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## Modelling approach adopted to investigate aging mechanisms

IFP Énergies nouvelles (IFPEN) has recently started to work on the development of simplified electrochemical and thermal battery models, particularly lumped-parameter (0D) approaches that allows for a good reproduction of dynamics behaviours of the systems.145-148 These 0D developments are used into vehicle simulators to optimize the architecture of the full system or to design model-based estimators for Battery Management System onboard applications. As aging phenomena should be taken into account, a specific effort is made to investigate and model aging mechanisms for Li-ion batteries. To achieve this engineering objective, the approach of Newman and White will be adopted and reduced order models will be designed. This choice is detailed in the present section.

Concerning the aging item, it appears that most of the reported aging models concern the LiCoO2/C technology which is the more common chemistry for portable device applications, but will not be used for electrified vehicles applications. Indeed, the NCA/C, NMC/C and LFP/C are the most promising candidates for automotive applications. Based on literature analysis presented in 1.1 and 1.2, one can notice that a lot of studies are reported on the experimental investigation of the aging mechanisms of these chemistries. Also, different aging models have been reported on the NCA/C technology.

Concerning the LFP/C technology, empirical36 and physics-based132 aging models have recently been reported. To the best of our knowledge, these models show deviations compared to the experimental data especially as the systems approaches its End-Of-Life (EOL) state. In this context, this thesis is dedicated to the development of a simplified electrochemical and thermal aging model of a commercial LiFePO4-graphite Li-ion cylindrical cell with a special focus on power/energy fade thoretical correlations and EOL predictions. The choice of developing a simplified physics-based mathematical model has been done for three main reasons according to the IFPEN strategy on energy storage systems as represented in Fig 1.4. The first reason is related to simulations purposes. Indeed, most of the physics-based aging models reported in literature are built on the simplified Single- Particle model structure to save computing resources for long term aging simulations.

For comparison, the P2D model requires 27 h to simulate 800 charge/discharge cycles whereas the SP model only requires 27 s for the same scientific computer. The second reason is related to the use of these simplified models for BMS algorithms design. Indeed, BMS algorithms require simplified models to represent the behaviours of the energy storage system for onboard applicability.150,151 The third reason is directly related to the possibility of experimentally calibrating these electrochemical and thermal battery model thanks to the multi-scale laboratories available at the IFPEN (Cell opening, tests on both electrodes, tests on the full cell/module/pack). For all the abovementioned reasons, this level of battery predictive models seems to be the more accurate to fulfil the different engineering objectives at IFPEN.

### Model calibration and validation

Electrical tests— Experimental work was performed on commercial LiFePO4-graphite cells ANR26650 M1 (2.3 Ah) from A123 Systems. C/10, C/4, C/2, 1C, 2C, 4C, and 8C charges and discharges were performed in a climatic chamber at 0°C, 10°C, 23°C, and 33°C using a multipotentiostat (VMP, Biologic, Claix, France) outfitted with 20 A boosters for high C-rate measurements. For discharge experiments, the initial state of the cells was obtained by charging at a constant current (CC) of 1C until 3.6 V, then a constant voltage (CV) of 3.6 V was maintained until the current was lower than C/20, finishing with a rest period of 4 h (1CCC- 3.6 V-CV until I < C/20, rest 4h). Discharges at different rates were then carried out from the same initial state. For charge experiments, the initial state of the cells was obtained by discharging at a constant current of 1C until a cell potential of 2 V, then a constant voltage of 2 V was maintained until the current was lower than C/20, finishing with a rest period of 4 h (1D-CC-2V-CV until I < C/20, rest 4h). Charges at different rates were then carried out from the same initial state.

Electrochemical and thermal model calibration— The experimental characterization of the inherent properties of the materials under study is an integral part of the modeling effort.31 Indeed, parameterization of physics-based models requires multi-level and multi-physics experimental devices, even if some properties of the materials can be found in literature.

