A Doyle–Fuller–Newman (DFN) model for the charge and discharge of nano-structured lithium iron phosphate (LFP) cathodes is formulated 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 some 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 edge(s). These discharge fronts separate regions of fully utilised LFP electrode particles from those that are not. Motivated by this observation an asymptotic solution to the model is sought. The results of the asymptotic analysis of the DFN model lead to a reduced order model, which we term the reaction front model (or 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 or in engineering control systems.

用于纳米结构磷酸铁锂 (LFP) 阴极充电和放电的 Doyle-Fuller-Newman (DFN) 模型是基于纳米级 LFP 电极颗粒内的锂传输比电池放电快得多，因此是没有速率限制。我们对模型提出了一些数值解，并表明对于相关参数值和各种 C 率，尖锐的放电前沿可能会形成并从电极的外边缘侵入电极。这些放电前沿将充分利用的 LFP 电极颗粒区域与未充分利用的区域分开。受此观察的启发，寻求模型的渐近解。DFN 模型的渐近分析结果导致了一个降阶模型，我们称之为反应前沿模型（或 RFM）。在适当的参数制度下，RFM 的解决方案和完整的 DFN 模型之间显示出良好的一致性。与 DFN 模型相比，RFM 的求解成本要低得多，因此有可能用于计算成本过高的场景，例如优化和参数估计问题或工程控制系统。