Mathematical modeling of transport phenomena in lithium ion batteries

The identi…cation and quanti…cation ofthe relationship of battery system properties and operation conditions with the thermalissues as well as how does the degradation develop inside the

PHENOMENA IN LITHIUM-ION BATTERIES

TONG WEI

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2014

This work would not have been possible to be achieved without the help of manypeople I would like to express my deepest gratitude to my supervisors, Professor Arun S.Mujumdar, Assistant Professor Erik Birgersson and Associate Professor Christopher Yapfor their excellent and tireless guidance for the work done in this thesis It has been agreat honor and pleasure to work with them during the past four years Prof Mujumdarpaved the way for me as a PhD student to pursue my research in National University ofSingapore (NUS) He is a nice and thoughtful mentor and always provides rich knowledgeand experience Prof Erik Birgersson opened the door for me to the world of an excitingresearch area - mathematical modeling of electrochemical energy storage system Prof.Erik Birgersson always helped me to build my con…dence His dedication and enthusiasmfor research and work impress me very much and set a positive example for me during myfour-year study Prof Yap, although only having a short time working with him, helped

me a lot The discussion with him, especially in how to strategically organize researchpapers and the thesis, has been crucial to the completion of my research work

In addition, I would like to thank all my colleagues and friends for their assistance whichhas facilitated the completion of this work I would thank our group members: Dr AgusPulung Sasmito, Dr Jundika Candra Kurnia for the discussion with them Specially, Iwould like to thank Dr Karthik Somasundaram for his kind help in developing the math-ematical modeling

Furthermore, I extend my gratitude to the China Scholarship Council and National versity of Singapore for their …nancial support

Uni-Last but not least, I dedicate this thesis to my parents for their endless love, support and

have reached where I am today.

Acknowledgements i

1.1 Overview of lithium-ion batteries 2

1.1.1 Structure and operation principles of a lithium-ion battery cell 4

1.1.2 Types and applications 6

1.1.3 Heat generation 7

1.1.4 Capacity fade 9

1.2 Mathematical modeling of lithium-ion batteries 10

1.4 Challenges 12

1.5 Outline of the thesis 12

2 Literature review 15 2.1 Theories of mathematical modeling 15

2.1.1 Porous electrode theory 16

2.1.2 Concentrated solution theory 17

2.1.3 Electrode kinetics 17

2.1.4 Solid phase di¤usion 18

2.2 Review of mathematical models 19

2.2.1 Coupled electrochemical-thermal models 19

2.2.2 Capacity fade models 21

2.2.3 Models for thermal management systems 24

3 Mathematical formulation 27 3.1 Governing equations 29

3.2 Constitutive relations 33

3.3 Boundary and initial conditions 38

4 Numerical methodology 41 4.1 COMSOL Multiphysics 42

4.2 Finite element method 43

5 A Monte Carlo simulation of a lithium-ion battery model - Correlating the uncertainties of system parameters with safety issues 46

5.2 Mathematical formulation of lithium-ion battery model 49

5.3 Monte Carlo simulation 51

5.4 Numerics 57

5.5 Results and discussion 58

5.5.1 Sample selection 58

5.5.2 Sensitivity analysis 58

5.5.3 Final cell temperature distribution 65

6 Analysis of capacity fade distribution of a cylindrical lithium-ion battery 69 6.1 Introduction 69

6.2 Mathematical formulation 71

6.3 Numerics 77

6.4 Results and discussion 79

6.4.1 Validation 79

6.4.2 Global behavior 80

6.4.3 Distribution of capacity fade 81

7 Numerical investigation of air cooling for a lithium-ion battery module 89 7.1 Introduction 89

7.2 Mathematical formulation 90

7.2.1 Governing equations 91

7.2.2 Boundary and initial conditions 95

7.3 Numerics 97

7.4 Results and discussion 98

7.4.2 E¤ect of air inlet velocity 101

7.4.3 E¤ect of cell arrangement 104

7.4.4 E¤ect of cell distance 105

7.4.5 Reversal ‡ow 106

8 Numerical investigation of water cooling for a lithium-ion bipolar bat-tery pack 111 8.1 Introduction 111

8.2 Mathematical formulation 113

8.3 Numerics 119

8.4 Results and discussion 119

8.4.1 Limiting cases 120

8.4.2 Thermal management with water cooling 126

9 Concluding remarks 136 9.1 Summary and conclusions 136

9.2 Contributions of this study 139

9.3 Recommendations for future work 141

Worldwide energy shortage and environment problems have necessitated more e¢ cient, reliable and sustainable techniques for energy transfer and storage Electricity,which could produce electrical energy, must be reliably and continuously available formany applications Therefore, electricity storage devices are critical for the e¤ective uti-lization of these energy sources.

