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Aging of Li-ion batteries

The study of aging mechanisms (see FIGURE I-2) on the electrodes is a key issue as aging depends on the type of materials used for the electrodes and the operating conditions. It has been reviewed by Vetter et al. [3] who evaluated the aging on carbonaceous negative electrode, lithium manganese oxides ( 2 4) with spinel structure and lithium nickel cobalt mixed oxides [ ( , ) 2] with layered structures. All those aging mechanisms lead to the loss of battery performance in terms of capacity decay. The stress factors (temperature, current, state-of-charge) applied to the battery highly impact the battery loss of performance [4].

Aging mechanisms on the negative and positive electrode

One of the most documented phenomena in the literature is the growth of a passivation layer called SEI [5]–[8] (Solid Electrolyte Interphase) as shown in FIGURE I-2. The SEI is formed during the first charge cycle of the battery. Its formation leads to an irreversible loss of capacity within the cell. The SEI layer formed during the first charge reduces the SEI growth by slowing down the diffusion of the molecules of solvents towards the interface between graphite and SEI. Also, the SEI layer protects the graphite from the intercalation of the molecules of solvents in the layers of the negative electrode that may cause its deformation (graphite exfoliation).
On the positive electrode, a passivation layer may also appear due to the decomposition of the electrolyte on the positive electrode/electrolyte surface [9].
Another mechanism often mentioned in the literature is lithium plating [10], which corresponds to the deposition of Li-ions on the surface of the negative electrode. Part of the plated lithium will be consumed irreversibly due to either the reaction with electrolyte to form new SEI film or the formation of “dead” lithium which is electrically isolated with anode [11]. The rest of plated lithium is considered as a reversible part. The reversible part of plated lithium can re-intercalate in the negative electrode known as ‘‘lithium stripping’’. Finally, this accumulation of lithium can promote the formation of dendrites [12] and thereby cause a short circuit between the two electrodes leading to a possible thermal runaway of the battery.
Another type of aging mechanism on the electrodes is the deactivation of the material particles, which are electrically insulated from the current collectors. On the negative electrode, the graphite exfoliation due to the solvent intercalation, the material delamination as well as the particle cracking due to the intercalation/extraction of the lithium are considered as a cause of graphite particle deactivation. On the positive electrode, the particles cracking, and active material dissolutions are also considered as deactivation of the active material.
Some studies in the literature evoke the influence of the positive electrode on the negative electrode during cycling, in particular the positive electrode materials based on Manganese ( 2+ ions) which can contaminate the negative electrode [13] or be found in the SEI [14]. The main hypothesis evoked in the literature is that these 2+ ions can diffuse into the SEI layer and destabilize it. This can possibly create cracks in this layer during cycling and increase the SEI formation. Another hypothesis different from the latter is proposed by Wang et al. [15] which associated the destabilization of the SEI layer due to acid impurities (HF) as the only cause of capacity fade. However, this hypothesis has been contradicted by Charles Delacourt et al. [16] who demonstrated that delamination of the LMO material is also a cause of capacity loss as it produces 2+ ions which are trapped on the SEI layer. The capacity loss is even higher when the 2+ are trapped in the SEI layer compared to when they simply diffuse into the SEI layer and intercalate in the graphite electrode because they provoke more structural change of the SEI.

Degradation modes on the electrodes

The degradation modes are the direct consequence of the degradation mechanisms. From what we mentioned previously, they can be categorized into two groups: Loss of Lithium Inventory (LLI) and Loss of Active Material (LAM).
The definition of loss of lithium inventory diverges in the literature. It can account for either the loss of Li ions only due to the parasitic reaction of SEI formation ([8], [17]) or the total Li loss included the Li trapped in the active material ([18], [19]). The loss of active mass occurs when Li can no longer be inserted in (or extracted from) active material due to the electrode deterioration.
Some factors such as current, temperature, and state of charge can accentuate the physical and chemical interactions within the battery. The degradation modes listed in the literature are summed up in FIGURE I- 3 [19].

Aging modes

There are generally two modes of aging for Li-ion batteries, calendar and cycling aging:
• Calendar aging represents the capacity loss of the battery during storage. There are generally two types of capacity losses: reversible capacity losses and irreversible losses. Reversible capacity losses correspond to the self-discharge of the battery. The quantity of Ah that failed to be fully charged is called the irreversible part [4]. The temperature and state of charge stress factors are important during calendar aging. Li-ion cells generally undergo higher aging at high temperatures and states of charge, but often the effect of temperature is predominant.
• Aging during cycling is synonymous with deterioration of battery performance following a charge/discharge sequence. It depends on the temperature, current, and depth of discharge profiles applied to the cell.

