Theoretical bounds on the accuracy of state and parameter estimation for batteries
Paper i proceeding, 2017

Today it is standard to use equivalent circuit models to describe the dynamic behavior of Li-ion vehicle batteries. The parameters and states change with operating point and are therefore continuously estimated using bayesian observers, though without knowing to what degree the performance can be improved. Posterior Cramér-Rao Lower Bounds (CRLBs) can be used to theoretically quantify the optimal accuracy of bayesian estimators. In this paper we apply this to a second-order nonlinear equivalent-circuit model of a lithium-ion battery. It is shown, by numerical calculations, how the posterior Cramér-Rao Lower Bounds depend on the amplitude and frequency of the current, and on the slope of the Open Circuit Voltage (OCV) curve. Furthermore, it is investigated how much the accuracy is reduced in combined estimation of the states and the resistance compared to when the resistance is perfectly known. More importantly, it is also shown that the Mean Square Errors (MSE) of an Extended Kalman Filter (EKF) are close to the posterior CRLBs, which means that, under the investigated circumstances, it is not possible to significantly reduce the MSEs by replacing the EKF by any other observer.

Secondary batteries

Circuit simulation

Numerical calculation

Open circuit voltage

Kalman filters

Parameter estimation

Circuit theory

State and parameter estimations

Equivalent circuits

Theoretical bounds

Nonlinear equivalent circuit

Dynamic behaviors

Lithium-ion batteries

Equivalent circuit model

Extended Kalman filters

Mean square error

Electric batteries

Bayesian estimators

Optimal accuracy


Anton Klintberg

Chalmers, Signaler och system, System- och reglerteknik

Torsten Wik

Chalmers, Signaler och system, System- och reglerteknik

B. Fridholm

Volvo Cars

American Control Conference

0743-1619 (ISSN)






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