Dr. Song-Yul Choe
Professor
Auburn University
High Resolution Modeling of Lithium Ion Battery and
its Applications
Auburn University
Mechanical engineering
Advanced Propulsion Research Lab.
Song-Yul (Ben) Choe
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Trend of advanced propulsion systems
Fuel Improvement
Mass
E-Drive
(40miles)
Toyota
“PRIUS”
Proto
Test
GM
“Chevy-Volt”
50%
Power
support
Toyota
“PRIUS”
GM
“Tahoe”
Honda
30%
Nissan
“INSIGHT”
“TINO”
VW
GOlf Daimler
Reneaut
“S-400”
Toyota
“Twingo”
Power
Assist
15%
“S-Class”Ford
“Focus 2.0,
GM
Explorer 4.0”
“Epsilon”
GM(Subaru)
Idle Stop
Functionality
Level of Voltage
“THS-M”
DCX
Regen.
Starter
Alternator
Ford
“ESCAPE”
“Elten-Custom”
Conv. vehicle
12V
1-3kW
Soft
HEV
Mild
HEV
42V
5-10kW
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96-144V
20-30kW
3
Hard/Split
HEV
Plug-In
HEV
288V
<<40kW
>288V Voltage(Power)
>40KW)
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Energy storage with battery
Nominal Capacity (Amp-hours):
Nominal Cell Voltage
3.73
Cell Dimensions (mm) 5.27
Cell Dimensions w/ terminals (mm)
Maximum Cell Temperature (°C)
Positive
Negative
Electrolyte
Separator
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15.7
164.2 X 249.6
75
Lithium Metal Oxide
Carbon
Organic Material
SRS
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Typical models for battery
• Models base on equivalent electrical circuit
Statics: resistors in series to a voltage source
Dynamics: a capacitor connected in parallel to a resistor
R dch_d
R dch_h
V oc
R cha_h
I dch
R cha_d
C dch
V b (t)
I cha
C cha
Ignored effects :
1.
Electrical behavior of the terminal as a function of SOC , T and material degradation, and O
CV as a function of hysteresis and SOC.
2.
Battery calendar life as a function of cycles and load profile
3.
Heat generation as a function of SOC , change of entropy and I (charge and discharge), heat tr
ansfer
4.
Various temperature effects caused by gradients of ion concentrations and side reactions
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Modeling of LiPB cell
Positive
electrode
area
•
T
L
Electrolyte
LixC6
Current collector (Al)
Negative
electrode
area
Separato
r
• ce
• Φe
• Φs
• ηSEI
•
cs
Current collector
(Cu)
Y
LiyMO2
Electrode
particle
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X
6
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Principle: Current, Concentration and State of Charge
• Current in micro cell
-
current
+
=
Ion current
-
+
+
Electron
current
-
+
Credit: huangqing
• SOC (state of charge) and cs (concentration in solid)
-
+
-
+
-
+
Credit: huangqing
Low SOC
Medium SOC
charging
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High SOC
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Electrochemical Thermal Mechanical Model
Charging and discharging processes: Heat generation, Elasticity and Degradation
Multi scale and Multi-physics coupled problems
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Overview of model
Single cell model
Initial conditions:
•Initial SOC
•Load profile
•Initial temperature
distribution
•Ambient
temperature
Temperature
distribution
•Cell voltage
•Temp. distribution
•Energy conservation
•Heat transfer
•Charge conservation
Potential
distribution
•SOC
•Overpotentials
•Reaction rate
•Concentration
•Efficiency
Micro cell model
Micro cell model
Micro cell model
Parameters:
•Battery geometry
•Maximum capacity
•Concentration
•Activity coefficient
•Diffusion
coefficient
•Change of enthalpy
•Conductivity
Heat source
Reaction rate
Standard
potential
•Butler-Volmer
Current
Overpotential
Nernst equ.
etc.
