent is in a major part inserted in the anode, site of the SEI growth reaction [4,23]. However, several OCVs range between 2 and 4.2 V, especially for batteries where the lithium intercalation in the cathode proceeds as solid solution (i.e. lithium nickel manganese cobalt, NMC, or lithium nickel cobalt aluminum, NCA) [1]. The aging rate of such batteries is thus more sensitive, than LFP batteries, to the SOC which highly influences the battery voltage [17,24]. Grolleau et al. has chosen a linear fitting for k function of SOC [12]. The aging rate expression is then described in (12) where Ai (i = 1; 2) represent the temperature effect governed by Arrhenius's law. From Table 5 and (10), c × SOC/d ranges between 0 and 1.15 when SOC is 0% and 100%, respectively. Thus, the exponential contribution to the aging of SOC in the Dakin aging rate expression, (10), could be linearly approximated by Taylor expansion. kðT; SOC Þ ¼ A1 ðT Þ  SOC þ A2 ðT Þ

ð12Þ

For batteries with a sensitive OCV to SOC (NMC or NCA based cathode) a linear fitting of the SOC effect on aging underestimates the aging rate [17]. Ecker et al. have found that the impact of SOC on an NMC battery aging rate is as important as the temperature impact which requires an exponential fitting [24].

Fig. 4. Arrhenius plots function of aging SOCs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The capacity model is developed using Eqs. (2), (10) and the averaged α detailed in Fig. 2. Simulation results are presented in Fig. 6. The model shows relatively good fitting results especially for 30 and 45 °C tests. The average error is the highest for 60 °C where it is equal to 3.16, 6 and −4.3% for SOC 100, 65 and 30%, respectively. In fact, from Fig. 5 the aging rate model underestimates the rate value at 60 °C. Likewise, the capacity fade for T 60 °C SOC 30% are well modeled until days 200. However, a model divergence is noted after 200 days which could be explained by the low R2 in α identification process suggesting a different aging mechanism. Nevertheless, simulation results are accurate for lower temperatures. In fact, the worse error is noted for 45 °C and 100% of SOC. However, average errors are near 0% for the remaining conditions. The accuracy is comparable with Grolleau et al. model [12]. 4.4. Lifetime estimation Generally, a battery is considered at end of life for power application when its capacity decays of 20% (C/C0 = 0.8). Thus, from Dakin model, the corresponding battery lifetime (L) for batteries stored at constant aging conditions is described in (13). 1

L ¼ ð− ln ð0:8ÞÞ

=αðT Þ

, ð13Þ ð365kðSOC;T ÞÞ

The lifetime results at same conditions (SOC = 100% and different temperatures) are presented in Table 6 for both models. Grolleau et al. model consider a constant α for temperatures below 30 °C as α(T) were identified only for 60 °C and 45 °C, but manually set for 30 °C. Nevertheless, both models results are close. At 20 °C, the battery lifetime is about 20 years which is compatible with vehicular application. However, a 10 °C increase of storage temperature cuts in half the expected battery lifetime. On the other hand, the power cycling impact should be taken into account as it highly contributes to the total aging [7]. An NMC and NCA based technology batteries were tested under calendar and

Fig. 5. Simulated aging rates vs. experimental rates.

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The developed model is analyzed and compared to a similar model in the literature and both model simulation results are equivalent and in agreement with experiment.

Acknowledgements The data used in this work are from SIMCAL1 project funded by National Research Agency (ANR). The current work is funded by the French FUI (United Interministerial Fund) under the MOBICUS2 industrial research program. The continuity of the research programs is enabled by the partner network: Renault1,2, CEA1,2, Controlsys2, DBT-CEV2, EDF1,2, EIGSI1,2, Enedis2, IFPEN1,2, IFSTTAR1,2, IMS1,2, La Poste2, LEC1,2, LMS-Imagine/ Siemens1,2, LRCS1, MTA1, Peugeot-Citroën1,2, SAFT1,2, Valeo1,2, and WattMobile2. Fig. 6. Simulation results (lines) vs. experiment (markers).

power cycling aging modes within the SIMCAL and SIMSTOCK projects [17]. In fact, both batteries were aged under several temperatures, SOCs and current magnitudes and the data were similarly analyzed with Dakin's degradation approach. The time dependent factors were found constant and slightly sensitive to aging conditions (α = 1 and α = 0.5 for NMC and NCA batteries, respectively) suggesting a different aging mechanism compared to the LiFebatt battery where α is sensitive to the temperature [17,25]. The total aging rate expression function of SOC, temperature and current magnitude (I) of both batteries is described in (14) [17]. ktot ¼ expðaðT ÞIÞ  expð

cSOC a

Þ  expðdaÞ  expð−b aT Þ

ð14Þ

where a(T) (A−1) represents the cell temperature effect on power cycling. In addition, a(T) highly increases with decreasing temperatures leading to an increase of aging rate at low temperatures with a cycling optimum (observed near 25 °C) [17]. In real applications, a battery pack is aged at variable operating conditions depending on geography, seasons, and driving style. The developed aging model should be coupled to electro thermal models to take into account battery self-heating, variable SOC, and power solicitation [26]. Therefore, the models should be interconnected to represent the battery pack, assembly of cells connected in serial and parallel. This allows studying the aging propagation and dispersion within the battery pack. 5. Conclusions The calendar aging of a lithium battery based on iron phosphate cathode is studied at several temperatures and state of charges. 9 different aging conditions including 3 temperatures (30, 45 and 60 °C) at 3 SOCs (30, 65 and 100%) were analyzed using Dakin's degradation approach which is inspired from chemical kinetics. The model parameters were identified by fitting linearly the experimental results in the logarithmic scale. The identified time dependent factors decrease with increasing temperature. The capacity aging rate expression is identified and found equivalent to Eyring's law. In fact, capacity aging rate increases exponentially with temperature and SOC. However, the temperature impact on aging is higher than the SOC impact. Table 6 Lifetime estimation comparison between Dakin and Grolleau et al. models. Model/T (°C)

20

25

30

Dakin, (years) Grolleau et al. [12] (years)

18 20

12 13.5

8 9

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Please cite this article as: I. Baghdadi, et al., Chemical rate phenomenon approach applied to lithium battery capacity fade estimation, Microelectronics Reliability (2016), http://dx.doi.org/10.1016/j.microrel.2016.07.058