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Modeling an identification of battery electrochemical-thermal model under fast charging

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Title:
Modeling an identification of battery electrochemical-thermal model under fast charging
Creator:
Aldhafeeri, Rashed
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
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English

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Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical engineering
Committee Chair:
Dey, Sandra
Committee Members:
Radenkovic, Miloje
Park, Jae-Do

Notes

Abstract:
Lithium-ion batteries, nowadays, have received much attention in the last few years. Because of their better energy density and power comparing to lead-acid batteries, Lithium-ion batteries have become a leading choice for electrified vehicles. Recently, fast charging of Lithium-ion batteries has gained significant focus. If successful, such fast charging will enable higher commercial penetration of electric vehicles due to reduced re-fueling time. To monitor and control such Lithium-ion batteries efficiently, advanced Battery Management Systems (BMSs) are essential. BMS, in general, contains hardware and software that are used to charge and discharge the Lithium ion cells safely. In the last couple of years, compared to phenomenological type electrical circuit models, coupled electrochemical-thermal models for batteries have gained more attention for BMS applications. Electrochemical-thermal models have the ability to precisely predict cell behavior along with information about the internal cell states. In this thesis, we focus on modeling and parameter identification of coupled electrochemical-thermal model of Lithium-ion batteries under fast charging utilizations. Such identified model will be essential to design estimation and fast charging control algorithms. Specifically, we identify the model parameters of a fresh battery cell (i.e. in the beginning of life) and an aged battery cell (i.e. in the end of life). The distinction from one another, the fresh cell and aged cell parameters will provide some insights about how the battery cell ages under fast charging.

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Full Text
MODELING AND IDENTIFICATION OF BATTERY ELECTROCHEMICAL-THERMAL MODEL UNDER FAST CHARGING
by
RASHED ALDHAFEERI
Bachelor of Science, University of Hafr A1 Batin, 2015
A thesis submitted to the Faculty of the Graduate School of the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Science Electrical Engineering 2019


This thesis for the Master of Science degree by
Rashed Aldhafeeri has been approved for the Electrical Engineering Program by
Satadru Dey, Chair Miloje Radenkovic Jae-Do Park
July 22, 2019


Aldhafeeri, Rashed (M.S., Electrical Engineering)
Modeling and Identification of Battery Electrochemical-Thermal Model under Fast Charging Thesis directed by Assistant Professor Satadru Dey
ABSTRACT
Lithium-ion batteries, nowadays, have received much attention in the last few years. Because of their better energy density and power comparing to lead-acid batteries, Lithium-ion batteries have become a leading choice for electrified vehicles. Recently, fast charging of Lithium-ion batteries has gained significant focus. If successful, such fast charging will enable higher commercial penetration of electric vehicles due to reduced re-fueling time. To monitor and control such Lithium-ion batteries efficiently, advanced Battery Management Systems (BMSs) are essential. BMS, in general, contains hardware and software that are used to charge and discharge the Lithium ion cells safely. In the last couple of years, compared to phenomenological type electrical circuit models, coupled electrochemical-thermal models for batteries have gained more attention for BMS applications. Electrochemical-thermal models have the ability to precisely predict cell behavior along with information about the internal cell states.
In this thesis, we focus on modeling and parameter identification of coupled electrochemical-thermal model of Lithium-ion batteries under fast charging utilizations. Such identified model will be essential to design estimation and fast charging control algorithms. Specifically, we identify the model parameters of a fresh battery cell (i.e. in the beginning of life) and an aged battery cell (i.e. in the end of life). The distinction from one another, the fresh cell and aged cell parameters will provide some insights about how the battery cell ages under fast charging.
The form and content of this abstract are approved. I recommend its publication.
Approved: Satadru Dey


Table of Contents
CHAPTER 1......................................................................1
INTRODUCTION AND OVERVIEW......................................................1
1.1 Classifications of Batteries.............................................1
1.1.1 Basic Terminology of Batteries.......................................2
1.2 Significance of Fast Charging in Li-ion Batteries.......................2
1.3 Aging Mechanism..........................................................4
1.3.1 The growth of solid-electrolyte interface (SEI) layer................4
1.3.2 The Lithium Plating..................................................5
1.4 Modeling and Identification of Electrochemical-thermal Models............5
CHAPTER II.....................................................................6
MODELING AND MODEL APPROXIMATION...............................................6
2.1 Battery Electrochemical-Thermal Model....................................6
2.2 Nominal Electrochemical Model............................................7
2.2.1 Finite Difference Approximation of SPM...............................9
2.3 Nominal Thermal Model and Finite Difference Approximation...............10
CHAPTER III...................................................................14
3.1 Genetic Algorithm (GA) Overview.........................................14
3.2 Experimental Setup......................................................15
3.3 Fresh Cell Electrochemical and Thermal Model Identification.............17
3.4 Aged Cell Electrochemical and Thermal Model Identification..............21
3.5 Observations............................................................23
CONCLUSION....................................................................25
REFERENCES....................................................................26
IV


List of Figures
Fig. 3. 1: Experimental Setup........................................................15
Fig. 3. 2: Cylindrical Cell Construction Cited from [35].............................16
Fig. 3.3: NMC Battery Cell...........................................................17
Fig. 3. 4: The Current Applied to the Cell...........................................18
Fig. 3. 5: Fresh Cell Terminal Voltage Verses Time...................................19
Fig. 3. 6: Fresh Cell Temperature Verses Time........................................20
Fig. 3.7: After Aging Terminal Voltage verses Time...................................22
Fig. 3. 8: After Aging Temperature Verses Time.......................................23
v


List of Tables
Table 2. 1: Li-ion Battery Model Nomenclature......................................7
Table 3. 1: Test Cell Specifications...............................................16
Table 3.2: Fresh Cell Optimized Parameters.........................................17
Table 3.3: Fresh Cell Optimized Parameters.........................................19
Table 3.4: Fresh Cell Temperature and Voltage RMS Errors...........................21
Table 3. 5: After Aging Optimized Parameters.......................................21
Table 3.6: After Aging Temperature and Voltage RMS Errors..........................22
VI


