system-level modeling, estimation and control of battery ... · system-level modeling, estimation...

System-Level Modeling, Estimation and Control of Battery System

Dr. Xinfan Lin

Department of Vehicle Controls and Systems Engineering Center of Research and Advanced Engineering

Ford Motor Company

5/26/2016 /29 Xinfan Lin Presentation

Outline

System-level battery management - Temperature estimation of battery system - Reduced battery voltage sensing

Physics-based Investigation and Modeling - Neutron Imaging

Work Experiences at Ford Motor Company - EV DC fast charging system - University collaboration

5/26/2016 Xinfan Lin Presentation /29

Li-ion Cells : Human Like

• Poke them and they can bleed and burst into flames

• Hate to be over-worked • Picky about temperature • Diversity • All cells must die

They need to be taken care of! Battery Management:

• State Estimation - State of charge (SOC)

- State of health (SOH)

- Power capability • Thermal Management - Temperature control

- Temperature imbalance control • Cell Balancing…


Existing Studies on Battery Management

BMS: States Estimation Thermal Management Cell Balancing …

Temp Sensor

Voltage & Current Sensors

State of Art: Cell-level Battery Management

Chevy Volt: 288 cells Nissan Leaf: 192 cells Tesla Model S: >7000 cells

Reality: Battery systems come in packs.


System-Level Battery Management under Sparse Sensing,

Limited Computational Capacity and System Uncertainty

Cell-Level Battery Management with Full Sensing

Temp Sensor

Voltage & Current Sensors

BMS: Thermal Management SOC estimation …

Battery Cell

Goal: System-level BMS

Battery System


A lesson learned from Industry

Outline





Issue: ineffective temperature sensing:

Limited number of sensors: ~ 1 in every 10 cells

Only measuring surface but not the internal cell temperature

Solution: combining sparse sensing with model-based estimation Cells

Sensor Housing

Temperature Estimation of Battery System

Temperature Sensing

Modeling System Identification

State Estimation

Sponsored by US Army TARDEC 5/26/2016 Xinfan Lin Presentation /29

Single-Cell Model and Identification

0 5 10 15 20 25 3025

30

35

40

t (min)

T s (o C)

0 5 10 15 20 25 300

100

200

300

400

t (min)

Par

amet

er

cp,si(JK-1)

cp,so(JK-1)

Re(0.01mΩ)

Rc(0.01(KW-1)

Core temp Tc

Surface temp Ts

2c s cc e

c

dT T TC I Rdt R

−= +

f ss s cs

u c

T TdT T TCdt R R

− −= −

0 10 20 30 40 50 60 70 80 9026

27

28

29

30

31

32

33

34

35

t (min)

T (o C

)

Measured TsEstimated TsMeasured TcEstimated Tc

System Identification • To determine model parameters • Online ID using Ts and I • Experimental validation

Lin, et al., IEEE Transaction, Control Systems and Technology 2013 Lin, et al., American Control Conference 2012

Ts

Tc


, 2 , ,

, , ,, , , , 1 , 1 ,2

c i s i c ic e

c

f in i s is i s i c i s i s i s is

u c cc

dT T Tdt R

T TdT T T T T Tdt R R R

C I R

C − +

−+

− − + −

=

= − +

, , , , 1

, ,, , , ,

,

f in i f out i

f in i sf out i f in i

u p air

TT T

T

T TR c

−=

−= −

Single Cell Model Cell to Cell Conduction

Coolant Flow Dynamics

Battery System Thermal Model

Lin, et al., IFP RHEVE 2011 Lin, et al., Journal of Power Sources 2014


Model + output feedback

Observer for Temperature Estimation Issue caused by sparse temperature sensing:

• Inaccurate model parameters for cells with no sensor

Model-based Observer Design

Battery Thermal System

( , )

