A Closed Form Reduced Order Electrochemical Model for Lithium-Ion Cells

Abstract

The state of a lithium (Li)-ion cell as a function of measureable quantities like cell voltage and current is not available in closed form without simplifying assumptions like uniform reaction rate, thus limiting the applicability of reduced order electrochemical models for on-board estimation. In the present work, an analytic form for non-uniform reaction rate profile is derived under certain limiting conditions. Using this form and polynomial approximations for the concentration profiles, a direct non-iterative solution scheme is developed for estimation of cell voltage, state of charge (SOC) and other internal variables. The predicted cell voltage is validated against experimental results for commercial cells while the internal variables are verified against the full pseudo 2 dimensional (P2D) model. The results show that, in spite of the order reduction, the model predicts cell voltage as well as the physical processes of the Li-ion cell accurately with less than 1% error for a wide range (0.2C – 5C) of operating conditions. The self-consistent predictive capability along with low computational cost, makes the proposed model an ideal candidate for physics based on-board state estimation.