Circuit Model of 100 Ah Lithium Polymer Battery Cell: Bong G. Kim, Dipesh D. Patel, Ziyad M. Salameh
Circuit Model of 100 Ah Lithium Polymer Battery Cell: Bong G. Kim, Dipesh D. Patel, Ziyad M. Salameh
Circuit Model of 100 Ah Lithium Polymer Battery Cell: Bong G. Kim, Dipesh D. Patel, Ziyad M. Salameh
ABSTRACT
This paper presents a circuit model for a 100 Ah Lithium Polymer Battery that takes into account the effect of temperature and discharge rates. This is done by studying the behavior of two advanced 100 Ah Lithium Polymer Battery cells
under different load condition and at different temperatures, to extract the RC parameters needed to develop the equivalent circuit model. This paper presents a methodology to identify the several parameters of the model. The parameters
of the circuit model depend on both, battery cell temperature and discharging current rate. The model is validated by
comparing simulation results with experimental data collected through battery cell tests. The simulation results of the
battery cell model are obtained using MATLAB, and the experimental data are collected through the battery test system
at battery evaluation lab at University of Massachusetts Lowell. This model is useful for optimization of the battery
management system which is needed to run a battery bank safely in an electric car.
Keywords: Lithium Polymer Battery Cell; Battery Circuit Model; Battery Cell Model Simulation
1. Introduction
Battery powered electric vehicles are becoming more and
more attractive with the advancement of new battery
technology that have higher power and energy density,
and it becomes necessary reliable models for design and
simulation of the batteries. 100 Ah Lithium Polymer Battery cells have been tested for cycling, fast chargeability,
realistic load test, self discharge, and life cycle. From
these test results, the battery has high energy density
(373 Wh/L) and specific energy (146 Wh/kg), less self
discharge rate (less than 3% during month), it can be fast
charged, and the battery cell voltage remains within the
limit during the realistic load test. The battery cell has a
long life cycle, more over the battery capacity decreased
very slowly with cycling. The lithium polymer battery
cell is much lighter than other batteries cell and it is one
of the long term criteria for electric vehicle batteries (energy density greater than 300 Wh/L, life cycle over 1000
cycles, and recharge time between 3 to 6 hours) [1].
Two 100 Ah Lithium Battery cells were tested for model.
One is old battery cell which the battery has only 90% of
total capacity and the other one is new battery cell which
has fully 100% of capacity. The old battery cell lost more
than 10% of total capacity because the battery was cycled
more than 700 times. The reason to pick a new and an
old battery cell for the test is to find how the battery SOC
Open Access
Current Regulator
( Up to 10Volts and 320Amps)
Rs or Voc l m am k m SOC n
n0 m0
(1)
Li-Poly Battery
Cell
A/D and D/A
Converter
Chamber
(Heating and Cooling)
MUX
Computer
C(short)
C(long)
R(short)
R(long)
Vsoc
Rs
Cb
Rd
Voc
Current
Source
3.7
3.6
3.5
3.4
3.3
5700
5800
5900
6000 6100
Time (sec.)
6200
6300
6400
Open circuit voltage of new cell @ 0 deg celcious for different discharge rates
C/10 (sim.)
C/10 (meas.)
C/4 (sim.)
C/4 (meas.)
C/2 (sim.)
C/2 (meas.)
C (sim.)
C (meas.)
0.9
0.8
0.7
0.6
0.5
0.4
State of charge (SOC)
0.3
0.2
0.1
Figure 5. Simulation and experimental result for Voc at various discharge current rate and ambient temperature 0C (new
cell).
