Abstract
With the increasing use of electric vehicles (EVs), there is a growing interest in the thermal management of EVs. In this study, we first reduced the computational complexity of single particle model (SPM) for the battery cell by introducing a 4th order approximation for Li-ion concentration in the solid phase. In addition, by integrating it with an energy balance, the constructed model can calculate the battery temperature along with the terminal voltage and state of charge. To develop a model compatible with the experimental data requires parameter estimation. However, the estimation accuracy for each parameter depends on its sensitivity. We investigated the influence of 16 parameters on the measured data under general experimental conditions (constant C-rate discharge) through simulations and sensitivity analysis. We classified the radius of the particle, total active surface areas, electrode maximum concentration, and a heat transfer coefficient as dominant parameters. When dominant parameters were estimated using the virtual experimental data, the percent error was smaller than 3.1%. For the parameters with minor influence, the estimation error was large even with the excellent agreement of the experimental data. We confirmed which parameter could be estimated using the C-rate experimental data accurately and which parameter should be estimated with additional experiments.
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Abbreviations
- Acell :
-
total cell surface area exposed to surroundings [m2]
- C p :
-
specific heat capacity of the cell [J/kg·K]
- Cs, max, j :
-
maximum concentration of lithium ions j [mol/m3]
- \({\overline {\rm{c}} _j}\) :
-
volume-averaged Li+ concentration in the solid phase [mol/m3]
- Cs, j :
-
Li+ concentration at solid surface
- Ds, j :
-
electrolyte diffusivity coefficient in the solid phase [m2/s]
- \({{\rm{E}}_{{a_{d,j}}}}\) :
-
activation energy for the solid-phase diffusion coefficient of electrode j [kJ/mol]
- \({{\rm{E}}_{{a_{r,j}}}}\) :
-
activation energy for the reaction rate constant of electrode k [kJ/mol]
- F:
-
faraday constant [96,487C/mol]
- j:
-
Li+ mole flux at solid surface [mol/m2/s]
- kj :
-
rate constant for the electrochemical reaction of electrode j [m2.5/mol0.5·S]
- h:
-
heat transfer coefficient between the cell and the surroundings [W/m2·K]
- Q:
-
rate of heat transfer between the cell and surroundings [W]
- \({\overline {\rm{q}} _j}\) :
-
volume-average Li+ concentration flux in the solid phase [mol/m4]
- Sj :
-
total electroactive area of the electrode j [m2]
- Rj :
-
radius of spherical intercalation of electrode j [m]
- R:
-
ideal gas constant [8.314 J/mol·K]
- T:
-
cell temperature [K]
- Tamb :
-
ambient temperature [K]
- Tref :
-
reference temperature [298.15K]
- V:
-
terminal voltage [V]
- φ 1, j :
-
solid phase potential of electrode j [V]
- φ 2,j :
-
solution phase potential of electrode j [V]
References
M. Guo, G. Sikha and R. E. White, J. Electrochem. Soc., 158(2), A122 (2011).
V. R. Subramanian, V. D. Diwakar and D. Tapriyal, J. Electrochem. Soc., 152(10), A2002 (2005).
K. An, P. Barai, K. Smith and P. P. Mukherjee, J. Electrochem. Soc., 161(6), A1058 (2014).
Y. Choi and H. Kim, Korean Ind. Chem., 18(5), 47 (2015).
B. Wu, J. Power Sources, 243, 544 (2013).
Y. Ma, IEEE Access, 7, 156136 (2019).
K. Kumaresan, G. Sikha and P. E. White, J. Electrochem. Soc., 155(2), A164 (1993).
A. P. Schmidt, IFAC Symposium Advances in Automotive Control, 43(7), 198 (2010).
M. Farag, H. Sweity, M. Fleckenstein and S. Habibi, J. Power Sources, 360, 618 (2010).
R. Gu, IEEE Transactions on Transportation Electrification, 2(4), 417 (2016).
D. Bernardi, E. Pawlikoski and J. Newman, J. Electrochem. Soc., 132(5), 5 (1985).
W. Li, Appl. Energy, 269, 115104 (2020).
L. Zhang, J. Electrochem. Soc., 161(5), A762 (2014).
M. Chen and G. A. Rincón-Mora, IEEE Transactions on Energy Conversion, 21(2), 504 (2006).
H. Pang, Electrochm. Acta, 307, 474 (2019).
K. Jiang, J. Power Sources, 451, 1 (2020).
F. Xue, Electrochem. Acta, 53, 6636 (2008).
H. Wang, ACS NANo, 14, 2575 (2020).
Z. Mao, M. Farkhondeh, M. Pritzker, M. Fowler and Z. Chen, Electrochim. Acta, 222, 1741 (2016).
J. K. Park, Principles and applications of lithium secondary batteries, Wiley-VCH Verlag & Co. KGaA, Weinheim (2012).
J. J. Lee, J. Korean Electrochem. Soc., 4(4), 139 (2001).
Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2021R1C1C1004217), and by Hyundai Motor Company as Development of Battery Thermal Model considering Battery Aging for Integrated Thermal Management. The present research has been conducted by the Research Grant of Kwangwoon University in 2020.
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Hong, C., Oh, SK. & Kim, Y. Sensitivity analysis for parameter classification of energy balance-integrated single particle model for battery cells. Korean J. Chem. Eng. 39, 1396–1411 (2022). https://doi.org/10.1007/s11814-022-1081-8
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DOI: https://doi.org/10.1007/s11814-022-1081-8