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PSpice and LTspice model of a Lithium-Ion battery
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 1
Concept of Device Modeling
(Version 1.0)
Bee Technologies Inc
http://www.bee-tech.info/
PSpice model of a Lithium-Ion battery
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 2
OCV Table
• C, battery capacity in ampere-hours
• SOC=100, the initial state of charge = fully
• OCV, battery open circuit voltage
R1
GND
V1
Hi
IN-
OUT+
OUT-
IN+
G6
GVALUE
GND
C2
7
R2
IN-
OUT+
OUT-
IN+
G1
GVALUE
0
N
1
C1
0
IN+
IN-
OUT+
OUT-
E3
EVALUE
12
IN+
IN-
OUT+
OUT-
E2
EVALUE
0
3
VMAX
100
4
U1
ETABLE
2
R5
R4
GND
D1
D2
0
D3
9
SOC
PARAMETERS:
C = 1.4
Tscale = 3600
SOC = 100
C3
R3
OCV
1.Simulation result (Tscale = 1, 3600)
Tscale=1 Tscale=3600
• Simulated result shows battery voltage discharging.
• C cell (1.4 amp / 1hr, 3.6V) Spec.
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 3
Time
0s 1.0s 2.0s 3.0s 3.6s
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 10Ks 20Ks 30Ks 36Ks
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Total job time (using Solver 1) = 0.27s, 10ms/step.Total job time (using Solver 1) = 649.34s, 10ms/step.
1.Simulation result (Tscale = 1, 3600)
Tscale=1 Tscale=3600
• Simulated result shows battery voltage discharging.
• C cell (1.4 amp / 3600s, 3.6V) Spec.
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 4
Time
0s 1.0s 2.0s 3.0s 3.6s
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 10Ks 20Ks 30Ks 36Ks
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Total job time (using Solver 1) = 0.27s, 10ms/step.Total job time (using Solver 1) = 2.52s, 100s/step.
2.OCV table = Electrochemical characteristics of Li-ion
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 5
3
3.5
4
4.5
5
0 20 40 60 80 100
OCV[V]
SOC [%]
SOC(%) OCV(V)
1.03217 3.54396
5.60322 3.60771
10.1743 3.67558
16.2198 3.71877
24.6247 3.76401
29.3432 3.78252
36.7158 3.81131
44.6783 3.83393
52.9357 3.8545
59.866 3.87918
65.7641 3.89974
74.0214 3.94293
79.9196 3.97172
87.4397 4.03136
93.3378 4.08483
100.854 4.1671
3.Simulation result (G6, Function)
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 6
V(U1.G6:OUT+,U1.G6:OUT-)
0V 1.0V 2.0V 3.0V 4.0V
I(U1.G6)
0A
1.0A
2.0A
3.0A
4.0A
4.Initial Voltage (Charge/Discharge)
Charge Discharge
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 7
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
5. Discharge Cycle
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 8
Value increase as
cycle time increase.
Value increase as
cycle time increase.
V1
Hi
IN-
OUT+
OUT-
IN+
G6
GVALUE
GND
C2
7
R2
IN-
OUT+
OUT-
IN+
G1
GVALUE
0
N
1
C1
0
IN+
IN-
OUT+
OUT-
E3
V(OCV)
EVALUE
R1
12
IN+
IN-
OUT+
OUT-
E2
EVALUE
0
GND
3
C3
VMAX
100
4
R3
{6.8/C}
U1
ETABLE
2
R5
R4
GND
D1
D2
0
D3
9
PARAMETERS:
C = 1.4
Tscale = 3600
SOC = 100
SOC
OCV
5. Discharge Cycle
Charge Discharge
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 9
Time
0s 1.0s 2.0s 3.0s 4.0s
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 1.0s 2.0s 3.0s 4.0s
V(Hi)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
cycle factor=1
cycle factor=2
cycle factor=1
cycle factor=2
6. E2
Charge Discharge
• E2={0.5*exp(-V(SOC)/A)}
• A=10
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 10
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
6. E2
Charge Discharge
• E2={0.5*exp(-V(SOC)/A)}
• A=20 [default]
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 11
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
6. E2
Charge Discharge
• E2={0.5*exp(-V(SOC)/A)}
• A=40
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 12
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
Time
0s 1.0s 2.0s 3.0s 4.0s
V(U1:Hi) V(U1.OCV)
0V
1.0V
2.0V
3.0V
4.0V
5.0V
V(U1.SOC)@1
0V 20V 40V 60V 80V 100V
V(U1.N)
0V
100mV
200mV
300mV
400mV
500mV
6. E2
• {0.5*exp(-V(SOC)/A)}
• List: 10, 20, 40
All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 13
A=10 A=20 A=40

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Concept of modeling of Lithium ion batteries (v1)

  • 1. PSpice and LTspice model of a Lithium-Ion battery All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 1 Concept of Device Modeling (Version 1.0) Bee Technologies Inc http://www.bee-tech.info/
  • 2. PSpice model of a Lithium-Ion battery All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 2 OCV Table • C, battery capacity in ampere-hours • SOC=100, the initial state of charge = fully • OCV, battery open circuit voltage R1 GND V1 Hi IN- OUT+ OUT- IN+ G6 GVALUE GND C2 7 R2 IN- OUT+ OUT- IN+ G1 GVALUE 0 N 1 C1 0 IN+ IN- OUT+ OUT- E3 EVALUE 12 IN+ IN- OUT+ OUT- E2 EVALUE 0 3 VMAX 100 4 U1 ETABLE 2 R5 R4 GND D1 D2 0 D3 9 SOC PARAMETERS: C = 1.4 Tscale = 3600 SOC = 100 C3 R3 OCV
  • 3. 1.Simulation result (Tscale = 1, 3600) Tscale=1 Tscale=3600 • Simulated result shows battery voltage discharging. • C cell (1.4 amp / 1hr, 3.6V) Spec. All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 3 Time 0s 1.0s 2.0s 3.0s 3.6s V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 10Ks 20Ks 30Ks 36Ks V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Total job time (using Solver 1) = 0.27s, 10ms/step.Total job time (using Solver 1) = 649.34s, 10ms/step.
