Abstract
This paper introduces a capacity fade model for Lithium-Ion batteries based on Single Particle model (SP model), a type of reformulated form of Psuedo 2D model first propose d by Doyle et al. The model simulates the loss of active material in the cathode and formation of solid electrolyte interphase(SEI) in the anode, resulting in capacity fade and resistance increase. The numerical model was suggested for the calculation of voltage profiles and parameters for capacity fades were determined so that cell testing data fit to calculated results. The results show that tested cell experienced about 34% loss of active material and 0.06 Ωm2 impedance increase after 3000 charge-discharge cycles. The developed methods can be used not only to calculate the performance degradation for battery pack by scaling up to vehicle level, but also to cascade targets for cell- module-pack-vehicle levels. The further studies were planned to investigate capacity fades for vehicle driving.
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Abbreviations
- A j :
-
surface area of the electrode ‘j’, m2
- C 1 j :
-
concentration of lithium in the solid phase inside electrode ‘j’, mol m−2
- C 1,max :
-
maximum concentration of lithium in the solid phase inside electrode ‘j’, mol m−2
- C s,j :
-
concentration of lithium at the surface of sphere for electrode ‘j’, mol m−2
- C e :
-
concentration of lithium in the electrolyte
- D 1 j :
-
diffusion coefficient of lithium in the solid phase inside electrode ‘j’, m2 s−1
- F :
-
Faraday’s constant, 9,6487 C mol−1
- i 0,j :
-
exchange current density for intercalation reaction for electrode ‘j’, A m−2
- i 0,j side :
-
exchange current density for the side reaction, A m−2
- J j :
-
current for electrode ‘j’, A
- J s,j :
-
current for the side reaction for electrode ‘j’, A
- k j :
-
rate constant for electrochemical reaction, Am2.5 mol−1.5
- k f :
-
film conductivity, Sm1
- M n :
-
molecular weight of side reaction product kgmol−1
- r :
-
radial coordinate, m
- R :
-
universal gas constant, 8.3143 J mol−1K−1
- R j :
-
radius of solid particles for electrode ‘j’, m
- R SEI :
-
resistance of SEI film, Ω m−2
- U ref,j :
-
local equilibrium potential for electrode ‘j’, V
- V j :
-
volume of active material for electrode ‘j’, m3
- x j :
-
stoichiometric number (C s,j /C 1,max) for electrode ‘j’
- α a :
-
anodic transfer coefficient of electrode
- α c :
-
cathodic transfer coefficient of electrode
- ε :
-
volume fraction of a phase
- ρ s :
-
density of the side reaction product, kg m−3
- ϕ 1,j :
-
local potential for electrode ‘j’, V
- ϕ 2 :
-
potential for electrolyte, V
- δ :
-
film thickness, m
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Baek, K.W., Hong, E.S. & Cha, S.W. Capacity fade modeling of a Lithium-ion battery for electric vehicles. Int.J Automot. Technol. 16, 309–315 (2015). https://doi.org/10.1007/s12239-015-0033-2
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DOI: https://doi.org/10.1007/s12239-015-0033-2