Aging modeling and lifetime optimization of Li-ion LiFePO4-graphite batteries according to the vehicle use.

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Direction Chimie et Physico-chimie Appliquées

Réf. formulaire : F110-QSEF30-rév2 – _{IFP Energies nouvelles – 1 et 4 avenue de Bois-Préau – 92852 Rueil-Malmaison Cedex – France}

N° étude :

XIG01001

N° référence: 62798

Partenaires : CNRS, LISE N° contrat: 178 638

Titre :

Modélisation du vieillissement et optimisation de la durée

de vie des batteries Li-ion de technologie LiFePO

4

-graphite suivant l'usage véhicule

Aging modeling and lifetime optimization of Li-ion

LiFePO

4

-graphite batteries according to the vehicle use

Thèse

Auteur(s) et

(appartenance) :

Eric PRADA

Diffusion

1-Public

Date de publication

Février 2013

Mots-clés : Batterie Li-ion LFP/C, modèle électrochimique et thermique, vieillissement calendaire _{et cyclage, charge rapide}

Résumé

Les batteries rechargeables assurent le stockage réversible de l'électricité sous forme électrochimique dans les véhicules électrifiés. Comprendre l'impact des mécanismes de vieillissement sur les performances énergie/puissance est critique pour la conception de systèmes de stockage sûrs, bon marché et durables. Cette démarche de recherche et développement s'appuie sur des modèles numériques. Dans cette thèse, un modèle électrochimique et thermique simplifié incluant le vieillissement a été conçu pour une cellule Li-ion LFP/C commerciale et enrichi des mesures de paramètres d'électrodes. Des corrélations théoriques entre pertes d'énergie et de puissance sont proposées et validées expérimentalement. Les limites du modèle sont mises en évidence par la confrontation des prédictions du modèle aux données de cyclage sous forts courants. Le modèle permet de discuter qualitativement et quantitativement la durée de vie en fonction des conditions opératoires. Une étude paramétrique sur les propriétés du design de l'électrode négative permet aussi d'expliquer les dispersions expérimentales sur l'apparition de l'état de fin de vie. Au terme de ces développements, des simulations de durée de vie de la batterie sont illustrées en phases de stockage et lors de charges rapides. La présence d'un optimum de durée de vie suivant l'usage véhicule est démontrée numériquement.

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Direction Chimie et Physico-chimie Appliquées

Réf. formulaire : F110-QSEF30-rév2 – _{IFP Energies nouvelles – 1 et 4 avenue de Bois-Préau – 92852 Rueil-Malmaison Cedex – France} Liste nominative de diffusion papier : Nombre d'exemplaires

Documentation 1 Eric Prada 5 V. Sauvant-Moynot 10 J. Bernard 1 Y. Creff 1 D. Di Dominico 1 R. Mingant 1 M. Petit 1 R. Revel 1 C. Edouard 1

Liste nominative d'accès électronique :

DS : A. Ehinger, H. Toulhoat, J. Jarrin V. Ruffier-Meray F. Badin Y. Creff A. Benkenida D. Di Dominico G. Corde P. Pognant-Gros J. Martin P. Tona V. Sauvant-Moynot Pour accord, V. Sauvant-Moynot

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THESE DE DOCTORAT DE L’UNIVERSITE PIERRE ET MARIE CURIE

Spécialité Electrochimie

Ecole Doctorale de Chimie Physique et de Chimie Analytique de Paris Centre

Présentée par

PRADA Eric

Pour obtenir le grade de

DOCTEUR de l’UNIVERSITÉ PIERRE ET MARIE CURIE

Sujet de la thèse :

Modélisation du vieillissement et optimisation de la durée de vie des batteries Li-ion de technologie LiFePO4-graphite suivant l'usage véhicule

Aging modeling and lifetime optimization of Li-ion LiFePO4-graphite batteries according to the vehicle use

soutenue le 23 Novembre 2012

devant le jury composé de :

M. Alain MAUGER, Directeur de Recherches Président

M. Jean-Michel VINASSA, Professeur Rapporteur

M. Marian CHATENET, Professeur Rapporteur

Mme Valérie SAUVANT-MOYNOT, Docteur Ingénieur Examinateur

M. Alain DOUARRE, Industriel Examinateur

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LIST OF SYMBOLS

as active surface area (m-1)

A geometric area of the electrodes (m²)

Acell geometric area of the cell (m²)

ce concentration of lithium in the electrolyte phase (mol m-3)

cs concentration of reduced lithium in the solid phase (mol m-3) s

s

c concentration of lithium at the solid-electrolyte interface (mol m-3)

Cp heat capacity (J kg-1 K-1)

De electrolyte phase diffusion coefficient (m² s-1)

Ds solid phase diffusion coefficient (m² s-1)

Dsolv solvent diffusion coefficient (m² s-1)

Ea activation energy (J mol-1)

F Faraday constant (C mol-1)

hconv thermal convective coefficient (W m-2 K-1)

i0 exchange current density (A m-2)

I current intensity flowing through the system (A) jf current per volume unit (A m-3)

k0 charge transfer rate constant (A mol-3/2m5/2) kf parasitic reaction rate constant (m.s-1)