CHAPTER I
INTRODUCTION AND OVERVIEW
Overall, Lithium-Ion (Li-ion) batteries are used for energy storage in numerous applications, for example, electric vehicles (EVs), smart grids, solar power storage, and drones. Such wide usage is due to their enormous advantages of high energy density, huge capacity, and long-life cycle. Currently, one of the most distinguished advantages of lithium material is that it is considered as the lightest among all other materials. It has also the best potential electrochemically. In fact, if lithium material is placed on the anode electrode, it can deliver extremely more energy densities. As a result, there will be some particles in which they penetrate the separator sheet of the battery and cause a short circuit. Recently, this type of Li-ion battery has suffered from safety issues, reliability, and high cost [1],
1.1 Classifications of Batteries
Batteries, generally, can be categorized as primary or secondary. Primary batteries can not be recharged; it has to be discarded after it has been fully discharged while the secondary batteries are rechargeable. Furthermore, there are three main battery chemistry types that are widely used: Li-ion, lead acid, and nickel metal hydride. In traditional internal combustion engine (ICE) vehicles, 12V lead acid (PbA) batteries were used to power the starter motor [27], Even though the higher energy nickel-metal hydride (NiMH) cells have powered up many of the first successful HEVs, they are being, generally, replaced by Li-ion batteries with better energy density and power. From power point of view, Li-ion and NiMH cells can, in fact, store same level of power; however, Li-ion cells can charge and discharge mroe faster than NiMH cells.
1


1.1.1 Basic Terminology of Batteries
Some common battery terms are listed below.
♦♦♦ Capacity: It can be described as the maximum level of charge that a battery can supply. Typically, capacity is expressed in Ampere-hour. Experimentally, it can be obtained by integrating the current / that is being applied from higher voltage level at the initial time t0 to the lower voltage level at final time tf.
Here 3600, is the scaling factor that is used for the conversion from seconds to hours. ♦♦♦ C-rate: It is value of current (/) expressed in terms of cell capacity (Q) :
♦♦♦ State-of-Charge (SOC): It can be described as an indication for the level of charge that is left in the cell. This is typically expressed as:
1.2 Significance of Fast Charging in Li-ion Batteries
Nowadays, intriguingly, most of EVs with a Level 11-240 V system can be completely charged from 6 to 8 hours [22]; eventually, charging period is considerably long and becomes unreasonable when recharges are required. To solve this problem, Level III fast charging levels are implemented, though they differ from place to place. More notably, because of the higher current that could cause degradation of the Li-ion batteries, and it could decrease Li-ion battery’s
I = C — rate x Q
2


lifetime, this fast charging technique has not been implemented on all EVs [23], Limited EVs leading companies allow the implementation of fast charging options, and they are recommended to be used rarely to reduce battery degradation phenomenon [21], To illustrate, because of a variety of chemical and physical processes under high current scenarios, the degradation in Li-ion battery cells is faster. Consequently, this degradation influences various components of the cells. For instance, the electrolyte, anode and cathode electrodes, the separator sheets, and the current collectors [25], In addition, as stated by the United States Advanced Battery Consortium (USABC), the long period of time objective to charge fast is to restore 40% battery’s SOC in 15 minutes [24]; still, fast charging generally includes high energy outputs, high temperatures, and high current rates. Subsequently, these will force to decline the electric characteristics of the Li-ion batteries and affect their functionalities. Yet, to tolerate such harmful conditions without major deterioration. Only sophisticated chemicals can be used for the fast charging. As a result, few Li-ion battery companies are presently able to supply cells that can accept both fast charging and have a long life.
Reduction of the charging time for Li-ion batteries that are installed in EVs and HEVs are primary concerns of most consumers. Therefore, for the safety factor and consistent operation, advanced battery management systems (BMS) are strongly required in order to develop the battery performance and optimize battery operation. Such BMS algorithms relies on mathematical models of batteries. There are different types of battery models that are available in existing literature. Data-driven battery models fit some mathematical equations that describe the battery voltage, current and temperature data [4], Electrical circuit based phenomenological models capture battery behavior in terms of electrical circuits [5, 6], Although these types of models can be useful in predicting battery voltage behavior, they may not be able to provide
3


insights about internal battery states. Under this scenario, coupled electrochemical-thermal models are useful which can capture the battery internal physics to a great extent [1, 2, 3],
1.3 Aging Mechanism
Interestingly, one of the most significant striking current discussions in Li-ion batteries area is the aging mechanism of Li-ion batteries. During batteries lifetime, their performance tends to decline gradually because of the unalterable chemical and physical changes. Thus, cells tend to lose their capacities, and the internal resistance is increased. Mainly, the capacity loss results in the decrease in the electric range of EVs, while the growth in internal resistance reduces the availability of power. Depending on the chemistry of the cell and working conditions, aging phenomenon can be triggered by various degradation mechanisms. These degradation mechanisms are detailed below.
1.3.1 The growth of solid-electrolyte interface (SEI) layer
Recently, researchers have shown an increased interest in the aspect of the growth of SEI layer that is considered as a major cause of fading capacity in Li-ion cells. As a consequence of side reactions that occur between the electrolyte solution and the active electrode material, the SEI layer forms. Subsequently, this reaction consumes some lithium metal, so the SEI layer grows and results in a gradual capacity fade as the SEI layer becomes, over time, thicker. Because of the low potential at the negative electrode, SEI growth occurs primarily at the negative electrode mostly at higher SOC. SEI film is formed, particularly, at the negative electrode because, during charging, electrolytes are not stable at this electrode. In addition, the growth of SEI is worsened when the temperature is high because the rate of the reaction increases with heat [27, 30],
4


1.3.2 The Lithium Plating
Lithium plating or deposition is the creation of lithium metal, during charging, around the anode of Li-ion batteries; likewise, it can take place at the negative electrode during higher charging current scenario; This eventually cause the loss of lithium and in turn, cell’s capacity.
All in all, the leading aging mechanisms at the anode electrode are SEI layer evolution and lithium plating; meanwhile, the aging at the electrode on the cathode is mostly because of the loss of active materials [31],
1.4 Modeling and Identification of Electrochemical-thermal Models
As mentioned before, models are essential to design algorithms for advanced BMS. In this work, we consider electrochemical-thermal model of Li-ion batteries. Our goal is to develop, simulate, and identify the model parameters of a fresh and aged battery cell. We have employed a combination of numerical and experimental techniques to achieve these goals. To reiterate, such models will be useful in designing advanced control and estimation algorithms under battery fast charging applications.
The rest of the thesis is organized as follows. Chapter II discusses modeling and model approximation of both electrochemical-thermal and nominal electrochemical model of theNMC Li-ion battery cell. Chapter III discusses the detailed model identification, experimental setup, and simulation results. Finally, conclusions are presented with a brief discussion on future problems.
5


