Dr. Song-Yul Choe Professor Auburn University. High Resolution Modeling of Lithium Ion Battery and...

Dr. Song-Yul ChoeProfessorAuburn University

Ben Choe, [email protected] ; Research on HEV&EV 2 Copying this presentation is illegal and strictly forbidden.

High Resolution Modeling of Lithium Ion Battery and its Applications

Auburn University Mechanical engineering

Advanced Propulsion Research Lab.Song-Yul (Ben) Choe


Trend of advanced propulsion systems

ProtoMass Test

Voltage(Power)12V 42V 96-144V 288V >288VLevel of Voltage

Conv. vehicle

GM(Subaru)“Elten- Custom”

Toyota“THS-M”

Ford“Focus 2.0,Explorer 4.0”GM

“Epsilon”

DCX“S-Class”

Reneaut“Twingo”

Honda“INSIGHT”

Toyota“PRIUS”

SoftHEV

MildHEV

Hard/SplitHEV

Plug-In HEV

E-Drive(40miles)

Power support

PowerAssist

Regen.

Idle Stop

StarterAlternator

15%

30%Nissan“TINO”

Fuel Improvement

Functionality

1-3kW 5-10kW 20-30kW <<40kW >40KW)

Daimler“S-400”

50%

GM“Chevy-Volt”

Toyota“PRIUS”

GM“Tahoe”

VWGOlf

Ford“ESCAPE”


Energy storage with battery

Nominal Capacity (Amp-hours): 15.7Nominal Cell Voltage 3.73Cell Dimensions (mm) 5.27Cell Dimensions w/ terminals (mm) 164.2 X 249.6Maximum Cell Temperature (°C) 75

Positive Lithium Metal OxideNegative CarbonElectrolyte Organic MaterialSeparator SRS


Typical models for battery

• Models base on equivalent electrical circuit Statics: resistors in series to a voltage sourceDynamics: a capacitor connected in parallel to a resistor

Ignored effects :1. Electrical behavior of the terminal as a function of SOC , T and material degradation, and

OCV as a function of hysteresis and SOC. 2. Battery calendar life as a function of cycles and load profile3. Heat generation as a function of SOC , change of entropy and I (charge and discharge), heat

transfer 4. Various temperature effects caused by gradients of ion concentrations and side reactions

R dc h_ dR dc h_ h

R c ha_ dR c ha_ h

C dc h

C c ha

VocVb(t)

Idc h

Ic ha


Modeling of LiPB cell

• T

• ce

• Φe

• Φs

• ηSEI• cs

Sep

arat

or

LixC6 LiyMO2

Cur

rent

col

lect

or

(Cu)

Cur

rent

col

lect

or

(Al)

Electrolyte

Positive electrode

area

Negative electrode

area

Electrode particle

L

X

Y


- +

Principle: Current, Concentration and State of Charge

current = +Ion current Electron current- + - + - +

- +- +

Low SOC Medium SOCcharging

High SOC

• Current in micro cell

• SOC (state of charge) and cs (concentration in solid)

Credit: huangqing

Credit: huangqing


Electrochemical Thermal Mechanical Model

Charging and discharging processes: Heat generation, Elasticity and Degradation Multi scale and Multi-physics coupled problems


Overview of model

Micro cell model

Micro cell model

•Energy conservation•Heat transfer •Charge conservation

Temperature distribution

Parameters:•Battery geometry•Maximum capacity•Concentration•Activity coefficient•Diffusion coefficient•Change of enthalpy•Conductivity

etc.

•Cell voltage•Temp. distribution

•SOC•Overpotentials•Reaction rate•Concentration•Efficiency

•Butler-Volmer

Mass balance•In electrolyte•In solid

Reaction rate

Current

Overpotential

Concentration

Nernst equ.

Standard potential

Micro cell model

Initial conditions:•Initial SOC•Load profile•Initial temperature distribution•Ambient temperature

Single cell model

Potential distribution

Heat source


Static and dynamic behavior of the battery

Characteristics at different current rates (T=300K and SOC=100%)

0.0 0.2 0.4 0.6 0.8 1.02.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

Te

rmin

al V

olta

ge

(V

)

DOD=1-SOC

1C

5C10C

20C20C

50C

0 20 40 60 803.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.0

Te

rmin

al V

olta

ge

(V

)

Time (s)

70% SOC 60% SOC 50% SOC 40% SOC 30% SOC

0 20 40 60 80

-72

0

72

Cu

rre

nt

(A)


Transient behavior of ion concentration (Discharging behavior at a step current of 10C)

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.5

1

r

Concentration in solid (1s, discharge at 10C)

L

Cs/

Cs,

max

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.5

1

r


L

Cs

/Cs

,ma

x

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

At 1sec

At 20 sec

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.