Table 1. Constant values for open circuit voltage of new battery.
bn
a2
a1
a0
b7
7.3705
14.741
0.51075
6.1005
26.39
b6
29.075
77.1571
42.848
47.19625
123.7646
60.662
b5
48.6737
167.355
153.79
64.16424125
186.641083
17.9
b4
45.1448
192.389
219.71
47.6905
164.7134
64.28
b3
25.0809
125.036
159.4
22.174825
94.42635
77.062
b2
8.2449
45.3
61.088
6.8331875
34.532775
36.402
b1
1.4449
8.3407
11.983
1.263825
6.9768
7.851
b0
0.1049
0.622
2.6403
0.1084125
0.623575
0.6342
a2
a1
b7
0.0119488
0.1033125
b6
0.0598998
0.4332045
a0
0.00246575
0.0653805
0.075432
0.06938275
0.4711365
0.07543
b5
0.1059938
0.6961025
0.22984
0.164565
0.96775
0.22984
b4
0.0790638
0.5003425
0.20603
0.19417
1.12784
0.20603
b3
0.0179244
0.1190662
0.0082249
0.119324363
0.82481618
0.008225
b2
0.0065888
0.035942
0.075254
0.03827267
0.41748149
0.074943
b1
0.0050703
0.02809715
0.035913
0.0065727
0.1515841
0.03675
b0
0.000772
0.0046413
0.0083023
0.00163701
0.037337975
0.010669
Open Access
JPEE
a2
a1
a0
b7
15.4438
30.8875
26.99555
71.132
23.85
b6
62.5562
125.1125
104.2017
269.6585
106.18
b5
103.4
213.155
26.862
164.184
424.648
167.458
b4
90.2385
200.6955
83.366
136.5385
364.2105
106.674
b3
44.966
114.8915
100.83
64.7615
187.6575
7.43
b2
12.9533
40.8165
58.564
17.671425
59.75125
22.635
b1
2.0656
8.4375
16.704
2.633675
11.147
9.8573
b0
0.1541
0.814
1.6986
0.181375
0.9936
1.273
a2
a1
a0
b8
0.3272625
0.654525
0.3272625
0.654525
b7
2.3734983
8.657718
7.8229
1.73876075
4.849293
2.745
b6
6.915181
31.568974
35.4135
7.5499185
35.377399
40.4914
b5
10.79453
55.20962
67.017
13.353155
70.56137
87.486
b4
9.9834525
54.46981
68.734
14.25865925
80.1097235
102.913
b3
5.63988
31.99052
41.288
9.46780248
54.9051424
71.799
b2
1.9100685
11.099369
14.544
3.888754375
22.8884275
30.2023
b1
0.3561925
2.10245615
2.7878
0.94612048
5.58207315
7.3937
b0
0.0281117
0.1681538
0.22801
0.122444075
0.71324865
0.94818
4.5
4.375
4.25
4.125
4
3.875
3.75
3.625
3.5
3.375
3.25
3.125
3
Open circuit voltage of old cell @ C/10 discharge rate for different temperature
40 deg cel. (sim.)
40 deg cel. (meas.)
20 deg cel. (sim.)
20 deg cel. (meas.)
0 deg cel. (sim.)
0 deg cel. (meas.)
0.9
0.8
0.7
0.6
0.5
0.4
State of charge (SOC)
0.3
0.2
0.1
Figure 6. Simulation and experimental result Voc at C/10 and various ambient temperatures (old cell).
12
11
10
9
8
7
6
5
4
3
2
x 10
-3
0.9
0.8
0.7
0.6
0.5
0.4
State of charge (SOC)
0.3
0.2
0.1
DC resistance (ohm)
Figure 7. Simulation and experimental result for Rs at variousdischarge current ratesand ambient temperature 0C (old cell).
0.012
0.011
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
0.9
0.8
0.7
0.6
0.5
0.4
State of charge (SOC)
0.3
0.2
0.1
Figure 8. Simulation and experimental result for Rs at C/10 and various ambient temperatures (old cell).
Terminal voltage different cells @ C discharge rate @ 20 deg celcious
4.2
old (meas.)
old (sim.)
new (meas.)
new (sim.)
4
3.8
3.6
3.4
3.2
3
2.8
1000
2000
3000
7000
8000
9000
10000
Figure 9. Simulation and experimental pulse discharge test result at C and ambient temperature 20C.
Open Access
JPEE
3.8
3.6
3.4
3.2
3
2.8
2.6
1000
2000
3000
4000
Time (sec.)