-The lithium-ion battery is an electrochemical energy storage system that has attractedincreasing attention in recent years because of many advantages over competing technolo-gies These include high operating voltage, high energy density, no memory e¤ect andlow self-discharge rate However, the performance of lithium-ion batteries is closely as-sociated with thermal and degradation e¤ects The identi…cation and quanti…cation ofthe relationship of battery system properties and operation conditions with the thermalissues as well as how does the degradation develop inside the battery cell are thereforecritical for the e¤ective and safe utilization of lithium-ion batteries Furthermore, betterunderstanding of the parameters and mechanisms involved will enable the improvement

in design of battery thermal management systems

In tandem with experimental investigations of lithium-ion battery systems, tational study has become an e¤ective tool for identifying the salient features that can

compu-be found in lithium-ion battery systems Mathematical modelling not only captures thetransport phenomena occurring inside the battery cells which are generally di¢ cult toquantify experimentally, but also saves time and cost in experimental setup Generally,

conservation of species, charge and energy in both solid and liquid phases is based on theporous electrode theory In this thesis, the following work has been undertaken using thelithium-ion battery model.

Firstly, safety issues arising from a lithium-ion battery during operation can be tributed to the variation of its temperature which is, in turn, associated with the uncer-tainties in the parameters such as system properties and operating conditions Hence, aMonte Carlo simulation (MCS) of a lithium-ion battery model is conducted to capture theprobabilistic nature of uncertainties in the parameters and their relative importance to thetemperature of a lithium-ion battery cell Sensitivity analysis is statistically performedand the varied parameters are ranked according to their contributions to the variation ofthe battery temperature

at-Besides studying thermal e¤ects, a simulation is conducted that aims to determine ifnon-uniform distributions of capacity fade will develop during the cycling of a cylindricallithium-ion battery It is observed that locally non-uniform distributions of capacity fadewill develop across the surface of a single electrode during cycling while the average ca-pacity fade among electrodes of di¤erent wounds is uniform

As part of the applied research, the lithium-ion battery model is used to evaluatethermal management systems for lithium-ion batteries at a module or pack level Di¤er-ent active thermal management systems-forced air or liquid cooling are evaluated for twodesigns (cylindrical batteries and cells with bipolar con…gurations) of lithium-ion batter-

performance of the thermal management system.

This thesis presents the study on the modeling of transport phenomena in lithium-ionbattery systems The following publications are based on research carried out for thisdoctoral thesis

Journals:

1 Richard Hong Peng Liang, Tangsheng Zou, Karthik Somasundaram, Wei Tong andErik Birgersson, Mathematical Modeling and Reliability Analysis of a 3D Li-ionBattery, Journal of Electrochemical Science and Engineering, 4(1), 1-17, 2014

2 Wei Tong, Erik Birgersson, Arun S Mujumdar and Christopher Yap Correlatinguncertainties of a lithium-ion battery - A Monte Carlo simulation (Accepted byInternational Journal of Energy Research)

3 Wei Tong, Wei Qiang Koh, Erik Birgersson, Arun S Mujumdar and ChristopherYap Numerical Investigation of Water Cooling for a Lithium-ion Bipolar BatteryPack (Resubmitted to International Journal of Thermal Sciences)

4 Wei Tong, Erik Birgersson, Arun S Mujumdar and Christopher Yap Analysis

of capacity fade distribution of a cylindrical lithium-ion battery (Manuscript inpreparation)

5 Wei Tong, Erik Birgersson, Arun S Mujumdar and Christopher Yap tational Study of Air Cooling for a Lithium-ion Battery Module (Manuscript in

1 1) Tong Wei, Erik Birgersson, Arun S Mujumdar and Christopher Yap NumericalStudy of Passive Thermal Management of a Cylindrical Lithium-ion battery, The3rd International Conference on Informatics, Environment, Energy and Applications(IEEE 2014), Shanghai, China, March 27-28, 2014, DOI: 10.7763/IPCBEE 2014.V66 11