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.5

1

r


L

Cs/

Cs,

max

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1At 80 sec

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.5

1

r


L

Cs

/Cs

,ma

x

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

At 180 sec


Potentials/Current density at positive and negative current collector

-2 0 2 4 6 8 10 12

0

5

10

15

3.6114

3.6116

3.6118

3.612

3.6122

02

46

810

0

5

10

153.6112

3.6114

3.6116

3.6118

3.612

3.6122

3.6124

-2 0 2 4 6 8 10 12

0

5

10

15

-7

-6

-5

-4

-3

-2x 10

-4

02

46

810

0

5

10

15-8

-6

-4

-2

0

x 10-4


Validation of a single pouch cell at 1C/2C/5C discharge/charge

0 1000 2000 30002.5

3

3.5

4

Time, s

Vol

tage

, V

Terminal voltage comparison @ 1C/2C/5C discharge

simulationexperiment

0 1000 2000 3000 4000290

295

300

305

310

315

320

Time, s

Tem

pera

ture

, K

Temperature comparison @ 1C/2C/5C discharge


0 500 1000 1500 2000 2500 3000298

300

302

304

306

308

Time, s

Tem

pera

ture

, K

Temperature comparison @ 20A/40A/60A/80A charge


0 500 1000 1500 2000 25003.5

4

Time, s

Vol

tage

, V

Terminal voltage comparison @ 20A/40A/60A/80A charge


0 500 1000 1500 2000 2500-80-60-40-20

0

Time, s

Cur

rent

, A

Current comparison @ 20A/40A/60A/80A charge



Thermal validation – 5C cycle 2D


Heat generation using the model and calorimeter

0 200 400 600

0

30

60

90

120

Discharging time, s

Hea

t, W

-110

0

110

Cur

rent

, A

2.5

3

3.5

4

Vol

tage

, V

0 200 400 600Chargeing time, s

7C6.3C5.7C5C4.1C

Measured

(OCV-Vt)I+Q

rev


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.


Mechanical stress of cells at 0.5C, 1C and 2C cycling

Ben Choe, [email protected], Research on HEV and Fuel cell 18 Copying of this presentation is strictly forbidden.

Maximum Stress as a Function of Position during discharge (at one instant)

Sep

arator

Cath

ode cu

rrent collector

An

ode cu

rrent collector

• 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.

Ben Choe, [email protected], Research on HEV and Fuel cell 19 Copying of this presentation is strictly forbidden.

Fracture is Observed near the Separator

• 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.

Q. Horn and K. White, 2007 [8]

J. Christensen, 2010 [7]


Block Diagram for battery management system (BMS)

BatteryPack/Module

CurrentVoltageTemperature

TRAY Temp.

Predefined Map

Ri(Charging)

Ri(SOC)

Voc(Charging)

Voc(SOC)

I,V(SOC)

Imean

Vaverage &Temp. Compensation

Search IVSOCbyIV Voltage MAP

TemperatureCharging/Discharging power

Health monitoring & Protection

Voltage Imbalance detection

Diagnosis

HCU

User Interface

Aging Coefficient &SOC CalculationAccumulated SOC Error Comp.

Charging/Discharging Control

Cooling Control

Thermal Management

SENSOR


Review of models for Battery

Empirical Model:Peukert’s equation

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

Electric equivalent circuit Model (EECM): Randles models with the 1st,

2nd and 3rd order

Reduced order of Electrochemical thermal Model (ETM: ROM ): Empirical OCV Polynomial, State space, Páde approx., POD, Galerkin Reformulation and others

Comp. timeAccuracy

Improvement of cell designs

BMS Functionalities

High

Intermediate

Low

Low Moderate High


Reduced order of the model (ROM) for real time applications

Parameters:• Cell geometry• Kinetic and trans-port properties

Initial conditions:• Terminal voltage• Load profile• Ambient tempera-ture

• Cell voltage• Temperature• SOC

Ion concentration in electrolyte Ce

Ion concentration in electrodes Cs

Potentials Φ

SOC estimation

Input:

Out-put:

Battery :

Steps Approaches Results

Order reduction • Ce State space approach

• Cs Polynomial approach

• Φ Parameters simplification

• Higher accuracy with less computational time

• Implicit method to solve PDEs• Optimization of the ROM for real time

applications


Validation of the ROM

0 0.5 1 1.5 2 2.5 3 3.5

x 104

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Time/s

Vt/V

exp@45oC

sim@45oC

exp@25oC

sim@25oC

exp@0oC

sim@0oC

0 0.5 1 1.5 2 2.5 3 3.5

x 104

-10

0

10

20

30

40

50

60

Time/s

T/o

C

exp@45oC

amb@45oC

sim@45oC

exp@25oC

amb@25oC

sim@25oC

exp@0oC

amb@0oC

sim@0oC

0 5 10 15 20-5

0

5

Time/h

Cu

rre

nt/C

0 5 10 15 202.5

3

3.5

4

Time/hV

t/V

0 5 10 15 2025

30

35

Time/h

T/o

C

exp@25oC

amb@25oC

sim@25oC

2. Test condition:Mode: Depleting Cycle #: 2Temperature: 25ºCCurrent: 1C, 2C, 5CInitial SOC: 0%

1. Test condition:Mode: Depleting Cycle #: 5Temperature: 0ºC, 25ºC, 45ºCCurrent: 1C, 2C, 5CInitial SOC: 0%

Xueyan Li, [email protected] , Nov.,2012 24 Copying this presentation is strictly forbidden.

