A Study on the Controllability of Lithium-Ion Batteries

TL;DR

This paper analyzes the controllability of lithium-ion batteries, linking the condition number of their models to control effort, and examines how aging affects controllability and assembly selection.

Contribution

It introduces a nonlinear controllability analysis for battery cells and connects model conditioning to control effort, providing insights into aging effects and assembly optimization.

Findings

Poorly conditioned cell dynamics require more control effort.

Aging impacts the controllability condition number of cells.

Optimal assemblies can be identified based on conditioning analysis.

Abstract

This work explores controllability and the control effort required for lithium-ion batteries. Battery packs have become a critical technology in both personal and professional applications as a means to store large amounts of energy. Management of cells in a pack becomes increasingly difficult though, with charging and discharging operations requiring more complex strategies due to parameter variations between the cells. There are numerous studies which develop effective estimation and control schemes to reduce the impact of the imbalances present in battery packs, but the receptiveness of the individual cells to these schemes is much less explored. This paper performs a nonlinear controllability analysis for experimentally parameterized cells. A connection is shown between the condition number of a battery's controllability matrix and the amount of control effort that battery will require. This reveals that if a cell's dynamics are poorly mathematically conditioned, it will require more time or higher power to control than one that is not. The controllability condition number of each cell's model is then determined both with new and aged parameters, and a sensitivity analysis shows that the cells' conditioning is equally impacted by all parameters. This offers insight into the increased control effort required for a battery as it ages and the culprit of said increase. The results of this analysis are then used to determine the best conditioned assemblies for a batch of cells with a mix of new and second-life parameters.