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Integration of capacity fading in an electrochemical model of Li-ion batteries

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Abstract

We have developed a new method to describe a fading model integrated with a parasitic reaction of rechargeable Li-ion batteries in the present work. In our work, the Li-ion battery reactions and the parasitic reaction are incorporated into one model. A new governing equation and a new field variable are presented in the new model to characterize the parasitic reaction and the relationship to the battery fading. Due to the new variations, the parameters that are changed with the battery’s aging are able to be calculated and updated automatically in the model. The parasitic reaction is assumed to obey a Tafel equation. The simulating results show that the distribution of overpotential of the parasitic reaction as function of x shapes, a figure close to a “V,” suggests the nonuniform distribution of the parasitic current. The parasitic reaction’s equilibrium potential is proved to be one of most important factors that determine the rate of the reaction. In addition, the cutoff charging state of charge (SOC) has a large influence on the parameters related to the rate of the parasitic reaction. Therefore, controlling the charging SOC can be seen as an effective method to protect the battery from aging.

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Abbreviations

S a :

Specific interfacial area of porous electrode (m2 m−3)

c :

Lithium concentration (mol m−3)

D :

Diffusion coefficient

F :

Faraday’s constant (96,487 C mol−1)

i :

Current density (A m−2)

i 0 :

Exchange current density (A m−2)

I :

Current (A)

k :

Rate constant to lithium intercalation/deintercalation (Am2.5 C−1 mol−0.5)

M :

Molecular weight (kg mol−1)

Q loss :

Volume-averaged capacity lost due to parasitic reaction (C m−3)

r :

Radius of particles (m)

R :

Universal gas constant (8.314 J mol−1 K−1)

R film :

Film resistance at the anode (Ω m2)

S :

Geometric surface area of electrode (m2)

SOC :

State of charge

t :

Time (s)

T :

Temperature (K)

E :

Local potential (V)

V :

Battery output voltage (V)

L :

Length (m)

β :

Anodic transfer coefficient of an electrochemical reaction

α :

Cathodic transfer coefficient of an electrochemical reaction

ε :

Volume fraction of a phase

φ :

Potential of a phase (V)

η :

Overpotential of an electrochemical reaction (V)

κ :

Conductivity of a phase (S m−1)

ρ :

Density of film (kg m−3)

e:

Electrolyte phase

eff:

Effective

i :

Positive or negative electrode

Li:

Li-ion intercalation/deintercalation

m:

Membrane separator

max:

Maximum value

N:

Cycle number

n:

Negative

p:

Positive electrode

film:

SEI film or SEI film reaction

grow:

Increased length of SEI film

ref:

In reference to Li+/Li electrode

s:

Solid/electrolyte interface

s/e:

Solid/electrolyte interface

0:

Initial state

con:

Consumed by the parasitic reaction

y :

Stoichiometric number of lithium ion

x :

Intercalation/deintercalation stoichiometric number of lithium ion

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under the grant number of 51106115 and the Fundamental Research Funds for the Central Universities under the grant number of WUT: 2014-IV-119.

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Authors and Affiliations

  1. School of Automotive Engineering, Wuhan University of Technology, Wuhan, 430070, People’s Republic of China

    Jianqiang Kang

  2. Center for Automotive Research, Mechanical and Aerospace Engineering Department, The Ohio State University, Columbus, OH, 43212, USA

    Jianqiang Kang, A. T. Conlisk & Giorgio Rizzoni

Authors
  1. Jianqiang Kang
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  2. A. T. Conlisk
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  3. Giorgio Rizzoni
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Correspondence to Jianqiang Kang.

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Kang, J., Conlisk, A.T. & Rizzoni, G. Integration of capacity fading in an electrochemical model of Li-ion batteries. J Solid State Electrochem 18, 2425–2434 (2014). https://doi.org/10.1007/s10008-014-2479-y

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  • DOI: https://doi.org/10.1007/s10008-014-2479-y

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