Two-level Electrochemical-model-based Estimation of Li-ion Battery State of Charge – Real-data Validation on an Electric Vehicle Use Case

This paper proposes a two-level hierarchical estimation structure of a lithium-ion battery state of charge (SoC) based on the parabolic-partial-differential-equation Single Particle Model (SPM). Using a suitable linear finite-dimensional approximation of this model, it is proposed that the SoC estimation to be done in two dynamically-separated levels, consistent with the multi-time-scale nature of battery internal phenomena: a fast level implementing a dynamic inversion, in charge of retrieving surface concentrations of lithium based on output voltage measures, and a slow level, in which internal lithium concentrations are estimated by employing a Luenberger observer. After having first suitably calibrated the model, this structure is easy to tune and allows avoiding estimation convergence issues frequently occurring in the case of a global, one-level estimation and which are partly due to a numerically ill conditioned linear approximated model. SoC estimation accuracy is validated by using real data issued from battery cycling in an electric vehicular application, that is, under standard driving cycle scenarios. Estimation errors – computed against Coulomb counting taken as baseline estimation of battery SoC – are smaller than 3.5%, thus suggesting very satisfactory performance.