CHAPTER II
MODELING AND MODEL APPROXIMATION
2.1 Battery Electrochemical-Thermal Model
Electrochemical battery models are attracting considerable interest due to its remarkable accuracy than the other approaches of modeling [7], Among the existing electrochemical models, a complete order electrochemical model that is known as pseudo-2D (P2D) model is widely adopted. However, the complexity and computational burden of P2D model demands some model reduction before applying it in real-time applications [8], Some model techniques have been suggested for some SOC estimation methods, including a residue grouping method with a linear Kalman filter (KF) [9], a Partial Differential Equation (PDE) type Luenberger observer [10], and particle filter (PF) [11],
A specific reduction of the P2D electrochemical model is called the single-particle model (SPM) in which both negative and positive electrodes are approximated as spherical particles. The SPM based modeling framework has been widely used in real-time applications such as SOC estimation. For example, an extended KF [12, 13], an Cinscented Kalman Filter [14], backstepping PDE estimator [15], Particle Filter (PF) [16], adaptive PDE observer [17], and geometric observer [18], nonlinear observer [19], and sliding mode observer [20] have been proposed that utilized SPM framework. The primary advantage of SPM framework the model is computationally efficient and at the same time captures certain internal physical behavior of Li-ion batteries. In the following sections, we describe this model in detail.
6


2.2 Nominal Electrochemical Model
The schematic of then SPM is shown in Fig. 2.1 below along with the list of variables Table 2.1.
V
Fig. 2. 1: Schematic of SPM
Table 2.1: Li-ion Battery Model Nomenclature
Symbol Definition and Unit
A Current collector area (m2)
a Specific surface area (m2/m3)
c Solid phase Li-ion concentration (mol/m3)
Q Heat generation (W/m3)
Y Cell radius (m)
D Effective diffusion coefficient in solid phase (m2/s)
F Faraday’s constant (C/mol)
I Current (A)


L Length of the electrodes (m)
X Radial coordinate (m)
P Cell density (kg/w?)
cp Specific heat (J/kg — K)
Rf Contact film resistance (Q)
k Thermal conductivity (W/m — K)
h Convection coefficient (W/m2 — K)
T Temperature (K)
vb Cell volume (m3),
u Open circuit voltage (V)
R Universal gas constant (J/mol — K)
ea Active material volume fraction (dimensionless)
Superscript ± Positive/Negative electrode
a, c Anode/Cathode
Essentially, anode and cathode, in the SPM framework, are approximated as single spherical particles in which lithium ions can diffuse in and out during charging and discharging. This approximation leads to two linear Partial Differential Equations (PDEs) that describe the diffusion of Lithium ions in two particles demonstrating each electrode. Note that the concentration of electrolytes solution is assumed to be constant [32], In this work, the focus will be only on the dynamics of anode that is given by the following PDE diffusion equation, and its boundary conditions.
dca(x,t) _ D d / 2dca(x, t)\ dt x25x\ dt )
(1)
dca(x, t)
dx
= 0,
x=0
5ca(x, t)
dx
x=X
-m
aaFDAaLa
(2)
8


where x is the radial coordinate of the particle in m, t is the time in s, ca is the Lithium concentration along the particle in mol/m3, D is the anode diffusion coefficient in m2/s, R is radius of the particle in m, / is the applied current in A with / > 0 that is indicating discharging and / < 0 which is indicating the charging, aa is the anode specific surface area in m2/m3 that is calculated as aa = 3 Ea/X where Ea is the active material volume fraction, F is Faraday’s constant in C/mol, Aa is the anode current collector area in m2, and La is the anode thickness in m. Under certain assumptions, the cathode Lithium concentration can be expressed in terms of anode Lithium concentration as cr = — &aAaLa c -|—llL— where n,,- is the total moles of
L ecAcLc a ecAcLc Ll
Lithium.
2.2.1 Finite Difference Approximation of SPM
To implement the aforementioned PDE model, we adopt the method of lines technique.
In method of lines technique, we discretize the spatial dimension into a finite number of nodes, and subsequently, approximate the spatial derivatives with central finite difference approximation keeping the time derivatives intact. Such approximation converts the PDE model to a set of Ordinary Differential Equations (ODEs) model.
From Eq. (1), we can write that
Next, consider a node 'm' in the discretized domain shown in Fig. 2.1. Using central difference method, the Lithium concentration dynamics at node 'm' can be written as:
dcam _ f _2_ /Ca(m+1) ~ Ca(m-1)\ Ca(m+1) ~ ^Cam + Ca(m-1) \
dt y mA V 2A / A2 J
9


= D
((-
(m+l) Ca(m-1)\ Ca(m+1) 2cam + Ca(.jn_1^)
mA2

A2
with discretization step A= —. Taking cm+1 and cm_1 as common factors from the above
equation, we get:
dCam D
dt
- A2 (cHm+1) {1 + m) + cHm-1) (/ m) 2c«™)
By defining, a = — and rearrange the equation, we get:
= a (l + —)ca \ m/
(m+i) 2acam +
a (l - —)ca
\ m/
(m-l)
Similarly, we apply same approximation at the other nodes. Consequently, we end up with the following set of ODEs:
Cam - (l ac&(m—i) a2cam + (l + m) aca(jn+
CaM = aCa(M-1) “ (* ~~ m) aCflM ~~ (* + m) ^
with m = 1,..(M — 1), discretization step A= —, and b = l/aaFDAaLa .
(3)
(4)
2.3 Nominal Thermal Model and Finite Difference Approximation
Temperature plays a crucial role in internal battery dynamics. Hence, it is essential to model the temperature dynamics of the battery. In this section, in order to capture the temperature variation along the cell radius, a distributed parameter thermal model is adopted [35],
Consider a cylindrical battery cell. The following distributed parameter thermal model captures the temperature variation along the radius of the cylinder:
10


(5)
pCp
dT,
(y.t)
dt
= k-
d2T,
(y.t)
dyi
+
1 dT(y,t) <2(Q
y dy F,
With its boundary conditions:
dT(y,t)
dy
y=o
= 0,
dT(y,t)
dy
y=Y
h
--(rQO-roo)
(6)
where t is time in s, y is the radial coordinate of the cell in m, Y is the cell radius in m, p is the cell density in kg/m3, Cp is the specific heat in J/kg — K, k is thermal conductivity in W/m — K, h is the convection coefficient in W/m2 — K ,Tm is the cooling/ambient temperature, Vb is the cell volume in m3, and Q is the heat generation term that is computed by:
<2(0 = I(t){Uc(alCa(X) + a2) + Ua(ca(X)) - Vt(t)} (7)
where Uc and Ua are the open circuit voltage maps of cathode and anode, respectively;
a1 = — (Ga AaLa)/(Ec ACLC) and a2 = mLj/(Gc ACLC); mLj is total moles of Lithium in the cell, and Vt is the battery terminal voltage that can be computed as:
Vt(0 = Uc(alCa(X) + a2) + Ua(ca(X)) - Rb /(t)
<8)
cccF \2acAcLci0c/ ^aF ''2&ai4aLaiQa'
where R is the universal gas constant in ]/mol — K, ac and aa are unitless charge transfer coefficients of cathode and anode, respectively; ac is specific surface area in m2/m3, Ac and Aa are the current collector area of cathode and anode, respectively in m, Lc and La are length of the electrodes of cathode and anode, respectively in m, t0c and i0a are the exchange current densities of cathode and anode, respectively in A/m2, Rb is the internal resistance of the cell in Q.
From Eq. (5), we can write
11


