Chemo-economic analysis of battery aging and capacity fade in lithium-ion battery

Journal of Energy Storage 25 (2019) 100911

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Chemo-economic analysis of battery aging and capacity fade in lithium-ion battery

T

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Abhishek Sarkar, Pranav Shrotriya , Abhijit Chandra, Chao Hu Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Capacity fade Solid Electrolyte Interface Reduced-order model Battery aging Battery recycling

Degradation due to capacity fade is a major cause of concern involved in the design and implementation of lithium-ion battery. In particular, the formation and growth of Solid Electrolyte Interface (SEI) have been considered as one of the primary degradation mechanisms affecting the cycle life of the battery. Over the past decade, several models have been reported towards simulation of SEI growth-induced degradation and prediction of cycle life. In this work, an efficient reduced-order electrochemical model was developed for a lithium cobalt oxide/graphite battery. A reaction–diffusion based SEI model was integrated with the electrochemical model to predict the cyclic capacity loss due to electrolyte deposition on the anode. The algorithm developed for this battery module was designed to reduce the computational time for capacity fade calculation with any (dis) charging protocol. The model was also applied for a lithium ferrous phosphate/graphite cell and in both cases, the fade predictions were within ± 1% deviation from the experimental results. A comparison of two charging protocols was undertaken to identify approaches that improve capacity fade characteristics of battery. The electrochemical benefit of a reduced fading rate for aged (or used) lithium battery was investigated. A concept of “aged-battery” was proposed to be used as an advantage for better cycle-life in battery for biomedical devices and recycling of electric vehicle battery for solar panels applications. An economic analysis was performed to justify the benefits from lower fade that was weighed against the additional cost involved in aging the battery.

1. Introduction Advancements in the lithium-ion battery technology over the past couple of decades have revolutionized the electronic, automotive and power industries [1,2]. Now, lithium-ion batteries have high energy density (>150 Wh/kg), high cycle life (>2000 cycles) and high columbic efficiency (>95%), making these energy storage units long lasting, portable and efficient [3]. A lithium-ion battery, being an electrochemical system, has transport of both ions and electrons. During the intercalation process, the lithium ions and the electrons would combine at the electrolyte/electrode interphase, making this the most critical domain in the entire battery [4–9]. The concept of the solid electrolyte interface (SEI) was first established by Peled et al. [5], as an electronically insulating but ionically conductive passivation layer at the electrode/electrolyte interface and the composition of the film was determined and summarized by Peled et al. [6] and Aurbach et al. [7]. The SEI is formed when the redox potential of the electrode lies outside the potential range for the battery [10]. The formation and growth of the SEI layer are both beneficial and detrimental for the

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battery. As the SEI layer grows, its poor electronic conductivity restricts the electron tunneling from the electrolyte thus prohibiting further electrolyte reduction. This improves the electrochemical stability of the battery. On the other hand, the formation and growth of the SEI layers occur due to consumption of the active lithium material from the electrolyte, thereby reducing the capacity of the battery [8,9]. Experimental analysis of SEI film growth can reveal the composition, growth rate and fade ability of battery due to an active SEI. However, it is not feasible to monitor the kinetics and thermodynamics of the SEI layer with the available experimental methodology. Therefore, prognostic modeling of SEI growth and the prediction of capacity fade using electrochemical degradation models provide a suitable means for monitoring battery life. There have been several works performed on modeling the anode reduction during SEI formation using techniques like molecular dynamics and quantum chemistry [11–13]. Continuum level modeling of lithium-ion battery with SEI was initially started as a modification on the Newman electrochemical model to incorporate SEI current as the irreversible loss parameter [14,15]. Peled et al. [5] modeled a parabolic SEI growth mechanism and later the model got modified to derive the experimentally observed t nature

Corresponding author. E-mail address: [email protected] (P. Shrotriya).

https://doi.org/10.1016/j.est.2019.100911 Received 23 January 2019; Received in revised form 10 April 2019; Accepted 21 August 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Single particle electrolyte model representation of a lithium-ion battery with SEI growth.

affordable, like an electric vehicle or biomedical applications. Finally, an economic analysis was performed to provide a cost versus capacity comparison involved the selection of aged lithium-ion battery based on the application.

