Modeling and State Estimation for Lithium Sulfur Batteries as a Piecewise Affine System

Lithium-sulfur (Li-S) is a promising battery chemistry for applications demanding high energy densities, such as electrified aircraft and heavy-duty trucks, among others. A critical challenge in modeling the Li-S chemistry lies in the use of differential algebraic (DAE) equations for representing the electrochemical dynamics. Due to their constrained and stiff nature, these equations are not conducive to real-time state estimation. In this study, we propose a novel approach to constrained state estimation for Li-S batteries by integrating a piecewise affine (PWA) model into a moving horizon estimation (MHE) framework. We begin by deriving the PWA model using a linear tree algorithm based on data obtained from simulations of a calibrated DAE model. We further leverage the unique structural advantages of the proposed PWA model to formulate a real-time state estimation algorithm grounded in a mixed-integer quadratic program. Overall, our initial findings, based on a single constant current trajectory, demonstrate that our approach offers an accurate and computationally efficient method for modeling and state estimation of Li-S batteries. The coupled PWA-MHE framework effectively captures the dynamics of the DAE system, even in the presence of high observational noise (20mV).