Low-order, explicit models of lithium ion cells are critical for real-time battery management system (BMS) applications. This paper presents a seventh-order, electrolyte enhanced single particle model (ESPM) with electrolyte diffusion and temperature dependent parameters (ESPM-T). The impedance transfer function coefficients are explicit in terms of the model parameters, simplifying the implementation of temperature dependence. The ESPM-T model is compared with a commercially available finite volume based model and results show accurate matching of pulse responses over a wide range of temperature (T) and C-rates (I). The voltage response to 30 s pulse charge–discharge current inputs is within 5% of the commercial code for 25°C<T<50°C at I12.5C and -10°C<T<50°C at I1C for a graphite/nickel cobalt manganese (NCM) lithium ion cell.

References

References
1.
Office of the Press Secretary,
2013
, The White House Press Release,
Washington, DC
, http://www.whitehouse.gov/the-press-office
2.
Thomas
,
C. E. S.
,
2009
, “
Transportation Options in a Carbon-Constrained World: Hybrids, Plug-In Hybrids, Biofuels, Fuel Cell Electric Vehicles, and Battery Electric Vehicles
,”
Int. J. Hydrogen Energy
,
34
(23)
, pp.
9279
9296
.10.1016/j.ijhydene.2009.09.058
3.
Rahn
,
C. D.
, and
Wang
,
C. Y.
,
2013
,
Battery Systems Engineering
,
Wiley
,
State College, PA
.
4.
Plett
,
G. L.
,
2004
, “
Extended Kalman Filtering for Battery Management Systems of LiPB-Based HEV Battery Packs Part 1. Background
,”
J. Power Sources
,
134
(2)
, pp.
252
261
.10.1016/j.jpowsour.2004.02.031
5.
Plett
,
G. L.
,
2004
, “
Extended Kalman Filtering for Battery Management Systems of LiPB-Based HEV Battery Packs Part 2. Modeling and Identification
,”
J. Power Sources
,
134
(2)
, pp.
262
276
.10.1016/j.jpowsour.2004.02.032
6.
Plett
,
G. L.
,
2004
, “
Extended Kalman Filtering for Battery Management Systems of LiPB-Based HEV Battery Packs Part 3. State and Parameter Estimation
,”
J. Power Sources
,
134
(2)
, pp.
277
292
.10.1016/j.jpowsour.2004.02.033
7.
Verbrugge
,
M. W.
, and
Conell
,
R. S.
,
2002
, “
Electrochemical and Thermal Characterization of Battery Modules Commensurate With Electric Vehicle Integration
,”
J. Electrochem. Soc.
,
149
(
1
), pp.
A45
A53
.10.1149/1.1426395
8.
Verbrugge
,
M. W.
, and
Liu
,
P.
,
2007
, “
Electrochemical Characterization of High-Power Lithium Ion Batteries Using Triangular Voltage and Current Excitation Sources
,”
J. Power Sources
,
174
(1)
, pp.
2
8
.10.1016/j.jpowsour.2007.03.019
9.
Schweighofer
,
B.
,
Raab
,
K. M.
, and
Brasseur
,
G.
,
2003
, “
Modeling of High Power Automotive Batteries by the Use of an Automated Test System
,”
IEEE Trans. Instrum. Meas.
,
52
(
4
), pp.
1087
1091
.10.1109/TIM.2003.814827
10.
Moss
,
P. L.
,
Au
,
G.
,
Plichta
,
E. J.
, and
Zheng
,
J. P.
,
2008
, “
An Electrical Circuit for Modeling the Dynamic Response of Li-Ion Polymer Batteries
,”
J. Electrochem. Soc.
,
155
(
12
), pp.
A986
A994
.10.1149/1.2999375
11.
Smith
,
K. A.
,
Rahn
,
C. D.
, and
Wang
,
C. Y.
,
2007
, “
Control Oriented 1D Electrochemical Model of Lithium Ion Battery
,”
Energy Convers. Manage.
,
48
(9)
, pp.
2565
2578
.10.1016/j.enconman.2007.03.015
12.
Smith
,
K. A.
,
Rahn
,
C. D.
, and
Wang
,
C. Y.
,
2008
, “
Model Order Reduction of 1D Diffusion Systems Via Residue Grouping
,”
ASME J Dyn. Syst. Meas. Control
,
130
(
5
), p.
011012
.10.1115/1.2807068
13.
Doyle
,
M.
, and
Newman
,
J.