M cell mass (kg)

MSEI Molar Mass of the SEI layer (kg.mol-1)

OCV Open Circuit Voltage (V)

Q charge capacity of an electrode (Ah) r radial coordinate in the 1D model R ideal gas constant (8.314 J mol−1 K−1) Rohm ohmic resistance ()

RSEI Solid Electrolyte Interphase resistance ()

Rs radius of spherical particles (m)

Rth thermal resistance (K W-1)

t time (s)

t+ Li ion transference number

U thermodynamic equilibrium potential (V) V cell voltage (V)

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x intercalated ratio of Li in the negative electrode y intercalated ratio of Li in the positive electrode z spatial coordinate in the 1D model (m)

Greek

ox charge transfer coefficient of anodic reaction

red charge transfer coefficient of the reduction reaction

 lengths of electrodes and separator (m)

SEI Solid Electrolyte Interphase (SEI) thickness (m)

e volume fraction of the electrolyte

s volume fraction of the active material

f volume fraction of the filler

 normalized inserted Li ion concentration SEI density of the SEI layer

 electrode overpotential (V)  thermal conductivity (W m-1 K-1)  ionic conductivity (S m-1)

 thermal flux (W)

 electric potential of electrolyte or solid phase (V)  solid phase conductivity (S m-1)

 hysteresis parameter

Subscripts, superscripts and acronyms 0 initial or equilibrium state a adjusted

amb ambient (temperature) bat / cell relative to the full cell Brugg Bruggman coefficient c calculated ch charge dch discharge

e relative to electrolyte es estimated

eff relative to effective values of parameters D relative to diffusion phenomenon

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gen relative to generated thermal flux int relative to core temperature m measured

n negative electrode ox relative to oxidation reaction p positive electrode red relative to reduction reaction ref reference temperature

skin relative to skin temperature of the cell solv relative to the solvent of the electrolyte tra relative to transferred thermal flux CC constant current protocol

CV constant voltage protocol

EIS Electrochemical Impedance Spectroscopy AM Average Model

P2D Pseudo Two Dimensional

PP Porous electrode with Polynomial approximation SP Single Particle

EV Electric Vehicle HEV Hybrid Electric Vehicle

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I would like to acknowledge all the people who contributed to this work from my collegues at IFPEN (Valérie, Mimmo, Yann, Serge, Julien, Rémy, Dominique, Martin,...), to my family who has always supported me, especially during this three-year period. I particularly thank Pr François Huet for his help, for the quality of his scientific work and for all the discussions we had.

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General Introduction

Motivated by energy security and environmental concerns, policy makers around the world are directing attention to electrified vehicles as a partial solution to reducing fossil fuel consumption and carbon emissions. Onboard an electrified vehicle, the secondary battery pack is discharged as it provides current intensity to the electric machine (EM), and is recharged via a generator during regenerative braking for a Hybrid Electric Vehicles (HEV), and also via a charger for Plug-In Hybrid Electric Vehicles (PHEV) and Battery Electric Vehicles (BEV). The success of market penetration of these environmental-friendly vehicles strongly depends on the industrialization of new battery technologies that must meet at the same time, performances, security, durability and cost requirements. Indeed, a battery pack is a key and complex component of the electrified vehicle. It is composed of a combination of serial/parallel elements or cells (that may be arranged into modules) controlled by an electronic management system (Battery Management System – BMS) ensuring a safe and optimized use of the stored electrical energy. The massive introduction of new battery technologies is an ambitious objective which still raises scientific and technical issues.1,2 In this context, due to their good energy and power performances, the Li-ion battery technologies are promising candidates to promote the development of electrified vehicles in the next years. However, the diversity of electrode materials and electrolytes, the diversity of vehicle usages, the understanding and management of battery aging phenomena, and finally the risk of thermal runaway constitute scientific and technical challenges. First of all, selecting a battery technology and sizing it to fulfil the energy and power requirements for a desired electrified vehicle (HEV, PHEV or EV) is a difficult task to realize from an engineering point of view.3 In order to design battery packs and to optimize the full architecture of electrified vehicles, engineering tools like numeric models of the components can be helpful. Indeed vehicle simulations are generally used in the preliminary design steps. The second engineering challenge deals with the control and the management of battery system to ensure safe operation during the vehicle usage. This control is based on an accurate and reliable real-time determination of the sate of charge (SOC) and state of health (SOH) of each element of the battery pack, to monitor the balancing functions between elements and determine the available power at any time. Beyond the classic SOC determination algorithms based on integration of the current flowing through the battery systems, research efforts tend to develop physical non destructive gauges of the SOC and the SOH.4 On the other hand, the development of model-based embedded algorithms appears as a promising solution to estimate during operation the internal state of the battery and to improve the BMS robustness.5-9

Last but not least, the third technical challenge deals with the reliable prediction and improvement of the battery lifetime through a better electrical and thermal management. This critical point is directly linked with the cost of the battery system. As a function of the various usages of an electrified vehicle (Driving Mode, Charging Mode or Parking mode), different operating factors such as the SOC, the current intensity and the temperature can significantly impact the aging rate of the battery system i.e. a loss of capacity and a loss of power. The optimization of charge/discharge strategies relies on the knowledge of the aging mechanisms kinetics occurring at the material scale. Li-ion batteries aging mechanisms have been extensively investigated for many years. The complexity of the underlying mechanisms depends on the chemistry of the systems and the operating conditions of the vehicle.10-13 To investigate these purposes, mathematical models of the battery physical behaviours and the integration of degradation mechanisms can be useful in predicting the system lifetime as a function of the application.14,15 Despite intensive research on aging mechanisms and modelling for traditional Li-ion technologies, the aging behaviors of the chemistries used for

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automotive applications such as LiNi0.8Co0.15Al0.05O2/Carbon (NCA/C) and LiFePO4/Carbon

(LFP/C) still remain difficult to model with accuracy.

