There are two special situations where our method described before is not effective

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```					A Universal SOC Model

Prof. Lei He
Electric Engineering Department, UCLA
http://eda.ee.ucla.edu
LHE@ee.ucla.edu

2010. 7
Outline
   Motivation

   Existing Work

   Proposed Approach

   Experimental Results

   Conclusions

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Motivation
   Demand for Rechargeable Batteries
Portable Products such as laptops and cell phones
Electric Vehicles and smart grid
   Battery Management System
To improve the efficiency of charging and discharging
To prolong life span
To satisfy the real-time requirement of power
   Key Models: SOC, SOH, and SOP
SOC = State of Charge, energy remaining in a battery
SOH, SOP = State of health, state of power

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Why It is Challenging
 Battery cell is a two-terminal “black box”
 Battery ages (more than NBTI)
 SOC needs to be monitored real-time and life-long
 SOC depends on temperature (like leakage)
 SOC needs to be measured for each cell
 Measurement method should not use complicated
circuits and systems
 It has to be reliable against rare events
 It needs to be tolerant to abuse to certain degree
 ….

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Outline
   Motivation

   Existing Work

   Proposed Approach

   Experimental Results

   Conclusions

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Existing Work
   Coulomb-Counting Based Estimation
 SoC is an integration function of time.
1 t
SOCc (t ) = SOCc (0) -  I (t ) dt ,
Q 0
 However, error will be accumulated over time.
   Voltage-Based Estimation
 Bijection between SoC and Open-Circuit Voltage (OCV)
 Then how to obtain OCV from the terminal voltage and
current?

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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Existing Voltage-based SOC
   A variety of methods
 Weighted Recursive Least Square Regression
 Extended Kalman Filter
 Radial Basis Function Neural Network
…
Simplified circuit models applied to reduced the complexity

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Regression for Existing Models

to be                                predetermined
decided

Source: M. Verbrugge, D. Frisch, and B. Koch, “Adaptive Energy Management of Electric and   Source: H. Asai, H. Ashizawa, D. Yumoto, and H. Nakam, “Application of an Adaptive Digital
Hybrid Electric Vehicles,” Journal of Power Sources, 2005.                                  Filter for Estimation of Internal Battery Conditions,” in SAE World Congress, 2005.

Parameters need to be tuned for different battery types and individual
battery cells
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Outline
   Motivation

   Existing Work

   Proposed Approach

   Experimental Results

   Conclusion

9 of 34
Proposed Approach
   Problem of Existing Work
Models are developed for specific types of batteries
   Characteristics of Proposed Approach
Using linear system analysis but without a circuit model
Low complexity for real-time battery management
   The Only Assumption Used in Proposed Approach
Within the short observing time window, a battery is
treated as a time-invariant linear system and the SoC and
accordingly the OCV is treated as constants.

+                                     +
Linear           V
V

-
System               -

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Initial Time Window
0                                                                                                    1
Current (A/m 2)

Current (A/m 2)
-200                                                                                                 0.5

-400
0
2      4       6       8   10   12                                                                   0              2             4           6              8    10   12
T ime (s)                                                                                                                      T ime (s)

Voltage Response                                                                                 x 10
4                                   Vf
5

Voltage (V)
4.1
Voltage (V)

4
3.9                                                                                                       0
3.8
3.7                                                                                                 -5
2             4           6              8    10   12
2      4       6
T ime (s)
8   10   12
Convolute with f (t)                                                                                 T ime (s)
unknown
region                                                               which satisfies
= OCV                     f (t )  i(t )   (t )                                                4
= OCVf
x 10
Voltage (V)

5

Voltage (V)
4.2
in the window.                                             0
4.1                                                                                                 -5
2      4       6       8   10   12                                                                                  2             4           6              8    10   12
T ime (s)                                                                                                                      T ime (s)
v f (t )
lim                OCV
+ Zero-State Response                                                                                                + Impulse Response                                       t    u f (t )
0
Voltage (V)
Voltage (V)

-2
10

-0.5
2      4       6       8   10   12                                                                        0.1               0.2           0.3          0.4       0.5   0.6
T ime (s)                                                                                                                       T ime (s)

Unit Step Function                                                                                      x 10
4                              uf
1
Voltage (V)

2
Voltage (V)

0
1
-1
2             4        6             8    10   12
0
2      4       6       8   10   12                                                                                                         T ime (s)
T ime (s)

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Following Windows
Voltage Response                                                                                                           Stimulation
Current Vf
4
4.1                                                                                                          1000
0