5.1 List of varied parameters 52

5.2 Physical and geometry parameters 53

5.3 pKS-value of K-S test on samples distribution 59

6.1 Physical and geometry parameters 78

6.2 Values of parameters used for the capcity fade model 79

7.1 Geometry and air properties 92

7.2 Standard deviations of temperature of cells at di¤erent positions at the end of discharge (base-case conditions) 103

7.3 Standard deviations of temperature of cells at di¤erent positions at the end of discharge: staggered arrangement with 9 mm cell distance 105

8.1 Coolant and insulator properties 118

1.1 Schematic of (a) a simpli…ed Ragone plot showing energy density vs powerdensity for various energy storage devices; (b) a comparision of energystorage capability of common rechargeable battery systems [2, 3] 31.2 Schematic of a lithium-ion battery operation principle 51.3 Lithium-ion batteries of various shapes and components: a cylindrical; b.coin; c prismatic; d pouch; …gure cited from Ref [2] 73.1 Schematic of (a) a single lithium-ion battery cell with various functionallayers; (b) agglomerate structure of lithium in active material in the elec-trodes 304.1 Applied discharge current with a smoothed Heaviside function (time scaleequals to 0.01s) - N: the time current starts to ramp up from zero, H: thetime current reaches its speci…ed value 445.1 Schematic of the computational domain of the lithium-ion battery 515.2 Flow chart of Monte Carlo simulation 545.3 Rankings of varied parameters at (a) 1 C-rate; (b) 5 C-rate using thecoe¢ cient of variance method 61

normalized derivative method 635.5 Scatter plots of battery temperaturevs top three ranked parameters in thesensitivity analysis at 5 C-rate: (a, c, e) varied each parameter individually;(b, d, f) varied all the parameters simultaneously 645.6 Sample distribution of battery temperature for the scenario of all the pa-rameters varied simultaneously at (a) 1 C-rate; (b) 5 C-rate Solid curve:normal density function …tted from sample mean and standard deviation 676.1 Schematic of (a) a cylindrical 18650 lithium-ion battery; (b) an axisymmetric-section of the spiral-wound battery with the structure of various functionallayers; (c) a basic unit of the jelly roll comprising a single cell; (d) ag-glomerate structure of lithium in active material in the electrodes Romannumerals: indicating the interfaces and boundaries of these layers 726.2 Validation of capacity fade model with experimental data [52] 806.3 Cell potential (solid line) / current density (dotted line) vs time duringthe 50th cycle 816.4 History of side reaction current density for the negative electrode of theoutermost wound during the 50th cycle: current collector side (solid line);separator side (dotted line) 826.5 Surface distributions of side reaction overpotential and side reaction currentdensity for the negative electrode of the outermost wound during the 50thcycle: (a, b) 5000 s (halfway of constant current charge); (c, d) 7000 s(halfway of constant voltage charge) 84

most electrode (solid line); innermost electrode (dotted line) 866.7 Comparison of the normalized capacity loss during the 50th cycle: outer-most electrode (solid line); innermost electrode (dotted line) 866.8 Comparison of (a) cumulative resistance increase and (b) cumulative nor-malized capacity loss with cycles of the outermost (solid line) and innermost(dotted line) electrodes 877.1 Schematic of a lithium-ion battery module 917.2 Schematic of the computational domain of two-dimensional battery module

of di¤erent con…gurations: (a) in-line; (b) staggered 937.3 Coupling of the one-dimensional and the two-dimensional models 957.4 Cell voltage curves/current densities vs time for the cells at P1 (solidlines) and P11 (dotted lines) 1007.5 Maximum temperature variation vs air inlet velocity of the battery moduleoperated under base-case conditions 1027.6 Maximum temperature variation of the two arrangements of the batterymodule operated under the base-case conditions 1047.7 E¤ects of cell distance on the maximum temperature variation for the bat-tery with staggered con…guration 1067.8 Average temperature history of cells at di¤erent positions under di¤erentfrequencies of reversal ‡ow 1087.9 Instantaneous average temperature of cells at di¤erent positions 109

sentative bipolar pack (named repeating-module) with the roman numeralsindicating the interfaces and boundaries of stacks and coolant plates; (c)cross-section of a stack with the roman numerals indicating the interfacesand boundaries of cells and various functional layers; (d) cross-section of asingle cell; (e) agglomerate structure of active material in the electrodes 1148.2 Voltage vs capacity of the battery pack during discharge at various C-rates under two limiting conditions: cooling (solid lines); without cooling(dashed lines) 1228.3 Concentration pro…le of Li+ in the electrolyte at the cut-o¤ voltage at a