Based on the abovementioned technical challenges, a complete chain has to be investigated to encourage electrified technologies penetration, from electrodes materials to the integrated battery onboard a vehicle (see fig. below).

Figure 0.1. Technological chain, from electrode materials to the integrated battery

In this report entitled "Aging modeling and optimization of Li-ion battery lifetime according

to the vehicle usage", a simplified electrochemical and thermal mathematical model

integrating the main aging mechanisms of a commercial LiFePO4/Carbon cell (A123 Systems

2.3 Ah) is developed. In the first chapter, a review of the reported aging mechanisms of different Li-ion chemistries is presented and the main modeling approaches are mentioned. In the second chapter, the simplified physics based model is detailed. This model is validated on classic charge/discharge profiles and is used to investigate fast charging phases for PHEV and EV.

In the third chapter, a simplified physics-based aging model is proposed and developed on the basis of the aforementioned electrochemical and thermal model. It is experimentally validated on different operating conditions such as calendar mode (Parking Mode) and cycling mode (Charging Mode and Driving Mode). The limits of the simplified model are evidenced by the comparisons between predictions and experimental data under high loads operating conditions. Empirical functions are integrated within the theoretical set of equations to account for the impact of current intensity on the battery aging.

Then in the fourth part, through a simulation study, the model is used to investigate the aging behavior of the LiFePO4/Carbon cell until its end-of-life (EOL) state.

In the fifth chapter, the model is used to discuss the battery lifetime in terms of capacity and power loss of the system during the calendar mode of the HEVs and EVs. Real climatic data are used to investigate the aging of the battery packs as a function of temperature and SOC in three cities (Paris, Moscow and Dubai). Simulations results are then analysed and used to specify some strategies to mitigate the aging of the energy storage system. A second simulation study deals with the impact of the charging protocols on the battery lifetime.

Finally, a conclusion is drawn and research perspectives are presented to investigate future developments possibilities.

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Chapter 1 : Context of the study

In this first chapter, an attempt to briefly review the main aging mechanisms occurring at both negative and positive composite electrodes of Li-ion batteries is successively done. The n the different approaches encountered in literature for batteries modeling are presented. The effects of different aging mechanisms are qualitatively correlated to their impact on energy and power performances. Finally, the approach investigated in the present work to model aging is introduced.

1.1 Main aging mechanisms of Li-ion battery systems

Physical and chemical degradation mechanisms of energy storage systems are numerous, complex and difficult to investigate experimentally. The aging of a battery is generally defined by a degradation of internal parameters of the system such as the capacity and the electrical resistance, respectively images of its energy and power performances. The characteristic changes of a battery consist of a reduction of the capacity (energy loss) and a rise of the resistance (power loss) as a function of time.

These degradation mechanisms have been intensively investigated and reported. Concerning Li-ion technologies, Vetter et al.13_{, reviewed the aging mechanisms occurring at the positive}

lamellar electrodes (LiMeO2), spinel materials (LiMn2O4) and on the carbonaceous negative

electrodes pointing out which were the causes, the consequences and the operational stress factors impacting the degradation processes. The stress factors impacting the battery lifetime are the temperature (T), the SOC and the current intensity (I) flowing through the cell. Later, Delacourt et al.16 _{during the SIMSTOCK Project extended the review to the LiFePO}

4 positive

electrode material. In his study, he used the impedance spectroscopy technique to discuss and quantify the aging mechanisms occurring in the composite porous electrodes of the Li-ion technology such as the active material loss and the growth of surface layers. Two types of aging phases can be distinguished: cycling (Driving Mode) and calendar aging (Parking Mode) when no current flows through the system. The effects of these two types of aging cause degradation evolutions that are difficult to analyse while performing accelerated life tests. Thus, experimental tests campaigns are generally designed to try to distinguish the respective contributions of cycling and calendar to the lifetime of the battery.

Literature provides important databases for different systems and electrodes materials. During the 90's, LiCoO2 and LiNi0.8Co0.15Al0.05O2 positive electrode materials were intensively

studied in cycling mode17-22_{as well as in calendar mode.}14,23_{Other systems such as}

LiMn2O4/Carbon24-31, or LiFePO4/Carbon32-46 were characterized during aging but databases

are not always easy to analyse. Also, establishing comparison between the different chemistries still remain a complex analysis work to perform despite the important literature databases.