Concentration
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Mass balance
•In electrolyte
•In solid
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Static and dynamic behavior of the battery
Characteristics at different current rates (T=300K and SOC=100%)
Current (A)
4.0
3.8
0
-72
3.4
0
20
40
60
80
4.0
3.2
3.9
3.0
1C
2.8
10C
2.6
20C
Terminal Voltage (V)
Terminal Voltage (V)
3.6
72
5C
20C
2.4
50C
2.2
3.8
3.7
3.6
70% SOC
60% SOC
50% SOC
40% SOC
30% SOC
3.5
3.4
3.3
2.0
3.2
0.0
0.2
0.4
0.6
0.8
1.0
0
40
60
Time (s)
DOD=1-SOC
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80
Transient behavior of ion concentration
(Discharging behavior at a step current of 10C)
At 1secConcentration in solid (1s, discharge at 10C)
Concentration in solid (80s, discharge at 10C)
At 80 sec
1
1
0.9
0.8
0.9
1
0.8
0.7
Cs/Cs,max
Cs/Cs,max
1
0.6
0.5
0.5
0.6
0.5
0.5
0.4
0
0
0.4
0
0
0.7
0.3
0
0.2
0.3
0
0.2
0.2
0.2
0.4
0.6
L
0
r
1
0.8
0.8
1
L
0.8
1
0.1
0.6
0.1
0.6
0.8
At 20 sec
0.4
0.4
0.6
0.2
0.2
0.4
0
r
1
Concentration in solid (180s, discharge at 10C)
1
Concentration in solid (20s, discharge at 10C)
1
At 180 sec
0.9
0.8
0.9
1
0.7
Cs/Cs,max
Cs/Cs,max
0.8
1
0.7
0.6
0.5
0.5
0.3
0.2
0.4
0.4
0.3
0
0.2
0
0.2
0.5
0
0
0.4
0
0
0.6
0.5
0.2
0.4
0.2
0.6
0.6
0.4
0.6
0.6
0.8
L
0.8
1
1
r
0.2
0.4
0.8
0.1
L
0.8
1
1
r
0.1
0
0
As lithium ion leaves from negative electrode and deposited in positive electrode, concentration at the interface
of the negative electrode drops rapidly when compared with that of inners, while opposite phenomena occurs in
the positive electrode.
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Potentials/Current density at positive and negative current
collector
15
3.6122
3.6124
3.612
3.6122
10
3.612
3.6118
3.6118
3.6116
3.6114
5
3.6116
3.6112
15
10
8
5
0
4
2
0
10
6
3.6114
0
-2
0
2
4
6
8
10
12
-4
x 10
-2
15
-4
x 10
0
-3
10
-2
-4
-4
-6
-5
5
-8
15
-6
10
8
5
0
0
2
4
6
10
0
-2
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4
6
8
10
12
-7
0
2
12
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Validation of a single pouch cell at 1C/2C/5C discharge/charge
Terminal voltage comparison @ 1C/2C/5C discharge
simulation
experiment
Temperature, K
4
Voltage, V
Temperature comparison @ 1C/2C/5C discharge
320
simulation
experiment
315
3.5
3
310
305
300
295
2.5
0
1000
2000
Time, s
290
0
3000
4
3.5
0
simulation
experiment
500
1000
1500 2000 2500
Time, s
Current comparison @ 20A/40A/60A/80A charge
0
-20
-40
simulation
-60
experiment
-80
0
500
1000 1500 2000 2500
Time, s
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2000
Time, s
3000
4000
Temperature comparison @ 20A/40A/60A/80A charge
308
simulation
experiment
306
Temperature, K
Current, A
Voltage, V
Terminal voltage comparison @ 20A/40A/60A/80A charge
1000
304
302
300
298
0
13
500
1000
1500 2000
Time, s
2500
3000
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Thermal validation – 5C cycle 2D
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Voltage, V Current, A
Heat generation using the model and calorimeter
110
0
-110
4
3.5
7C
6.3C
5.7C
5C
4.1C
3
Heat, W
2.5
120
90
Measured
(OCV-Vt)I+Qrev
60
30
0
0
200
400
600
Discharging time, s
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0
15
200
400
Chargeing time, s
600
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Measurement of Thickness
•
The change of battery thickness caused by the volume change of
electrodes is calculated by the model.
•
In experiment, thickness of the battery is measured by measuring both
sides of the battery during cycling.
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Mechanical stress of cells at 0.5C, 1C and 2C cycling
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Maximum Stress as a Function of Position
during discharge (at one instant)
•
The plotted stress at each position is the maximum value of the
stress in the local electrode particle.
The highest stress is found in the electrode near the separator.
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Cathode current collector
Separator
Anode current collector
•
Fracture is Observed near the Separator
Q. Horn and K. White, 2007 [8]
J. Christensen, 2010 [7]
•
Other researchers took SEM images at the cross-section of cell, where
fractures are found in the electrode near the separator [7] [8].
•
Our simulation shows that the highest stress locates at the electrode near
the separator, where fractures are most likely to happen.
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Block Diagram for battery management system (BMS)
Battery
Pack/Module
Predefined Map
Current
Voltage
SENSOR
Temperature
Ri(SOC)
Ri(Charging)
TRAY Temp.
Voc(SOC)
Voc(Charging)
Thermal Management
Imean
Cooling Control
Charging/Discharging Control
HCU
Aging Coefficient &
SOC Calculation
Accumulated SOC Error Comp.
