1

Model based management system (BMS) for

Lithium-ion Batteries

M.A.P.L.E.

Modeling, Analysis, and Process-control Laboratory

for Electrochemical systems

Department of Chemical Engineering

University of Washington, Seattle

2

Current research topics:

– New materials (Si, Ge), ionic liquids,

core shell (magic bullet), hybrid

organic/inorganic materials

– Electrolyte decomposition, insitu

measurements, stress/phase field

modeling and measurements

– May take 20-30 years before

commercialization

Battery Research

While we wait

– Can we get more life, energy

density and improve safety with

better design?

– 10% increase in energy density at

high power for 20% additional life

– Move phase field and detailed

models to applications

If fundamental/systems engineering approaches are established for short term

goals, they are valid for next generation materials and systems

3

Outline

• Introduction

– Lithium-ion batteries and available models

Pseudo-two-dimensional thermal model (P2D)

• Problems with high-rate charging

– Overpotential

– Thermal effect

– Stress-strain effect

• Model reformulation

• Optimal charging profiles

• Conclusion

Separator

Anode

Container

Anode Cathode

Anode lead

4

Lithium-ion battery

Cathode Separator Anode

Curr

ent

Colle

cto

r Curre

nt C

olle

cto

r

Li+

Charging

e

Charge

1y x yLiMO Li MO xLi xe

Charg

6 6

e

xxL x Le Ci i C

Li+ Li+

Li+

Li+

5

Motivates design of architecture and operational strategies based on engineering

scaleup principles

Wide range of energy and power demands

ICD

Cell Phones

&

MP3 players

Laptops

& Tablets

Satellites

Plug-in hybrid

vehicles

Electric vehicles

Energy

Po

wer

Power grid

(images taken from the internet from various sources)

6

Sandwich Level

SEI layer growth

Side reactions

Non uniform current

Stress related cracking

Ohmic resistance

Mass transfer resistance

Lithium-ion batteries – Current limitations

Market Issues

Cost

Life

Safety

System Level

Underutilization

Capacity fade

Lower energy density

Thermal runaway

(V. Ramadesigan+, JES, 2012)

7

Current design practice is not good enough

8

Reverse engineering flight

[from Frank Doyle’s 2005 AIChE CAST award lecture]

9

But really, batteries are just like us

• Operate best between 65-75°F

65°F

75°F

65°F

75°F

65°F

75°F

Too Cold! Too Hot! Just Right

10

Which charging protocol is better?

• Protocol 1 reaches 4.2 V first and stays there

• Protocol 2 reaches 4.2 V at a later time but goes well above

4.2 V

Time (s) Time (s)

0

0.5

1

1.5

2

2.5

3

3.5

4

0 400 800 1200 16003.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

0 400 800 1200 1600

Vo

lta

ge

(V

)

Cu

rre

nt

(C-r

ate

)

Voltage Current

11

100% 0%

20%

40% 60%

80%

SOC

Battery

• No way to directly measure state of charge (SOC)

• No way to measure state of health (SOH)

• Only voltage, current are measurable

Can’t look inside the battery

12

Models for batteries

Predictability

CP

U t

ime

Porous

Electrode P2D

x

r

x

r

x

r

Single

Particle

Model

Stack

Thermal

Model

MD, KMC, etc

Empirical

Models Intercalation + Faraday’s law

Electrochemical Engg. +

Faraday’s law + intercalation

P2D +

Stress-strain

Plane shifts

Li+

stress & strain in graphite during intercalation / deintercalation

Stress effects on Graphite structure

P2D + Population

balance

Adding more physics provides more fidelity

and functionality for the model and the BMS

Comes at a higher computational cost

SOC

SOC

(+),(-)

SOC(x),

SOH,

T(x)

SOC(x,y),

SOH,

T(x,y)

13

Equivalent Circuit Model

• Very fast, 2-3 ordinary differential

algebraic equations (DAEs)

• No temperature or life effects, needs

to be updated when battery fades

UOC

RO

UTh

UTh

CTh ITh

IL

UL

Th LTh

Th Th Th

U IU

R C C

L OC TH L OU U U I R

14

Singe-particle model

• Fast, 20-30 DAEs (for a finite difference

formulation)

• Captures intercalation and kinetics in

lumped form

• Not valid for low temperature, high rates,

fast charging

Cathode Anode

15

Porous electrode two-dimensional (P2D)

model – electrolyte phase

+

-

Cu

rren

t co

llecto

r

- +

-

+

- +

-

+

-

+

-

+ - +

- +

Cu

rren

t co

llecto

r

Anode Cathode Separator

Solvated Anions

Solvated Lithium ion

Solvent

graphite particle

cathode particle

2

p p peff,p 2

( is the electrolyte concentration)