5 C-rate under two limiting conditions (y = 3 10 2 m): cooling (solidline) and without cooling (dashed line) 1248.4 Temperature window of the battery pack: upper limit (dashed line); lowerlimit (solid line); operating line of temperature (dotted line) 1258.5 Average temperature di¤erence vs number of stacks at the cut-o¤ voltage

at various C-rates (1 C: H; 2 C: ; 5 C: N) with uc = 2.5 10 3 m s 1

and wc= 5 10 2 cm) 1288.6 Local temperature distribution at the cut-o¤ voltage at 5 C-rate for thebattery pack of (a) ms = 5, uc = 2.5 10 3 m s 1, wc = 5 10 2 cm;(b) ms = 15, uc = 2.5 10 3 m s 1, wc = 5 10 2 cm; (c) ms = 15, uc

= 2.5 10 2 m s 1, wc = 5 10 2 cm; (d) ms = 15, uc = 2.5 10 3 m

s 1, wc = 2 10 1 cm 129

at various C-rates (1 C: H; 2 C: ; 5 C: N) with ms = 15 and wc= 5

10 2 cm 1318.8 Average temperature di¤erence vs thickness of coolant plate at the cut-o¤voltage at various C-rates (1 C:H; 2 C: ; 5 C:N) with ms = 15 and uc=2.5 10 3 m s 1 133

As speci…c interfacial area per unit volume, m 1

cl electrolyte concentration, mol m 3

c0

l initial electrolyte concentration, mol m 3

cavgs average concentration of lithium in the active material, mol m 3

cmax

s maximum concentration of lithium in the active material, mol m 3

csurfs surface concentration of lithium in the active material, mol m 3

c0

s initial concentration of lithium in the active material, mol m 3

cv;i coe¢ cient of variation

Cp speci…c heat capacity, J kg 1 K 1

Dl di¤usion coe¢ cient of electrolyte, m2 s 1

Ds di¤usion coe¢ cient of lithium in the active material, m2 s 1

Ea activation energy for a variable, J mol 1

Erab absolute error

Erre relative error

F Faraday’s constant, 96,487 C mol 1

iapp applied current density, A m 2

is solid phase current density, A m

j sequence number of simulation runs

J local charge transfer current per unit volume, A m 3

k e¤ective thermal conductivity, W m 1 K 1

k0 reaction rate constant, mol2:5 m 0:5 s 1

ls di¤usion length, m

n total number of varied parameters

Nl species ‡ux, mol m 2 s 1

p probability

Q volumetric heat generation, W m 3

q conductive heat ‡ux, W m 2

R gas constant, J mol 1 K 1

Rs radius of active material in the electrodes, m

sxi standard deviation of sample (input)

sy standard deviation of sample (output)

Tref reference temperature, K

Uref;i open circuit potential of the electrode i, V

wi thickness of the functional layer i, m

xi mean of sample (input)

X i population (input)

Y population (output)

signi…cance level

a anodic transfer coe¢ cient

c cathodic transfer coe¢ cient

Bruggemann constant

"f volume fraction of conductive …ller additive

"l volume fraction of electrolyte

"p volume fraction of polymer phase

overpotential, V

ne state of charge of negative electrode

pe state of charge of positive electrode

e¤ective density, kg m 3

l ionic conductivity of electrolyte, S m 1

s electronic conductivity of solid matrix, S m 1

X i standard deviation of population (input)

Y standard deviation of population (output)

l liquid phase potential, V

s solid phase potential, V

X i mean of population (input)

Y mean of population (output)

ab absolute value

critical critical value

f ara faradaic process related value

avg average value

Generally, electrical energy is stored in another form of energy As a type of commonlyapplied energy storage device, a battery indirectly stores the electrical energy in the form

of chemical energy When the battery releases electrical energy, redox reactions of theelectrochemical active reactants inside the battery is induced to create charges performingthe electrical work at the external electric circuit