1.1.1 Aging mechanisms at the carbonaceous negative electrodes

Aging phenomena occurring at the negative carbonaceous electrodes are mainly related to the modification of the electrode/electrolyte interface, the modification of the active material and the modification of the composite electrode parameters (porosity).16 These mechanisms are represented in Fig.1.1. Peled et al.47-50 widely contributed to understand the underlying growth mechanisms of the solid electrolyte interphase (SEI) in addition to its modelling.51

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Figure 1.1. Physical and chemical phenomena occurring at the electrode/electrolyte interface13

A synthesis of the main degradation phenomena of the negative carbonaceous electrodes is presented in the Table 1.1. This table is taken form Vetter et al.'s work.

Table 1.1. Aging of negative carbonaceous electrodes: Mechanisms, Effects, Impacts on

performances13

Physical Mechanisms Effects _performancesImpacts on Operating Stress _Factors

Electrolyte decomposition Loss of Lithium _{Impedance Rise} _{Capacity Loss}Power Loss High Temperature _{High SOC} Solvent Co-intercalation, gas evolution,

cracking

Active material Loss (exfoliation) Loss of Lithium

Capacity Loss Overcharge

Reduction of the active area due to the

SEI growth Impedance Rise Power Loss High Temperature High SOC

Porosity modification due to the SEI

growth Impedance Rise Power Loss High currents High SOC Loss of electronic contact between

particles due to cycling Loss of active material Capacity Loss

High currents High DOD Binder Decomposition Loss of Lithium Capacity Loss High Temperature _{High SOC} Current collector corrosion Impedance Rise Other Overdischarge

Lithium Plating Loss of Lithium Capacity Loss Low Temperature _{High currents}

1.1.2 Aging mechanisms at the positive electrodes

One can generally classify the commercially used positive electrodes materials into three groups. The first group consists of lamellar oxides such as LiCoO2, LiNi0.8Co0.15Al0.05O2, and

LiCo1/3Ni1/3Mn1/3O2. The second one includes the spinel-type oxide (LiMn2O4). Finally, the

olivine-type iron phosphate (LiFePO4) represents the third group. As for the negative

electrodes, aging can result in a loss of active material (dissolution, phase transformation...) or can be due to the degradation of the composite electrode (Binder degradation, delaminating...)

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or to the electrolyte degradation at the interface with the electrode material (leading to surface films formation), as illustrated in Fig. 1.2.

Figure 1.2. Main physical and chemical phenomena occurring at the positive electrodes13

A synthesis of the main aging phenomena occurring at the positive electrodes is presented in the Table 1.2. This table is extracted from the work of Delacourt.16

Table 1.2. Aging of positive electrodes: Mechanisms, Effects, Impacts on performances16

Physical Mechanisms Effects _performancesImpacts on Operating Stress _Factors

Phase Transition, volume change Loss of Lithium _{Impedance Rise} _{Capacity Loss}Power Loss High Temperature _{High SOC} Structural disorder Loss of active material _{Impedance Rise} Capacity Loss _{Power Loss} High currents Oxygen release from the

cristallographic structure Impedance Rise

Power Loss Capacity Loss

Destruction

High Temperature High SOC Oxidation reaction of the electrode

leading to resistive surface layers Loss of Lithium _{Impedance Rise} _{Capacity Loss}Power Loss High Temperature High SOC (Li(Ni,Co,Al)xO4) Active material dissolution (or

iron-based impurities in the case of

LiFePO4) Loss of active material Capacity Loss

High Temperature (LiMn2O4) High/Low SOC Loss of contact between particles due to

the cycling operations Loss of active material Capacity Loss High DOD Binder decomposition Loss of Lithium Capacity Loss High Temperature _{High SOC}

1.2 State of the art of battery modelling

In order to introduce the various electrical and thermal modelling approaches of the energy storage systems, one can distinguish two main classes: either empirical models, or physics-based models:

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i) Empirical models, such as Equivalent electrical circuit models (EEC) have simple mathematical structures. These models are based on series/parallel association of resistances and capacitances elements. Simple to develop, these are classically used to mimic the electrical and thermal dynamics of the battery systems.52,53The electrical parameters can be identified thanks to frequential analysis54(Electrochemical Impedance Spectroscopy) or thanks to temporal analysis (HPPC Freedom car manual)55. These electrical parameters can typically depend on state-of-charge, state-of-health, temperature and current intensity. All these dependencies can be stored in multidimensional look-up tables.

ii) Electrochemical and thermal models, initially reported by Newman et al.56,57, are based on the knowledge of chemical reactions and physical phenomena occurring at the micro-macro scales in the battery cell.

