Reduced-Order Model of Lithium-Iron Phosphate Battery Dynamics: A POD-Galerkin Approach

Lithium iron phosphate batteries with plateau in the open circuit voltage, hysteresis, and path dependence dynamics due to phase transition during intercalation/de-intercalation are challenging to model and even more challenging to control. A core-shell electrochemical modeling approach is able to capture the phase transition behavior at the cost of using a fine-grained spatial grid to transform the governing Partial Differential Algebraic Equations into Ordinary Differential Algebraic Equations, resulting in a computationally expensive system intractable for the design of real-time battery management system algorithms. This letter presents a reduced-order modeling paradigm to transform the high-dimensional model into a low-dimensional yet accurate control oriented electrochemical model. The Proper Orthogonal Decomposition-Galerkin method is used to reduce the state variable vector from 169 to a meager 9 with negligible loss in fidelity. The reduced-order model is validated against both experimental data and the high-dimensional model for discharging-charging load profiles of different C-rates and real driving cycles. Promising results with one-third the computational burden and a voltage RMS error of less than 0.6% are achieved.