Research Papers

A Computationally Efficient Approach for Optimizing Lithium-Ion Battery Charging

[+] Author and Article Information
Ji Liu

Department of Mechanical
and Nuclear Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: jxl1081@psu.edu

Guang Li

School of Engineering
and Material Sciences,
Queen Mary University of London,
Mile End Road,
London E1 4NS, UK
e-mail: g.li@qmul.ac.uk

Hosam K. Fathy

Department of Mechanical
and Nuclear Engineering,
Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@psu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 6, 2015; final manuscript received November 17, 2015; published online December 23, 2015. Assoc. Editor: Beshah Ayalew.

J. Dyn. Sys., Meas., Control 138(2), 021009 (Dec 23, 2015) (8 pages) Paper No: DS-15-1207; doi: 10.1115/1.4032066 History: Received May 06, 2015; Revised November 17, 2015

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


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.
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. [CrossRef]
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.
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
Huntington, G. T. , 2007, “ Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control Problems,” Ph.D. thesis, University of Florida, Gainesville, FL.
Benson, D. , 2005, “ A Gauss Pseudospectral Transcription for Optimal Control,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
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.
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. [CrossRef]
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. [CrossRef]
Laroche, B. , Martin, P. , and Rouchon, P. , 2000, “ Motion Planning for the Heat Equation,” Int. J. Robust Nonlinear Control, 10(8), pp. 629–643. [CrossRef]
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. [CrossRef]
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
Rahn, C. D. , and Wang, C.-Y. , 2013, Battery Systems Engineering, Wiley, Chichester, UK.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Mutambara, A. G. , 1999, Design and Analysis of Control Systems, CRC Press, Boca Raton, FL.
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. [CrossRef]
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).


Grahic Jump Location
Fig. 3

Computational time versus the number of collocation points

Grahic Jump Location
Fig. 1

Simulation results for problem (23) applying the flatness-based GPM for two current upper limits: Imax=5A (solid lines) and Imax=2A (dashed lines). The initial SOC in (a) 0.7 and (b)0.4.

Grahic Jump Location
Fig. 2

Simulation results for problem (42) applying the flatness-based GPM for two current upper limits: Imax=5A (solid lines) and Imax=2A (dashed lines): (a) results with initial SOC as 0.7 and voltage upper bound as 3.7 V and (b) results with initial SOC as 0.4 and voltage upper bound as 4.0 V



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In