m

T f T IT CT==

I

ˆˆ ˆ( , )ˆ ˆm

T f T I

T CT

=

=

mT ˆy m me T T= −

mT

T

[ ]21 21 ...s sT

c c cn snT T T T T T T= 1 ...T

m s sjT T T =

10n j≥

( )yh e+

ˆf f≠


Problem Formulation

5/26/2016 Xinfan Lin Presentation

Battery thermal model in state-space representation: 2

m

T AT BIT CT= +=

Model uncertainty: resistance imbalance among cells

,0 ,1 ,2 ,1 [ ,0, ., ,..0 0]T

e e e e e e nc

R R R R R RC

∆ = − = ∆ ∆ ∆ , ,0| 0.1| e i eR R≤∆

Goal: to design an optimal “worst-case” observer

( )man )i x (me

eRJ e R

∆∆F

,1 ,2 ,1 0 0 ... 0

Tee e e n

c c

RC

B R R RC

= =

ˆ: ˆ

ˆ ˆh h m

h

T T I GTA By C x

+ +==

F

ˆe T T= −

,1 ,2 ,

,0 , ,0

0 0 0 ,

. . 0.1 0.1 , 1,2, ,

Te e e e n

e e i e

R R R R

s t R R R i n

∆ = ∆ ∆ ∆ − ≤ ∆ ≤ =

Guarantee minimized worst-case error under all possible degree of uncertainties!

/29

Robust H∞ observer: solving linear matrix inequality (LMI)

22

, , , , ,

2

min

*. . 0,

* ** * *

1,2,...0

hR X M N D

T T T T T T T T Tj h

T T T T T Th

T Th

RA A R RA A X C Z M R B W C D NA X XA C Z ZC XB ZD W C D

s tD D

j qR X

γγ

γ

+ + + + ∆ − − + + + + − < − −

− ∀ =

− <

II

, 0, 1,q q

j j j jj j

B Bα α α∆ = ≥ =∑ ∑If ΔB belongs to a polytope:

In our case: ,1 ,2 ,

, ,0 ,0

1 0 0 0 ,

0.1 , 0.1 , 1,2, ,

Tj e e e n

c

e i e e

B R R RC

R R R i n

∆ = ∆ ∆ ∆

∆ ∈ − =

Method: Robust H∞ Observer

Lin, Ph.D. Dissertation Lin, et al., ASME DSCC 2014

[0, 2),m main ( )x

eeuR

G jω

ω∈ +∞ ∆F


Results for 1 Sensor

Observer Performance

Worst-case Estimation Deviation Under the 10% Resistance Uncertainty

Estimated Temperature Distribution in the pack (core and surface T of each cell)

0 500 1000 1500 2000 2500 300025

30

35

40

45

50

55

time (s)Te

mp

(o C)

Temp Est.Worst-case deviation

0 500 1000 1500 2000 2500 300025

30

35

40

45

50

55

time (s)

Tem

p (o C

)


Outline





Sensor Housing

Voltage Sensing

SOC Estimation Under Reduced Voltage Sensing

Issue: Too much voltage sensing - Need to measure the voltage of single cells - For overvoltage protection

Disadvantages: - High cost and complexity - Difficulty for maintenance

Solution: reduced voltage sensing - Measuring the total voltage instead of cell voltage - Estimating the cell voltage from the total voltage


Are sensors such a big deal? Yes for auto industry!

Two cells in series • x1 ǂ x2 (SOC: state of charge) • Analysis using a battery electrical model • Goal: to estimate x1, x2 based on V1 + V2

SOC Imbalance

SOC1, SOC2

I V1+V2

Observer

1, 1,1

1, 1, 1 , ( )kk kk k

tIx V g xx IRQ−

−= + = +∆

, 1, 2,T

str k k kx x x=

Problem Formulation

V1, V2

2, 2,1

2, 2, 1 , ( )kk kk k

tIx V g xx IRQ−

−= + = +∆

, 2,1, 2, 1,( ) ( ) 2str k k k k kV V g x g xV IR= + = ++


0 0.2 0.4 0.6 0.8 1

2.7

3

3.3

3.6

SOC

Volta

ge, g

(x) (

V)

Single point: indistinguishable. Trajectory: distinguishable.

Consider 3 combinations:

0 50 100 1506.85

6.9

6.95

7

7.05

time (s)

Tota

l Vol

tage

, Vst

r (V)

0 50 100 1506.85

6.9

6.95

7

7.05

time (s)

Tota

l Vol

tage

, Vst

r (V)

0 50 100 1506.85

6.9

6.95

7

7.05

time (s)

Tota

l Vol

tage

, Vst

r (V)

0.85 0.9 0.95 13.4

3.45

3.5

3.55

3.6

SOC

Volta

ge (V

)

0.85 0.9 0.95 13.4

3.45

3.5

3.55

3.6

SOC

Volta

ge (V

)

0.85 0.9 0.95 13.4

3.45

3.5

3.55

3.6

SOC

Volta

ge (V

)

Two-Cell String Voltage

Feasibility?

