Research into reduced-order models (ROM) for Lithium-ion batteries is motivated by the need for a real-time embedded model possessing the accuracy of physics-based models, while retaining computational simplicity comparable to equivalent-circuit models. The discrete-time realization algorithm (DRA) proposed by Lee et al. (2012, “One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics,” J. Power Sources, 220, pp. 430–448) can be used to obtain a physics-based ROM in standard state-space form, the time-domain simulation of which yields the evolution of all the electrochemical variables of the standard pseudo-2D porous-electrode battery model. An unresolved issue with this approach is the high computation requirement associated with the DRA, which needs to be repeated across multiple SoC and temperatures. In this paper, we analyze the computational bottleneck in the existing DRA and propose an improved scheme. Our analysis of the existing DRA reveals that singular value decomposition (SVD) of the large Block–Hankel matrix formed by the system's Markov parameters is a key inefficient step. A streamlined DRA approach that bypasses the redundant Block–Hankel matrix formation is presented as a drop-in replacement. Comparisons with existing DRA scheme highlight the significant reduction in computation time and memory usage brought about by the new method. Improved modeling accuracy afforded by our proposed scheme when deployed in a resource-constrained computing environment is also demonstrated.

References

References
1.
Weiss
,
M.
,
Bonnel
,
P.
,
Hummel
,
R.
,
Provenz
,
A.
, and
Manfredi
,
U.
,
2011
, “
On-Road Emissions of Light-Duty Vehicles in Europe
,”
Env. Sci. Tech
,
45
(
19
), pp.
8575
8581
.
2.
Ibrahim
,
H.
,
Ilinca
,
A.
, and
Perron
,
J.
,
2008
, “
Energy Storage Systems—Characteristics and Comparisons
,”
Renewable Sustainable Energy Rev.
,
12
(
5
), pp.
1221
1250
.
3.
Andrea
,
D.
,
2010
,
Battery Management Systems for Large Lithium Ion Battery Packs
,
Artech House
,
Boston, MA
.
4.
Bergveld
,
H. J.
,
Kruijt
,
W. S.
, and
Notten
,
P. H. L.
,
2002
,
Battery Management Systems
, Vol. 1,
Springer
,
Dordrecht, The Netherlands
.
5.
Plett
,
G. L.
,
2006
, “
Sigma-Point Kalman Filtering for Battery Management Systems of LiPB-Based HEV Battery Packs—Part 1: Introduction and State Estimation
,”
J. Power Sources
,
161
(
2
), pp.
1356
1368
.
6.
Sun
,
F.
,
Hu
,
X.
,
Zou
,
Y.
, and
Li
,
S.
,
2011
, “
Adaptive Unscented Kalman Filtering for State of Charge Estimation of a Lithium-Ion Battery for Electric Vehicles
,”
Energy
,
36
(
5
), pp.
3531
3540
.
7.
Doyle
,
M.
,
Fuller
,
T. F.
, and
Newman
,
J.
,
1993
, “
Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell
,”
J. Electrochem. Soc.
,
140
(
6
), pp.
1526
1533
.
8.
Fuller
,
T. F.
,
Doyle
,
M.
, and
Newman
,
J.
,
1994
, “
Simulation and Optimization of the Dual Lithium Ion Insertion Cell
,”
J. Electrochem. Soc.
,
141
(
1
), pp.
1
10
.
9.
Bizeray
,
A.
,
Zhao
,
S.
,
Duncan
,
S.
, and
Howey
,
D.
,
2015
, “
Lithium-Ion Battery Thermal-Electrochemical Model-Based State Estimation Using Orthogonal Collocation and a Modified Extended Kalman Filter
,”
J. Power Sources
,
296
, pp.
400
412
.
10.
Dao
,
T.-S.
,
Vyasarayani
,
C. P.
, and
McPhee
,
J.
,
2012
, “
Simplification and Order Reduction of Lithium-Ion Battery Model Based on Porous-Electrode Theory
,”
J. Power Sources
,
198
, pp.
329
337
.
11.
Subramanian
, V
. R.
,
Boovaragavan
,
V.
, and
Diwakar
, V
. D.
,
2007
, “
Toward Real-Time Simulation of Physics Based Lithium-Ion Battery Models
,”
Electrochem. Solid-State Lett.
,
10
(
11
), pp.
A255
A260
.
12.
Cai
,
L.
, and
White
,
R. E.
,
2009
, “
Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations
,”
J. Electrochem. Soc.
,
156
(
3
), pp.
A154
A161
.
13.
Rahn
,
C. D.
, and
Wang
,
C.-Y.
,
2013
,
Battery Systems Engineering
,
Wiley
,
Chichester, UK
.