1
(9)
dT,
(y.t)
k (d2T,
(y.O \ + ^ ^
dt pCp\ dy2 ) pCpy\ dy ) pCpVb
<2 CO
Next, we apply the finite difference approximation to convert the PDE to a group of ODEs. We discretize the radial direction into M number of nodes. At node'm', the PDE (9) can be approximated as:
dTm k {T(jn+1) 2Tm + m-l)^ ^ (T(m+1) ^(m-l)
dt pC-
V
A2
iw—r.
/ pCpmA \
2A
) + nr 1/ *2(0
/ p Cp Vjj
Y 1
with discretization step A= —. Denoting = — , we get
_ nl (T(m+1) , fik ^f(m+i) ^(m-l)') , P A
A5 2A
T - r>7- I (T(m+1) 7(m-l)\ P a
m ljk\ A2 A2 A2 / mA V 2A 2A / + ^
(10)
(11)
Bk
Defining ax = —, and applying similar approximation to other nodes, we can write the following set of ODEs that capture the thermal dynamics:
T-l — —1.5a17(1') + 1.5a!7(2) 1?
P_A
(14)
- (l - 2^) «i7(m-i) - 2a17’(m) + (l + —) air(m+i) + (15)
Tm - (i - 2]jj) + (“2ai + %(! - y)(l + ^)) T\
i l\hA P .
+ ai{1 + 2M) TTm+VhQ
(16)
with m = 2,..., (M — 1), and discretization step A= — .
12


With the above formulation, we now have a group of ODEs that capture the SPM electrochemical dynamics and another group of ODEs that capture the distributed parameter thermal dynamics. Next, our goal is to identify the parameters of these discretized electrochemical-thermal model. This is detailed in the next chapter.
13


CHAPTER III
MODEL IDENTIFICATION
3.1 Genetic Algorithm (GA) Overview
A genetic algorithm (GA) is defined as a method that is used to solve both constrained and unconstrained optimization problems to reach the optimal solutions. In other words, the fundamental idea of GA is to repeatedly modify a group of individual solutions. This method can applied to solve problems that are not suitable for typical optimization algorithms. In this work, we use GA to identify the unknown parameters of the electrochemical-thermal model developed in the previous chapter. Essentially, the optimization problem is of the following form:
min rms(Xm(0) — Xe) with subject to: M and 0min < 0 < 0max 0
where Xm is the output of the model M, Xe is the experimental data, 0 is the unknown parameters of the model M, and 0min and 0max are the lower and upper bounds of the parameters 0.
In the electrochemical model identification case Xm denotes the model voltage, M denotes the discretized version of SPM, Xe denotes the experimental voltage data, and 0 denotes a set of unknown electrochemical parameters to be discussed later.
In the thermal model identification case Xm denotes the model surface temperature, M denotes the discretized version of distributed parameter thermal model, Xe denotes the experimental temperature data, and 0 denotes a set of unknown thermal parameters to be discussed later. In the next section, we discuss the experimental setup used to collect the experimental voltage and temperature data from an NMC battery cell.
14


3.2 Experimental Setup
The experiments were carried out on a 3000 mAh Nickel Manganese Cobalt (NMC) lithium ion battery cell. The experimental data have been collected using an Arbin battery test equipment along with type T thermocouples. Arbin testing system, generally, is used for charge/discharge, and cycling. In this research, particularly, it is used to charge and discharge the battery cells and record the cell voltage, current and temperature. The experimental setup is shown in Fig. 3.1.
Fig. 3. 1: Experimental Setup
15


The Internal construction of a typical cylindrical cell is shown in Fig. 3.2.
Fig. 3. 2: Cylindrical Cell Construction Cited from [35]
The specifications of the cell that is used in the research are listed in Table 3.1 below. A snapshot of the cell used is shown in Fig. 3.3.
Table 3. 1: Test Cell Specifications
Height 65.0 ± 0.2 (mm)
Mass 47.0 (g)
Nominal capacity 3000 (mAh)
Maximum charge voltage 4.20 ±0.05 (V)
Nominal voltage 3.60 (V)
Charge Operating Temperature 0 ~ 50 (°C)
Discharge Operating Temperature -20 ~ 75 (°C)
Maximum charge current 4000 (mA)
Maximum discharge current 20000 (mA)
16


Fig. 3.3: NMC Battery Cell
3.3 Fresh Cell Electrochemical and Thermal Model Identification
In this section, we identify some electrochemical parameters of the fresh cell (in the beginning of life). We choose to identify the following parameters: D, La, X, Rf, and nLi. Rest of the model parameters are assumed known from [36], We have used MATLAB to perform the GA optimization. The optimized parameters values are shown in Table 3.2 below.
Table 3. 2: Fresh Cell Optimized Parameters
D 9.114 x 1(T15
La 1.248 x 1(T4
X 9.144 x 10-6
nLt 0.1796
Rf 0.005
17


where D is the effective diffusion coefficient for solid phase in the negative electrode in m2/s, La is the length of negative electrode in m, X is the radius of solid particles in negative electrode in m, Rf is the film resistance in Q, and nLi is the total moles of Lithium.
The current profile applied to the cell is shown in Fig. 3.4. Corresponding voltage plots are shown in Fig. 3.5.
Fig. 3. 4: The Current Applied to the Cell
18


Fig. 3.5: Fresh Cell Terminal Voltage Verses Time
Following a similar approach, we identify the thermal parameters of the cell. We choose to identify the following parameters: k, h, and Cp. The optimized parameters values are shown in Table 3.3 below.
Table 3.3: Fresh Cell Optimized Parameters
k 1.8000
cp 907.0570
h 16.6172
19


where k is the thermal conductivity in W/m — K, h is the convection coefficient in W/m2 — K, and Cp is the specific heat in J/kg — K.
Also, Fig. 3.6 shows the temperature plots.
Fig. 3. 6: Fresh Cell Temperature Verses Time
The Root Mean Square (RMS) errors between the model and experimental data are shown in Table 3.4.
20