SOC estimation using Extended Kalman Filter

Output:

Battery

Measurement update

Time update with the ROM

SOC calculation

Input:

t̂V kx̂

aves,c

tVambTI ,

SOC

• Error of SOC 7-10%• Initial errors of BMS

Feedback controls and real time model

Xueyan Li, [email protected] , Nov.,2012 25 Copying this presentation is strictly forbidden.

Results of the estimation based on ROM + EKF

0 5 10 15 20-6

-4

-2

0

2

4

6

Time/h

Cu

rre

nt/C

Exp

0 5 10 15 20

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

Time/h

Vt/V

ExpROMROM+EKF

0 5 10 15 20-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Time/h

SO

C e

rro

r

ROMROM+EKFAhAh w/o bias

Test condition:Mode: JSTemperature: 25ºCInitial SOC: 100%Initial error: 0.2V (30% SOC)

Test condition:Mode: Depleting Temperature: 25ºCInitial SOC: 0%Initial error: 0.5V (6.5% SOC)

0 200 400 600 800 10000

10

20

30

40

50

60

70

Time/s

Cu

rre

nt/A

Exp

0 200 400 600 800 10003.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

Time/s

Vt/V

ExpROMROM+EKF

0 200 400 600 800 10000.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Time/s

SO

C

ExpROMROM+EKFAhAh w/o bias

Current: Voltage: SOC:

Current: Voltage: Error of SOC:


Health monitoring of battery

SOH

SOHQ

SOHP

Capacity fade

Power fade

Other mechanism

Research interests for SOH

SOH

Current iBattery

pack

ROM Model&

SOH detection algorithm

Output states value ( V T )

States estimation(Vt SOC T )

Compare

Aging parameters estimation( as ɛs )

error


Estimation of SOHQ

0 50 100 150 200 250 300 3507

8

9

10

11

12

13

14

15

16

Number of cycles

Qm

ax

(Ah

)

ExperimentalSimulation(Curve fitting)

• The simulation of Qmax is calculated by the semi-empirical model whose aging parameters are obtained from curve fitting.


Fast charging: limiting factors

Effects of Lithium plating: Capacity

• 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

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:

66 CLieLiC xxx

s)(LieLi

Cause of Lithium plating: Large current rate during charging,

especially at high Li ion concentration Low temperature

Reference: C. J. Mikolajczak, J. Harmon, From Lithium plating to Lithium –ion cell runaway Exponent [Ex(40)]annual report, 2009

Observed Li plating


Comparison of simulation results and experimental results: Charging

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Vt/

V

time/s

Sim1C

Exp1C

Sim2CExp2C

Sim5C

Exp5C

Test condition:Temperature=25°C Initial Vt= 2.9VCharge current: 1C/2C/5C rate

Terminal Voltage (V)Surface Concentration (mol/cm3)

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000.01

0.015

0.02

0.025

0.03

0.035

0.04

time/s

Sur

face

con

cent

ratio

n

Sim1C

Sim2C

Sim5C


New Charging method

Battery

i(t)Positive Terminal

Estimated concentrations, SOC and temperature

+ -

ROM Model

Ambient Temperature; T

Terminal Voltage: VT

Charging/Discharging current Negative Terminal

Reference: Maximum allowed concentrations and temperature, and desired SOC

Pulse generator• Two level or• Three level


Experimental Data for Charging at 4C

0 500 1000 1500-5

-4

-3

-2

-1

0

1

time/s

curr

ent/

A

Pulse

CC/CV

0 500 1000 15003

3.2

3.4

3.6

3.8

4

4.2

4.4

time/s

Vt/

V

Pulse

CC/CV

sim

Qmax by CC and CV charging and the proposed charging method


Fast Charging Algorithm

Cell No. 1 2

Ambient temperature (°C) 25 25

Charging method CC/CV Pulse

Charging current (C) 4 4

Discharging current (C) 2 2

Rest time (min) 10 10

Cycles 100 100

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

Test conditions:

0 20 40 60 80 10015.4

15.5

15.6

15.7

15.8

15.9

cycle

Qm

ax/A

h

Experiment

0 100 200 300 400 50014

14.5

15

15.5

16

cycle

Qm

ax/A

h

Estimation

CC/CV-exp

Pulse-expCC/CV-est

Pulse-estIf there is no significant degradation,

Qmax = Cycle*P1 + P2


Summary

Modeling

Design Diagnosis and Prognosis

Health monitoring (Growth of SEI, Change of conductivities, Losses of active materials and others)

• Power fade• Capacity fade

Multi-scale and Multi-physics high resolution electrochemical, thermal and mechanical modeling considering degradations of materials.

1. Cell design

2. System design • Series and parallel

connection 3. Cooling systems

4. Controls1. SOC estimation2. Temperature

controls

5. Rapid charging and discharging

Dr. Song-Yul ChoeProfessorAuburn University

Dr. Song-Yul Choe Professor Auburn University. High Resolution Modeling of Lithium Ion Battery and...

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