of the capacity loss over battery cycling [16,17]. Reduced-order models like the single particle model have been popularly used with the assumption of constant reaction current to reduce the complexity of the Newman model by decoupling the governing equations [18]. Investigations by Prada et al. [19] and Ekstrom and Lindbergh [20] have modeled the capacity and power fade for a lithium ferrous phosphate (LFP)/graphite (C) battery. Reduced-order models have been also used to simulate battery degradation due to SEI formation [21–25]. In the work done by Baek et al. [22], a linear SEI profile was assumed by replacing the reaction coefficient for the SEI current by a constant. Jin et al. [21], proposed a non-linear model for the reaction coefficient and used a numerical optimization to predict capacity fade in LFP/C cell. The rapid growth of electric vehicle (EV) in the automobile industry has shown a rising trend in lithium battery utilization. In the year 2020, about 0.45–4 million EVs will be sold in the US and 5.2–19.8 million in the international market [26–28]. The growing demand for lithium batteries increases the pressure on consumption of lithium, cobalt, nickel, and manganese [27,29]. Since, cobalt, nickel, and manganese are not primarily mined in the US, a potential instability is eminent in the future of lithium battery production. Therefore, sustainable utilization and recycling of EV lithium battery systems for electric grids and solar panel applications would be key towards the stable growth of battery industry in the future. Several studies have reported the potential technical, economical and energetic analysis towards the application of recycled EV batteries for solar panel grids and in the electric supply chain [30]. In the current work, an efficient reduced-order electrochemical model was developed for a lithium-ion battery with a non-linear kinetic formulation to model the SEI current. The proposed model was applied with a Euler Implicit scheme for accurate and rapid prediction of capacity fade in lithium-ion battery with any (dis)charging protocol. The model was adjusted for graphite-based anodes based on experimental data acquired from lithium cobalt oxide (LCO)/graphite (C) cells and validated for LCO/C and LFP/C cells. The electrochemical benefit of aged/used lithium-ion battery was studied targeting recycling of used EV batteries for solar panel grids. A concept of aging the lithium-ion battery prior to commercialization was proposed based on the work by Fathi et al. [31], and simulated to predict the capacity loss for an aged lithium-ion cell. The aging process was designed to reduce the effective capacity loss over the operation period of the battery and would be advantageous for applications where battery replacement is not

2. Mathematical model A continuum level modeling of lithium-ion battery requires solving a set of six coupled ODEs and PDEs governing the diffusion, kinetics and charge conservation as developed by Newman et al. [15]. Modeling the SEI growth-induced degradation involves modifying the Newman model to include the SEI kinetics and growth. A reduced-order battery degradation model was developed with the ability to predict capacity fade over multiple cycles. A single particle electrochemical model [18] (SPM) was utilized to simulate a lithium-ion battery with a constant-current (CC) discharge and a constant-current-constant-voltage (CCCV) charge protocol. The lithium-ion cell was assumed to have a dilute reaction species behavior with the electrolyte to be a lithium source/sink providing a uniform reaction current to the electrode particles. The ionic/electronic current variation throughout the electrode was assumed to be linear. However, the overall lithium species conservation was maintained in the analysis. The electrochemical SPM model was integrated with a battery degradation model that captures SEI formation and growth [24,32]. A lithium-ion battery was modeled with electrode particles having SEI deposition on the anode, as represented in Fig. 1. The electrode particles were assumed to be spherical and the average particle radius was considered across the electrode. The diffusion of lithium ions into the electrode was governed by Fick's Second Law [33]. The surface of the particle was subjected to the reaction current flux (jn).

∂cs ∂ 2c 2 ∂cs ⎞ = Ds ⎛ 2s + ∂t r ∂r ⎠ ⎝ ∂r ⎜

− Ds

∂cs ∂r

⎟

= jn Re

(1)

(2)

The reaction current flux is related to the gradient of the ionic current in Eq. (4). Since the ionic current varies linearly with the electrode thickness, the reaction current flux is a constant.

Il + Is = Iapp 2

(3)

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(Fa). jn = ∇ . Il = −∇ . Is =

Iapp Ls

(4)

where, Il, Is, Iapp is the ionic, electronic and applied current flux, cs is the solid-phase lithium-ion concentration, Ds is the lithium diffusion coef3ϵ ficient of the electrode, a = R is the effective reaction area per unit s volume, ϵ, Ls are the porosity and thickness of the electrode, Rs is the average electrode particle radius, and F is the Faraday's constant. The current and surface over-potential (η = ϕs − ϕl − UOCV ) for the positive electrode, were expressed as a function of the normalized lic thium-ion concentration ( c ) , using the Butler-Volmer kinetics [15].