Table 3.4: Fresh Cell Temperature and Voltage RMS Errors
Temperature rms error 0.2134
Voltage rms error 0.0189
3.4 Aged Cell Electrochemical and Thermal Model Identification
In this section, we optimize a set of electrochemical and thermal parameters that are assumed to change with battery aging. The NMC cell is cycled repeatedly until end of life is reached. Here end of life is defined as 20% drop from initial capacity of the cell. We assume that the following parameters are changed due to battery aging: /r, Rf and nLi. The identified parameter values are shown in Table 3.5 below. The rms errors between the model and the experimental data are shown in Table 3.6. Figure 3.7 and 3.8 show the voltage and temperature plots.
Table 3.5: After Aging Optimized Parameters
Rf 0.0115
nLt 0.1715
k 6.6
21


Table 3.6: After Aging Temperature and Voltage RMS Errors
Temperature rms error 0.8392
Voltage rms error 0.0328
Fig. 3.7 shows that the modeled and experimental data are almost matched for the terminal voltage verses time.
Fig. 3.7: After Aging Terminal Voltage verses Time
22


Fig. 3. 8: After Aging Temperature Verses Time
3.5 Observations
In the above experimental identification, we have found the following;
The total moles of Lithium, denoted by the parameter nLi, is changed from 0.1796 to 0.1715. This essentially indicates that the battery capacity is faded during cycling of the battery cell.
The film resistance, denoted by the parameter Rf, is changed from 0.005 Q to 0.0115 Q. This essentially indicates that the battery internal resistance has been increased during cycling.
23


Finally, we have also observed that the thermal conductivity of the cell has also been changed from 1.8 W/m-K to 6.6 W/m-K.
24


CONCLUSION
In this thesis, we have conducted modeling and identification of battery electrochemical-thermal model under fast charging. Specifically, we have chosen Single Particle Model (SPM) to capture the electrochemical dynamics, and a distributed parameter thermal model to capture temperature dynamics. Next, we have collected experimental voltage, current, and temperature data from a cylindrical battery cell. These experimental data has been used to identify parameters of the electrochemical and thermal models. We have identified the parameters of a fresh cell, and an aged cell which was cycled to reach end of life. We have observed that the total moles of Lithium is reduced after cycling, and internal resistance is increased. These changes essentially indicates capacity and power fade of the battery. We have also noticed change in thermal conductivity due to cycling. As future work, these identified models will be used for designing estimation and control algorithms to enable safe fast charging.
25


REFERENCES
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Full Text

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MODELING AND IDENTIFICATION OF BATTERY ELECTROCHEMICAL THERMAL MODEL UNDER FAST CHARGING by RASHED ALDHAFEERI Bachelor of Science, University of Hafr Al Batin, 2015 A thesis submitted to the Faculty of the Graduate School of the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Science Electrical Engineering 2019

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ii This thesis for the Master of Science degree by Rashed Aldhafeeri h as been approved for the Electrical Engineering Program b y Satadru Dey , Chair Miloje Radenkovic Jae Do Park July 22, 2019

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iii Aldhafeeri , Rashed (M.S., Electrical Engineering) Modeling and Identification of Battery Electrochemical Thermal Model under Fast Charging Thesis directed by Assistant Professor Satadru Dey ABSTRACT L ithium ion batteries, nowadays, have received much attention in the last few years . Because of their better energy density and power comparing to lead acid batteries , Lithium ion batteries have become a leading choice for electrified vehicles . Recently, fast charging of Lithium ion batteries has gained significant focus. If successful, such fast charging will enable higher commercial penetration of electric vehicles due to reduced re fueling time. To monitor and control such Lithium ion batteries efficiently, a dvanced B attery M anagement S ystems (BMSs) are essential . BMS, in general, contains hardware and software that are used to charge and discharg e the Lithium ion cells safely . In the last couple of years , compar ed to phenomenological type electrical circuit models , coupled electrochemical thermal models for batteries have gained more attention for BMS applications . Electrochemical thermal models have the ability to precisely predict cell behavior along with information about the internal cell states. In this thesis , we focus on modeling and parameter identification of coupled electrochemical thermal model of Lithium ion batteries under fast charging utilizations . Such identified model will be essential to design estimation and fast charging control algorithms. Specifically, we identify the model parameters of a fresh battery cell (i.e. in the beginning of life) and an aged battery cell (i.e. in the end of life). The distinction from one another , the fresh cell and aged cell parameters will provide some insights about how the battery cell ages under fast charging. The form and content of this abstract are approved. I recommend its publication. Approved: Satadru Dey

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iv Table of Contents CHAPTER I ................................ ................................ ................................ .............. 1 INTRODUCTION AND OVERVIEW ................................ ................................ .. 1 1.1 Classifications of Batteries ................................ ................................ ................................ .................. 1 1.1.1 Basic Terminology of Batteries ................................ ................................ ................................ .... 2 1.2 Significance of Fast Charging in Li ion Batteries ................................ ................................ ............... 2 1.3 Aging Mechanism ................................ ................................ ................................ ............................... 4 1.3.1 The growth of solid electrolyte interface (SEI) layer ................................ ................................ .. 4 1.3.2 The Lithium Plating ................................ ................................ ................................ ..................... 5 1.4 Modeling and Identification of Electrochemical thermal Models ................................ ...................... 5 CHAPTER II ................................ ................................ ................................ ............ 6 MODELING AND MODEL APPROXIMATION ................................ ............... 6 2.1 Battery Electrochemical Thermal Model ................................ ................................ ............................ 6 2.2 Nominal Electrochemical Model ................................ ................................ ................................ ........ 7 2.2.1 Finite Difference Approximation of SPM ................................ ................................ .................... 9 2.3 Nominal Thermal Model and Finite Difference Approximation ................................ ...................... 10 CHAPTER III ................................ ................................ ................................ ........ 14 3.1 Genetic Algorithm (GA) Overview ................................ ................................ ................................ .. 14 3.2 Experimental Setup ................................ ................................ ................................ ........................... 15 3.3 Fresh Cell Electrochemical and Thermal Model Identification ................................ ........................ 17 3.4 Aged Cell Electrochemical and Thermal Model Identification ................................ ........................ 21 3.5 Observations ................................ ................................ ................................ ................................ ..... 23 CONCLUSION ................................ ................................ ................................ ....... 25 REFERENCES ................................ ................................ ................................ ....... 26