ε 1

c

c cD a t j

t x

Material balance

eff,p

eff,p1 2eff,p

1 2

2κ lnκ 1

( , are the solid- & liquid-phase potentials)

x

RT ct I

x F x

Charge balance

(J.S. Newman+, 1993-2012)

16

+

-

Cu

rren

t co

llecto

r

-

+

-

+

-

+

-

+ -

+

-

+ - +

- +

Cu

rren

t co

llecto

r

Anode Cathode Separator

Solvated Anions

Solvated Lithium ion

Solvent

graphite particle

cathode particle

P2D model – solid phase

LiyMO2 Lithiated

Graphite

s

p s

s,p p c

D T ct

2

1eff,p p p2

1( is the solid-phase potential)

a Fjx

17

+

-

Cu

rren

t co

llecto

r

-

+

-

+

-

+

-

+ -

+

-

+ - +

- +

Cu

rren

t co

llecto

r

Anode Cathode Separator

Solvated Anions

Solvated Lithium ion

Solvent

graphite particle

cathode particle

P2D model – kinetics

LiyMO2 Graphite

Reaction

Reaction

Li+

S

surfp p1 2, sinh

2o T CF

j i URT

18

+

-

Cu

rren

t co

llecto

r

-

+

-

+

-

+

-

+ -

+

-

+ - +

- +

Cu

rren

t co

llecto

r

Anode Cathode Separator

Solvated Anions

Solvated Lithium ion

Solvent

graphite particle

cathode particle

P2D model – thermal behavior

• >1000 DAEs (for standard finite difference

formulation)

, rxn,i rev,i ohm,ii i

i p i i

dT TC Q Q Q

dt X X

19

Why P2D model?

• Control schemes can only include the physics/

phenomena modeled Empirical

Model

• Terminal Cell

voltage

• Total SOC

Single Particle

Model

• Electrode Voltage

• Electrode SOC

• Average SEI growth

• Temperature of cell

P2D Model

• Local electrode

Overpotential

Concentration

SOC

Current density

Stress • Spatial SEI growth

• Ohmic drop

• Mass/heat transfer

x

r

[Doyle+, JES (1993); P.W.C. Northrop+, JES (2014)]

20

CYCLE 25

Dsn= 1.415E-13

kn = 2.503E-09

CYCLE 1

Dsn= 3.455E-13

kn = 1.207E-09

CYCLE 100

Dsn= 8.267E-14

kn = 1.213E-09

CYCLE 200

Dsn= 6.755E-14

kn = 2.035E-10

Parameter estimation

[ V. R. Subramanian+, FOCAPD 2009, V. Ramadesigan+ (ECS, 2010 )]

21

Experimental Verification – US Government Cells

[V. Ramadesigan+, ECST 2009 ]

22

Experimental Validation – US Government Cells

0

500

1000

0.20.40.60.811.21.41.61.8

x 10-13

0

5

10

15

x 1014

cycle

Dsn

(m2/s)

PD

F

[ V. Ramadesigan+, ECST 2009, V. Ramadesigan+ ECS (2010) ]

23

Bayesian Estimation

3 4 5 60

2

4

6x 10

15

Dsn

(10-14

m2/s)

PD

F

Dsn

at cycle 500

2.5 3 3.5 4 4.50

5

10x 10

15

Dsn

(10-14

m2/s)

PD

F

Dsn

at cycle 1000

4 5 6 7 80

1

2x 10

11

kn (10-11

mol/(mol/m3)1.5

)

PD

F

Kn at cycle 500

3.5 4 4.50

1

2x 10

12

kn (10-11

mol/(mol/m3)1.5

)P

DF

Kn at cycle 1000

Bayesian estimation for the solid-phase diffusion

coefficient Dsn and the reaction rate constant kn for the

negative electrode at cycle 500 and 1000

24

Bayesian Estimation

0 200 400 6000

1

2x 10

-13

cycle number (N)

Dsn,

m2/s

Dsn

=4.110-14

N-0.35

0 200 400 6000

2

4

6x 10

-9

cycle number (N)

kn,

m2/s

kn=510

-7N

-1.4

0 2500 5000 7500 100002.5

3

3.5

4

4.5

Discharge time, s

Voltage,

V

Data

Simulated

[ V. R. Subramanian+, FOCAPD 2009, V. Ramadesigan+ ECS (2010) ]

25

Outline

• Introduction

– Lithium-ion batteries and available models

Pseudo two-dimensional thermal model (P2D)

• Problems with high-rate charging

– Overpotential

– Thermal effect

– Stress-strain effect

• Model reformulation

• Optimal charging profiles

• Conclusion

Separator

Anode

Container

Anode Cathode

Anode lead

26

• Negative potential at the anode

causes lithium to plate

– Anode overpotential < 0

Lithium plating

x

r

(www.ifw-dresden.de/de)