  • 4. 1.Simulation result (Tscale = 1, 3600) Tscale=1 Tscale=3600 • Simulated result shows battery voltage discharging. • C cell (1.4 amp / 3600s, 3.6V) Spec. All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 4 Time 0s 1.0s 2.0s 3.0s 3.6s V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 10Ks 20Ks 30Ks 36Ks V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Total job time (using Solver 1) = 0.27s, 10ms/step.Total job time (using Solver 1) = 2.52s, 100s/step.
  • 5. 2.OCV table = Electrochemical characteristics of Li-ion All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 5 3 3.5 4 4.5 5 0 20 40 60 80 100 OCV[V] SOC [%] SOC(%) OCV(V) 1.03217 3.54396 5.60322 3.60771 10.1743 3.67558 16.2198 3.71877 24.6247 3.76401 29.3432 3.78252 36.7158 3.81131 44.6783 3.83393 52.9357 3.8545 59.866 3.87918 65.7641 3.89974 74.0214 3.94293 79.9196 3.97172 87.4397 4.03136 93.3378 4.08483 100.854 4.1671
  • 6. 3.Simulation result (G6, Function) All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 6 V(U1.G6:OUT+,U1.G6:OUT-) 0V 1.0V 2.0V 3.0V 4.0V I(U1.G6) 0A 1.0A 2.0A 3.0A 4.0A
  • 7. 4.Initial Voltage (Charge/Discharge) Charge Discharge All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 7 Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V
  • 8. 5. Discharge Cycle All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 8 Value increase as cycle time increase. Value increase as cycle time increase. V1 Hi IN- OUT+ OUT- IN+ G6 GVALUE GND C2 7 R2 IN- OUT+ OUT- IN+ G1 GVALUE 0 N 1 C1 0 IN+ IN- OUT+ OUT- E3 V(OCV) EVALUE R1 12 IN+ IN- OUT+ OUT- E2 EVALUE 0 GND 3 C3 VMAX 100 4 R3 {6.8/C} U1 ETABLE 2 R5 R4 GND D1 D2 0 D3 9 PARAMETERS: C = 1.4 Tscale = 3600 SOC = 100 SOC OCV
  • 9. 5. Discharge Cycle Charge Discharge All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 9 Time 0s 1.0s 2.0s 3.0s 4.0s V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 1.0s 2.0s 3.0s 4.0s V(Hi) 0V 1.0V 2.0V 3.0V 4.0V 5.0V cycle factor=1 cycle factor=2 cycle factor=1 cycle factor=2
  • 10. 6. E2 Charge Discharge • E2={0.5*exp(-V(SOC)/A)} • A=10 All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 10 Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V
  • 11. 6. E2 Charge Discharge • E2={0.5*exp(-V(SOC)/A)} • A=20 [default] All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 11 Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V
  • 12. 6. E2 Charge Discharge • E2={0.5*exp(-V(SOC)/A)} • A=40 All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 12 Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V Time 0s 1.0s 2.0s 3.0s 4.0s V(U1:Hi) V(U1.OCV) 0V 1.0V 2.0V 3.0V 4.0V 5.0V
  • 13. V(U1.SOC)@1 0V 20V 40V 60V 80V 100V V(U1.N) 0V 100mV 200mV 300mV 400mV 500mV 6. E2 • {0.5*exp(-V(SOC)/A)} • List: 10, 20, 40 All Rights Reserved Copyright (C) Bee Technologies Corporation 2009 13 A=10 A=20 A=40