0
Research Papers

A Temperature Dependent, Single Particle, Lithium Ion Cell Model Including Electrolyte Diffusion

[+] Author and Article Information
Tanvir R. Tanim

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: trt140@psu.edu

Christopher D. Rahn

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

Chao-Yang Wang

Professor
William E. Diefenderfer Chair
of Mechanical Engineering,
and Director of the Electrochemical
Engine Center,
Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: cxw31@psu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 21, 2013; final manuscript received July 30, 2014; published online August 28, 2014. Assoc. Editor: Jwu-Sheng Hu.

J. Dyn. Sys., Meas., Control 137(1), 011005 (Aug 28, 2014) (11 pages) Paper No: DS-13-1280; doi: 10.1115/1.4028154 History: Received July 21, 2013; Revised July 30, 2014

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Office of the Press Secretary, 2013, The White House Press Release, Washington, DC, http://www.whitehouse.gov/the-press-office
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. [CrossRef]
Rahn, C. D., and Wang, C. Y., 2013, Battery Systems Engineering, Wiley, State College, PA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Gu, W. B., and Wang, C. Y., 2000, “Thermal-Electrochemical Modeling of Battery Systems,” J. Electrochem. Soc., 147(8), pp. 2910–2922. [CrossRef]
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]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Verbrugge, M. W., and Koch, B. J., 2003, “Electrochemical Analysis of Lithiated Graphite Anodes,” J. Electrochem. Soc., 150(3), pp. A374–A384. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Ji, Y., Zhang, Y., and Wang, C. Y., 2013, “Li-Ion Cell Operation at Low Temperatures,” J. Electrochem. Soc, 160(4), pp. A636–A649. [CrossRef]
Jacobsen, T., and West, K., 1995, “Diffusion Impedance in Planar, Cylindrical and Spherical Symmetry,” Electrochem. Acta, 40(2), pp. 255–262. [CrossRef]
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. [CrossRef]
Shi, Y., Prasad, G. K., Shen, Z., and Rahn, C. D., 2011, “Discretization Methods for Battery Systems Modeling,” American Control Conference, CA.
Gebhart, B., 1993, Heat Conduction and Mass Diffusion, McGraw-Hill, New York.
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. [CrossRef]
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. [CrossRef]
Frankline, G. F., Powell, J. D., and Naeini, A. E., 2011, Feedback Control of Dynamic Systems, Pearson, New Delhi, India.
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. [CrossRef]
EC Power, 2013, “Software Products,” http://ecpowergroup.com/products-2/software-licensing

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of a pseudo 2D Li-ion cell model

Grahic Jump Location
Fig. 4

Voltage response of AutoLion-ST, ESPM, and ESPM-T from 10 °C initial temperature and 50% initial SOC: (a) magnified voltage during 2.5 C discharge pulse (left box in Fig. 4(c)), (b) magnified voltage during 20 C discharge pulse (right box in Fig. 4(c)), (c) voltage response, (d) cell temperature, and (e) pulse current input

Grahic Jump Location
Fig. 5

Voltage response of AutoLion-ST and ESPM-T from 0 °C and 50% initial SOC: (a) voltage response, (b) cell temperature, and (c) pulse current input

Grahic Jump Location
Fig. 2

Voltage response of AutoLion-ST, ESPM, and SPM at 25 °C and 50% initial SOC: (a) magnified voltage during 8.5 C discharge pulse (left box in Fig. 2(c)), (b) magnified voltage during 20 C discharge pulse (right box in Fig. 2(c)), (c) voltage response, (d) electrolyte potential difference, and (e) pulse current input

Grahic Jump Location
Fig. 3

Voltage response of AutoLion-ST and ESPM at 25 °C and 50% initial SOC: (a) magnified voltage during 20 C pulse (left box in Fig. 3(c)), (b) magnified voltage during 15 C pulse (right box in Fig. 3(c)), (c) voltage response, (d) SOC, and (e) pulse current input

Grahic Jump Location
Fig. 6

Voltage response of AutoLion-ST and ESPM-T from 10 °C and 50% initial SOC: (a) voltage response, (b) cell temperature, and (c) 7.5C–30 s hybrid pulse charge–discharge cycle

Grahic Jump Location
Fig. 7

ESPM-T error relative to AutoLion-ST for different C-rate pulse cycles (see Fig. 6(c)) versus cell temperature. The solid dot corresponds to the dot in Fig. 6(a).

Tables

Errata

Discussions

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