This paper presents a framework for optimizing lithium-ion battery charging, subject to side reaction constraints. Such health-conscious control can improve battery performance significantly, while avoiding damage phenomena, such as lithium plating. Battery trajectory optimization problems are computationally challenging because the problems are often nonlinear, nonconvex, and high-order. We address this challenge by exploiting: (i) time-scale separation, (ii) orthogonal projection-based model reformulation, (iii) the differential flatness of solid-phase diffusion dynamics, and (iv) pseudospectral trajectory optimization. The above tools exist individually in the literature. For example, the literature examines battery model reformulation and the pseudospectral optimization of battery charging. However, this paper is the first to combine these four tools into a unified framework for battery management and also the first work to exploit differential flatness in battery trajectory optimization. A simulation study reveals that the proposed framework can be five times more computationally efficient than pseudospectral optimization alone.

References

1.
Klein
,
R.
,
Chaturvedi
,
N.
,
Christensen
,
J.
,
Ahmed
,
J.
,
Findeisen
,
R.
, and
Kojic
,
A.
,
2011
, “
Optimal Charging Strategies in Lithium-Ion Battery
,”
American Control Conference
(
ACC
), San Francisco, CA, June 29–July 2, pp.
382
387
.
2.
Rahimian
,
S. K.
,
Rayman
,
S.
, and
White
,
R. E.
,
2011
, “
Optimal Charge Rates for a Lithium Ion Cell
,”
J. Power Sources
,
196
(
23
), pp.
10297
10304
.
3.
Moura
,
S.
,
Chaturvedi
,
N.
, and
Krstic
,
M.
,
2013
, “
Constraint Management in Li-Ion Batteries: A Modified Reference Governor Approach
,”
American Control Conference
(
ACC
),
Washington, DC
, June 17–19, pp.
5332
5337
.
4.
Methekar
,
R.
,
Ramadesigan
,
V.
,
Braatz
,
R. D.
, and
Subramanian
,
V. R.
,
2010
, “
Optimum Charging Profile for Lithium-Ion Batteries to Maximize Energy Storage and Utilization
,”
ECS Trans.
,
25
(
35
), pp.
139
146
.
5.
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
.
6.
Moura
,
S. J.
,
Forman
,
J. C.
,
Bashash
,
S.
,
Stein
,
J. L.
, and
Fathy
,
H. K.
,
2011
, “
Optimal Control of Film Growth in Lithium-Ion Battery Packs Via Relay Switches
,”
IEEE Trans. Ind. Electron.
,
58
(
8
), pp.
3555
3566
.
7.
Bashash
,
S.
,
Moura
,
S. J.
,
Forman
,
J. C.
, and
Fathy
,
H. K.
,
2011
, “
Plug-In Hybrid Electric Vehicle Charge Pattern Optimization for Energy Cost and Battery Longevity
,”
J. Power Sources
,
196
(
1
), pp.
541
549
.
8.
Mamun
,
A.-A.
,
Narayanan
,
I.
,
Wang
,
D.
,
Sivasubramaniam
,
A.
, and
Fathy
,
H. K.
,
2015
, “
Multi-Objective Optimization to Minimize Battery Degradation and Electricity Cost for Demand Response in Datacenters
,” ASME Paper No. DSCC2015-9812.
9.
Hu
,
X.
,
Li
,
S.
,
Peng
,
H.
, and
Sun
,
F.
,
2013
, “
Charging Time and Loss Optimization for LiNMC and LiFePO4 Batteries Based on Equivalent Circuit Models
,”
J. Power Sources
,
239
, pp.
449
457
.
10.
Huntington
,
G. T.
,
2007
, “
Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control Problems
,”
Ph.D. thesis
, University of Florida, Gainesville, FL.
11.
Benson
,
D.
,
2005
, “
A Gauss Pseudospectral Transcription for Optimal Control
,”
Ph.D. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
12.
Kehs
,
M. A.
,
Beeney
,
M. D.
, and
Fathy
,
H. K.
,
2014
, “
Computational Efficiency of Solving the DFN Battery Model Using Descriptor Form With Legendre Polynomials and Galerkin Projections
,”
American Control Conference
(
ACC
),
Portland, OR
, June 4–6, pp.
260
267
.
13.
Suthar
,
B.
,
Northrop
,
P. W.
,
Braatz
,
R. D.
, and
Subramanian
,
V. R.
,
2014
, “
Optimal Charging Profiles With Minimal Intercalation-Induced Stresses for Lithium-Ion Batteries Using Reformulated Pseudo 2-Dimensional Models
,”
J. Electrochem. Soc.
,
161
(
11
), pp.