1.1 Overview of lithium-ion batteries

Figure 1.1a is the Ragone plot of various energy storage and/or conversion systems teries can generally store signi…cantly more speci…c energy than conventional capacitorsand electrochemical capacitors due to the faradaic processes, i.e., electrochemical reactions[1] Fuel cells have relatively high speci…c energy However, they are energy conversionsystems In a fuel cell, the chemical energy from a fuel is converted into electrical energy

Bat-by the redox reaction The fuel is stored isolated from the device The requirements forthe fuel storage and transportation restrict the usage of fuel cells which make fuel cellsless attractive than batteries Today commercially available rechargeable batteries includelithium-ion, nickel-metal-hydrid, and nickel-cadmium devices As shown in Figure 1.1b,lithium-ion batteries and other lithium-based batteries have the highest energy densitiesamong all rechargeable batteries

Lithium-ion batteries, …rst commercialized by SONY in 1991, are now widely utilized

in portable, computing and electronic applications The main advantages of a lithium-ionbattery, including high energy density, high operating voltage, no memory e¤ect, slowself-discharge rate, and good cycle life (greater than 1000 cycles), make it a promisingcontender for energy storage in consumer electronics Although they are likely to beamong the most important energy storage devices in the future, lithium-ion batteries arestill su¤ering from some undesirable drawbacks like increasing internal resistance duringcharge/discharge cycles, capacity loss, ageing e¤ects on battery life, thermal runawaywhen overcharged or improperly operated Accurate understanding of working mecha-nisms and appropriate management measures are thus critical to achieve greater reliabilityand longevity of lithium-ion battery systems

Figure 1.1: Schematic of (a) a simpli…ed Ragone plot showing energy density vs powerdensity for various energy storage devices; (b) a comparision of energy storage capability

1.1.1 Structure and operation principles of a lithium-ion battery

cell

A basic lithium-ion battery cell consists of several functional layers: a current collector ofaluminum coated with a positive lithium-metal-oxide electrode (cathode), a current col-lector of copper coated with a negative graphite carbon electrode (anode), and a separator

in between the electrodes The electrodes and the separator are of porous structure thatare …lled with a non-aqueous electrolyte Di¤erent chemistries of lithium-ion batteriesare developed The most commercialized negative electrode is graphite and hard carbon.The positive electrode is typically made of a metal oxide, such as lithium cobalt oxide(LiCoO2), lithium manganese oxide (LiMn2O4) and lithium iron phosphate (LiFePO4).The electrolyte is usually an organic carbonate solvent such as ethylene carbonate (EC)

or dimethyl carbonate (DMC) mixed with a lithium salt such as lithium phate (LiPF6), lithium perchlorate (LiClO4) and lithium tetra‡uoroborate (LiBF4) [4].During charge and discharge, lithium ions are transferred from one electrode to another

hexa‡uorophos-by the intercalation and the deintercalation processes, as illustrated in Figure 1.2 withelectrode reactions expressed as

Positive electrode: LiMO2 Li1 xMO2+ xLi++ xe (1.1)Negative electrode: C + x Li++ xe LixC (1.2)Overall: LiMO2+C LixC + Li1 xMO2 (1.3)where M represents the transition metal employed for the positive electrode

Figure 1.2: Schematic of a lithium-ion battery operation principle.

1.1.2 Types and applications

More recently, lithium-ion batteries are becoming the heart of many electric-poweredapplications For some applications such as the mobile phone and tablet computer, a singlelithium-ion battery cell is su¢ cient for the device to work; while for large scale applicationssuch as electric vehicles [5] and large scale stationary energy storage [6], high voltage andhigh capacity output are required In order to meet these requirements, the batterycells are not simply combined together, but organized regularly to perform in terms of

a battery module/pack system with advantages of minimized weight, compact, secure,good thermal management, as well as safety and protection against external interference

In particular, those battery cells may be con…gured in series, parallel or mixture of bothmodes to deliver the desired voltage, capacity and power density, e.g., the Panasonic highenergy lithium-ion battery module [7] In addition, supervisory control and managementcircuits are integrated into the pack to ensure optimal performance by minimizing thenon-uniformities among cells and modules

Lithium-ion batteries can be classi…ed by cell shape, generally including cylindricalcells, coin/button cells, prismatic cells and pouch cells as shown in Figure 1.3 There arealso cells with bipolar con…guration and other special designs for civil and military use.Lithium-ion battery cells in di¤erent shapes are applied to di¤erent end applications Forexample, the mobile phone battery is generally of a prismatic cell while the laptop battery

is usually a battery pack composed of 6 or 9 cylindrical cells

Figure 1.3: Lithium-ion batteries of various shapes and components: a cylindrical; b.coin; c prismatic; d pouch; …gure cited from Ref [2].