−ve

αF iSEI = −i 0 exp ⎛− (ϕs − ϕl − USEI − RSEI in ) ⎞ ⎠ ⎝ RT

δ κ

= cl

= −Dl ∇cl

− int

− int

(14) (15)

∂lnf± ⎞ ∂lncl ∂ϕ 2RT (1 − tc0) ⎛⎜1 + σl ⎛ l ⎞ = −in + σl ⎟ F ∂lnce ⎠ ∂x ⎝ ∂x ⎠ ⎝

(16)

V = ϕs+ − ϕs−

(17)

⎟

∫0

tdischarge

Iapp dt

(18)

The capacity fade (Qfade) was calculated as the time integral of the current component lost in the formation of the SEI film. As the SEI layer grew, the SEI current increased and the capacity fade progressed. The relative capacity (Qrel) was calculated as the relative capacity at the end of each charge cycle with respect to the first cycle.

(7)

Qfade =

Qrel =

∫0

tcharge

a. Ls . iSEI dt

N Qcap − Qfade

Qcap − Q1fade

(19)

× 100[%] (20)

3. Economic analysis (8)

dδ i M = − SEI SEI dt 2FρSEI

An economic analysis was presented to demonstrate the cost versus fade relation for aged lithium-ion batteries. The process of aging is defined as a controlled electrochemical cycling of the battery in, (a) industrial setup, where the battery is aged in a controlled fashion prior to commercialization; and (b) recycling of commercial applications such as EV for application in solar panels, where the cycling in closely controlled and monitored by the electronics in the automobile. The lithium storage capacity of a lithium battery depends on the material property of the electrodes and the active lithium available in the electrolyte. With cycling of the battery, the active lithium gets consumed in the form of an irreversible reaction forming a film called SEI. The rate of fading of the capacity decreases with the number of cycles as the SEI layer creates an insulating barrier over the electrode restricting ion transport. The observed behavior of capacity fade in lithium-ion batteries underlies the square root of time-type ( t ) characteristics [16,17,24,39,40]. This implies that the relative capacity change (ΔQrel = Qrel |N − Qrel |N + ΔN ) over a certain duration of cycles (consider ΔN = 100 cycles) would reduce as N progresses, although the absolute relative fade (Qrel|N) would increase with N. The initial capacity for an aged battery can be defined as the starting capacity of the battery prior to aging (i.e., right after manufacturing), while the commercial capacity can be defined as the capacity of the battery from the point of commercial utilization. So, a 200-cycle aged battery, having the same commercial capacity as a new battery, must have a higher initial capacity than a new battery. The concept of battery aging arrives considering this reduction in the change in relative capacity (ΔQrel) as the cell ages. The electrochemical advantage of aging a lithium battery could be reflected as longer cycle life compared to a new cell given the same threshold of relative capacity fade. On the other hand, to maintain the absolute capacity to be the same for aged and new cells, the initial capacity of the aged-cell has to be comparatively higher than the new cell. Let us consider an example problem where a new cell has an initial capacity of 100 [mAh] (Qrel = 100%) and fades to 90 [mAh] (Qrel = 90%) and 85 [mAh] (Qrel = 85%) by the end of 100 and 200 cycles,

(9)

The SEI rate coefficient is modeled as an adjusting parameter for the graphite electrode.

D δ ⎞ 4πRs2 ⎛ ⎞ Cr (N )−0.5 i 0 = βFcEC ⎛ EC ⎝ δ2 ⎠ ⎝ As ⎠

(10)

δ = δ0 f (N )

(11)

⎜

⎟

The SEI thickness grows over the process of battery cycling with the initial SEI thickness to be δ0. The simulation could only be modeled considering an initially developed SEI layer. The SEI formation mechanism is a highly involved reaction mechanism with the formation time-scale being negligibly small during the first cycle charging. The SEI grows with the number of cycles (N). The reaction current coefficient for the SEI current was modeled with a set of material properties and a constant (β). The combination of material properties was selected to establish the dimension for current flux. Here, cEC is the ethylene carbonate concentration in the electrolyte, and DEC is the diffusion D coefficient of lithium-ion in SEI. The term FcEC ( δEC 2 ) represents the

volumetric current through the SEI film and 4πRs2 δ represents the SEI volume. The product of these two terms per unit effective particle area ( As = 4πRs2 ) represents the reaction current flux through the SEI. The power law for the SEI reaction flux was assumed, i.e., ξ = −0.5, such that upon integrating over the number cycles the capacity fade would follow the traditional N characteristic. The electrolyte-phase lithium concentration (cl) balance was performed based on the diffusion of the lithium ions through the electrolyte [34]. The electrolyte lithium-ion follows conservation of flux and species at the interface, while the electrolyte lithium-ion flux is zero at the current collectors.

