Mathematical Modelling of Lithium Iron Phosphate Electrodes

  • Michael Jack Castle

Student thesis: Doctoral Thesis


A Doyle-Fuller-Newman (DFN) model for the charge and discharge of lithium iron phosphate (LFP) cathodes is formulated and non-dimensionalised, and some popular reduced-order models are derived. The DFN model is then solved numerically using both the Finite Difference Method (FDM) and the Finite Element Method (FEM), and simulations of the DFN using both methods are compared. On the basis that lithium transport within the nanoscale LFP electrode particles is much faster than cell discharge, and is therefore not rate limiting, we present numerical solutions to the model and show that for relevant parameter values, and a variety of C-rates, it is possible for sharp discharge fronts to form and intrude into the electrode from its outer edges. These discharge fronts separate regions of fully utilised LFP electrode particles from regions of LFP electrode particles not yet utilised. Motivated by this observation a novel asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a novel reduced order model, which we term the Reaction Front Model (RFM). Favourable agreement is shown between solutions to the RFM and the full DFN model in appropriate parameter regimes. The RFM is significantly cheaper to solve than the DFN model and therefore has the potential to be used in scenarios where computational costs are prohibitive, e.g. in optimisation and parameter estimation problems, and in battery control systems. Upon re-evaluation of the RFM, we observe that it is possible to relieve the assumption that the LFP particles are small enough to not be rate limiting whilst maintaining the key features of the reduced order model, which is significantly less computationally expensive than the DFN. This model, which we term the RFM-D, is then validated against experiment and, due to the simplicity of the RFM-D, we show that a full parametrisation is possible using only discharge curves. Additionally, we show that the RFM-D reveals key features of the discharge curves for LFP half-cells, where the most prevalent rate limiting factors can be easily identified through qualitative analysis, which has applications to cell design.
Date of AwardJan 2023
Original languageEnglish
Awarding Institution
  • University of Portsmouth
SupervisorJamie Foster (Supervisor), William Lee (Supervisor) & Andrew Osbaldestin (Supervisor)

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