A highly efficient reduced order electrochemical model for a large format LiMn₂O₄/Carbon polymer battery for real time applications

Mechanisms for ion transport, diffusion and intercalation/deintercalation processes in batteries during charging and discharging are described by governing equations that consist of partial differential equations and nonlinear functions. Solving these equations numerically is computational intensive, particularly when the number of cells connected in series and parallel for high power or energy increases, whereas tolerance of errors should be kept under specified limits. Reduction of the computational time is required not only for enabling simulation of the behavior of packs, but also for development of a model capable of running in real time environments, so that new advanced estimation methods for state of charge (SOC) and state of health (SOH) can be developed. In our previous research work, a reduced order model (ROM) was developed using different techniques including polymoninal approximation and residue grouping, which represents the physical behaviors of a battery. However, computational time has not been optimized. In this paper, methods to reduce the computational time are analyzed and employed to reduce the computational time while considering the accuracy. Apart from retaining the residue grouping method for the ion concentration in electrolyte and linearization of the Butler–Volmer equation, the Padé approximation is introduced to simplify the calculation of ion concentration in electrode particles governed by the Fick's second law. Meanwhile, discretized governing equations for potentials in electrodes and electrolytes are reduced by employing proper orthogonal decomposition (POD). In addition, expressions of the equilibrium potentials for anodes and cathodes are fitted to different order polynomials. The reduced equations are coupled to construct a single cell model for a large format lithium polymer battery that is validated against experimental data. The results show that the ROM proposed can reduce the computational time at least to one-tenth of the models developed previously, while overall accuracies can be maintained