F3144
F3155
.
14.
Fliess
,
M.
,
Lévine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples
,”
Int. J. Control
,
61
(
6
), pp.
1327
1361
.
15.
Laroche
,
B.
,
Martin
,
P.
, and
Rouchon
,
P.
,
2000
, “
Motion Planning for the Heat Equation
,”
Int. J. Robust Nonlinear Control
,
10
(
8
), pp.
629
643
.
16.
Rao
,
A. V.
,
Benson
,
D. A.
,
Darby
,
C.
,
Patterson
,
M. A.
,
Francolin
,
C.
,
Sanders
,
I.
, and
Huntington
,
G. T.
,
2010
, “
Algorithm 902: Gpops, a Matlab Software for Solving Multiple-Phase Optimal Control Problems Using the Gauss Pseudospectral Method
,”
ACM Trans. Math. Software
,
37
(
2
), pp.
22:1
22:39
.
17.
Gong
,
Q.
,
Kang
,
W.
,
Bedrossian
,
N.
,
Fahroo
,
F.
,
Sekhavat
,
P.
, and
Bollino
,
K.
,
2007
, “
Pseudospectral Optimal Control for Military and Industrial Applications
,” 46th
IEEE
Conference on Decision and Control
, New Orleans, Dec. 12–14, pp.
4128
4142
.
18.
Ross
,
I. M.
, and
Fahroo
,
F.
,
2003
, “
Legendre Pseudospectral Approximations of Optimal Control Problems
,”
New Trends in Nonlinear Dynamics and Control and Their Applications
,
Springer
, Berlin, Heidelberg, pp.
327
342
.
19.
Liu
,
J.
,
Li
,
G.
, and
Fathy
,
H.
,
2015
, “
Efficient Lithium-Ion Battery Model Predictive Control Using Differential Flatness-Based Pseudospectral Methods
,”
ASME
Paper No. DSCC2015-9765.
20.
Ramadesigan
,
V.
,
Northrop
,
P. W.
,
De
,
S.
,
Santhanagopalan
,
S.
,
Braatz
,
R. D.
, and
Subramanian
,
V. R.
,
2012
, “
Modeling and Simulation of Lithium-Ion Batteries From a Systems Engineering Perspective
,”
J. Electrochem. Soc.
,
159
(
3
), pp.
R31
R45
.
21.
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
.
22.
Rahn
,
C. D.
, and
Wang
,
C.-Y.
,
2013
,
Battery Systems Engineering
,
Wiley
, Chichester, UK.
23.
Guo
,
M.
,
Sikha
,
G.
, and
White
,
R. E.
,
2011
, “
Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior
,”
J. Electrochem. Soc.
,
158
(
2
), pp.
A122
A132
.
24.
Chaturvedi
,
N. A.
,
Klein
,
R.
,
Christensen
,
J.
,
Ahmed
,
J.
, and
Kojic
,
A.
,
2010
, “
Modeling, Estimation, and Control Challenges for Lithium-Ion Batteries
,”
American Control Conference
(
ACC
),
Baltimore, MD
, June 30–July 2, pp.
1997
2002
.
25.
Burns
,
J.
,
Stevens
,
D.
, and
Dahn
,
J.
,
2015
, “
In-Situ Detection of Lithium Plating Using High Precision Coulometry
,”
J. Electrochem. Soc.
,
162
(
6
), pp.
A959
A964
.
26.
Ross
,
I. M.
, and
Fahroo
,
F.
,
2004
, “
Pseudospectral Methods for Optimal Motion Planning of Differentially Flat Systems
,”
IEEE Trans. Autom. Control
,
49
(
8
), pp.
1410
1413
.
27.
Mutambara
,
A. G.
,
1999
,
Design and Analysis of Control Systems
,
CRC Press
, Boca Raton, FL.
28.
Arora
,
P.
,
Doyle
,
M.
, and
White
,
R. E.
,
1999
, “
Mathematical Modeling of the Lithium Deposition Overcharge Reaction in Lithium-Ion Batteries Using Carbon-Based Negative Electrodes
,”
J. Electrochem. Soc.
,
146
(
10
), pp.
3543
3553
.
29.
Liu
,
J.
,
Rothenberger
,
M.
,
Mendoza
,
S.
,
Mishra
,
P.
,
Jung
,
Y.-S.
, and
Fathy
,
H.
,
2016
, “
Can an Identifiability-Optimizing Test Protocol Improve the Robustness of Subsequent Health-Conscious Lithium-Ion Battery Control? An Illustrative Case Study
,”
American Control Conference
(
ACC
),
Boston
, July 6–8 (not yet published).
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