OCV measurements at different aging states

The SOH is defined by: (%) = ( ) ∗ 100 (1.4) ( = 0)
( ) being the current total capacity and ( = 0) the total capacity measured at the Beginning-Of-Life (BOL), expressed in Ah.
The SOC is calculated as the ratio between remaining capacity ( ) and the nominal one ( ) as follows: (%) = ( ) ∗ 100 (1.5)
The OCV, at a given battery SOH, is commonly characterized versus the SOC.
Experimentally, the OCV-SOC signal is measured using two methods:
The first method is the Galvanostatic Intermittent Titration Technique (GITT). This is the most common method used. This method is performed by successive charge (or discharge) the battery at different SOCs followed by a resting time. This resting time allows the battery to reach the equilibrium state. The OCV is then measured at that equilibrium state. Following this step, we can deduct the OCV-SOC curve.
The second method is the continuous OCV measurement at a low rate (≤ C/10). Initially, the battery is fully discharged (or charged). Then a constant current I is applied until the battery reaches the SOC 100% (or 0%). The same current is applied to completely discharge the battery to reach 0% of SOC (or completely charge to reach the SOC 100%). The main advantage of this method is that it required less time than the GITT method. Between the two phases (complete charge and discharge), a resting time is applied to stabilize the cell voltage as shown FIGURE I- 4 [20]. In fact, the OCV signal in FIGURE I- 5 is considered as a pseudo-OCV. Even at low current, the battery is still influenced by the polarization effect.
So, to build the real cell OCV ( ), the pseudo-OCV charge signal ( ) and discharge signal ( ) are averaged as illustrated in FIGURE I- 5.
The OCV-SOC change is dependent upon the operating conditions and aging stages and must be experimentally characterized depending on the cell SOH [21]. An example is given in FIGURE I- 6 where the OCV has been characterized at different SOH for the cell battery. The data come from an internal project conducted at the French Atomic Energy and Alternative Energies Commission (CEA).

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Prognosis of lithium-ion batteries SOH and OCV

The prognosis of the battery SOH and OCV can be performed using data-driven methods. These data-driven methods correspond to prognosis models such as aging models [22] or machine learning methods [23]. In this thesis work, we will only focus on aging models for the prognosis of the battery SOH and OCV. Two types of models are studied in this section: the one-tank and the dual-tank aging models.

One-tank OCV and aging models

The one-tank aging models developed in the literature predict the evolution of the cell SOH (or capacity), which is used to update the OCV versus SOC signal during aging, as illustrated in

One-tank OCV model

In the literature, the OCV-SOC signal along with aging is updated using three approaches.
In the first approach, the OCV-SOC (or OCV-Q) signal is measured at the BOL. Then the OCV curve is transversely shrunk knowing the cell SOH. Wang et al. [24] studied the characteristic of OCV-Q for LiFePO4 by transversely shrinking the OCV curve when the battery loses a certain amount of capacity, as shown in FIGURE I- 8. This shrinking is equivalent to multiply the remaining Q abscissa by a constant ratio (SOH). As a result, the shape of the OCV curve is kept constant but it is simply shifted to the left during aging.
In fact, the shape of the OCV curve can also be distorted with aging as illustrated in FIGURE I- 6. The second and third methods used in the literature to update the OCV are model-based approaches:
● The second approach used for the correction of the OCV signal consists of using a look-up table OCV function of SOC and SOH and performing a linear interpolation at a given SOH to determine the OCV-SOC signal [25].
● The third approach is based on the mathematical functions of OCV versus SOC. Yu et al. [26] reviewed a total of eighteens OCV-SOC functions models in the literature. Those mathematical models include polynomial, exponential, and logarithmic functions. The OCV-SOC signal along with aging is updated by performing an optimization process[27].

Table of contents :