27

Charging problem – plating overpotential

0

( , ) ( , ) ( , )film

plating s e s s

n

Rx t x t U j x t

a

at the

anode-separator

interface

plating

Separator Cathode Separator Anode

28

Charging problem – plating overpotential

at the

anode-separator

interface

plating

0

( , ) ( , ) ( , )film

plating s s s s

n

Rx t x t U j x t

a

Cathode Separator Anode

29

Local variation of current density and stress

[B. Suthar, JES (2014)]

30

Conventional charging (CC-CV) and

drawbacks

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 500 1000

Cu

rren

t (C

ra

te)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

3.753.8

3.853.9

3.954

4.054.1

4.154.2

4.25

0 500 1000

Vo

lta

ge

(V)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

295

300

305

310

315

320

325

0 500 1000

Tem

per

atu

re (

K)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

-0.05-0.04-0.03-0.02-0.01

00.010.020.030.040.05

0 500 1000

Ov

erp

ote

nti

al

(V)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

31

Silicon nano-structured electrodes

31

Cycling

Nanowires

1D electron

transport

Strain

relaxation

Good contact with current collector

Good: Use Si nano-structured

electrodes

- Relaxation of strain

- Efficient electron transport

- Good current collector

contact

- Decreases dead weight

(Chan+, Nat. Nano, 2008)

Bad: High stress development during intercalation

- Volume expansion, De-lamination from substrate

32

CC-CV charging and drawbacks

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 500 1000

Cu

rren

t (C

ra

te)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

3.753.8

3.853.9

3.954

4.054.1

4.154.2

4.25

0 500 1000

Vo

lta

ge

(V)

Time (Sec)

CC-CV with 3C

CC-CV with 4C

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 500 1000

Str

ess

(sca

led

)

Time (s)

Tangential Stress (Near Separator)

CC-CV with 3C

CC-CV with 4C

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 500 1000

Str

ess

(sca

led

)

Time (s)

Radial Stress (Near Separator)

CC-CV with 3C

CC-CV with 4C

33

Outline

• Introduction

– Lithium-ion batteries and available models

Pseudo two-dimensional thermal model (P2D)

• Problems with High-rate charging

– Overpotential

– Thermal effect

– Stress-strain effect

• Model reformulation

• Optimal charging profiles

• Conclusion

Separator

Anode

Container

Anode Cathode

Anode lead

34

Finite difference solution

Np

Positive Electrode Separator Negative Electrode

x=0 x=lp x=lp+ls x=lp+ls+ln

Nn Ns Nr Nr

Li-ion cell pseudo-2D model

1000-10000 DAEs, Time: 1-2 min

35

• Lumped Parameter Models

– Drop the physics?

• Proper Orthogonal Decomposition

• Mathematical Reformulation

– Spectral methods + analytical solution

– OCFE

Different order reduction approaches

(L. Cai and R.E. White, JES, 2009)

(V.R. Subramanian +, ESL, 2007; ECS 2009)

(P.W.C. Northrop+, JES, 2011)

36

Mathematical reformulation

Coordinate

Transformation

Original System 3000-10000 DAEs

A

0X 1X

C A

px l

p sx l l

p s nx l l l

0x

S

C

S

-1 1 0

x

-1

1

0 f(x

)

Analytical

Solutions

Final System 30-50 DAEs

Reduces

into

Orthogonal

Collocation

(P.W.C. Northrop+, JES, 2011) (Patent US20140136169)

37

Reformulated model

Computation Details Full-order

FD model

Reformulated

model

Number of equations for charge or

discharge curve

>1000

DAEs

27 DAEs

Computation time for charge or

discharge curve

1-2 min 15-45 ms

• Memory requirement < compared to full-order finite difference (FD) models

• Reformulated model conserves mass and charge

Stabilizes coupled multiscale codes

38

Outline

• Introduction

– Lithium-ion batteries and available models

Pseudo two-dimensional thermal model (P2D)

• Problems with high-rate charging

– Overpotential

– Thermal effect

– Stress-strain effect

• Model reformulation

• Optimal charging profiles

• Conclusion

Separator

Anode

Container

Anode Cathode

Anode lead

39

Dynamic optimization methodology

• Simultaneous discretization

Large Nonlinear

Program

PDE

( , ) . ( , )nx x tt

N x t

Spatial

Discretization

Algebraic

Equations

1, , , appk k k kk

F z z y i

, , appk k kkG z y i

DAEs

'( ) , , , appz t f t z y i

0 , , , appg t z y i

Path Constraints

and Obj. Function

maxmin

maxmin

maxmin

( ) ,

( ) ,

( )

appi i k i

y y k y

z z k z

Optimal Charging/

Discharging Profile

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

Scaled time

Scale

d c

urr

en

t (C

Rate

)

with PID

without PID

Nonlinear

Programming

Solver

Temporal

Discretization

(L.T. Biegler, JPC, 2004)

