(229a) A Reduced Order Lithium ION Battery MODEL Based On Smoothed Unit STEP Functions

Abstract

Rigorous, physics based models for lithium ion batteries (LIB) have been developed over the past twenty years, beginning with Doyle et al. and Fuller et al. and continued by others [1-2]. These models are characterized by a large number of simultaneous partial differential equations (PDE) that require the solution of very large systems of non-linear algebraic differential equations (ADE). Problems that arise with the non-linear nature of the Butler-Volmer kinetics equation are perhaps even more significant than the computational time requirements for large systems. There is also a limited understanding of some of the physical parameters for lithium batteries that is compounded by variations in battery design and mass manufacturing processes. These uncertainties and the highly non-linear nature of the rigorous model pose problems for simulation and especially for control applications. These issues have led several researchers to develop reduced order models (ROM) based on various simplifications to the rigorous model.  This paper presents a ROM that exploits the fact that the governing PDE’s for the battery’s positive electrode, separator and negative electrode differ only by the magnitude of certain physical parameters.  Smoothed “If Then” unit functions are incorporated in a finite element LIB model at the battery’s interfaces to switch physical parameters without injecting discontinuities into the model.

Key Words: Lithium Ion Battery, Reduced Order Model, Fuzzy If Then Logic