1.2.1 Equivalent electrical circuit modelling

Equivalent electrical circuit models are frequently adopted for simplicity reasons since the related mathematical structures are rather easy to implement and to calibrate. These structures are either lumped-parameter models (time-dependent variables) or spatially resolved ones.58,59 In order to design a dynamic electro-thermal cell model, a refined knowledge of the underlying physical and chemical phenomena occurring at each electrodes is generally not required.60-64 The prediction accuracy of these dynamic models depend on the quantity of experimental data used to calibrate the electrical parameters dependencies upon the various operating conditions (SOC, I, T). The experimental work thus represents an important part of the design of such models. These modelling approaches have been successfully adapted to different technologies. ISEA (Institut für Stromrichtertechnik und Elektrische Antriebe) researchers have largely contributed to these modelling approaches on Pb-Acid63,65-68, Ni-MH64,69, Li-ion70,71 technologies and ultracapacitors.72-75

Nevertheless, these modelling approaches present some limitations in accurately predicting the systems dynamics as a function of the operating conditions. The first issue is related to the diffusion phenomena modelling. The diffusion phenomena are due to concentration gradients that develop within the systems as current flows in it. Depending on boundaries conditions of the underlying diffusion processes, one can model the mass transport thanks to concentration impedances. The impedance functions are generally identified through electrochemical impedance spectroscopy technique in the frequential domain. These impedance functions are then implemented in the temporal domain for simulation purposes.54,76,77 Kuhn et al.52,53,78 studied the implementation mathematical modes of the classical diffusion impedances with electrical networks of Foster or Cauer type. Other authors worked on the temporal realization of more complex diffusion impedance.79 The second issue concerns the integration of parameters dependencies upon current intensity.62,64,76,77,80,81Additional mechanisms like redistribution of charges or long term relaxations can be integrated in these model approaches as electrical branches in parallel with the main electrical structure.75,82 Finally, the third issue is related to the numerous models structures. As shown in the literature, it is difficult to define a unique electrical circuit model able to accurately and extensively describe the dynamics of the battery systems. Indeed, the electrical behaviour of the batteries can be strongly impacted at low temperatures inducing complex evolutions of the impedance spectra shapes and thus modifying the structure and the parameterization of the model.83,84

Despite all the abovementioned inherent difficulties of this modelling approach, equivalent circuit models are commonly used to investigate the physical processes occurring at the electrode scale (charge transfer, diffusion phenomena,...). Fitting impedance spectra on the

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basis of equivalent electrical circuit models is a powerful tool to follow the evolution of physical phenomena during battery aging for instance.81,85-87

1.2.2 Electrochemical modelling

In these physics-based modelling approaches, the kinetics equations of the main electrochemical reactions, the mass and charge conservation equations and the energy balance constitute the mutli-physics framework of this class of models characterized by an algebro-differential mathematical structures. Previously developed by Newman et al, these approaches try to reproduce the physical and chemical phenomena occurring within the positive electrode/separator/negative electrode assembly. The implementation and resolution of these models is not an easy work to do compared to the equivalent electrical circuit models. The electrochemical models have been successfully adapted to numerous battery chemistries such as Pb-Acid88, Ni-MH89-93 and Li-ion3,57,94-99 at the cell level. Many fundamental studies were dedicated to model the complex behaviours of different positive electrode materials like LiCoO2, LiFePO4 and negative electrode materials like Meso Carbon Micro Beads (MCMB)

and Li4Ti5O12.100-103 The design of such models requires electrochemical, mathematical and

experimental expertise. A refined knowledge of electrode materials behaviours is essential. Indeed, the main difficulty of these approaches relies on the model calibration which requires the determination of geometric, electrochemical and thermal properties of each subsystem, namely the positive and negative electrodes. Most of the reported electrochemical models are isothermal ones for simplicity reasons. However, different authors like Lee102 and Zhang104 pointed out the difficulties of isothermal models in accurately predicting the capacity restitution at different current regimes.102,105 Within the theoretical framework of these physics-based models, corrections have been proposed on the solid state diffusion coefficient106, on the exchange current densities107, and on the size of particles to fit the experimental data.108 More complex models that couple electrochemical and thermal phenomena have been proposed especially for the Li-ion technologies.3,109 In the electrochemical models, it is possible to define the SOC of the battery as a function of the concentration of active species in each electrodes which allows for a better indication of the stored energy compared to EEC models. However, parasitic reactions occurring as the battery ages can modify the active material quantities and thus modify the SOC estimation. Concerning the electrochemical approaches, Bergveld et al. published another electrochemical modelling approach without considering the characteristics of the porous electrodes. They used equivalent circuit analogies to solve and implement the main physical and chemical phenomena occurring in the battery cell110 (mass transport in the electrolyte, in the solid phases, double layer capacitances...). This electronic-network representation of the battery assembly is well suited for simulations purposes and BMS applications. Indeed, the electrical parameters are directly correlated to the concentration of the active species in both electrolyte and solid phases. Bergveld et al. adapted their modelling approach on different battery technologies. This approach has been used to investigate the optimization of Li-ion batteries charging protocols for instance.110-112

1.2.3 Aging modelling

Lots of research efforts have been done for more than two decades on the aging mechanisms understanding/modelling of the different technologies of Li-ion battery systems. The reported aging models tend to describe/predict the evolution of internal parameters of the storage systems. The main internal parameters are the capacity and the resistance, respectively images

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of the energy and power performances of the system. A review of the literature allows for a classification of the different aging modelling approaches into two categories.113

i) The empirical or semi-empirical models that reproduce the evolution of the internal parameters as a function of the operating conditions used to calibrate the model. These approaches are rarely predictive and non useable for ab initio design especially when the operating conditions of the battery are not known.

ii) The physics-based models in which the degradation mechanisms occurring at the electrode interfaces or inside the active material are considered. The experimental effort to calibrate these models is important too. These approaches are more predictive and can be used to investigate the impact of various operating conditions (charges/discharges/floating) on the aging of the battery systems.

