Observability analysis and state estimation of lithium-ion batteries in the presence of sensor biases

TL;DR

This paper analyzes the observability of lithium-ion battery models and proposes a method to estimate state of charge despite sensor biases, using nonlinear Kalman filters and differential geometric analysis.

Contribution

It derives observability conditions for nonlinear battery models and demonstrates bias estimation with various nonlinear Kalman filters using experimental data.

Findings

Biases can be effectively estimated with nonlinear Kalman filters.

Observability conditions differ between linearized and nonlinear models.

UKF outperforms EKF variants in bias estimation accuracy.

Abstract

This paper investigates the observability of one of the most commonly used equivalent circuit models (ECMs) for lithium-ion batteries and presents a method to estimate the state of charge (SOC) in the presence of sensor biases, highlighting the importance of observability analysis for choosing appropriate state estimation algorithms. Using a differential geometric approach, necessary and sufficient conditions for the nonlinear ECM to be observable are derived and are shown to be different from the conditions for the observability of the linearised model. It is then demonstrated that biases in the measurements, due to sensor ageing or calibration errors, can be estimated by applying a nonlinear Kalman filter to an augmented model where the biases are incorporated into the state vector. Experiments are carried out on a lithium-ion pouch cell and three types of nonlinear filters, the first-order extended Kalman filter (EKF), the second-order EKF and the unscented Kalman filter (UKF) are applied using experimental data. The different performances of the filters are explained from the point of view of observability.