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v List of Figures Fig. 3. 1: Experimental Setup ................................ ................................ ................................ ....... 15 Fig. 3. 2: Cylindrical Cell Construction Cited from [35] ................................ .............................. 16 Fig. 3. 3: NMC Battery Cell ................................ ................................ ................................ .......... 17 Fig. 3. 4: The Current Applied to the Cell ................................ ................................ .................... 18 Fig. 3. 5: Fresh Cell Terminal Voltage Verses Time ................................ ................................ .... 19 Fig. 3. 6: Fresh Cell Temperature Verses Time ................................ ................................ ............ 20 Fig. 3. 7: After Aging Terminal Voltage verses Time ................................ ................................ .. 22 Fig. 3. 8: After Aging Temperature Verses Time ................................ ................................ ......... 23

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vi List of Tables Table 2. 1: Li ion Battery Model Nomenclature ................................ ................................ ............. 7 Table 3. 1: Test Cell Specifications ................................ ................................ ............................... 16 Table 3. 2: Fresh Cell Optimized Parameters ................................ ................................ .............. 17 Table 3. 3: Fresh Cell Optimized Parameters ................................ ................................ .............. 19 Table 3. 4: Fresh Cell Temperature and Voltage RMS Errors ................................ ..................... 21 Table 3. 5: After Aging Optimized Parameters ................................ ................................ ............. 21 Table 3. 6: After Aging Temperature and Voltage RMS Errors ................................ ................... 22

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1 CHAPTER I INTRODUCTION AND OVERVIEW Overall, Lithium Ion (Li ion) batter ies are used for energy storage in numerous applications , for example, electric vehicles (EVs) , smart grids , solar power storage, and drones . Such wide usage is due to their enormous advantages of high energy density, huge capacity, and long life cycle . Currently, one of the most distinguished advantages of l ithium material is that it is considered as the lightest among all other materials. It has also the best potential electrochemically . In fact, if lithium material is placed on the anode electrode, it can deliver extremely more energy densities . As a result, there will be some particles in which they penetrate the separat or sheet of the battery and cause a short circuit . Recently , this type of Li ion battery ha s suffered from safety issues, reliability, and high cost [1] . 1.1 Classifications of Batteries B atteries, generally, can be categorized as primary or secondary . Primary batteries can not be recharged; it has to be discarded after it has been fully discharged while the secondary batteries are rechargeable. Furthermore, th ere are three main battery chemistry types that are widely used: Li ion, lead acid , and nickel metal hydride . In traditional internal combustion engine (ICE) vehicles , 12 V lead acid (PbA) b atteries were used to power the starter motor [27]. Even though the higher energy nic kel metal hydride (NiMH) cells have powered up many of the first successful HEVs, they are being, generally , replaced by Li ion batteries with better energy density and power . From power point of view, Li ion and NiMH cells can, in fact , store same level of power; however, Li ion cells can charge and discharge mroe faster than NiMH cells.

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2 1.1.1 Basic Terminology of Batteries Some common battery terms are listed below. Capacity: It can be described as the maximum level of charge that a battery can supply . Typically, capacity is expressed in Am pere hour. Experimentally, it can be obtained by integrating the current that is being applied from higher voltage level at the initial time to the lower voltage level at final time : Here 3600, is t he scaling factor that is used for the conversion from seconds to hours. C rate : It is value of current ( ) expressed in terms of cell capacity ( : State of Charge (SOC): It can be described as an indication for the level of charge that is left in the cell . This is typically expressed as: 1.2 Significance of Fast Charging in Li ion Batteries Nowadays, intriguingly, most of EVs with a Level II 240 V system can be completely charged from 6 to 8 h ours [22] ; eventually, charging period is considerably l ong and becomes un reasonable when recharges are required . To solve this problem , Level III fast charging levels are implemented , though they differ from place to place . More notably , because of the high er current that could cause degradation of the Li ion batteries , and it could decrease Li

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3 lifetime , this fast charging technique has not been implemented on all EVs [23]. Limited EV s leading companies allow the implementation of fast charging options , and they are recommended to be used rarely to reduce battery degradation phenomenon [ 21 ]. To illustrate, because of a variety of chemical and physical processes under high current scenarios , the degradation in Li ion battery cells is faster . Consequently, this degradation influences various components of the cells . For instance, the electrolyte, anode and cathode electrodes, the separator sheets, and the current collectors [25 ]. In addition, as stated by the United S tates Advanced Battery Consortium (USABC), the long period of time objective to charge fast is to re store 40% in 15 min utes [ 24 ]; still, fast charging generally includes high energy outputs , high temperatures , and high current rates . S ubsequently , these will f orce to decline the electric characteristics of the Li ion batteries and affect their functionalities. Yet , to tolerate such harmful conditions without major deterioration . Only sophisticated chemicals can be used for the fast charging . As a result, few Li ion battery companies are presently able to supply cells that can accept both fast charging and have a long life . R eduction of the charging time for Li ion batteries that are installed in EVs and HEVs are primary concerns of most consume rs . Therefore, for the safety factor and consistent operation, advanced battery management systems (BMS) are strongly required in order to develop the battery performance and optimize battery operation . Such BMS algorithms relies on mathematical models of batteries. There a re different types of battery models that are available in existing literature . Data driven battery models fit some mathematical equations that describe the battery voltage, current and temperature data [4]. Electrical circuit based phenomenological models capture battery behavior in terms of electrical circuits [5, 6]. Although these types of models can be useful in predicting battery voltage behavior, they may not be able to provide

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4 insights about internal battery states. Under this scenario, coupled elec trochemical thermal models are useful which can capture the battery internal physics to a great extent [1 , 2 , 3 ] . 1.3 Aging Mechanism Interestingly, o ne of the most significant striking current discussions in Li ion batteries area is the aging mechanism of Li ion batteries. During batteries lifetime , their performance tends to decline gradually because of the unalterable chemical and physical changes . Thus, cells tend to lose their capacities, and the internal resistance is increase d . Mainly , the capacity loss results in the decr ease in the electric range of EV s , while the growth in internal re sistance reduces the availability of power. Depending on the chemistry of the cell and working conditions, aging phenomenon can be triggered by various degradation mechanisms. These d egradation mechanisms are detailed below. 1.3.1 The growth of solid electrolyte interface (SEI) layer Recently, researchers have shown an increased interest in t he aspect of the growth of SEI lay er that is considered as a major cause of fading capacity in Li ion cells . As a consequence of side reaction s that occur between the electrolyte solution and the active electrode material , t he SEI layer forms . Subsequently, this reaction consumes some lithium metal , so the SEI layer grows and results in a gradual capacity fade as th e SEI layer becomes, over time, thicker . B ecause of the low potential at the negative electrode , SEI growth occurs p rimarily at the negative electrode mostly at high er SOC . SEI film is formed , particularly, at the negative electrode because , during charging , electrolytes are not stable at this electrode. In addition, the growth of SEI is worsened when the temperature is high because the rate of the reaction increases with heat [27, 30].

