A Universal SOC ModelA Universal SOC Model

Prof. Lei HeElectric Engineering Department, UCLA

http://eda.ee.ucla.eduLHE@ee.ucla.edu

2010. 7

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MotivationMotivation

Existing WorkExisting Work

Proposed ApproachProposed Approach

Experimental ResultsExperimental Results

ConclusionsConclusions

OutlineOutline

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Demand for Rechargeable BatteriesDemand for Rechargeable BatteriesPortable Products such as laptops and cell phonesPortable Products such as laptops and cell phonesElectric Vehicles and smart gridElectric Vehicles and smart grid

Battery Management SystemBattery Management SystemTo improve the efficiency of charging and dischargingTo improve the efficiency of charging and dischargingTo prolong life spanTo prolong life spanTo satisfy the real-time requirement of powerTo satisfy the real-time requirement of power

Key Models: SOC, SOH, and SOPKey Models: SOC, SOH, and SOPSOC = State of Charge, energy remaining in a batterySOC = State of Charge, energy remaining in a batterySOH, SOP = State of health, state of power SOH, SOP = State of health, state of power

MotivationMotivation

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Battery cell is a two-terminal “black box”Battery cell is a two-terminal “black box” Battery ages (more than NBTI)Battery ages (more than NBTI) SOC needs to be monitored real-time and life-long SOC needs to be monitored real-time and life-long SOC depends on temperature (like leakage)SOC depends on temperature (like leakage) SOC needs to be measured for each cellSOC needs to be measured for each cell Measurement method should not use complicated Measurement method should not use complicated

circuits and systemscircuits and systems It has to be reliable against rare eventsIt has to be reliable against rare events It needs to be tolerant to abuse to certain degreeIt needs to be tolerant to abuse to certain degree ……..

Why It is ChallengingWhy It is Challenging

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MotivationMotivation

Existing WorkExisting Work

Proposed ApproachProposed Approach

Experimental ResultsExperimental Results

ConclusionsConclusions

OutlineOutline

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Coulomb-Counting Based EstimationCoulomb-Counting Based EstimationSoC is an integration function of time. SoC is an integration function of time.

However, error will be accumulated over time.However, error will be accumulated over time.

Voltage-Based EstimationVoltage-Based EstimationBijection between SoC and Open-Circuit Voltage (OCV)Bijection between SoC and Open-Circuit Voltage (OCV)Then how to obtain OCV from the terminal voltage and Then how to obtain OCV from the terminal voltage and

current?current?

Existing WorkExisting Work

c c 0

1SOC ( ) = SOC (0) - ( ) ,

tt I t dt

Q

Source: P. Moss, G. Au, E. Plichta, and J. P. Zheng, “An electrical circuit for modeling the dynamic response of li-ion polymer batteries,” Journal of The Electrochemical Society, 2008.

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A variety of methodsA variety of methodsWeighted Recursive Least Square RegressionWeighted Recursive Least Square RegressionAdaptive Digital FilterAdaptive Digital FilterExtended Extended KalmanKalman Filter FilterRadial Basis Function Neural NetworkRadial Basis Function Neural Network……

Simplified circuit models applied to reduced the complexitySimplified circuit models applied to reduced the complexity

Existing Voltage-based SOCExisting Voltage-based SOC

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Parameters need to be tuned for different battery types and individual Parameters need to be tuned for different battery types and individual battery cellsbattery cells

Regression for Existing ModelsRegression for Existing Models

predeterminedto bedecided

Source: H. Asai, H. Ashizawa, D. Yumoto, and H. Nakam, “Application of an Adaptive Digital Filter for Estimation of Internal Battery Conditions,” in SAE World Congress, 2005.

Source: M. Verbrugge, D. Frisch, and B. Koch, “Adaptive Energy Management of Electric and Hybrid Electric Vehicles,” Journal of Power Sources, 2005.