ϵ

+ int

Qcap =

where, i0 is the reaction rate coefficient for the SEI current, USEI is the SEI open circuit voltage, RSEI is the SEI film resistance which is dependent on the SEI film thickness (δ) and electrical conductivity of the SEI film (κ). The growth rate of the SEI film thickness (dδ/dt) depends on the SEI current (iSEI), molar mass and density of SEI (MSEI, ρSEI).

RSEI =

+ int

⎜

(5)

(6)

= ie + iSEI

− Dl ∇cl

(13)

=0

The electrolyte lithium concentration was used to predict the electrolyte phase potential (ϕl) [34]. The overall cell potential (V) was found as the difference between the solid-phase potentials (ϕs) at the current collector. Finally, the cell's capacity (Qcap) was calculated from the current over a period of one discharge cycle.

For the negative electrode, the reaction current flux (in = Fjn ) was accounted as a summation of the electrode current (ie) and the SEI current (iSEI). The electrode current (ie) was the same as in the positive electrode (in |+ve ) Eq. (5). The SEI current was driven by the Tafel kinetic [24] as it was dominated by the cathodic potential.

in

cc

cl

max

αF in +ve = 2Fkr cl (cmax − cs ) cs sinh ⎛ η⎞ ⎝ RT ⎠

− Dl ∇cl

∂cl = ∇ . (Dl ∇cl ) + (1 − tc0) jn ∂t

(12) 3

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respectively. The change in relative capacity from 0 to 100 cycles is 10 [mAh] (ΔQrel |ΔN = 100 = 10%). If the relative capacity at the end of 100 ′ |⎧ N ′= 1 ⎫ = 100%, then the cycles is considered Qrel |N = 100 = 90% → Qrel ⎨ ⎩ N = 100 ⎬ ⎭

relative capacity at the end of 200 cycles ′ |⎧ N ′= 100 ⎫ ≈ 94.44%, and the change in relative Qrel

Table 1 Chemo-thermal properties for cathode (LCO and LFP), anode materials (C) and SEI. [24,35–38]

becomes capacity

⎨ ⎩ N = 200 ⎬ ⎭

ΔQ ′rel|ΔN = 100 ≈ 5.56%. However, to market a new and an aged cell, both with the beginning of life capacity of 100 [mAh], the aged cell must have an initial capacity of 111 [mAh] upon the completion of cell fabrication (or 11 [mAh] worth of extra material). The advantage of aged lithium-ion battery was focused towards, (a) applications needing longer cycle life (or slower fade), and (b) recycling of used batteries. Applications like solar panel modules, electric vehicles, and biomedical devices need to have a long cycle life (e.g., 10+ years) with minimal allowable fade [31]. In one case, industrially aged lithium battery could satisfy the need for longer cycle life for batteries in EV and biomedical devices. On the other hand, commercially used batteries from EV could be directly used in solar panel electric grids [27]. The industrial aging of lithium battery comes with an economic disadvantage and needs a capacity vs economic optimization. As the battery was aged, there was a need for more capital investment (Ccapex) in starting material to compromise for the inherent fade involved in aging. Furthermore, the electricity consumed in aging of the cell adds as an operational cost (Copex).

Ccapex =

Qcap

desired

Qrel

× Capital

N

Material property

LCO

LFP

C

Rs (μm) ϵ Le (μm) D (m2/s)

4.2 0.38 100

0.4 0.38 100

15 0.45 150

kr (

5 m2

2 × 10−13

8 × 10−16

3.9 × 10−14

1 × 10−10

3.12 × 10−12

5 × 10−11

)

mol . m3 ∂UOCV mV ( ) ∂T K

0.25

0.30

0.14

ρs (Ω.m)

1 × 104

1 × 105

W kth ( ) m.K mol cmax ( 3 ) m

0.32

2.70

6 × 10−4 80

49, 900

21, 200

30, 500

–

–

SEI 4540

cEC (

mol ) m3

DEC (m2/s)

–

–

δ0 (nm) β

– – –

– – –

1 × 10−19 5 0.2 162

–

–

1690

kg ) kmol kg ρSEI ( 3 ) m

MSEI (

Table 2 Cost analysis data for 18650 cell [41,42].