,
1996
, “
Comparison of Modeling Predictions With Experimental Data From Plastic Lithium Ion Cells
,”
J. Electrochem. Soc.
,
143
(
6
), pp.
1890
1903
.10.1149/1.1836921
14.
Doyle
,
M.
, and
Fuentes
,
Y.
,
2003
, “
Computer Simulations of a Lithium-Ion Polymer Battery and Implications for Higher Capacity Next-Generation Battery Designs
,”
J. Electrochem. Soc.
,
150
(6)
, pp.
A706
A713
.10.1149/1.1569478
15.
Gu
,
W. B.
, and
Wang
,
C. Y.
,
2000
, “
Thermal-Electrochemical Modeling of Battery Systems
,”
J. Electrochem. Soc.
,
147
(8)
, pp.
2910
2922
.10.1149/1.1393625
16.
Smith
,
K. A.
,
Rahn
,
C. D.
, and
Wang
,
C. Y.
,
2010
, “
Model-Based Electrochemical Estimation and Constraint Management for Pulse Operation of Lithium Ion Batteries
,”
IEEE Trans. Control Syst. Technol.
,
18
(
3
), pp.
654
663
.10.1109/TCST.2009.2027023
17.
Prasad
,
G. K.
, and
Rahn
,
C. D.
,
2012
, “
Development of a First Principles Equivalent Circuit Model for a Lithium Ion Battery
,”
ASME
Paper No. DSCC2012-MOVIC2012-8607.10.1115/DSCC2012-MOVIC2012-8607
18.
Lee
,
J. L.
,
Chemistruck
,
A.
, and
Plett
,
G. L.
,
2012
, “
One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics
,”
J. Power Sources
,
220
, pp.
430
448
.10.1016/j.jpowsour.2012.07.075
19.
Klein
,
R.
,
Chaturvedi
,
N. A.
,
Christensen
,
J.
,
Ahmed
,
J.
,
Findeisen
,
R.
, and
Kojic
,
A.
,
2010
, “
State Estimation of a Reduced Electrochemical Model of a Lithium-Ion Battery
,”
American Control Conference
, Baltimore, MD, June 30–July 2, pp.
6618
6623
. 10.1109/ACC.2010.5531378
20.
Klein
,
R.
,
Chaturvedi
,
N. A.
,
Christensen
,
J.
,
Ahmed
,
J.
,
Findeisen
,
R.
, and
Kojic
,
A.
,
2013
, “
Electrochemical Model Based Observer Design for a Lithium-Ion Battery
,”
IEEE Trans. Control Syst. Technol.
,
21
(
2
), pp.
289
301
.10.1109/TCST.2011.2178604
21.
Haran
,
B. S.
,
Popov
,
B. N.
, and
White
,
R. E.
,
1998
, “
Determination of the Hydrogen Diffusion Coefficient in Metal Hydrides by Impedance Spectroscopy
,”
J. Power Sources
,
75
(1)
, pp.
56
63
.10.1016/S0378-7753(98)00092-5
22.
Chaturvedi
,
N. A.
,
Klein
,
R.
,
Christensen
,
J.
,
Ahmed
,
J.
, and
Kojic
,
A.
,
2010
, “
Algorithms for Advanced Battery-Management Systems
,”
IEEE Control Syst. Mag.
,
30
(
3
), pp.
49
68
.10.1109/MCS.2010.936293
23.
Moura
,
S. J.
,
Chaturvedi
,
N. A.
, and
Krstić
,
M.
,
2012
, “
PDE Estimation Techniques for Advanced Battery Management Systems—Part I: SOC Estimation
,”
American Control Conference
, Montreal, QC, Canada, June 27–29, pp.
559
565
. 10.1109/ACC.2012.6315019
24.
Santhanagopalan
,
S.
,
Guo
,
Q.
,
Ramadass
,
P.
, and
White
,
R. E.
,
2006
, “
Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries
,”
J. Power Sources
,
156
(2)
, pp.
620
628
.10.1016/j.jpowsour.2005.05.070
25.
Rahimian
,
S. K.
,
Rayman
,
S.
, and
White
,
R. E.
,
2013
, “
Extension of Physics-Based Single Particle Model for Higher Charge–Discharge Rates
,”
J. Power Sources
,
224
, pp.
180
194
.10.1016/j.jpowsour.2012.09.084
26.
Marcicki
,
J.
,
Canova
,
M.
,
Conlisk
,
A. T.
, and
Rizzoni
,
G.
