Reduced order model for a lithium ion cell with uniform reaction rate approximation

The detailed isothermal electrochemical model for a lithium ion cell comprises of 10 coupled partial differential equations (PDEs). It is computationally intensive to use this model for detailed parameter estimation, battery packs, battery management system algorithms, calendar or cycle life predictions etc. This work describes a reduced order model framework, which reduces the detailed model PDEs, to a manageable set of ordinary differential equations (ODEs), which can be used for the above applications. Volume averaging PDEs yield ODEs. Hence volume averaging is the basic method used for model reduction. The gradient or profile information lost on volume averaging is recovered through profile based approximations. For the lowest order reduced order model (ROM), a uniform reaction rate, quadratic electrolyte concentrations and quartic solid phase concentrations are assumed. In this ROM only 5 linear ODEs are solved, and the rest are nonlinear algebraic evaluations. When compared with the detailed electrochemical model of a lithium ion cell, this ROM gives negligible error at nominal currents and a maximum error of about 3% at high currents, for a typical commercial cell. (c) 2012 Elsevier B.V. All rights reserved.