State of Charge Estimation in Li-ion Batteries Using an Isothermal Pseudo Two-Dimensional Model

The dynamics of Li-ion batteries are often defined by a set of coupled nonlinear partial differential equations called the pseudo two-dimensional model. It is widely accepted that this model, while accurate, is too complex for estimation and control. As such, the literature is replete with numerous approximations of this model. For the first time, an algorithm for state-of-charge estimation using the original pseudo two-dimensional model is provided. A discrete version of the model is reformulated into a state-space model by separating linear, nonlinear, and algebraic states. This model is high dimensional (of the order of tens to hundreds of states) and consists of implicit nonlinear algebraic equations. The degeneracy problems with high-dimensional state estimation are circumvented by developing a particle filter algorithm that sweeps in time and spatial coordinates independently. The implicit algebraic equations are handled by ensuring the presence of a ‘tether’ particle in the algorithm. The approach is illustrated through simulations.