,
2013
, “
Design and Parametrization Analysis of a Reduced-Order Electrochemical Model of Graphite/LiFeO4 Cells for SOC/SOH Estimation
,”
J. Power Sources
,
237
, pp.
310
324
.10.1016/j.jpowsour.2012.12.120
27.
Christofides
,
P. D.
, and
Daoutidis
,
P.
,
1997
, “
Finite-Dimensional Control of Parabolic PDE Systems Using Approximate Inertial Manifolds
,”
J. Math. Anal. Appl.
,
216
(2)
, pp.
398
420
.10.1006/jmaa.1997.5649
28.
Baker
,
J.
, and
Christofides
,
P. D.
,
2000
, “
Finite-Dimensional Approximation and Control of Nonlinear Parabolic PDE Systems
,”
Int. J. Contr.
,
73
(5)
, pp.
439
456
.10.1080/002071700219614
29.
Verbrugge
,
M. W.
, and
Koch
,
B. J.
,
2003
, “
Electrochemical Analysis of Lithiated Graphite Anodes
,”
J. Electrochem. Soc.
,
150
(
3
), pp.
A374
A384
.10.1149/1.1553788
30.
Yabuuchi
,
N.
,
Makimura
,
Y.
, and
Ohzuku
,
T.
,
2007
, “
Solid-State Chemistry and Electrochemistry of LiCo1∕3Ni1∕3Mn1∕3O2 for Advanced Lithium-Ion Batteries III. Rechargeable Capacity and Cycleability
,”
J. Electrochem. Soc
,
154
(
4
), pp.
A314
A115
.10.1149/1.2455585
31.
Fang
,
W.
,
Kwon
,
O. J.
, and
Wang
,
C. Y.
,
2010
, “
Electrochemical–Thermal Modeling of Automotive Li-Ion Batteries and Experimental Validation Using a Three-Electrode Cell
,”
Int. J. Energy Res.
,
34
(2)
, pp.
107
115
.10.1002/er.1652
32.
Ji
,
Y.
,
Zhang
,
Y.
, and
Wang
,
C. Y.
,
2013
, “
Li-Ion Cell Operation at Low Temperatures
,”
J. Electrochem. Soc
,
160
(
4
), pp.
A636
A649
.10.1149/2.047304jes
33.
Jacobsen
,
T.
, and
West
,
K.
,
1995
, “
Diffusion Impedance in Planar, Cylindrical and Spherical Symmetry
,”
Electrochem. Acta
,
40
(2)
, pp.
255
262
.10.1016/0013-4686(94)E0192-3
34.
Forman
,
J. C.
,
Bashash
,
S.
,
Stein
,
J. L.
, and
Fathy
,
H. K.
,
2011
, “
Reduction of an Electrochemistry-Based Li-Ion Battery Model Via Quasi-Linearization and Padé Approximation
,”
J. Electrochem. Soc.
,
158
(
2
), pp.
A93
A101
.10.1149/1.3519059
35.
Shi
,
Y.
,
Prasad
,
G. K.
,
Shen
,
Z.
, and
Rahn
,
C. D.
,
2011
, “
Discretization Methods for Battery Systems Modeling
,”
American Control Conference
, CA.
36.
Gebhart
,
B.
,
1993
,
Heat Conduction and Mass Diffusion
,
McGraw-Hill
,
New York
.
37.
Subramanian
,
V. R.
,
Ritter
,
J. A.
, and
White
,
R. E.
,
2001
, “
Approximate Solutions for Galvanostatic Discharge of Spherical Particles
,”
J. Electrochem. Soc.
,
148
(
11
), pp.
E444
E449
.10.1149/1.1409397
38.
Subramanian
,
V. R.
,
Tapriyal
,
D.
, and
White
,
R. E.
,
2004
, “
A Boundary Condition for Porous Electrodes
,”
Electrochem. Solid State Lett.
,
7
(
9
), pp.
A259
A263
.10.1149/1.1773751
39.
Frankline
,
G. F.
,
Powell
,
J. D.
, and
Naeini
,
A. E.
,
2011
,
Feedback Control of Dynamic Systems
,
Pearson
,
New Delhi, India
.
40.
Valøen
,
L. O.
, and
Reimers
,
J. N.
,
2005
, “
Transport Properties of LiPF6-Based Li-Ion Battery Electrolytes
,”
J. Electrochem. Soc.
,
152
(
5
), pp.
A882
A891
.10.1149/1.1872737
41.
EC Power,
2013
, “
Software Products
,” http://ecpowergroup.com/products-2/software-licensing
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