Journal of Applied Electrochemistry

, Volume 48, Issue 6, pp 663–674 | Cite as

Lithium iron phosphate electrode semi-empirical performance model

  • B. Rajabloo
  • A. Jokar
  • W. Wakem
  • M. Désilets
  • G. Brisard
Research Article


The galvanostatic performance of a pristine lithium iron phosphate (LFP) electrode is investigated. Based on the poor intrinsic electronic conductivity features of LFP, an empirical variable resistance approach is proposed for the single particle model (SPM). The increasing resistance behavior observed at the end of discharge process of LFP batteries can be justified by the increased ohmic resistance, a resistive-reactant feature of LFP as the positive electrode active materials. The model is validated for two different laboratory made Li/LFP coin cells: a high-energy and a high-power configuration. Comparisons between the experimental results and the model predictions reveal that a variable resistance is successful to tackle the increasing overpotential.

Graphical Abstract

Schematic of the coated LFP active material particles in (a) beginning of discharge with well-connected particles, (b) end of discharge with poor-connected particles


Lithium-ion battery Single particle model Lithium iron phosphate Parameter estimation 

List of symbols

\(c_{{s,k}}^{{\max }}\)

Maximum concentration of Li+ in the particle of positive electrode (mol m−3)


Li+ diffusion coefficient in the particle of positive electrode (m2 s−1)


Faraday’s constant (C mol−1)


Applied current density, (A m−2)


Reaction rate constant of electrode k (k = p,n), (m2.5 mol−0.5 s−1)


Unknown parameter vector


Universal gas constant (J mol−1 K−1)


Radius of the particles of positive electrode (m)


Total electroactive area of electrode k (k = p,n) (m2)


State of charge of positive electrode


Initial state of charge of positive electrode


Time (s)


Absolute temperature (K)


Open-circuit potential of positive electrode (V)


Total volume of positive electrode (m3)


Model’s estimation of the cell potential (V)


\({\varepsilon _p}\)

Volume fraction of active material

\({\delta _p}\)

Dimensionless flux of lithium ion at positive electrode

\({\lambda _k}\)

The kth eigenvalue



Initial state


Positive electrode


Negative electrode


Solid phase



The authors are very grateful to Hydro-Québec and to the Natural Sciences and Engineering Council of Canada (NSERC) for their financial support.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemical and Biotechnological EngineeringUniversité de SherbrookeSherbrookeCanada
  2. 2.Department of ChemistryUniversité de SherbrookeSherbrookeCanada

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