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
 Adaptive Digital Filter
 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
decided
predetermined
Source: M. Verbrugge, D. Frisch, and B. Koch, “Adaptive Energy Management of Electric and
Hybrid Electric Vehicles,” Journal of Power Sources, 2005.
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.
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
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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.
+
V
-
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Linear
System
+
V
-
Initial Time Window
Impulse Stimulation
Current Load
-200
-400
2
4
6
T ime (s)
8
10
1
Current (A/m 2)
Current (A/m 2)
0
12
0.5
0
0
Voltage (V)
4
8
10
12
= OCV
0
-0.5
2
in the window.
2
4
6
T ime (s)
8
10
12
4
6
T ime (s)
8
10
1
0
2
x 10
5
2
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4
6
T ime (s)
8
10
12
10
12
4
6
T ime (s)
8
10
12
10
12
= OCVf
4
0
-5
2
4
6
T ime (s)
8
lim
+ Impulse Response
10
t 
-2
0.1
12
Unit Step Function
8
0
+ Zero-State Response
2
6
T ime (s)
Vf
Convolute with f (t)
which satisfies
Voltage (V)
4.1
4
4
-5
f (t )  i(t )   (t )
4.2
Voltage (V)
Voltage (V)
Voltage (V)
unknown
region
6
T ime (s)
Voltage (V)
2
x 10
5
Voltage (V)
Voltage (V)
Voltage Response
4.1
4
3.9
3.8
3.7
2
1
x 10
0.2
0.3
T ime (s)
0.4
0.5
0.6
uf
4
0
-1
2
4
6
T ime (s)
8
10
12
v f (t )
u f (t )
 OCV
Following Windows
Current V
Stimulation
f
History Influence
3.90
-10
3.8
-20
3.8
5
10
3.7
3.7
3.6
12
0
15
convolution
20
14 5
16 10
1000
0
-200
500
-400
00
5
18
15 20
T ime (s)
2022
24
25
Current (A/m 2)
Current (A/m 2)
0
-200
16
18
T ime (s)
20
22
-1000
12
-2
10
14
16
0.2
24
Voltage (V)
Voltage (V)
1
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16
18
T ime (s)
20
22
25
20
0.4
22
0.5
24
0.6
1
0.5
0
12
14
16
18
T ime (s)
20
22
24
uf
2
14
18
T ime (s)
0.3
T ime (s)
Unit Step Function
0
12
20
Impulse Stimulation
Current Stimulation
14
15
Impulse Response
0.1
-400
12
10
T ime (s)
-500
T ime (s)
Voltage (V)
Voltage(V)
(V)
Voltage
-3
4
3.9 x 10
VoltageCurrent
(V)
(A/m 2)
Voltage Response
4.14
24
200
100
0
-100
12
14
16
18
T ime (s)
20
22
24
lim
t 
v f (t )
u f (t )
 OCV
Special Situations

Case I:
lim
t 
v f (t )
u f (t )
 OCV
 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.
Simulated
Ours
100
80
40
20
0
SOC %
60
Current (A/m2)
SOC %
80
0
Simulated
Ours
100
0
-20
60
Current (A/m2)

40
-40
1000
500
1010
Time (s)
20
1020
1000
Time (s)
1500
0
2000
0
Simulated
Ours
1000
Time (s)
1000
Time (s)
2000
1500
2000
Simulated
Ours
100
0
-18
60
-20
40
-22
20
0
500
1000
Time (s)
2000
1000
Time (s)
(c) Constant Load
1500
2000
0
Current (A/m2)
40
SOC %
60
Current (A/m2)
SOC %
0
80
20
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-28
(b) Constant Power
80
0
-26
500
(a) Periodical Discharge
100
-24
0
0
-20
-40
0
500
1000
Time (s)
1000
Time (s)
2000
1500
(d) Piecewise Discharge
2000
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
SOC error
8%
Tungsten oxide/Perchlorate/CoO2
Graphite/30% KOH in H2O/V2O5
6%
4%
2%
0%
0
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500
1000
Time (s)
1500
2000
Robustness
The algorithm converges quickly to the correct SoC
despite an upset on SoC.
100%
OCV error
SOC error

50%
0%
0.1
0.2
0.3
Time (s)
0.4
0.5
0.1
0.2
0.3
Time (s)
0.4
0.5
20%
10%
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0%
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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