State of health estimation for battery modules with parallel-connected cells under cell-to-cell variations

State of health (SOH) estimation for lithium-ion battery modules with cells connected in parallel is a challenging problem, especially with cell-to-cell variations. Incremental capacity analysis (ICA) and differential voltage analysis (DVA) are effective at the cell level, but a generalizable method to extend them to module-level SOH estimation remains missing, when only module-level measurements are available. This paper proposes a new method and demonstrates that, with multiple features systematically selected from the module-level ICA and DVA, the module-level SOH can be estimated with high accuracy and confidence in the presence of cell-to-cell variations. First, an information theory-based feature selection algorithm is proposed to find an optimal set of features for module-level SOH estimation. Second, a relevance vector regression (RVR)-based module-level SOH estimation model is proposed to provide both point estimates and three-sigma credible intervals while maintaining model sparsity. With more selected features incorporated, the proposed method achieves better estimation accuracy and higher confidence at the expense of higher model complexity. When applied to a large experimental dataset, the proposed method and the resulting sparse model lead to module-level SOH estimates with a 0.5% root-mean-square error and a 1.5% average three-sigma value. With all the training processes completed offboard, the proposed method has low computational complexity for onboard implementations.