I,V(SOC)
Health monitoring & Protection
Vaverage &
Temp.
Compensation
Temperature
Charging/Discharging power
User
Interface
Diagnosis
Search IVSOC
by
IV Voltage MAP
Voltage Imbalance detection
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Review of models for Battery
High
Improvement of
cell designs
Intermediate
BMS
Functionalities
Full order of Electrochemical, thermal
and mechanical Model (ETMM:
FOM): Electrochemical kinetics,
Potential theory, energy and mass
balance, and charge conservation , Ohm’s
law, Empirical OCV and elasticity
Reduced order of Electrochemical thermal
Model (ETM: ROM ): Empirical OCV
Polynomial, State space, Páde approx.,
POD, Galerkin Reformulation and others
Electric equivalent circuit Model
(EECM): Randles models with the 1st,
2nd and 3rd order
Low
Empirical Model:
Peukert’s equation
Comp. time
Accuracy
Low
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Moderate
21
High
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Reduced order of the model (ROM) for real time applications
Input:
Parameters:
• Cell geometry
• Kinetic and transp
ort properties
Initial conditions:
• Terminal voltage
• Load profile
• Ambient temperat
ure
Steps
Approaches
Order reduction
•
•
•
Battery :
Ion concentration
in electrolyte Ce
Output
Ion concentration
in electrodes Cs
•
•
•
: voltage
Cell
Temperature
SOC
Potentials Φ
SOC estimation
Results
Ce  State space approach
Cs  Polynomial approach
Φ  Parameters simplification
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•
•
•
Higher accuracy with less computational
time
Implicit method to solve PDEs
Optimization of the ROM for real time
applications
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Validation of the ROM
4.2
exp@45oC
4
sim@45oC
Vt/V
exp@25oC
3.8
sim@25oC
3.6
exp@0oC
sim@0oC
3.4
2. Test condition:
Mode: Depleting
Cycle #: 2
Temperature: 25ºC
Current: 1C, 2C, 5C
Initial SOC: 0%
1. Test condition:
Mode: Depleting
Cycle #: 5
Temperature: 0ºC, 25ºC, 45ºC
Current: 1C, 2C, 5C
Initial SOC: 0%
3.2
3
Current/C
5
2.8
2.6
0
0.5
1
1.5
2
Time/s
2.5
3
3.5
x 10
60
0
-5
4
0
5
10
Time/h
15
20
0
5
10
Time/h
15
20
10
Time/h
15
20
exp@45oC
amb@45oC
50
4
Vt/V
sim@45oC
exp@25oC
40
o
3.5
3
amb@25 C
o
sim@25 C
T/ C
30
2.5
o
exp@0oC
amb@0oC
20
sim@0oC
10
o
exp@25 C
T/ C
35
-10
amb@25oC
o
0
0
0.5
1
1.5
2
Time/s
2.5
3
0
4
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sim@25oC
25
3.5
x 10
30
23
5
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SOC estimation using Extended Kalman Filter
•
•
Error of SOC 7-10%
Initial errors of BMS
Input:
Feedback controls and
real time model
Output:
I , Tamb
Vt
Battery
Time update with the
ROM
Vˆt
cs,ave
Xueyan Li, xzl0017@tigermail.auburn.edu , Nov.,2012
Measurement update
SOC calculation
x̂ k
SOC
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Results of the estimation based on ROM + EKF
Current:
Voltage:
SOC:
1.1
4.3
70
Exp
ROM
ROM+EKF
Exp
4.2
60
4.1
50
Exp
ROM
ROM+EKF
Ah
Ah w/o bias
1
0.9
0.8
3.9
30
0.7
3.8
20
10
0
0.6
3.7
0.5
3.6
0
200
400
600
800
1000
3.5
0
200
400
600
800
1000
0.4
0
200
400
Current:
Voltage:
1000
Error of SOC:
Exp
ROM
ROM+EKF
4.2
4
800
0.12
4.4
Exp
600
Time/s
Time/s
Time/s
6
4
ROM
ROM+EKF
Ah
Ah w/o bias
0.1
0.08
3.8
0.06
3.6
0.04
0
SOC error
Vt/V
2
Current/C
Test condition:
Mode: Depleting
Temperature: 25ºC
Initial SOC: 0%
Initial error: 0.5V
(6.5% SOC)
SOC
40
Vt/V
Test condition:
Mode: JS
Temperature: 25ºC
Initial SOC: 100%
Initial error: 0.2V
(30% SOC)