Numerous examples of the two abovementioned categories can be found in the literature. Concerning the empirical or semi-empirical approaches114,115, Spotnitz116 described the different phases of life and the related evolution shapes of the internal parameters for Li-ion technologies. Four phases are identified as described in the Fig. 1.3. The Phases A, B and C are generally those considered during the battery lifetime with a End-Of-Life (EOL) criterion set at 20 % capacity loss. The phase D represents the real battery EOL. This phase is characterised by abrupt evolutions of capacity and internal resistance. The prediction of the phase D is difficult to assess with semi-empirical models.

Figure 1.3. Schematic evolution of the residual capacity as a function of cycle number116

Collaborative projects between the Argonne National Laboratory (ANL) and the Idaho National Laboratory (INL) provided insight into the understanding of the underlying mechanisms responsible of the complex shapes of residual capacity and internal resistance during the aging of the batteries. 17,18,117-118 They used experimental techniques like EIS in 3-electrode configuration to follow the behaviours of each 3-electrodes during the aging

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tests.124,125 From the results of these investigations, the phases A, B and C could be controlled by the degradation phenomena occurring at the negative electrode. The overpotentials induced by the aging of the negative electrode could induce in turn aging of the positive that would then promote and control the ultimate step D. The abovementioned experimental results were used to design semi-empirical aging models.21,22 Bloom et al.18,126,127 proposed a para-linear law to describe the capacity fade and the impedance increase of the NCA/C technology. These models take the form of power laws integrating the dependencies upon SOC, temperature and, current intensity as has been recently reported by Wang et al.36 on the LFP/C technology. The aging model parameters are determined thanks to experimental curve fitting procedures. The general form of the semi-empirical models is presented in the Table 1.3.

Table 1.3. General form of the semi-empirical aging model. Impedance and capacity evolution laws

Evolution Laws Semi-empirical aging models References

Resistance rise model R(t)a'₁tz a'₂



tt₀



a'₃ 18,21,22,128

Capacity fade model a rate z

t RT C a E a t Q          2 1exp ) ( 22,36,127,129,130

The z exponent of the power laws is generally equal to 0.5, showing that the aging mechanisms are mainly governed by diffusion phenomena.14,23,131 These aging models have been integrated into dynamic electro-thermal models of Li-ion technologies, Electrochemical Double Layer Capacitors (EDLC)72,73 and into 1D electrochemical models10_{. These evolution}

laws can be used for ab initio design if the operating conditions are similar to those used for the aging model calibration (calendar or simple cycling operating conditions). However, as soon as the operating conditions differ from those used for the calibration procedure, these approaches are not adapted anymore. It is then preferable to adopt predictive approaches like physics-based models.

Numerous developments of physics-based models of Li-ion battery systems have been proposed in the literature. Based on the Newman's approach, Doyle et al.57,132,133set the equations of the SEI layer growth mechanisms at the negative carbonaceous electrodes which is one of the most reported aging phenomenon in traditional Li-ion systems. Ploehn et al.134 and then Safari et al.135 integrated the mechanism of SEI layer growth by solvent diffusion inside the layer, pointing out the kinetics and diffusion limitations of the parasitic reaction. They validated their developments with literature experimental data on the NCA/C showing excellent results. These approaches have been validated on classic cycling operating conditions57,133,136-141 and on more complex driving mission profiles142,143. Also, Bashash144_{and Peterson}41_{have recently integrated a physics-based battery aging model into a}

complete vehicle simulator to predict the system aging as a function of the vehicle mission profile and to investigate the optimization of the vehicle architecture. However, the quality of the correlation between model prediction and experimental data is not always fully demonstrated in the reported investigations.

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1.3 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.140,149 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.

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Figure 1.4. Synthesis of battery models : Comparison between computation effeciciency vs model predictivity and capability

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Chapter 2 : Simplified Electrochemical and