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5 1.3.2 The Lithium Plating Lithium plating or deposition is the creation of lithium metal , during charging , around the anode of Li ion batteries ; likewise, it can take place at the negative electrode during higher charging current scenario; This eventually cause the loss of lithium and in turn, capacity . All in all, the leading aging mechanisms at the anode electrode are SEI layer evolution and lithium plating ; meanwhile, the aging at the electrode on the cathode is mostly because of the loss of active material s [31]. 1.4 Modeling and Identification of Electrochemical thermal Models As mentioned before, models are essential to design algorithms for advanced BMS. In this work, we consider electrochemical thermal model of Li ion batteries. Our goal is to develop, simulate, and identify the model parameters of a fresh and aged battery ce ll. We have employed a combination of numerical and experimental techniques to achieve these goals. To reiterate, such models will b e useful in designing advanced control and estimation algorithms under battery fast charging applications. The rest of the thesis is organized as follows. Chapter II discusses modeling and model a pproximation of both electrochemical thermal and nominal electrochemical model of the NMC Li ion battery cell. Chapter III discusses the detailed model identifi cation, experimental se tup, and simulation results . Finally, conclusions are presented with a brief discussion on future problems .

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6 CHAPTER II MODELING AND MODEL APPROXIMATION 2.1 Battery Electrochemical Thermal Model Electrochemical battery model s are attracting considerable interest due to its remarkable accuracy than the other approaches of modeling [7]. Among the existing electrochemical models, a complete order electrochemical model that is known as pseudo 2D (P2D) model is widely adopted. Howe ver, t he complexity and computational burden of P2D model demands some model reduction before applying it in real time applications [8]. Some model technique s ha ve been suggested for some SOC estimation methods, including a residue grouping method with a l inear Kalman filter (KF) [9], a Partial Differential Equation (PDE) type Luenberger observer [10], and particle filter (PF) [11]. A specific reduction of the P2D electrochemical model is called the single particle model (SPM) in which both negative and po sitive electrodes are approximated as spherical particles. The SPM based modeling framework has been widely used in real time applications such as SOC estimation . For example, an extended KF [12, 13], an Unscented Kalman Filter [14], backstepping PDE estim ator [15] , Particle Filter ( PF ) [16], adaptive PDE observer [17], and geometric observer [18] , nonlinear observer [19] , and sliding mode observer [20] have been proposed that utilized SPM framework . The primary advantage of SPM framework the model is computationally efficient and at the same time captures certain internal physical behavior of Li ion batteries. In the following sections, we describe this model in detail.

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7 2. 2 Nominal Electrochemical Model The schematic of then SPM is shown in Fig. 2. 1 below along with the list of variables in Table 2 .1. Fig. 2. 1 : Schematic of SPM Table 2. 1 : Li ion Battery Model Nomenclature Symbol Definition and Unit Current collector area ( Specific surface area ( / Solid phase Li ion concentration (mol/ Heat generation (W/ Cell radius (m) Effective diffusion coefficient in solid phase ( Current (A)

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8 Length of the electrodes (m) Radial coordinate ( ) Cell density ( ) Specific heat ( ) T hermal conductivity ( ) C onvection coefficient ( ) Temperature (K) C ell volume ( , Open circuit voltage ( V ) U niversal gas constant ( ) Active material volume fraction (dimensionless) Superscript Positive/N egative electrode Anode/Cathode Essentially , anode and cathode, in the SPM framework, are approximated as single spherical particles in which l ithium ions can diffuse in and out during charging and discharging . This approximation lead s to two linear Partial Differential Equations ( PDEs ) that describe the diffusion of Lithium ions in two particles demonstrating each electrode. Note that the concentration of electrolytes solution is assumed to be constant [32] . In this work , the focus will be only on the dynamics of anode that is given by the following PDE diffusion equation , and its boundary conditions. ( 1 ) ( 2 )

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9 where is the radial coordinate of the particle in , is the time in , is the Lithium concentration along the particle in , is the anode diffusion coefficient in , is radius of the particle i n , is the applied current in with that is indicating discharging and which is indicating the charging, is the anode specific surface area in / that is calculated as where is the active material volume fraction, constant in C/mol, is the anode current collector area in , and is the anode thickness in Under certain assumptions, the cathode Lithium concentration can be expressed in terms of an ode Lithium concentration as where is the total moles of Lithium. 2.2.1 Finite Difference Approximation of SPM To implement the aforementioned PDE model, we adopt the method of lines technique . In m ethod of lines technique, we discretize the spatial dimension into a finite number of nodes, and subsequently, approximate the spatial derivatives with central finite difference approximation keeping the time derivatives intact. Such approximation converts the PDE model to a set of Ordinary Differential Equations (ODEs) model. From Eq. (1), we can write that Next, consider a node in the discretized domain shown in Fig. 2.1. Using central difference method, the Lithium concentration dynamics at node can be written as:

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10 with discretization step . Taking and as common factors from the above equation, we get: By defining, and rearrange the equation, we get: Similarly, we apply same approximation at the other nodes. Consequent ly , we end up with the following set of ODEs : ( 3 ) ( 4 ) with discretization step and . 2.3 Nominal Thermal Model and Finite Difference Approximation Tem perature plays a crucial role in internal battery dynamics. Hence, it is essential to model the temperature dynamics of the battery. In this section, in order to capture the temperature variation along the cell radius , a distributed parameter thermal model is adopted [ 35 ] . Consider a cylindrical battery cell. T he following dist ributed parameter thermal model captures the temperature variation along the radius of the cylinder :

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11 ( 5 ) With its boundary conditions: ( 6 ) where is time in , is the radial coordinate of the cell in , is the cell radius in is the cell density in is the specific heat in is thermal conductivity in , is the convection coefficient in is the cooling/ambient temperature, is the cell volume in , and is the heat generation term that is computed by : ( 7 ) where and are the open circuit voltage maps of cathode and anode, respectively ; and ; is total moles of Lithium in the cell , and is t he battery terminal voltage that can be computed as : ( 8 ) where is the universal gas constant in and are unitless charge transfer coefficients of cathode and anode, respectively; is s pecific surface area in and are the current collector area of cathode and anode, respectively in , and are l ength of the electrodes of cathode and anode, respectively in , and are the exchange current densities of cathode and anode , respectively in , is the internal resistance of the cell in From Eq. (5), we can write

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12 ( 9 ) Next, we apply the finite difference approximation to convert the PDE to a group of ODEs. We discretize the radial direction into M number of nodes. At node , the PDE (9) can be approximated as: with discretization step . Denoting , we get ( 10 ) ( 11 ) Defining , and applying similar approximation to other nodes, we can write the following set of ODEs that capture the thermal dynamics : ( 14 ) ( 15 ) ( 16 ) with and discretization step .

