Lithium-Ion Battery State of Charge and Critical Surface Charge Estimation Using an Electrochemical Model-Based Extended Kalman Filter

摘要

This paper presents a numerical calculation of the evolution of the spatially resolvednsolid concentration in the two electrodes of a lithium-ion cell. The microscopic solidnconcentration is driven by the macroscopic Butler–Volmer current density distribution,nwhich is consequently driven by the applied current through the boundary conditions. Thenresulting, mostly causal, implementation of the algebraic differential equations that describenthe battery electrochemical principles, even after assuming fixed electrolyte concentration,nis of high order and complexity and is denoted as the full order model. Thenfull order model is compared with the results in the works of Smith and Wang (2006,n“Solid-State Diffusion Limitations on Pulse Operation of a Lithium-Ion Cell for HybridnElectric Vehicles,” J. Power Sources, 161, pp. 628–639) and Wang et al. (2007 “Controlnoriented 1D Electrochemical Model of Lithium Ion Battery,” Energy Convers. Manage.,n48, pp. 2565–2578) and creates our baseline model, which will be further simplified forncharge estimation. We then propose a low order extended Kalman filter for the estimationnof the average-electrode charge similarly to the single-particle charge estimation in thenwork of White and Santhanagopalan (2006, “Online Estimation of the State of Charge ofna Lithium Ion Cell,” J. Power Sources, 161, pp. 1346–1355) with the following twonsubstantial enhancements. First, we estimate the average-electrode, or single-particle,nsolid-electrolyte surface concentration, called critical surface charge in addition to thenmore traditional bulk concentration called state of charge. Moreover, we avoid thenweakly observable conditions associated with estimating both electrode concentrationsnby recognizing that the measured cell voltage depends on the difference, and not thenabsolute value, of the two electrode open circuit voltages. The estimation results of thenreduced, single, averaged electrode model are compared with the full order modelnsimulation.