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MotivationMotivation

Existing WorkExisting Work

Proposed ApproachProposed Approach

Experimental ResultsExperimental Results

ConclusionConclusion

OutlineOutline

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Problem of Existing WorkProblem of Existing WorkModels are developed for specific types of batteriesModels are developed for specific types of batteries

Characteristics of Proposed ApproachCharacteristics of Proposed ApproachUsing linear system analysis but without a circuit modelUsing linear system analysis but without a circuit model

Low complexity for real-time battery managementLow complexity for real-time battery management The Only Assumption Used in Proposed ApproachThe Only Assumption Used in Proposed Approach

Within the short observing time window, a battery is Within the short observing time window, a battery is treated as a time-invariant linear system and the SoC and treated as a time-invariant linear system and the SoC and accordingly the OCV is treated as constants.accordingly the OCV is treated as constants.

Proposed ApproachProposed Approach

+

-

VLinearSystem

+

-

V

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Initial Time WindowInitial Time Window

0.1 0.2 0.3 0.4 0.5 0.6

10-2

Time (s)

Vol

tage

(V

)

2 4 6 8 10 120

1

2

Time (s)

Vol

tage

(V

)

Current Load

Voltage Response

= OCVf

+ Zero-State Response

Unit Step Function

Convolute with f (t) which satisfies

in the window.

( ) ( ) ( )f t i t t

+ Impulse Response

Vf

= OCV

uf

Impulse Stimulation

( )lim OCV

( )f

tf

v t

u t

unknownregion

2 4 6 8 10 12

3.73.83.9

44.1

T ime (s)

Vol

tage

(V

)

2 4 6 8 10 124.1

4.2

T ime (s)

Vol

tage

(V

)

2 4 6 8 10 12-0.5

0

Time (s)

Vol

tage

(V

)

2 4 6 8 10 12-5

0

5x 10

4

Time (s)

Vol

tage

(V

)

2 4 6 8 10 12-1

0

1x 10

4

Time (s)

Vol

tage

(V

)

2 4 6 8 10 12-5

0

5x 10

4

Time (s)

Vol

tage

(V

)

2 4 6 8 10 12

-400

-200

0

Time (s)

Cur

rent

(A

/m2 )

0 2 4 6 8 10 120

0.5

1

Time (s)

Cur

rent

(A

/m2 )

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0 5 10 15 20 253.6

3.7

3.8

3.9

4

4.1

T ime (s)

Vol

tage

(V

)

12 14 16 18 20 22 243.6

3.7

3.8

3.9

4

Time (s)

Vol

tage

(V

)

0 5 10 15 20 253.6

3.7

3.8

3.9

4

4.1

T ime (s)

Vol

tage

(V

)

Voltage Response Current Stimulation

12 14 16 18 20 22 24-1000

-500

0

500

1000

Time (s)

Vol

tage

(V

)

Following WindowsFollowing Windows

12 14 16 18 20 22 24

-400

-200

0

Time (s)

Cur

rent

(A

/m2 )

0 5 10 15 20 25

-400

-200

0

Time (s)

Cur

rent

(A

/m2 )

0.1 0.2 0.3 0.4 0.5 0.6

10-2

Time (s)

Vol

tage

(V

)

12 14 16 18 20 22 240

1

2

Time (s)

Vol

tage

(V

)

12 14 16 18 20 22 24

-1000

100

200

Time (s)

Vol

tage

(V

)

12 14 16 18 20 22 240

0.5

1

Time (s)

Cur

rent

(A

/m2 )

Current Stimulation

Unit Step Function

Vf

uf

Impulse Stimulation

( )lim OCV

( )f

tf

v t

u t

5 10 15 20-20

-10

0

x 10-3

Time (s)

Vol

tage

(V

)

Impulse Response

History Influence convolution

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Special SituationsSpecial Situations Case I:Case I:

uuff also converges to zero as also converges to zero as tt approaches infinity. approaches infinity. I.e., I.e., uuff((tt) = 0 for ) = 0 for tt > 0. > 0.