Current/A
4
3.4
3.2
-2
0
5
10
Time/h
15
0
3
-0.02
2.8
-0.04
2.6
-0.06
-4
-6
0.02
20
Xueyan Li, xzl0017@tigermail.auburn.edu , Nov.,2012
0
5
10
Time/h
15
20
-0.08
0
5
25 Copying this presentation is strictly forbidden.
10
Time/h
15
20
Health monitoring of battery
Research
interests for
SOH
SOHQ
SOH
Capacity fade
SOHP
Power fade
Other mechanism
Current i
Battery
pack
Output states value
(V T)
Compare
error
ROM Model
&
SOH detection
algorithm
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States estimation
(Vt SOC T )
Aging parameters
estimation
( as ɛs )
SOH
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Estimation of SOHQ
16
Experimental
Simulation(Curve fitting)
15
14
Qmax (Ah)
13
12
11
10
9
8
7
•
0
50
100
150
200
Number of cycles
250
300
350
The simulation of Qmax is calculated by the semi-empirical model
whose aging parameters are obtained from curve fitting.
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Fast charging: limiting factors
 The reaction on the negative electrode is described as:
 When operated improperly, Li-ions are deposited on the
anode surface instead of intercalating during charging:
C6  xLi   xe   Li x C6
Li   e   Li (s)
Cause of Lithium plating:
 Large current rate during charging,
especially at high Li ion concentration
 Low temperature
Observed Li plating
Effects of Lithium plating:
Reference: C. J. Mikolajczak, J. Harmon, From Lithium plating to
 Capacity
Lithium –ion cell runaway Exponent [Ex(40)]annual report, 2009
• Irreversible loss of active Lithium
 Safety
• Dendrites can cause shorting within the electrodes
 Heat generation
• A mat of dead lithium and dendrites can increase the chances minor shorts will
lead to thermal runway
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Comparison of simulation results and experimental results:
Charging
Test condition:
Temperature=25°C
Initial Vt= 2.9V
Charge current: 1C/2C/5C rate
Surface Concentration (mol/cm3)
Terminal Voltage (V)
0.04
4.2
4
Sim1C
Sim2C
Sim5C
0.035
Sim1C
Exp1C
Sim2C
Exp2C
Sim5C
Exp5C
Vt/V
3.6
3.4
3.2
Surface concentration
3.8
0.03
0.025
0.02
3
0.015
2.8
2.6
0.01
0
500
1000
1500
2000
2500 3000
time/s
3500
4000
4500
5000
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0
500
1000
1500
2000
2500 3000
time/s
3500
4000
4500
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5000
New Charging method
Charging/Discharging current
i(t)
Positive Terminal
+
Negative Terminal
Battery
Ambient Temperature; T
Terminal Voltage: VT
ROM Model
Estimated concentrations, SOC and temperature
Pulse generator
• Two level or
• Three level
Reference: Maximum allowed concentrations
and temperature, and desired SOC
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Experimental Data for Charging at 4C
1
4.4
0
4.2
4
-2
Pulse
CC/CV
Vt/V
current/A
-1
-3
Pulse
CC/CV
sim
3.6
3.4
-4
-5
3.8
3.2
0
500
1000
time/s
3
1500
0
500
1000
time/s
1500
Qmax by CC and CV charging and the
proposed charging method
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Fast Charging Algorithm
Test conditions:
Cell No.
1
2
Ambient temperature (°C)
25
25
CC/CV
Pulse
Charging current (C)
4
4
Discharging current (C)
2
2
Rest time (min)
10
10
Cycles
100
100
Charging method
Benefits:
1. Less capacity losses after 100 cycles;
• 0.34Ah by the CC and CV.
• 0.24Ah losses by the proposing
method
• Estimate losses at 500 cycles: 0.5 Ah
2. Less temperature rise
3. Reduction of charging time
Experiment
Estimation
15.9
16
CC/CV-exp
Pulse-exp
CC/CV-est
Pulse-est
15.7
If there is no significant
degradation,
15.6
Qmax = Cycle*P1 + P2
15.5
Qmax/Ah
Qmax/Ah
15.8
15
14.5
15.5
15.4
0
20
40
60
80
14
100
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0
100
200
300
400
500
cycle
cycle
32
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Summary
Multi-scale and Multi-physics high resolution electrochemical, thermal and
mechanical modeling considering degradations of materials.
Modeling
1. Cell design
2. System design
• Series and parallel
connection
3. Cooling systems
Health monitoring (Growth of
SEI, Change of conductivities,
Losses of active materials and
others)
Diagnosis
•
•
Power fade
Capacity fade
and
Prognosis
Design
4. Controls
1. SOC estimation
2. Temperature
controls
5. Rapid charging and
discharging
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Dr. Song-Yul Choe
Professor
Auburn University