(21)

Copex = V × Qcap × ΔN × Elec

(22)

Ctotal = Ccapex + Copex

(23)

Parameter

The capital expenditure is calculated as the cost per unit capacity (Capital, $/mAh) times the initial capacity needed. The operational expenditure is the electricity per unit (Elec, $/kWh) times the energy consumed to age the cell over ΔN number of cycles (Table 2). .

Value

Capital (

3.07

Elec

$ ) Ah $ ( ) kWh

0.139a

Qcap|desired (mAh) V (V) ΔN (cycles)

3400 3.7 100

a Electricity rate in the state of Iowa was considered for the analysis.

the lithium-ion in the electrode particle. Fig. 2a represents the schematic of the standard charge profile considered to simulate the electrochemical SPM for the lithium-ion cell. The discharge was performed at constant current followed by zero current. The β constant in the SEI reaction current of the degradation model was adjusted against the long-term cycling experiments described in Hu et al. [43] for Fig. 2b. The same β parameter was used for performing analysis for Fig. 2c. The primary driving parameter found in the analysis was the growth rate of SEI film [31]. The simulation was performed over a span of 1000 cycles and the initial capacity (at N = 1) was considered to be 100%. An initial SEI thickness of 5[nm] was assumed at the beginning of the first cycle charging to accommodate the preformed SEI. The initial SEI formation mechanism was not considered in the analysis because the SEI layer forms almost instantaneously compared to the time taken to charge the cell. The formation of SEI is a kinetic driven parameter while the growth of SEI is diffusion driven. Hence, only SEI growth was considered in the model. Fig. 2b shows the comparison of the model predicted capacity variation against the experimental data for LCO/C cells [43]. The model was able to capture the trend of capacity fade in the LCO/C cells with a high degree of accuracy. The deviation of the model predicted data from the average of the four cells used in the experiment was calculated (Fig 2d). The deviation was calculated as follows,

4. Results and discussion A reduced-order multiscale mathematical model was developed to simulate battery degradation in the lithium-ion battery due to the SEI formation and growth, and to predict capacity fade in LCO/C and LFP/ C batteries. The material properties were considered from Table 1. The particle level and electrolyte level diffusion models were solved with a Euler Implicit solver with the spatial discretization completely vectorized in Matlab. This presented an algorithm which was unconditionally stable in the temporal domain, allowing the possibility of selecting larger time steps. This making the computation several orders of magnitude faster. Each cycle iteration was recorder to be performed in 150 ms, with a 1000 cycle fade run taking less than three minutes of solution time. The solution for voltage and SEI parameters were solved using a Newton Raphson code allowing very accurate predictions in a short number of iterations. 4.1. Battery life and capacity fade prediction The electrochemical model was simulated over multiple charge/ discharge cycles following a charging profile followed in experimental studies from literature. The initial charging protocol followed in the simulation assumed a constant current charging (galvanostatic), until the cell voltage achieves the higher cut-off voltage. Then the current was allowed to decay gradually, following a constant voltage (potentiostatic) charging. The potentiostatic condition was applied till the current reduced to 10–20% of Iapp. At the end of the potentiostatic charging, the current was made zero to equilibrate the concentration of

Qrel theory ⎞ Δ exp → theory = ⎜⎛1 − ⎟ × 100% Qrel exp ⎠ ⎝

(24)

The deviation for the LCO/C cell simulation was found to be within ± 1% of the experimental results over the span of 700 cycles. For the 4

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Fig. 2. Single particle electrolyte model with battery degradation due to SEI formation, (a) Representation of the charging protocol, (b) Comparison of the model predicted data for LCO/C against long-term cycling experiments described in Hu et al. [43], (c) Comparison of model predicted data for LFP/C against experimental data from Liu et al. [44], (d) Deviation of model prediction from experimental data (%) for LCO/C and LFP/C.