Then, the terminal current is constant and the battery becomes Then, the terminal current is constant and the battery becomes a pure resistance network.a pure resistance network.

Case II:Case II:The first sample of terminal current in the window is close to 0.The first sample of terminal current in the window is close to 0.Then move the window to the next sample as the starting Then move the window to the next sample as the starting

point.point.The extreme case is that the sampled current is keeps 0The extreme case is that the sampled current is keeps 0

battery in open-circuit state.battery in open-circuit state.

( )lim OCV

( )f

tf

v t

u t

OCV = ( ) ( ) effV t I t R

OCV = ( )V t

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MotivationMotivation

Existing WorksExisting Works

Proposed ApproachProposed Approach

Experimental ResultsExperimental Results

ConclusionConclusion

OutlineOutline

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Verified via Verified via dualfoil5dualfoil5, a popular battery simulator, a popular battery simulatorSimulation input: current waveform, load or power.

Battery materials: a library containing common materials.

Simulation output: SOC, OCV, terminal voltage and current. Implementation Environment

MATLAB 7.01 running on a dual-core Pentium 4 CPU at a 1.73GHz clock frequency.

Experimental SettingsExperimental Settings

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The extracted SoC fits well with the simulated data The extracted SoC fits well with the simulated data (labeled as simulated) for different current profiles.(labeled as simulated) for different current profiles.

AccuracyAccuracy

0 500 1000 1500 20000

20

40

60

80

100

Time (s)

SOC

%

SimulatedOurs

1000 1010 1020

-40

-20

0

Time (s)

Cur

rent

(A

/m2 )

(a) Periodical Discharge

0 500 1000 1500 20000

20

40

60

80

100

Time (s)

SOC

%

SimulatedOurs

0 1000 2000-28

-26

-24

Time (s)

Cur

rent

(A

/m2 )

(b) Constant Power

0 500 1000 1500 20000

20

40

60

80

100

Time (s)

SOC

%

SimulatedOurs

0 1000 2000-22

-20

-18

Time (s)

Cur

rent

(A

/m2 )

(c) Constant Load

0 500 1000 1500 20000

20

40

60

80

100

Time (s)

SOC

%SimulatedOurs

0 1000 2000

-40

-20

0

Time (s)

Cur

rent

(A

/m2 )

(d) Piecewise Discharge

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Error within 4% for different materials for active positive material / electrolyte / negative positive material of batteries (Labeled).

For each type of batteryOnly a discharge from fully-charged to empty-charged is conducted to build up the bijection between OCV and SoC.

No other tuning is needed.

UniversalityUniversality

0 500 1000 1500 2000

0%

2%

4%

6%

8%

10%

Time (s)

SOC

err

or

Graphite/LiPF6/CoO2

Tungsten oxide/Perchlorate/CoO2

Graphite/30% KOH in H2O/V2O5

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The algorithm converges quickly to the correct SoC despite an upset on SoC.

RobustnessRobustness

0.1 0.2 0.3 0.4 0.50%

50%

100%

Time (s)

SOC

err

or

0.1 0.2 0.3 0.4 0.50%

10%

20%

Time (s)

OC

V e

rror

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A Universal State-of-Charge Algorithm for BatteriesA simple yet accurate algorithm to calculate open-circuit A simple yet accurate algorithm to calculate open-circuit voltage (OCV) based on terminal voltage and current of voltage (OCV) based on terminal voltage and current of the battery.the battery.

Only linear system analysis used without any circuit Only linear system analysis used without any circuit model and hence universality to discharge current profile model and hence universality to discharge current profile and any battery types without modification.and any battery types without modification.

Experiments showing less than 4% SoC error compared to Experiments showing less than 4% SoC error compared to detailed battery simulation.detailed battery simulation.

Future workFuture workFixed point and FPGA implementationFixed point and FPGA implementation

Hardware in loop testingHardware in loop testing

ConclusionsConclusions