Thermal Model of LiFePO

₄

-Graphite Li-Ion

Batteries for Fast Charge Applications

2.1 Introduction

Over the past 15 years, Li-ion batteries have received much attention for their application as leading candidates for next generations of electric vehicles (EVs), plug-in electric vehicles (PHEVs), even hybrid electric vehicles (HEVs), and also as a promising alternative for energy storage. In that context, it is essential to proceed with detailed mathematical modeling of the battery technology, to produce the optimum cell design, management and configuration. Even though the various aspects of performance required from a battery in terms of power and energy can be assessed experimentally, battery modeling can be of valuable use to explore electrical limitations and thermal behavior of a candidate technology. For all these purposes, refined electrochemical models are being more and more investigated. In comparison with empirical modeling approaches, physics-based models can provide detailed information for the optimization of a battery with respect to the efficient use of energy and are thus promising candidates for next generations of battery management systems (BMS). Initially developed by Newman and Tiedemann,1 the Pseudo Two-Dimensional (P2D) model is the reference in electrochemical battery models in terms of theoretical integration of mechanisms and prediction capabilities. The P2D model was especially validated on galvanostatic discharge operating conditions. It generally gives good results but requires heavy computing resources, which prohibits its use for onboard BMS application.2 In order to limit computing time for simulation purposes, mathematical reduction of the P2D model have led to the development of simplified electrochemical models like the Porous electrode model with the Polynomial approximation (PP) and the Single Particle (SP) model. Santhanagopalan et al.3 reviewed the main electrochemical battery models comparing the P2D, PP and SP models in terms of computing efficiency for cycling performance purposes. Comparisons were performed on basic discharge profiles. In the simplified SP model, the Li concentration in the electrolyte phase is assumed to be uniform along the cell. This hypothesis can strongly limit the capabilities of these models for design and specification issues, especially for high-load solicitations where mass transport limitations in liquid phase are not negligible.3 Neglecting electrolyte phase can also limit the model applicability for aging studies. Similarly to the SP model, Di Domenico et al. have recently developed an average model (AM) for charge estimation in BMS applications, with fixed electrolyte concentration, as detailed below.4 The present chapter focuses on the development of a simplified and computationally efficient electrochemical and thermal Li-ion model, which integrates the main design parameters of battery and some specific features of LiFePO4 and graphite electrodes, with the aim to predict

the voltage dynamics and capacity restitution for LiFePO4-graphite Li-ion batteries under

slow or fast galvanostatic charge and discharge operating conditions. Indeed, from a practical point of view for EVs and PHEVs, continuous high loads solicitations correspond to fast charge operating conditions that can daily occur. Fast charge situations have to be carefully investigated through both experimental and numerical tests to design safe and durable Li-ion battery packs.

In the first section of the chapter, theoretical considerations, hypotheses and the mathematical structure of the model are presented. Specific features and behaviors of electrode materials such as hysteresis of LiFePO4 and graphite electrodes are pointed out. In the second part, the

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properties. Then, electrical and thermal model predictions are compared with experimental data on various charge and discharge profiles. The concept of a current-dependent radius of the particle reported in the literature on the SP model is used to account for the difference in capacity restitution after charge or discharge at same rate. Finally, the third part is dedicated to a simulation study on constant current fast charging protocols. The capabilities and limits of this simplified electrochemical and thermal model are highlighted and different ways to improve the present model are also mentioned.

2.2 Model Development

State-of-the-Art on electrochemical and thermal battery models— Literature on

electrochemical and thermal modeling of battery systems is quite extensive. In the porous electrode theory, the electrode is treated as a superposition of two continua, namely the electrolytic phase and the solid matrix. The solid matrix is modelled as microscopic spherical particles, where the Li ions diffuse and react at the surface of the spheres. A classical 1D representation of a Li-ion battery is shown in Fig. 2.1. The complete electrochemical system is composed of three porous media, namely the negative electrode, the separator and the positive electrode. The porosity of the three regions is filled by the electrolyte liquid phase.

Figure 2.1. Schematic of 1D (z-direction) electrochemical cell model.

Considering the LiFePO4-graphite system, the electrochemical storage reactions in charge can

be represented by Eqs. 1-2.

4 1

arg

4 yLi ye Li FePO

LiFePO Ch e     __y for the positive electrode [1]

6 arg 6 1 C LiC Li xe

xLi   __x Ch e for the negative electrode [2]

During discharge operating conditions, the reverse reactions occur in the cell. The nominal physical and chemical phenomena occurring in Li-ion systems can be expressed by the mass conservation of Li+ species (Eqs. 3-4), charge conservation (Eqs. 5-6) and electrochemical kinetics (Eqs. 7-8) that are presented in Table 2.1. All these equations are the framework of the P2D electrochemical model. Non isothermal electrochemical models have also been addressed by Gu and Wang5 in a 1D model at the electrode level whereas other researchers have introduced a simple lumped-parameter thermal model for the full cell.6-7 As presented in

z=sp

z=0 z=n z=L

Electrolyte

Separator Positive electrode Negative electrode

Solid Material

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Table 2.2., the energy balance (Eq. 14) integrates both generated (Eq. 15) and exchanged with environment (Eq. 16) thermal fluxes. Generated thermal flux takes into account both the irreversible and reversible contributions. Coupling between the electrochemical and thermal models is performed thanks to a classical Arrhenius law expressed by Eq. 17 for all mass transport and kinetic parameters. Readers can refer to the aforementioned literature for further detailed description of the mathematical developments. Based on the P2D mathematical structure, the theoretical set-up of the simplified model is detailed in section 2.2.