5000
6000
7000
Figure 10. Simulation and experimental constant discharge test at C/2 and at ambient temperature 0C.
(2)
Behavior of the battery in static as well as dynamic response is very non-linear. Several simulation methods
have been approached. Proposed method is circuit-parameter based procedure of equation solving. The equations are written in MATLAB. Simulation is for discharge only as we have done the test for discharge. Values of current for simulation are directly taken from test
results so that accuracy is maintained. For the static response the values of capacitances and resistances depend
on SOC. Value of capacitances at that SOC of battery
measured from dynamic response are taken. The effect of
capacitances, in both the static and dynamic response, die
out after the short and long time constants and resulting
terminal voltage depends on battery internal dc resistance,
short time dc resistance and long time dc resistance. Parameters in the circuit depend on SOC, temperature, rate
of discharge. Circuits response can be explained by
equation which is used for the simulation.
m = initial SOC of the battery before discharge;
Ccapacity = capacity of the battery.
T mCcapacity
t SOC t Ccapacity
T t
Rs Cs ,
t T
Vop t I t Rdc t I t Rs t 1 e
T s t
R C
V t Vop t I t Rdc t Rs t I t Rl t 1 e l l , t T s
Vop t I t Rdc t Rs t Rl t ,
t T s l
s Rs Cs , l Rl Cl
Open Access
(3)
JPEE
4.5
Terminal voltage (V)
4
3.5
3
2.5
2
1000
2000
3000
4000
5000
Time (sec.)
6000
7000
8000
9000
Figure 11. Simulation and experimental pulse discharge test result at C and ambient temperature 0C.
Terminal voltage different cells @ C discharge rate @ 40 deg celcious
4.5
old (meas.)
old (sim.)
new (meas.)
new (sim.)
4.25
4
3.75
3.5
3.25
3
1000
2000
3000
7000
8000
9000
10000
Figure 12. Simulation and experimental pulse discharge test result at C and ambient temperature 40C.
Terminal voltage of different cells @ C/4 discharge rate @ 0 deg celcious
4.5
new (meas.)
new (sim.)
old (meas.)
old (sim.)
3.5
2.5
2000
4000
6000
8000
Time (sec.)
10000
12000
14000
Figure 13. Simulation and experimental constant discharge test result at C/4 and ambient temperature 0C
Open Access
JPEE
than 30 mV, which is less than 3% error margin. Therefore, the simulation results of the battery cell circuit
model match well with the experimental data.
4. Conclusion
A nonlinear battery cell circuit model which is based on
relationship between the battery cell terminal voltage and
battery cell state of discharge (SOC) characteristic under
different discharge current rates and different ambient
temperatures condition has been developed. The nonlinear battery cell circuit model can be used to accurately
model and predict battery cell performance from the experimental and simulation test results. The model will
greatly help research on circuit simulation, multi-cell
battery analysis, battery cell performance prediction and
optimization, and battery cell management. The experimental and simulation of battery circuit cell modeling is
within 3% of error margin. The lithium battery cell has
the best performance when the cell is at room temperature (20C) and has C/10 discharge current rate. The
lithium polymer battery cell holds more than 70% of its
capacity between 3.2 and 3.7 volts. Based on this circuit
model, it could be developed with other models like
fuzzy or neuro-fuzzy logic.
[3]
[4]
[5]
[6]
J. C. Zhang, S. Ci and H. Sharif, An Enhanced CircuitBased Model for Single-CellBattery, IEEE Applied
Power Electronic Conference and Exposition (APEC),
February 21-25, 2010, Palm Springs, pp. 672-675.
[7]
B. G. Kim, F. P. Tredeau and Z. M. Salameh, Performance Evaluation of Lithium Polymer Batteries for Use in
Electric Vehicles, IEEE Vehicle Power and Propulsion
Conference (VPPC), September 3-5, 2008, Harbin, pp.
1-5.
REFERENCES
[1]
Z. M. Salameh and B. G. Kim, Advanced Lithium Polymer Batteries, IEEE Power and Energy Society General
Open Access
JPEE