VoltageCurrent (A/m 2)
4
3.9 x 10
-3   History Influence                                    convolution                              -200
500
Voltage (V)
Voltage (V)

(V)
0
3.9                                                                                                          -400
-10
3.8                                                                                                                 00               5               10                15         20     25
-20
3.8                                                                                                                                                       T ime (s)
5        10               15         20
3.7
3.7                              T ime (s)                                                                   -500
Impulse Response
3.6                                                                                                         -1000

Voltage (V)
0
12         14 5     16 10        18     15 20       2022   25
24                                                   12              14          16            18             20    22    24
-2
T ime (s)                                                                   10                                           T ime (s)

0.1             0.2              0.3           0.4       0.5    0.6
T ime (s)

Current Stimulation                                                                                           Impulse Stimulation
1

Current (A/m 2)
0
Current (A/m 2)

0.5
-200
v f (t )
-400
12            14       16           18            20    22    24
0
12              14          16            18             20        22    24     lim                OCV
T ime (s)                                t    u f (t )
T ime (s)

Unit Step Function                                                                                                                                 uf
200
Voltage (V)

2
Voltage (V)

100
1                                                                                                         0
-100
0                                                                                                            12           14             16            18             20     22    24
12      14       16           18            20    22    24
T ime (s)
T ime (s)

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Special Situations                            lim
v f (t )
 OCV
t    u f (t )
   Case I:
 uf also converges to zero as t approaches infinity.
 I.e., uf(t) = 0 for t > 0.
 Then, the terminal current is constant and the battery becomes
a pure resistance network.

OCV = V (t )  I (t ) Reff
Case II:
 The first sample of terminal current in the window is close to 0.
 Then move the window to the next sample as the starting point.
 The extreme case is that the sampled current is keeps 0
 battery in open-circuit state.

OCV = V (t )
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Outline
   Motivation

   Existing Works

   Proposed Approach

   Experimental Results

   Conclusion

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Experimental Settings
   Verified via dualfoil5, a popular battery simulator
Simulation 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.

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Accuracy
   The extracted SoC fits well with the simulated data
(labeled as simulated) for different current profiles.
100                                               Simulated              100                                               Simulated
Ours                                                                     Ours
80                                                                       80

SOC %
SOC %

60                                                                       60

Current (A/m2)
Current (A/m2)

0                                                                      -24

40                        -20                                            40                        -26
-40
20                         1000       1010     1020
20                        -28
0     1000     2000
Time (s)                                                                 Time (s)
0                                                                        0
0                     500        1000       1500    2000                 0                     500        1000      1500     2000
Time (s)                                                                 Time (s)
(a) Periodical Discharge                                                   (b) Constant Power

100                                               Simulated              100                                               Simulated
Ours                                                                     Ours
80                                                                       80
SOC %
SOC %

60                                                                       60       Current (A/m2)
Current (A/m2)

-18                                                                        0

40                                                                       40                        -20
-20
-40
20                        -22
0     1000     2000
20                              0     1000     2000
Time (s)                                                                 Time (s)
0                                                                        0
0                     500        1000       1500    2000                 0                     500        1000      1500     2000
Time (s)                                                                 Time (s)
(c) Constant Load                                                     (d) Piecewise Discharge

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Universality
   Error within 4% for different materials for active positive
material / electrolyte / negative positive material of
batteries (Labeled).
   For each type of battery
Only a discharge from fully-charged to empty-charged is
conducted to build up the bijection between OCV and SoC.
No other tuning is needed.
10%
Graphite/LiPF 6/CoO2
8%
Tungsten oxide/Perchlorate/CoO2
6%          Graphite/30% KOH in H2O/V2O5
SOC error

4%

2%

0%
0   500           1000           1500       2000
Time (s)
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Robustness
       The algorithm converges quickly to the correct SoC
despite an upset on SoC.

100%
SOC error

50%

0%
0.1   0.2       0.3    0.4   0.5
Time (s)
20%
OCV error

10%

0%
0.1   0.2       0.3    0.4   0.5
Time (s)

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Conclusions
   A Universal State-of-Charge Algorithm for Batteries
A simple yet accurate algorithm to calculate open-circuit
voltage (OCV) based on terminal voltage and current of
the battery.
Only linear system analysis used without any circuit
model and hence universality to discharge current profile
and any battery types without modification.
Experiments showing less than 4% SoC error compared
to detailed battery simulation.
   Future work
Fixed point and FPGA implementation
Hardware in loop testing

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