  In this paper, a novel electrochemical model for LiFePO$_4$ battery cells
that accounts for the positive particle lithium intercalation and
deintercalation dynamics is proposed. Starting from the enhanced single
particle model, mass transport and balance equations along with suitable
boundary conditions are introduced to model the phase transformation phenomena
during lithiation and delithiation in the positive electrode material. The
lithium-poor and lithium-rich phases are modeled using the core-shell
principle, where a core composition is encapsulated with a shell composition.
The coupled partial differential equations describing the phase transformation
are discretized using the finite difference method, from which a system of
ordinary differential equations written in state-space representation is
obtained. Finally, model parameter identification is performed using
experimental data from a 49Ah LFP pouch cell.