SOC1 = SOC2 = 0.94

SOC1 = 0.92, SOC2 = 0.952

SOC1 = 0.9, SOC2 = 0.958


Total voltage trajectory based on the string model

To be observable, δxstr,k and (δVstr,k, δVxstr,k+1) needs to be an one-to-one mapping, meaning that O(xstr,k) should be of full rank.

1, 2,, 1,

1, 2,, 1 2,

, ,

'( ) '( )

'( ) '( )

( )

k kstr k k

k kk kstr k k

str k str k

g x g xV xt tI I

Q QO

g x x

x

gV x

x

δ δδ δ

δ

+

= + +

∆ ∆

=

1, 2,

,1, 2,

'( ) '( )

' ))

((

( ) '

k k

str k k kk k

O x I Ig x g x

t tg x g xQ Q∆ ∆

= + +

Observability Matrix

Nonlinear observability: 2nd order gradient of g(x)

Math Underpinning: Observability

5/26/2016

1, 2,

1, 2,

'( ) '( )

''( ) ''( )

k k

k k

g x g xI Ig x g xQ Q

⇔

Xinfan Lin Presentation /29

Trajectory-based method: Moving Horizon Observer

500 1500 2500 35006

6.3

6.6

6.9

7.2

time (s)

V str (V

)

0 0

1,0 2,0

1,0 2,0

1 1

0

,0

,0

,

,0 2 00

1 ,

( ) ( )

( ) ( )

( )

( ) ( )

str

str

str kk k

i i

g x g xt tg x g x

VH x

Vt t

g x g x

I IQ Q

I I

Q Q

− −

+ ∆ ∆ +

= = ∆ ∆

+

+ +

+ +

∑ ∑

Use Newton’s method to calculate xstr,0 iteratively:

Algorithm

Lin, et al., IEEE Control Systems and Technology 2014 Lin, et al., American Control Conference 2013


0 10 20 303.35

3.4

3.45

3.5

3.55

3.6

Estimation step

Vol

tage

(V)

V1

Ve1

V2

Ve2

0 10 20 300.7

0.75

0.8

0.85

0.9

0.95

1

Estimation step

SO

C

SOC1

SOCe1

SOC2

SOCe20 0.2 0.4 0.6 0.8 1

2.7

3

3.3

3.6

SOC

g(x)

(V)

0 0.2 0.4 0.6 0.8 10

5

10

15

g'(x

) (V

)

SOC

0 0.2 0.4 0.6 0.8 1-400

-200

0

200

SOC

g''(x

) (V

)

A123 LiFePO4 battery:

g(x): Voltage vs. SOC

Application to Actual Battery

The SOCs are observable in high and low SOC ranges due to non-zero 2nd order gradient!


Battery Pack Temperature Estimation • Thermal Model: - Capture surface and core temperatures of all cells in the pack

• Online parameter ID algorithm: - Determine parameters by using onboard signals

• Robust Observer design: - Guarantee minimized worst-case estimation error under uncertainty SOC and Voltage Estimation under Reduced Voltage Sensing: • Observability Analysis: - Establish the conditions for the cell SOCs to be observable

• Nonlinear Observer Design: - Trajectory-based moving horizon observer …

• Extension to cell capacity and resistance estimation

Summary: System-Level Battery Management


Outline





Neutron Imaging of Li-ion Battery

Siegel, Lin, et al., J. Electrochemical Soc. 2011 Siegel, Lin, et al., American Control Conference 2011 Siegel, Lin, et al., American Control Conference 2012

5/26/2016 /29

1C

5C

lithium distribution inside battery

Xinfan Lin Presentation

Why we made our own cells? - customize shape/dimension - to know/control composition - need special materials Procedures: - Start with: LMO, graphite… - Mix and Grind - Dissolve and make paste - Paste on the mold - Bake and dry up - Assemble inside glove box

Design and Fabrication of Battery Cells


Processed Lithium Concentration


Outline





Work Experiences at Ford

Applying the system-level BMS to EVs

EV systems and components development • EV DC Fast Charging System

- Charging 80% range in 20 minutes

University Collaboration: • UMich, GE: ARPA-E AMPED

- Battery control based on strain/temp sensing

• Ohio State: Ford URP - Aging propagation in battery packs


Questions?


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