I.1. Lithium-ion battery presentation
I.2. Aging of Li-ion batteries
I.2.1. Aging mechanisms on the negative and positive electrode
I.2.2. Degradation modes on the electrodes
I.2.3. Aging modes
I.2.4. OCV measurements at different aging states
I.3. Prognosis of lithium-ion batteries SOH and OCV
I.3.1. One-tank OCV and aging models
I.3.1.1. One-tank OCV model
I.3.1.2. One-tank capacity aging model
I.3.1.3. One-tank aging models limitation
I.3.2. Dual-tank OCV and aging models
I.3.2.1. Dual-tank OCV model
I.3.2.2. Dual-tank aging model
I.4. Purpose of this thesis
II.1.1. Presentation and aims of the project
II.1.2. Production Gr/NMC-LMO cell and coin cells manufacture
II.1.2.1. Production cell characteristics
II.1.2.2. Coin cells manufacture
II.2. Protocol of check-up on 43 Ah Gr/NMC-LMO for aging tests
II.3. Aging campaign and experimental results
II.3.1. Experimental measurements of the cell SOH
II.3.1.1. Fixed calendar conditions
II.3.1.2. Thermal cycling, fixed SOC
II.3.1.3. Variable SOC, fixed temperature
II.3.2. Experimental measurements of the cell voltage at C-10
III.1. MOBICUS aging model
III.1.1. MOBICUS aging laws
III.1.1.1. Degradation rate 𝐽𝑐𝑎𝑙
III.1.1.2. Degradation loss function 𝑓𝑑𝑒𝑔
III.1.2. Identification of the parameters of the MOBICUS aging model
III.1.2.1. Identification method and results
III.1.2.2. Experimental and simulated cell SOH from the MOBICUS aging model
III.1.2.3. MOBICUS aging model error
III.1.3. Model validation
III.2. One-tank aging model
III.2.1. One-tank aging model laws
III.2.1.1. Degradation rate 𝐽𝑐𝑎𝑙
III.2.1.2. Degradation loss function 𝑓𝑑𝑒𝑔
III.2.2. One-tank aging model parameters identification
III.2.2.1. Identification method and results
III.2.2.2. Experimental and simulated cell SOH from the one-tank aging model
III.2.2.3. One-tank aging model error
III.2.3. Validation of the one-tank aging model
III.3. Comparison of the MOBICUS aging model prediction versus One- tank aging model
III.3.1. Identification process at 60°C and 65% of SOC
III.3.2. Validation process for the thermal cycling condition at SOC 65%
IV.1. Dual-tank OCV model
IV.1.1. Model presentation
IV.1.2. Parameter’s identification of the dual-tank model
IV.1.2.1. Identification method
IV.1.2.2. Dual-tank parameters evolution with aging
IV.1.2.3. Validation from the literature
IV.1.2.4. Influence of the degradation path
IV.2. Dual-tank aging model
IV.2.1. Dual-tank aging model equations
IV.2.2. Parameters identification
IV.2.2.1. 𝐶𝑝𝑜𝑠 aging model parameters identification
IV.2.2.2. 𝐶𝑛𝑒𝑔 aging model parameters identification
IV.2.2.3. 𝑂𝐹𝑆 aging model parameters identification
IV.2.3. Aging model validation
IV.3. Evolution of the dual-tank model parameters with aging
IV.3.1. Simulation of the calendar aging condition at T=45°C and SOC=65%: reference case
IV.3.1.1. Aging evolution of the dual-tank OCV parameters and full cell capacity.
IV.3.1.2. Evolution of the positive and negative electrode potential signals
IV.3.1.3. Evolution of the maximum and minimum lithium content
IV.3.2. Influence of the degradation rate on the electrode lithium contents
IV.3.2.1. Acceleration of the positive electrode capacity 𝐶𝑝𝑜𝑠 aging parameter
IV.3.2.2. Acceleration of the electrode capacity 𝐶𝑛𝑒𝑔 aging parameter
IV.3.2.3. Acceleration of OFS aging
IV.3.3. Influence of the electrodes sizing on the electrode potential signals and lithium content
IV.3.3.1. Positive electrode undersized
IV.3.3.2. Positive electrode oversized
V.1. SEI modeling
V.1.1. Full cell representation
V.1.2. SEI mechanisms and equations
V.1.2.1. Kinetic of intercalation of the lithium-ion :
V.1.2.2. SEI growth model and the parasitic reaction of lithium-ions consumption
V.2. Physics-based aging model
V.2.1. 𝑂𝐹𝑆 aging law
V.2.2. Influence of degradation modes on the offset aging
V.2.2.1. Influence of 𝐿𝐿𝐼 on the offset parameter
V.2.2.2. Influence of the loss of active mass 𝐿𝐴𝑀𝑝𝑜𝑠 on the offset parameter
V.2.2.3. Influence of the loss of active mass 𝐿𝐴𝑀𝑛𝑒𝑔 on the offset parameter
V.2.3. Identification of the parameters of the physics-based aging model
V.2.3.1. Identification method and results
V.2.3.2. SEI thickness growth
V.2.4. Aging evolution of the parameters of the physics-based aging model
V.2.4.1. Evolution of the electrode potential signals with aging
V.2.4.2. Evolution of the cell voltage and capacity with aging
V.2.5. Validation of the physics-based aging model and comparison with the one-tank aging model
VI.1. General conclusion
VI.2. Perspectives
VI.2.1. Dual-tank OCV model: hysteresis effect and validation of the identification process
VI.2.2. Dual-tank aging model: Effect of temperature and state-of-charge
VI.2.3. Physics-based aging model: modeling of the active mass loss on the electrodes
VI.2.4. Physics-based aging model: Introduction of other mechanisms for the SEI


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