Current imbalance in dissimilar parallel-connected batteries and the fate of degradation convergence

TL;DR

This paper develops an analytical framework to understand how initial differences in capacity and resistance among parallel-connected batteries influence their current and SOC imbalance dynamics, degradation trajectories, and system behavior.

Contribution

It introduces closed-form equations for imbalance dynamics, validates them experimentally, and explores how different degradation assumptions and chemistries affect battery system evolution.

Findings

Current imbalance can lead to convergent degradation trajectories.

Different degradation assumptions can cause divergent degradation paths.

Cell chemistry and OCV nonlinearities significantly influence system behavior.

Abstract

This paper proposes an analytical framework describing how initial capacity and resistance variability in parallel-connected battery cells may inflict additional variability or reduce variability while the cells age. We derive closed-form equations for current and SOC imbalance dynamics within a charge or discharge cycle. These dynamics are represented by a first-order equivalent circuit model and validated against experimental data. To demonstrate how current and SOC imbalance leads to cell degradation, we developed a successive update scheme in which the inter-cycle imbalance dynamics update the intra-cycle degradation dynamics, and vice versa. Using this framework, we demonstrate that current imbalance can cause convergent degradation trajectories, consistent with previous reports. However, we also demonstrate that different degradation assumptions, such as those associated with SOC imbalance, may cause divergent degradation. We finally highlight the role of different cell chemistries, including different OCV function nonlinearities, on system behavior, and derive analytical bounds on the SOC imbalance using Lyapunov analysis.