A highly efficient reduced order model considering aging effects for lithium ion polymer batteries

Abstract

Mechanisms for ion transport, diffusion, and intercalation/de-intercalation processes in batteries during charging and discharging are described by governing equations that consist of partial differential equations and nonlinear functions in an electrochemical model. Solving these equations numerically is computationally 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 the 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 order to represent the physical behaviors of a battery and optimize the computational time, advanced model order reduction techniques have been applied to reduce the model complexity for individual variables. Padé approximation, Residue Grouping and Proper Orthogonal Decomposition (POD) are introduced to simplify the calculation of ion concentration in electrode particles, ion concentration in electrolyte and potentials in electrode and electrolyte, respectively. Meanwhile, the Butler-Volmer equation is linearized and the equilibrium potential curves are fitted to different order polynomials. Additionally, the aging effects are considered in the model for prediction of the battery end of life. Our investigation on aging mechanisms of the lithium ion batteries has revealed that side reaction is the main cause among others for capacity and power fade of the battery. The production of the side reaction forms thin unsolvable layers that adhere to the surface of the graphite particles and grow as cycled, which is called solid electrolyte interphase (SEI). The iii growth of the SEI leads to loss of the lithium ions, loss of the electrolytes and loss of the active volume fraction. These effects are described using the Butler-Volmer kinetics and aging parameters. Particularly, electrolyte solvent diffusion described by Fick's law is integrated into the aging model, which results in quantifying the electrolyte solvent concentration in SEI. The exchange current density of the side reaction is formulated as a function of electrolyte solvent and lithium ion concentration, which justifies the reaction rate in the aspect of reactants. In addition, the temperature dependency of the model parameters is also considered by adopting the energy equations. Finally, the aging model is incorporated into the ROM. Performances of the ROM are compared with the experimental data collected from a high power pouch type lithium ion polymer battery with Li(MnNiCo)O2/Graphite chemistry.