capacity loss is a time integral of the SEI current, which in turn depends on the charge profile. Mathematically, a larger area under the current/ time profile would mean larger capacity fade. As long as the anode is supplied with current during charging, the SEI layer would keep growing. With this mathematical inference in consideration, two different charge profiles (Fig. 2a and b) were simulated with the same rate of charging for LCO/C cell over the same time frame. Profile I was considered the same as Fig. 2a, where the charging is done at constant current (C/6) till the higher cut-off voltage was reached, followed by 30min of pontentiostatic charging and ending with a zero current profile to equilibrate the concentration profile. Profile II was considered the similar to Profile I, where the charging is done at constant current (C/6) till the higher cut-off voltage was obtained, but the potentiostatic profile was considered till the current decayed almost to zero. So, for Profile I the battery is not charged to completely 100% which is in contrast to Profile II. The area under the current/time curve was larger in Profile II than Profile I. The relative capacity for Profile I and II were predicted from the model and compared in Fig. 3c and d. Fig. 3c shows that the capacity fade in Profile II is more than Profile I as inferred from Eq. (19). The deviation of the fade between profiles I and II was calculated (Fig. 3d) and by 1000 cycles Profile II would have 9% lower capacity than Profile I. The standard protocol of constant current constant voltage zero current (CCCVZC) has a higher cycle life and performance compared to a constant current constant voltage (CCCV) charging profile. Hence, it is advantageous to not charge the battery up to 100% of its depth-of-charge.

LCO/C cell model (Fig. 2b), a constant current profile of C/6 was applied, followed by a 30min of constant voltage profile and ending with a zero current (or rest) profile, in each cycle to match the referred protocol on Hu et al. [43]. After getting the adjusted parameter β and validating against the experimental results for LCO/C, the model was simulated considering LFP/C cell. Assuming that the anode was made of the same material, i.e. mesocarbon microbeads (MSMB) with the same average particle size for both battery systems. Since SEI grows on the anode and graphite being the anode for both LFP/C and LCO/C cell, the analysis was performed postulating that the SEI parameters for LCO/C cell would be applicable for the LFP/C cell. The model was simulated with LFP/C cell with the particle size for the cathode adjusted to observe the same non-dimensional time (tD∝r2/ D) as the LCO/C cell. The charge profile was changed to constant current at C/2 and constant voltage till 10% of Iapp, to match the protocol observed in Liu et al. [44]. The predicted capacity fade over 1000 cycles was compared against the experimental results predicted by Liu et al. [44] (Fig. 2c) with no adjustment made to β or any other parameter/ property effecting the anode. The predicted results were in close agreement with the experimental results. The results provide an indication that the model could be applicable for different cathode material with MCMB as anode with the considered particle size. However, further experimentation is needed to validate this postulation, which is beyond the scope of the current work. The deviation of the predicted and experimental data for the LFP/C cell over 1000 cycles was calculated (Fig. 2d). The deviation was observed to be within ± 0.5% validating the model and also providing a high degree of confidence on the level of accuracy of the model.

4.3. Battery ageing and economic analysis 4.2. Comparison of charging profiles based on capacity fade The electrochemical benefit of aged or used lithium battery was considered for analysis to predict better performing and longer cycle for battery. The capacity fade (or the relative capacity) for a lithium-ion

A set of simulations were performed to compare the effect of the charging protocol on the relative fade of the battery. From Eq. (19), the 5

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Fig. 3. Comparison of capacity fade on LCO/C cell with two charging protocols, (a) CCCVZC protocol, (b) CCCV protocol, (c) Comparison of relative capacity fade over 1000 cycles from Profile I and II, (d) Deviation of capacity between Profile I and II over 1000 cycles.

cell follows a N type profile, where N is the number of charging cycles, and the fade curve flattens out and starts to saturate as the number of cycle increases. So, the change in the relative capacity over a certain number of cycle decreases as the battery is cycled. A battery fade by 10% over the first 100 cycles would fade only by 4% in the next 100 cycles. However, the overall capacity would be much lower at the end of 200 cycles compared to that in 100 cycles. The object of interest in the case of aged lithium-ion batteries is the change in the relative capacity (or fade) over a definite number of cycles and not the absolute capacity of the cell. For testing the implication of this hypothesis, all aged lithium cells must have the same capacity from the time of testing (or time when the battery starts to be commercially used). An analysis was performed for a LCO/C cell similar to that shown in Fig. 2b. The cell was cycled for 1000 cycles with each 100 cycles representing 1 year of battery utilization (or aging). The aging was considered such that at the relative capacity at the beginning of the commercial utilization (or after the aging period) was made 100% and capacity in the cycles onwards was rescaled relatively. For example, for a two years aged battery the capacity at the end of 200 cycles from Fig. 2b, was made 100% and all the predicted capacity from 200 cycles onwards was scaled accordingly. The change in relative capacities of aged battery, from 0 to 9 years of aging, were compared over a duration of 100 cycles (or 1 year) (Fig. 4a). The relative capacity at the end of 100 cycles was the lowest for new batteries and increased as the battery was aged (Fig. 4b). In the current analysis, for a new battery, the relative capacity at the end of 100 cycles is 90% while for a 4 years aged cell the relative capacity by 100 cycles is 98.2%. This means that aged lithium-ion batteries having the same commercial capacity as new batteries would have a longer cycle life. The benefit of aging however grows out with