40

Halting lithium plating

• If overpotential goes below zero,

lithium plating will occur

• Solution: Restrict overpotential

𝟎 ≤ 𝛈

41

Optimal control for charging – avoid plating

• Problem formulation

• Model description

– Reformulated model

( )( )

f

Q appapp

t

i t0

max i t dt

such that

maxapplied

plating

0 i i ;

>0

3.5C

1

,s pC 2

,s pC

1

,e pC2

,e pC1

,e sC

2

,e sC

1

,s nC 2

,s nC

1

,e nC 2

,e nC1

,e pT

2

,e nT1

,e nT

2

,e pT

2

,e sT

1

,e sT

Maximize charge stored

(Patent US20140136169, “Systems and methods for improving battery

performance;” [P.W. C. Northrop+, JES (2014)]

42

Which charging protocol is better?

• Protocol 1 reaches 4.2 V first and

stays there

• Protocol 2 reaches 4.2 V at a later

time but goes well above 4.2 V

• Protocol 2 avoids lithium plating

(optimal control)

Time (s) Time (s)

Time (s)

0

0.5

1

1.5

2

2.5

3

3.5

4

0 400 800 1200 16003.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

0 400 800 1200 1600

Vo

lta

ge

(V

)

Cu

rre

nt

(C-r

ate

)

Pla

tin

g O

ve

rpo

ten

tial (V

)

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 400 800 1200 1600

[P.W.C. Northrop +, JES (2014)]

43

Is avoiding plating enough?

Time (s) Time (s)

Time (s)

0

0.5

1

1.5

2

2.5

3

3.5

4

0 400 800 1200 16003.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

0 400 800 1200 1600

Vo

lta

ge

(V

)

Cu

rre

nt

(C-r

ate

)

Pla

tin

g O

ve

rpo

ten

tial (V

)

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 400 800 1200 1600300

305

310

315

320

325

330

335

340

0 400 800 1200 1600

Te

mp

era

ture

(K

)

Time (s)

44

Optimal control for charging – avoid plating

and temperature rise

• Problem formulation

• Model description

– Reformulated thermal P2D

( )( )

f

Q appapp

t

i t0

max i t dt

( , )

such that

maxapplied

plating

max

0 i i ;

>0;

T x t T K

3.5C

335

1

,s pC 2

,s pC

1

,e pC2

,e pC1

,e sC

2

,e sC

1

,s nC 2

,s nC

1

,e nC 2

,e nC1

,e pT

2

,e nT1

,e nT

2

,e pT

2

,e sT

1

,e sT

Maximize charge stored

45

300

305

310

315

320

325

330

335

340

0 400 800 1200 1600

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

0 400 800 1200 1600

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 400 800 1200 1600

0

0.5

1

1.5

2

2.5

3

3.5

4

0 400 800 1200 1600

Time (s) Time (s)

Time (s)

Vo

lta

ge

(V

)

Cu

rre

nt

(C-r

ate

)

Pla

tin

g O

ve

rpo

ten

tial (V

)

Time (s)

Te

mp

era

ture

(K

)

Determining optimal charge profile

Optimal fast charge yields 10.5% increase in SOC

with no lithium plating or effects from temperature rise

46

User Interface

47

Control algorithm on microcontroller

48

Optimal profiles for solar-battery hybrids

Standard Protocol N

orm

ali

ze

d C

urr

en

t

t, time of the day (hr)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

4 8 12 16 20

Standard Charging

Max Charge Stored

Reduced Fade

Solar Insolation

Demand

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

4 8 12 16 20

Standard Charging

Max Charge Stored

Solar Insolation

Demand

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

4 8 12 16 20

Standard Charging

Solar Insolation

Demand

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

4 8 12 16 20

Solar Insolation

Demand

Optimal Energy Optimal Life

[M. Lawder+, Proc of IEEE (2014)]

49

Summary and future directions

• Summary

– Model-based optimal control leads to improved

charging profiles

Subtle differences in operating protocols correspond

to significant local variations in electrochemical,

thermal, and mechanical behaviors

– Reformulated models make the pseudo-2D model

manageable for control relevant applications

50

Acknowledgements

• Students, postdoctoral associates, and collaborators

(UW/WUStL/TTU)

• Sponsors

– NSF, DOE-ARPA-E, DOE (SERIIUS), MDA, NRO, Sun Edison, ACS PRF,

Hyundai Motor Company, NCSA, UW Clean Energy Institute

• For more info visit

depts.washington.edu/maple

51

“If you can’t model your process, you don’t

understand it. If you don’t understand it, you

can’t improve it. And, if you can’t improve it,

you won’t be competitive in the 21st century.”

Jim Trainham (RTI International)

Questions?

Thanks!

52

Multi-objective multi-disciplinary multi-scale problem

Optimal BMS

BMS based on MPC