Electrochemical characterization tests were conducted at both cell and electrode levels. In order to perform tests at the electrode level, some cells were operated in an argon-filled glove box after complete discharge at 2 V. Scanning electron microscopy was performed on both LiFePO4 and graphite electrodes to determine some of the design parameters. Pieces of the recovered electrodes were then separately reassembled in coin cells with a Li-foil counter electrode to determine the open circuit voltage and the electrochemical window for each electrode. For the LiFePO4-graphite system under study, both literature and measured data were collected and reported in Table 2.3.

#### Application to fast charging simulations

Fast charging protocols are being more and more investigated for automotive applications since these phases of vehicle battery life are critical in terms of durability, safety and usability. Different protocols are proposed in literature from classical CC-CV protocols to innovative pulse charging or boost charging.38 From a practical point of view, constant powe or CC charging protocols are the easiest to implement. In this part, a simulation study is proposed to investigate classical CC fast charging protocols in terms of efficiency, charge duration and thermal aspects. CC charges from 0.5C to 8C were considered on the 2.3 Ah commercial LiFePO4-graphite cell (Fig. 2.9.). The initial SOC was set to 0 % to investigate the complete fast charge. The upper cut-off voltage was set to 3.6 V, which is the value recommended by the manufacturer. The cooling temperature was considered to be 23°C under free convection. As can be observed in Fig. 2.9., good performances in cell charging are achieved with respect to the coulomb efficiency with, for example, 1.75 Ah charged at 7C. At current regimes higher than 7C, the upper cut-off voltage was rapidly reached and the experimental charging test prematurely stopped, which explains why the exchanged charge was so small. The same phenomenon can be observed in the experimental and simulation results presented in Fig. 2.6. with the 8C charge test. The experimental charges exchanged at C/2, 1C, 2C, 4C and 8C rates were measured. Figure 9 shows they are in good agreement with the simulated charges.

**Electrochemical and thermal aging model development**

Nominal electrochemical and thermal battery model.— A SP electrochemical and thermal model was developed in the previous chapter from the Pseudo-2D mathematical structure to study capacity restitution at different temperatures and constant current regimes for both charge and discharge operations.17 In this model, the radius of the active material particles was current-dependent to improve the model predictions under fast charging/discharging operating conditions. It was then difficult to address dynamic profiles because of the currentsign change during the cycle so that the model was applied to continuous galvanostatic regimes only. In the present chapter, for sake of simplicity the particle radius of the active material is not current-dependent, as traditionally performed in reported battery models.

The main electrochemical equations of the SP model are detailed in Table 3.1. Considering spherical particles at the negative and positive electrodes, the concentration, cs(r), of Li+ species in the solid phase is classically governed by Eq. 1 while the Li+ concentration, ce, in the electrolyte phase at any time along the negative electrode / separator / positive electrode cell of thickness L is given by Eq. 2. Adopting a lumped parameter approach, the overpotentials, , of both electrodes were expressed as the sum of the kinetic, k , and diffusion, diff , overpotentials (Eq. 4). Assuming a symmetry in the charge transfer coefficients (ox = red = = 0.5), the Butler-Volmer relations (Eq. 3) giving the Faradaic current density per unit volume, jf, can be inverted to express the kinetic overpotential as a function of j f (2as i0 ) (Eq 5). The diffusion overpotentials in the solid phase, diff , have been expressed as the difference between the thermodynamic equilibrium potentials, U, taken at the surface and at the centre of the spherical particles (Eq. 6). In this equation, s,max s s s c c and s,max b s b c c denote the normalized inserted Li ion concentration at the surface and in the bulk of the electrode. The mass-transport overpotential in the electrolyte, mt e , is expressed as the difference between the potentials of the electrolytic phase taken at the extremities of the electrodes (Eq. 7). Contrary to classical SP approaches, the masstransport overpotential, mt e , is simply added in the voltage calculation. Mass transport is not coupled with the intercalation kinetics as it is generally done in higher-order electrochemical models, so that the model presented in Ref 17 consists simply in a superposition of overpotentials due to kinetic and diffusion phenomena. Thus, in Eq. 8, the cell voltage can be expressed as a function of the design parameters.