14.
Ning
,
G.
, and
Popov
,
B. N.
,
2004
, “
Cycle Life Modeling of Lithium-Ion Batteries
,”
J. Electrochem. Soc.
,
151
(
10
), pp.
A1584
A1591
.
15.
Romero-Becerril
,
A.
, and
Alvarez-Icaza
,
L.
,
2011
, “
Comparison of Discretization Methods Applied to the Single-Particle Model of Lithium-Ion Batteries
,”
J. Power Sources
,
196
(
23
), pp.
10267
10279
.
16.
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
.
17.
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
.
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
.
19.
Pryce
,
J. D.
,
1993
,
Numerical Solution of Sturm–Liouville Problems
, Clarendon Press, New York.
20.
Lee
,
J. L.
,
Chemistruck
,
A.
, and
Plett
,
G. L.
,
2012
, “
Discrete-Time Realization of Transcendental Impedance Models, With Application to Modeling Spherical Solid Diffusion
,”
J. Power Sources
,
206
, pp.
367
377
.
21.
Lee
,
J. L.
,
2012
, “
Reduced-Order Physics-Based Model of Lithium-Ion Batteries
,”
Ph.D. thesis
,
University of Colorado
,
Colorado Springs, CO
.
22.
Plett
,
G.
,
2015
,
Battery Management Systems: Battery Modeling
(Artech House Power Engineering Series),
Artech House
,
Boston, MA
.
23.
Kalman
,
R.
, and
Ho
,
B.
,
1965
, “
Effective Construction of Linear State Variable Models From Input Output Data
,”
3rd Allerton Conference
, pp.
449
459
.
24.
Ljung
,
L.
,
1998
, “
System Identification
,”
Signal Analysis and Prediction, Part II
(Applied and Numerical Harmonic Analysis Series), Birkhauser, Boston, pp.
163
173
.
25.
Golub
,
G. H.
, and
Van Loan
,
C. F.
,
2013
,
Matrix Computations
, Vol.
3
,
John Hopkins University Press
,
Baltimore, MD
.
26.
Anderson
,
E.
,
Bai
,
Z.
,
Bischof
,
C.
,
Blackford
,
S.
,
Demmel
,
J.
,
Dongarra
,
J.
,
Du Croz
,
J.
,
Greenbaum
,
A.
,
Hammarling
,
S.
,
McKenney
,
A.
, and
Sorensen
,
D.
,
1999
,
LAPACK Users' Guide
,
SIAM
,
Philadelphia, PA
.
27.
Lehoucq
,
R.
,
Maschhoff
,
K.
,
Sorensen
,
D.
, and
Yang
,
C.
,
2013
,
Arpack: Solving Large Scale Eigenvalue Problems
, Vol.
1
,
Astrophysics Source Code Library
, Michigan Technological University, Houghton, MI, Record No. 1311.010.
28.
Larsen
,
R.
,
1998
, “
Propack–Software for Large and Sparse SVD Calculations
,”
Ph.D. thesis, Aarhus University
,
Aarhus, Denmark
.
29.
Björck
,
Å.
,
1994
, “
Numerics of Gram-Schmidt Orthogonalization
,”
Linear Algebra Appl.
,
197
, pp.
297
316
.
30.
Rosen
,
L. E.
,
2005
,
Open Source Licensing: Software Freedom and Intellectual Property Law
, Prentice-Hall, Upper Saddle River, NJ.
31.
Elsner
,
J. B.
, and
Tsonis
,
A. A.
,
1996
,
Singular Spectrum Analysis: A New Tool in Time Series Analysis
,
Springer
,
Boston, MA
.
32.
Korobeynikov
,
A.
,
2010
, “
Computation-and Space-Efficient Implementation of SSA
,”
Stat. Interf.
,
3
(
3
), pp.
357
368
.
33.
Golyandina
,
N.
,
Korobeynikov
,
A.
,
Shlemov
,
A.
, and
Usevich
,
K.
,
2015
, “
Multivariate and 2D Extensions of Singular Spectrum Analysis With the RSSA Package
,”
J. Stat. Software
,
67
(
1
), pp.
1
78
.
34.
Golyandina
,
N. E.
, and
Usevich
,
K. D.
,
2010
, “
2D-Extention of Singular Spectrum Analysis: Algorithm And Elements of Theory
,”
Matrix Methods: Theory, Algorithms, and Applications
, World Scientific, NJ, pp.
449
473
.
35.
COMSOL
,
2012
, COMSOL Multiphysics User Guide (Version 4.3a),
COMSOL, Inc.
,
Burlington, MA
.
You do not currently have access to this content.