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Two-point State of Charge Determination In Lithium-Ion Battery Packs

Matthieu Dubarry

[email protected]

Cyril Truchot, Arnaud Devie & Bor Yann Liaw

mailto:[email protected]

SOC estimation is of extreme importance for reliability of battery operation.

SOC estimation for an assembly remains a subject of great interest.

Previous study showed that StringSOC is obtainable from StringOCV not SCOCV

Not convenient: need to be recalculated with every assembly at every SOH

Time consuming

Need for a better method

Here, a viable method for SOC determination and tracking for multi-cell assemblies is proposed and validated.

Objectives & Motivation

C. Truchot, M. Dubarry and B.Y. Liaw, Applied Energy, 119, p.218 (2014).

: SOC if the most charged single cell

: SOC if the most discharged single cell

: Average single cell SOC

: SOC of the average single cell voltage

: Open String Voltage, no tie to single cells

-15

-10

-5

0

5

10

15

4.264 6.568 7.548 8.517 8.666 12.36 87.75

Err

or

(%)

C/5 C/2 C/1 3/2C 2C 5/2C

C/2

Charge

Discharge

SC

MinSOC

SC

MaxSOC

String

OSVSOC

String

Avg(OCV)SOC

String

MeanSOC

SC

MinSOC

SC

MaxSOC

String

OSVSOC

String

Avg(OCV)SOC

String

MeanSOC

The theoretical background behind the proposed method is based on three concepts:

(1) The SOC of a single cell can be accurately calculated from a rest cell voltage (RCV) and a universal OCV=(SCSOC) function.

This OCV= (SCSOC) function varies with aging.

(2) The capacity variations within cells of the same batch can be described by a quantity called capacity ration, Qr in mAh SOC–1.

(3) All OCV= (SOC) functions can be dissociated mathematically into two independent one-dimensional arrays, OCV and SOC, of the same size.

Arrays will always be represented in italics.

The goal is to express the correlation between single cell attributes (OCV and SCQr) and pack attributes (OPV and packQr).

Anakonu approach: Understand SC/Pack correlation

Principles

M. Dubarry, C. Truchot, A. Devie and B.Y. Liaw, J. Electrochem. Soc. , submitted

Lets start with 3 identical cells,…

Same OCV, Same Qr,


Ideal battery pack – Example of a 3S1P assembly

Cell #1

Cell #2

Cell #3


Same OCV, Same Qr, Same RCV1

… Connect them in series…

… And discharge a capacity Q



Cell #1

Cell #2

Cell #3

RPVj = i=1

𝑛

SCiRCVj = 𝑖=1

𝑛

𝑆𝐶𝑖𝑂𝐶𝑉(SCiSOCRCVj

)

= 𝑂𝑃𝑉 SC1SOCRCVj = 𝑖=1

𝑛

𝑂𝐶𝑉(SC1SOCRCVj

)

SC1RCV1

SC2RCV1

SC3RCV1

RPV1Pack







Cell #1

Cell #2

Cell #3

SC1RCV1

SC2RCV1

SC3RCV1

SC1RCV2

SC2RCV2

SC3RCV2

Q

RPV1

RPV2

SC1SOC

SC2SOC

SC3SOC

RPVj = i=1

𝑛

SCiRCVj = 𝑖=1

𝑛


)


𝑛


)

Pack







Cell #1

Cell #2

Cell #3

Pack

SC1SOC

packSOC

SC2SOC

SC3SOC

Q

Q = ∆SCiSOC SCiQr = ∆packSOC packQr

packQr =∆SCiSOC SCiQr

∆packSOC=

Q

∆packSOC

RPVj = i=1

𝑛

SCiRCVj = 𝑖=1

𝑛


)


𝑛


)

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑖=1

𝑛

𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶

𝑝𝑎𝑐𝑘𝑆𝑂𝐶 =)𝑆𝐶1𝑆𝑂𝐶 − 𝑆𝐶1𝑆𝑂𝐶(OPVmin)𝑆𝐶1𝑆𝑂𝐶(OPVmax) − 𝑆𝐶1𝑆𝑂𝐶(OPVmin

Ideal SC/Pack correlation

SC1RCV1

SC2RCV1

SC3RCV1

SC1RCV2

SC2RCV2

SC3RCV2

RPV1

RPV2

3 identical cells

Same OCV, Same Qr

But different initial SOC

Different RCV1

Need to address the

misalignment

Translation factor tf:


Cells with different initial SOC

SC1SOC

SC2SOC

SC3SOC

Q

SC1RCV1

SC2RCV1

SC3RCV1

SC1RCV2

SC2RCV2

SC3RCV2

Cell #1

Cell #2

Cell #3


𝑛


X

)SCi𝐭𝐟 = 𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV1

3 identical cells

Same OCV, Same Qr

But different initial SOC

Different RCV1

Need to address the

misalignment

Translation factor tf:


Cells with different initial SOC

Pack

0

SC1SOC

SC2SOC

SC3SOC

Q

SC1RCV1

SC2RCV1

SC3RCV1

SC1RCV2

SC2RCV2

SC3RCV2

Cell #1

Cell #2

Cell #3

packSOC

RPV1

RPV2

SC2tf

SC3tf


𝑛


X

)SCi𝐭𝐟 = 𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV1

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + 𝑖=2𝑛 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + SCi𝐭𝐟

SOC mismatch SC/Pack correlation

3 cells

Same OCV, Same RCV1

But different size

Different Qr

Need to address scaling

Scaling factor sf:


Cells with different capacity ration

SC1SOC

Q

SC1RCV1

SC1RCV2

SC2SOC

SC3SOC

SC2RCV1

SC3RCV1

SC2RCV2

SC3RCV2

Cell #1

Cell #2

Cell #3

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + 𝑖=2𝑛 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + SCitf

X

SCisf =SCiQr

SC1Qr=∆SCiSOC

∆SC1SOC

=)𝑆𝐶𝑖𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV2)𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶1𝑆𝑂𝐶(RCV2

3 cells

Same OCV, Same RCV1

But different size

Different Qr

Need to address scaling

Scaling factor sf:


Cells with different capacity ration

Pack

0

SC2SOC

SC3SOC

SC2RCV1

SC3RCV1

SC2RCV2

SC3RCV2

Cell #1

Cell #2

Cell #3

packSOC

RPV1RPV2

SC1SOC

Q

SC1RCV1

SC1RCV2

SC2sf

SC3sf

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + 𝑖=2𝑛 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + SCitf

X

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶

+ 𝑖=2𝑛 𝑂𝐶𝑉 SCi𝐬𝐟 𝑆𝐶1𝑆𝑂𝐶 + SCitf

SOC & Qr mismatch SC/Pack correlation

SCi𝐬𝐟 =SCiQr

SC1Qr=∆SCiSOC

∆SC1SOC

=)𝑆𝐶𝑖𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV2)𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶1𝑆𝑂𝐶(RCV2

Cell degradation modifies the cells

Same RCV1 but different OCV and Qr


Cells with different SOH

2.8

3

3.2

3.4

3.6

3.8

4

4.2

0 20 40 60 80 100

0% LLI4% LLI8% LLI12% LLI16% LLI20% LLI

Vo

lta

ge

(V

)

SOC (%)


+ 𝑖=2𝑛 𝑂𝐶𝑉 SCisf 𝑆𝐶1𝑆𝑂𝐶 + SCitf

X𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑺𝑪𝟏𝑶𝑪𝑽 𝑆𝐶1𝑆𝑂𝐶

+ 𝑖=2𝑛𝑺𝑪𝒊𝑶𝑪𝑽 SCisf 𝑆𝐶1𝑆𝑂𝐶 + SCitf

Cell #10% LLI

Cell #210% LLI

Cell #320% LLI





2.8

3

3.2

3.4

3.6

3.8

4

4.2

0 20 40 60 80 100


Vo

lta

ge

(V

)

SOC (%)



X

SC1SOC

Q

SC1RCV1

SC1RCV2

SC2SOC

SC3SOC

SC2RCV1

SC3RCV1

SC2RCV2

SC3RCV2

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑺𝑪𝟏𝑶𝑪𝑽 𝑆𝐶1𝑆𝑂𝐶

+ 𝑖=2𝑛𝑺𝑪𝒊𝑶𝑪𝑽 SCisf 𝑆𝐶1𝑆𝑂𝐶 + SCitf

Full SC/Pack correlation

M. Dubarry, C. Truchot and B.Y. Liaw, J.Power Sources, 219 (2012) 204-216

Cell #10% LLI

Cell #210% LLI

Cell #320% LLI





2.8

3

3.2

3.4

3.6

3.8

4

4.2

0 20 40 60 80 100


Vo

lta

ge

(V

)

SOC (%)



X𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑆𝐶1𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶

+ 𝑖=2𝑛𝑆𝐶𝑖𝑂𝐶𝑉 SCisf 𝑆𝐶1𝑆𝑂𝐶 + SCitf

Full SC/Pack correlationPack

0

SC2SOC

SC3SOC

SC2RCV1

SC3RCV1

SC2RCV2

SC3RCV2

packSOC

RPV1RPV2

SC1SOC

Q

SC1RCV1

SC1RCV2

M. Dubarry, C. Truchot and B.Y. Liaw, J.Power Sources, 219 (2012) 204-216

Cell #10% LLI

Cell #210% LLI

Cell #320% LLI

Full SC/pack correlation:

Anakonu : Single cell/Pack correlation

packQr =( )𝑆𝐶𝑖𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV2 )SCiQr

𝑝𝑎𝑐𝑘𝑆𝑂𝐶(RCV1) − 𝑝𝑎𝑐𝑘𝑆𝑂𝐶(RCV2=

Q

∆packSOC

RCV1 RCV2

𝑂𝑃𝑉 𝑆𝐶1𝑆𝑂𝐶 = 𝑆𝐶1𝑂𝐶𝑉 𝑆𝐶1𝑆𝑂𝐶 + 𝑖=2

𝑛

𝑆𝐶𝑖𝑂𝐶𝑉 SCisf 𝑆𝐶1𝑆𝑂𝐶 + SCitf

)SCitf = 𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV1SCisf =)𝑆𝐶𝑖𝑆𝑂𝐶(RCV1) − 𝑆𝐶𝑖𝑆𝑂𝐶(RCV2)𝑆𝐶1𝑆𝑂𝐶(RCV1) − 𝑆𝐶1𝑆𝑂𝐶(RCV2

. . .

With 2 sets of RCVs we can calculate the full OPV=f(packSOC) and packQr

3S1P string with a 10% SOC imbalance

Validation 1: Initial SOC imbalance

C. Truchot, M. Dubarry and B.Y. Liaw, Applied Energy, 119, p.218 (2014)


Illustrate approach benefits forcell-to-cell variation accommodation.

Remove the need for initial SOC calibration on assemblies.

3S1P with temperature gradient

Validation 2: Aging induced imbalance

0.5

0.6

0.7

0.8

0.9

1

1.1

0 100 200 300 400 500 600

25oC

60oC

3S1P

Cap

acity,

Ah

Cycle #

25°C

60°C


sftf

25°C 60°C 25°C

25°CRef: 25°CRef:

60°C

60°C

25°C

25°C

9.5

10

10.5

11

11.5

12

12.5

13

-5

0

5

10

15

20

25

30

0 20 40 60 80 100

Experimental OPV

FullAccOPV

NoAccOPV

SOC calaculation difference (%)

SOC calaculation difference with no OCV accomodation (%)SOC calaculation difference with no accomodation at all (%)

Vo

lta

ge (

V)

SO

C a

bsolu

te e

rror (%

)

SOC (%)

3

3.2

3.4

3.6

3.8

4

4.2

-10

-5

0

5

10

15

20

0 20 40 60 80 100

Initial SCOCV

SCOCV after 125 cycles at 25°C

SCOCV after 150 cycles at 60°C

E

F

Vo

ltag

e (

V)

SO

C a

bsolu

te e

rror (%

)

SOC (%)

Illustrate approach benefits forSOC & SOH tracking.

Quantify cells intrinsic & extrinsic degradation in-situ.

Unique and simple packSOC estimation method

No physical disassembly, no pack maintenance: reduced downtime

Requires only two measurements of rest cell voltages of all single cells

Reduce the complexity in the SOC & SOH tracking

Offers significant benefits to battery control and management

Two parameters, tf and sf to characterize and track cell imbalance

Enables RUL determination with improved accuracy.

Can be coupled with ‘alawa approach for degradation simulation

Pack-level and cell-level degradation factors could be distinguished and accurately quantified without complicated protocols and procedures.

Conclusions


Apply the technique on real size battery packs

HNEI is monitoring several MW size battery systems in Hawai’i

Future work

Acknowledgments

Cyril Truchot

FundingIdaho National Laboratory

US DOE EERE ABR

(Contract No. DE-AC07-05ID14517).

Mahalo for your attention! Questions ?

[email protected]

Full publication list available on



http://scholar.google.com/citations?user=G7OkgLAAAAAJ&hl=en

http://scholar.google.com/citations?user=G7OkgLAAAAAJ&hl=en

http://www.linkedin.com/pub/matthieu-dubarry/25/a2/764

http://www.linkedin.com/pub/matthieu-dubarry/25/a2/764

https://www.researchgate.net/profile/Matthieu_Dubarry/

https://www.researchgate.net/profile/Matthieu_Dubarry/

http://orcid.org/0000-0002-3228-1834

http://orcid.org/0000-0002-3228-1834

http://www.google.com/+MatthieuDubarry

http://www.google.com/+MatthieuDubarry

Download - Two-point State of Charge Determination In Lithium-Ion ... · Two-point State of Charge Determination In Lithium-Ion Battery Packs ... benefits to battery control and management

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