Table 2.1. 1D electrochemical model equations.7

Physical and chemical

mechanisms Eq. Boundary conditions

Solid phase: conservation of Li+_species ² ² 0 1 _              s s s c r D r r r c t [3] 0 0     r s s c r D , F a j c r D s f s R r s s_     Electrolyte phase: conservation of Li+_species ε 



1



0             F j t c z D z c t f e eff e e e [4] 0 0         z L e z e c z c z Solid phase: charge conservation  0      _      f s eff j z z [5] A I z z s_z _L eff z s eff _ _           0 σ 0             z _sp s n z s z z Electrolyte phase: charge conservation ln _ 0                 _      f e eff D e eff j c z z z z [6] 0 0           z L e z e z z Electrochemical kinetics









_            _ __ _         _ __ _  U RT F U RT F i a j s e red e s ox s f 0 exp exp [7] Electrode overpotential seU [8] Electrolyte ionic diffusivity Brugg e e eff e D D   [9] Electrolyte ionic conductivity Brugg e eff ___  [10] Electrolyte ionic diffusional conductivity             e eff eff D c d f d t F RT ln ln 1 ) 1 ( 2 [11]

Solid phase electronic

conductivity  s eff _[12] Specific interfacial surface area _s s s R a 3 _[13]

Table 2.2. Heat transfer and energy balance equations.

Heat transfer and energy balance Eq.

Energy balance



gen tra



p C M T dt d _ 1 _ __ [14]

Thermal flux generated

during operation









             I dT U U d T I U U V _p _n p n gen ( ) [15]

Transferred thermal flux

to environment trahconvAcell



TTamb



[16]

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Arrhenius law applied to mass transport and kinetic

parameters 

 

                     T T R E ref a ref 1 1 exp [17]

Within the framework of electrochemical models, one has to consider the properties of electrode materials in details. Indeed, even with the P2D model, non satisfactory results can be obtained if specific features of materials are not considered. Among all the electrode materials used in Li-ion batteries, LiFePO4, which is a phase transformation material as

initially reported by Padhi et al. in 1997,8 is one of the most promising chemistry due to its intrinsic safety, low cost and electrochemical performances. Nevertheless, LiFePO4 material

presents specific features like partial solid solution regions or differences in capacity restitution according to the charging or discharging path which makes the modeling of this material difficult. During the past decade, electrochemical modeling works on LiFePO4 have

been addressed to understand the complex mechanism of Li ions insertion/extraction that proceeds through a two-phase transition between a Li-poor LixFePO4 phase ( phase) and a

Li-rich LiyFePO4 phase (-phase). Srinivasan and Newman9 reported the first shrinking-core

model, but in order to obtain a good agreement with experimental data on discharge curves at different current rates, they had to consider a particle size distribution (PSD) effect with spherical particles of two different sizes. The original shrinking-core model was then extended to the planar geometry by Wang et al.10 who obtained good results on discharge operating conditions up to 20 C. The authors extended the original shrinking-core model by introducing the Li diffusion in both phases and the interface mobility as a model parameter. This model was then used to design new galvanostatic and potentiostatic intermittent titration techniques (GITT and PITT) to determine the diffusion coefficients of the respective phases in the composite (+).11_{Nevertheless, shrinking-core models can be difficult to program and}

issues related to the management of multiple interfaces can appear for complex charge/discharge profiles. Alternatively, Thorat et al.12 proposed the concept of phase-change diffusivity to account for LiFePO4 behavior in charge and discharge, introducing a

concentration-dependent diffusion coefficient of Li in the solid phases. Moreover, the authors considered the resistive-reactant feature of insulating LiFePO4, introducing the PSD effect

with four different particle sizes. The resistive-reactant concept was further developed by Safari and Delacourt who studied, with a simplified electrochemical model, the (dis)charge path dependence, the asymmetry and the electronic resistance distribution of this material.13 Good agreement was obtained with experimental data until 1C charge and discharge rates. Later, Delacourt and Safari14 proposed a simplified mathematical model to explain the insertion/extraction mechanism of Li ions for LiFePO4 material until 2C. In this simplified

approach based on the SP model without considering PSD effect, the authors determined relationships between particle radius and current density to fit experimental charge and discharge curves. In this work, the radius dependencies upon current were tentatively explained with the mosaic concept.

Simplified theoretical model and hypotheses.— In order to design a simplified

electrochemical model, the AM developed by Di Domenico et al.4 was adopted and extended. The AM consists of neglecting the solid concentration distribution along the electrode and considering the material diffusion, for each electrode, inside a representative solid particle at which the Li concentration is equal to the mean value of the concentration over the electrode thickness, c_s(r). Accordingly, the Faradaic current density per unit volume, jf, is equal to the

mean value of the current density over the electrode thickness, j_f. Therefore, the AM model

Aging modeling and lifetime optimization of Li-ion LiFePO4-graphite batteries according to the vehicle use.

Direction Chimie et Physico-chimie Appliquées

XIG01001

Titre :

Modélisation du vieillissement et optimisation de la durée

de vie des batteries Li-ion de technologie LiFePO

-graphite suivant l'usage véhicule

Aging modeling and lifetime optimization of Li-ion

LiFePO

-graphite batteries according to the vehicle use

Thèse

Eric PRADA

1-Public

Février 2013

Direction Chimie et Physico-chimie Appliquées

TABLE OF CONTENTS

LIST OF SYMBOLS

General Introduction

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

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1.3

Modelling approach adopted to investigate aging

mechanisms

1.4

References of Chapter 1

Chapter 2

: Simplified Electrochemical and

Thermal Model of LiFePO

-Graphite Li-Ion

Batteries for Fast Charge Applications

2.1

Introduction

2.2

Model Development

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