aging and from 5 to 9 years aged battery the capacity benefit is <1%. This concept of longer cycle life for an aged-battery could be applied to situations where replacement of batteries is not convenient. Lithiumion batteries used in electric vehicles and some biomedical applications do not have the freedom to be replaced in 10 years or plus. For such applications, the aged battery could be of potential interest. This concept is also applicable for used lithium battery from EV. EV batteries could be recycled with better electrochemical performance in applications needing lower capacity, like solar panel grids. The economic analysis is of importance when considering industrial aging of lithium battery prior to commercialization. The aging process involves a cost in the form of capital and operational requirements. An aged battery has a higher initial capacity than a new battery of the same commercial capacity. For batteries with higher capacity, more starting material is needed, thereby involving more capital cost. Moreover, cycling process involved to age the battery requires an operational cost in the form of electricity charges. An economic analysis was performed to calculate the cost of aged 18650 LCO/C batteries over a span of 0–9 years of aging. Fig. 5 plots the fade in capacity for aged battery and the equivalent cost of aging the battery over a span of 9 years. A simple optimization showed that the optimal fade to cost-benefit is achieved for a 1year aged battery. The capacity benefit was maximum at the end of 1 year of aging is the maximum and the curve gradually flattens out as the aging progresses. So, a little capacity benefit could be obtained beyond 5–6 years of aging. However, the cost increases steeply making the decision to age the battery though. So, there was a tradeoff between cost and capacity, especially where the application demands long cycle life battery units. For electric vehicle and biomedical applications where the commercial life is often >10 years, it would be beneficiary to move towards the 6

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Fig. 4. (a) Capacity fade over 100 cycles for aged-batteries from the aging span of 0–9 years, (b) Relative capacity of aged-battery at the end of 100 cycles.

∼ 100 × faster than commercial 1D lithium electrochemical models. The model was also validated against LFP/C cell proposing that different cathode material in combination with a graphite anode could be simulated with the current model. Two different charge profiles were considered for analysis to test the fade tendency for a CCCV protocol against CCCVZC protocol. It was established that a CCCVZC which does not charge the battery up to 100% shows a much better cycle performance than a 100% charging CCCV protocol. Finally, a novel concept was introduced in which aged (or used) lithium-ion batteries could be commercialized (or recycled) with lower capacity fade. Aging of lithium-ion battery would allow a reduced change in the relative capacity over the same the number of cycle period of a new battery due to the non-linear nature of the fade over time curve. The industrially controlled aging of battery would involve both capital and operational cost making it an optimization problem between electrochemical requirements and economic vantage point. However, recycling of used lithium battery from EV in electric grid applications would have the electrochemical benefit of longer cycle life with no cost involved in aging. Therefore, the industrially aged battery would be the prime candidate for electric vehicle and biomedical applications, where the cost inherent in the aging process is negligible compared to the cost in replacing the unit. On the other hand, recycling of used EV batteries could be eminent in sustainable reuse of critical electrode materials.

Fig. 5. Economic analysis of 18650 cells to compare the capacity fade performance of aged-batteries against the total cost of manufacturing and aging the cells.

Supplementary materials aged battery. The price paid in aging the battery was compensated by the price in replacing the battery. While for cell phone batteries, no aging was needed because the commercial life for the cell phone itself is 3–5 years and lower cycle performance is acceptable as the batteries were cheaper to replace. The cost analysis is not necessary when targeting the analysis for recycling of lithium batteries. The EVs have excellent electronically controlled charging protocols for the battery module. Recycling of these batteries after use in EVs would be a direct installation in designated applications, like solar panels in electric grid systems. This provides the electrochemical advantage of the aging process without involvement of the cost.

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