**Table of contents :**

**CHAPTER 1 : CONTEXT OF THE STUDY **

1.1 MAIN AGING MECHANISMS OF LI-ION BATTERY SYSTEMS

1.1.1 AGING MECHANISMS AT THE CARBONACEOUS NEGATIVE ELECTRODES

1.1.2 AGING MECHANISMS AT THE POSITIVE ELECTRODES

1.2 STATE OF THE ART OF BATTERY MODELLING

1.2.1 EQUIVALENT ELECTRICAL CIRCUIT MODELLING

1.2.2 ELECTROCHEMICAL MODELLING

1.2.3 AGING MODELLING

1.3 MODELLING APPROACH ADOPTED TO INVESTIGATE AGING MECHANISMS

1.4 REFERENCES OF CHAPTER 1

**CHAPTER 2 : SIMPLIFIED ELECTROCHEMICAL AND THERMAL MODEL OF LIFEPO4-GRAPHITE LI-ION BATTERIES FOR FAST CHARGE APPLICATIONS.**

2.1 INTRODUCTION

2.2 MODEL DEVELOPMENT

2.3 MODEL CALIBRATION AND VALIDATION

2.4 APPLICATION TO FAST CHARGING SIMULATIONS

2.5 CONCLUDING REMARKS

2.6 REFERENCES OF CHAPTER 2

**CHAPTER 3 : A SIMPLIFIED ELECTROCHEMICAL AND THERMAL AGING MODEL OF LIFEPO4-GRAPHITE LI-ION BATTERIES : POWER AND CAPACITY FADE PREDICTIONS **

3.1 INTRODUCTION

3.2 ELECTROCHEMICAL AND THERMAL AGING MODEL DEVELOPMENT

3.3 EXPERIMENTAL CALIBRATION AND VALIDATION OF THE AGING MODEL

3.4 DISCUSSION ON THE POWER LOSS AND CAPACITY FADE CORRELATIONS

3.5 CONCLUDING REMARKS AND PERSPECTIVES

3.6 REFERENCES OF CHAPTER 3

**CHAPTER 4 : A SIMPLIFIED ELECTROCHEMICAL AND THERMAL AGING MODEL OF LIFEPO4 GRAPHITE LI-ION BATTERIES : ANALYSIS AND PREDICTABILITY OF END-OF-LIFE MECHANISM OF A COMMERCIAL BATTERY **

4.1 INTRODUCTION

4.2 MODEL-BASED ANALYSIS AND PREDICTABILITY OF END-OF-LIFE FOR LIFEPO4 GRAPHITE CELLS

4.3 PARAMETRIC STUDY ON THE IMPACT OF DESIGN PARAMETERS ON THE END-OF-LIFE STATE OCCURRENCE

4.4 CONCLUDING REMARKS

4.5 REFERENCES OF CHAPTER 4

**CHAPTER 5 : APPLICATIONS TO CALENDAR AND CHARGE SIMULATIONS FOR PHEV AND EV **

5.1 APPLICATION TO CALENDAR SIMULATIONS FOR PHEV AND EV

5.2 APPLICATION TO CHARGING PROTOCOLS FOR PHEV AND EV

5.3 CONCLUDING REMARKS ON BATTERY MANAGEMENT STRATEGIES TO IMPROVE THE BATTERY LIFETIME

5.4 REFERENCES OF CHAPTER 5

CONCLUSIONS AND PERSPECTIVES

**ANNEXE 1:** SYNTHESIS OF THE PHYSICS-BASED AGING MODEL OF A LIFEPO4-

GRAPHITE LI-ION CELL

**ANNEXE 2:** RÉSUMÉ EN FRANÇAIS

RÉSUMÉ

ABSTRACT