A Descriptor System Approach for the Nonlinear State Estimation of Li-Ion Battery Series/Parallel Arrangements

The nonlinear state estimation for a series/parallel arrangement of lithium-ion (Li-ion) battery cells is addressed in this article assuming limited information. First, a unified model for series/parallel arrangements in terms of a nonlinear descriptor model is proposed in order to account for Kirchhoff's laws characterizing the interconnection. It relies on a simplified electrochemical model of the individual cells, the so-called equivalent-hydraulic model. Then, assuming that the system and output equation nonlinearities locally satisfy Lipschitz-like constraints, a linear matrix inequality (LMI)-based technique is proposed for designing a nonlinear state observer, which estimates the state of each individual cell (such as the state-of-charge and inner temperature) as well as the algebraic variables (currents or voltages for respectively parallel or series configurations). The proposed design conditions also provide an estimate of the region of guaranteed convergence while ensuring a peak-to-peak performance with respect to exogenous inputs and model uncertainties. The effectiveness of the approach is demonstrated on a detailed battery electrochemical simulator (based on the Doyle-Fuller-Newman model) for a series arrangement of two cells. Comparisons with a standard extended Kalman filter demonstrate the superior performance of the proposed approach.