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13 With the above formulation, we now have a group of ODEs that capture the SPM electrochemical dynamics and another group of ODEs that capture the distributed parameter thermal dynamics. Next, our goal is to identify the parameters of these discretized electrochemical thermal model. This is detailed in the next chapter .

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14 CHAPTER II I MODEL IDENTIFICATION 3.1 Genetic A lgorithm (GA) Overview A genetic algorithm (GA) is defined as a method that is used to solve both constrained and unco nstrained optimization problems to reach the optimal solutions . I n other words, t he fundamental idea of GA is to repeatedly modify a group of individual solutions . This method can applied to s olve problems that are not suitable for typical optimization algorithms. In this work, we use GA to identify the unknown parameters of the electrochemical thermal model developed in the previous chapter. Essentially, the optimization problem is of the following form: with subject to: and where is the output of the model , is the experimental data, is the unknown parameters of the model , and and are the lower and upper bounds of the parameters . In the electrochemical model identification case denotes the model voltage, denotes the discretized version of SPM, denotes the experimental voltage data, and denotes a set of unknown electrochemical parameters to be discussed later. In the thermal model identification case denotes the model surface temperature, denotes the discretized version of distributed parameter thermal model, denotes the experimental temperature data, and denotes a set of unknown thermal parameters to be discussed later. In the next section, we discuss the experimental setup used to collect the experimental voltage and temperature data from an NMC battery cell.

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15 3.2 Experimental Setup The experiments were carried out on a 3000 mAh Nickel Manganese Cobalt (NMC) lithium ion battery cell. The experimental data have been collected using a n Arbin battery test equipment along with type T thermocouple s . Arbin testing system , generally, is used for charge/discharge , and cycling . In this research, particularly, it is used to charge and discharge the battery cells and record the cell voltage, current and temperature. The experimental setup is shown in Fig . 3.1 . Fig. 3. 1 : Experimental Setup

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16 The Internal construction of a typical cylindrical cell is shown in Fig. 3 .2 . Fig. 3. 2 : Cylindrical Cell Construction Cited from [35] The specifications of the cell that is used in the research are listed in Table 3.1 below . A snapshot of the cell used is shown in Fig. 3.3. Table 3. 1 : Test Cell Specifications Height 65.0 ± 0.2 ( mm ) Mass 47.0 ( g ) Nominal capacity 3000 ( mAh ) Maximum charge voltage 4.20 ± 0.05 ( V ) Nominal voltage 3.60 ( V ) Charge Operating Temperature 0 ~ 50 ( ) Discharge Operating Temperature 20 ~ 75 ( ) Maximum charge current 4000 ( mA ) Maximum discharge current 20000 ( mA )

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17 Fig. 3. 3 : NMC Battery Cell 3.3 Fresh Cell Electrochemical and Thermal Model Identification In this section, we identify some electrochemical parameters of the fresh cell (in the beginning of life). We choose to identify the following parameters: , , , , and . Rest of the model parameters are assumed known from [ 36 ]. We have used MATLAB to perform the GA optimization. The optimized parameters values are shown in Table 3 .2 below . Table 3. 2 : Fresh Cell Optimized Parameters

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18 where is the e ffective d iffusion coefficient for solid phase in the negative electrode in , is the length of negative electrode in , is the r adius of solid par t icles in negative electrode in , is the film resistance in , and is the total moles of Lithium . The current profile applied to the cell is shown in Fig. 3.4. Corresponding voltage plots are shown in Fig. 3.5. Fig. 3. 4 : The Current Applied to the Cell

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19 Fig. 3. 5 : Fresh Cell Terminal Voltage V erses Time Following a similar approach, we identify the thermal parameters of the cell. We choose to identify the following parameters: , , and . The optimized parameters values are shown in Table 3. 3 below. Table 3. 3 : Fresh Cell Optimized Parameters 1.8000 907.0570 16.6172

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20 where is the thermal conductivity in , is the c onvection coefficient in , and is the specific heat in . Also, Fig. 3.6 shows the temperature plots . Fig. 3. 6 : Fresh Cell Temperature V erses Time The Root Mean Square (RMS) error s between the model and experimental data are shown in Table 3.4 .

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21 Table 3. 4 : Fresh Cell Temperature and Voltage RMS Errors Temperature rms error 0.2134 Voltage rms error 0.0189 3.4 Aged Cell Electrochemical and Thermal Model Identification In this section, we optimize a set of electrochemical and thermal parameters that are assumed to change with battery aging. The NMC cell is cycled repeated ly until end of life is reached. Here end of life is defined as 20% drop from initial capacity of the cell. We assume that the following p arameters are changed due to battery aging: , and . The identified parameter values are shown in Table 3.5 below . The rms errors between the model and the experimental data are shown in Table 3.6 . Figure 3.7 and 3.8 show the voltage and temper ature plots. Table 3. 5 : After Aging Optimized Parameters 6.6

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22 Table 3. 6 : After Aging Temperature and Voltage RMS Errors Temperature rms error 0.8392 Voltage rms error 0.0328 Fig. 3.7 shows that the modeled and experimental data are almost matched for the terminal voltage verses time . Fig. 3. 7 : After Aging Terminal Voltage verses Time

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23 Fig. 3. 8 : After Aging Temperature Verses Time 3.5 Observations In the above experimental identification, we have found the following; The total moles of Lithium, denoted by the parameter , is changed from 0.1796 to 0.1715. This essentially indicates that the battery capacity is faded during cycling of the battery cell. The film resistance, denoted by the parameter This essentially indicates that the battery internal resistance has been increased during cycling.

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24 Finall y, we have also observed that the thermal conductivity of the cell has also been changed from 1.8 W/m K to 6.6 W/m K.

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25 CONCLUSION In this thesis, we have conducted modeling and identification of battery electrochemical thermal model under fast charging. Specifically, we have chosen Single Particle Model (SPM) to capture the electrochemical dynamics, and a distributed parameter therma l model to capture temperature dynamics. Next, we have collected experimental voltage, current, and temperature data from a cylindrical battery cell. These experimental data has been used to identify parameters of the electrochemical and thermal models. We have identified the parameters of a fresh cell, and an aged cell which was cycled to reach end of life. We have observed that the total moles of Lithium is reduced after cycling, and internal resistance is increased. These changes essentially indicates ca pacity and power fade of the battery. We have also noticed change in thermal conductivity due to cycling. As future work, these identified models will be used for designing estimation and control algorithms to enable safe fast charging.

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