When the reaction is reversed, the heat is also reversed.

2 Irreversible heat generation The irreversible heat is caused by the polarization e¤ectwhen the current passes through the conducting material inside the battery Thepolarization e¤ect here refers to the deviation of the potential from its equilibriumstate

3 Ohmic heat generation The ohmic heat, also known as Joule heating related tothe resistance of the battery The ohmic heat is released during the passage of anelectric current through the battery cell In a lithium-ion battery cell, the ohmicheat generation is also irreversible and can be attributed to two e¤ects, i.e., theelectronic e¤ect from the solid matrix and the ionic e¤ect from the electrolyte phase[8]

During operation, excessive heat generation inside lithium-ion batteries will lead tounexpected temperature increase If this heat cannot be dissipated e¤ectively, the batterywill be overheated, resulting in thermal runaway or explosion in a worst-case scenario Infact, there have been several cases of lithium-ion batteries going into thermal runaway inlaptop and cellphone applications leading to recalls by manufacturers including Dell, IBM,Toshiba and Apple In large scale applications such as hybrid electric vehicles and electricvehicles, batteries are usually in the form of a battery module/pack If one or more cellsare failing, the high heat arising from these cells could propagate to the neighbor cells andcause the battery system to become thermally unstable, which can further induce chainreaction and even catastrophic destruction of the module/pack Therefore, appropriatethermal management system is crucial for better and safer operations of battery systems

Another issue is the non-uniformities between cells/modules in a battery pack out proper battery management and supervision, especially in large scale applications.Batteries in applications such as EV comprise long strings of cells in series in order toachieve the desired operating voltage and numbers of cells/modules in parallel in order

with-to achieve the required capacity or output power During operation, it is di¢ cult with-tomaintain the battery pack temperature, keeping all the cells at a constant temperature.The non-uniform temperature between cells can cause electrical imbalance over time, i.e.,non-uniform charge and discharge behavior of the battery pack When the non-uniformityoccurs between cells, the batteries will su¤er from a series of problems, such as overcharge(due to the electrical imbalance) which in turn can induce thermal runaway and capac-ity loss and eventually cause a module/pack level failure Hence, lithium-ion batteriesrequire e¤ective measures for thermal management and battery management to maintainthe batteries operating under safe and stable conditions

1.1.4 Capacity fade

Besides excessive heat generation, capacity fade is another main limitation of the mance of lithium-ion batteries The capacity fade refers to the loss in discharge capacityand occurs throughout the whole life of batteries Various mechanisms are responsible forthe loss of battery capacity Some of them lead to reversible capacity loss which can berecovered by recharging the batteries, while the others cause irreversible capacity loss thatthe active material, lithium, is consumed irreversible by side reactions As investigated,battery capacity fade is associated with various conditions (both internal and external)and factors In this thesis, only irreversible capacity fade is taken into account

perfor-1.2 Mathematical modeling of lithium-ion batteries

Mathematical modeling and computational analysis are extensively employed in the study

of lithium-ion battery systems Various mechanistic mathematical models are developed

to resolve the essential phenomena occurring within a lithium-ion battery cell which cannot be simply obtained by conducting experiments These models typically consider thetransient equations of conservation of species, charge and energy together with relevantboundary conditions at multiscales A more detailed literature review on the mathemat-ical modeling of a lithium-ion battery is presented in Chapter 2

As aforementioned, thermal related issues can be the major concern for lithium-ion teries Moreover, the understanding of mechanisms of capacity fade is also important forbetter utilization of such batteries According to these two points, two main objectives areproposed for this work: 1) theoretically study the factors that can cause the temperaturevariation and the distribution of capacity fade developing in a lithium-ion battery cell;2) numerically investigate the performance of di¤erent thermal management systems forlithium-ion batteries at a module/pack level

bat-The theoretical studies that are carried out include:

Capturing the random yet probabilistic nature of uncertainties in design and ation parameters of a battery cell and their relative e¤ects on the battery tempera-ture;

oper-Investigating if a non-uniform distribution of capacity fade will develop during

cy-cling of a lithium-ion battery.

