A combining electrochemical model for LiFePO₄-graphite lithium-ion battery considering cathode heterogeneous solid phase phenomenon

The mounting requirement for advanced lithium-ion batteries (LIBs) is based on the enhancement of their whole work life. The application of battery models is vital to improve the control and management ability of sophisticated battery system. Latest work has demonstrated that the open-circuit potential (OCP) of a full LiFePO₄-graphite battery (LFP) which is critical to model accuracy. But the OCP is inconsistent along with the charge and discharge cycles, which also varies with different discharge C-rates. In this study, to simulate the special discharge voltage of a commercial LiFePO₄-graphite cell, a mesoscopic model for LFP cathode solid particles is proposed, which is considering the dynamical reaction in the positive region by introducing of many-particle model. Different with the conventional way to capture the OCP by experimental measurement or empirical function, the mesoscopic model divides the electrode solid phase into several units possessing the non-monotonic reference potential which is employed the Margules equation. In this way, the potential can be integrally calculated, which is much approaching to the true OCP. Besides, the charge reaction resistance is regarded as equivalent direct current resistances assumed to be in line with the Gauss distribution law. We also considered the appearance and vanishment of the discharging platform during the high C-rates discharge cycles, which can be explained by the phase changing phenomenon of LFP OCP. And for the calculation of a full cell voltage, the electrolyte and anode part of model are retained from single-particle model with electrolyte dynamics (SPMe), so that it can be processed by Laplace transformation and followed by Padé approximation for the simplicity. The SPMe combined with our many-particle mesoscopic model is capable to ultimately simulate the characteristic of a full LiFePO₄-graphite battery discharge voltage.