The applied studies focus on the analysis of two di¤erent active thermal managementsystems designed for a battery module/pack, including:

Active thermal management system comprising forced air cooling for a battery ule of cylindrical cells;

mod-–Coupling of the one-dimensional battery models and the two-dimensional jugate heat transfer model;

con-–Identifying design and operation parameters of interest;

–Evaluating the performance of the thermal management by considering boththe maximum temperature variation and the uniformity of temperature distri-bution

Active thermal management system comprising forced liquid cooling for a batterypack;

–Designing the bipolar battery pack and the cooling system;

–Identifying design and operation parameters of interest;

–Evaluation the performance of the thermal management system

These two applied studies are motivated by the fact that no study has been carriedout for battery thermal management which accounts for both the local electrochemicaland the thermal behaviors

1.4 Challenges

The challenges to be overcome in this work are:

Exploring proper methods and procedures for sensitivity analysis of the batterysystem;

Coupling of the …rst principle capacity fade model into the lithium-ion batterymodel;

Reducing computational costs without sacri…cing computational accuracy for ulating complex battery systems such as the battery module and pack

This thesis consists of nine chapters, covering both theoretical investigations and appliedstudies of the lithium-ion battery system A brief outline of each chapter is given below:Chapter 1 describes the development of lithium-ion batteries as a type of electro-chemical energy storage and conversion system; applications and types of lithium-ionbatteries are then brie‡y introduced The issues - thermal e¤ects and degradation

- of lithium-ion batteries are identi…ed and these provide the motivations of thisstudy, followed by the objectives of the present research work

Chapter 2 presents a thorough literature review of the mathematical models veloped for predicting the electrochemical and the thermal behavior of lithium-ionbatteries as well as the existing thermal management designs

de-Chapter 3 provides the mathematical framework utilized in the whole thesis Thegoverning equations, constitutive relations, boundary and initial conditions are pre-sented in this chapter.

Chapter 4 introduces the numerical methodology employed in conducting the ulations

sim-Chapter 5 carries out a Monte Carlo simulation of a lithium-ion battery model tocapture the probabilistic nature of uncertainties in the system properties and theoperation conditions and their relative importance to the temperature of a lithium-ion battery cell

Chapter 6 reports a simulation to examine if a non-uniform distribution of capacityfade develops during the cycling of a cylindrical lithium-ion battery cell The bat-tery in this study is resolved by an axisymmetric two-dimensional cross-section Atransient mathematical model of lithium-ion battery integrated with capacity fadee¤ects is solved

Chapter 7 provides a numerical study to evaluate the e¤ects of several design andoperation parameters of a lithium-ion battery module on the performance of anactive thermal management system comprising forced air cooling The battery cell isresolved with a one-dimensional geometry and the battery module with air ‡ow …eld

is resolved with a two-dimensional geometry Each of the cells is solved separatelyand interactively coupled with the two-dimensional model

Chapter 8 presents a numerical investigation to evaluate the performance of abipolar-design battery pack in terms of operating and design parameters of an active

thermal management system comprising forced liquid cooling The behavior of thebattery pack during galvanostatic discharge under two limiting conditions are alsostudied.

Chapter 9 provides a summary of the key …ndings and contributions of this thesis;and then proposes recommendations for the future studies

Literature review

Mathematical modeling of electrochemical energy storage systems requires a series ofdi¤erential and algebraic equations to precisely describe the internal physical and electro-chemical behavior taking place during the various operating conditions These equationsspecifying the dependent variables of interest, along with boundary and initial conditionsconstitute the fundamental modeling framework The following literature review mainlyfocuses on the theories used in setting up the modeling framework of lithium-ion batter-ies Apart from reviewing the theories for battery modeling, a review of existing modelingworks that are relevant to the studies conducted in this thesis is also presented in thischapter

Employing mathematical modeling in the design of batteries has a long history In the late1950’s, the macroscopic models of the current and the potential distributions in porous