Optimal Assembly of Repurposed Lithium-Ion Battery Packs under Cell Heterogeneity and Screening Uncertainty

Abstract

The growing supply of retired electric vehicle batteries presents an opportunity for second-life stationary energy storage, but assembling heterogeneous retired cells into reliable packs is challenging due to substantial variation in capacity, DC internal resistance (DCIR), and self-discharge. This paper proposes a robust optimization framework for cell-to-pack assembly of second-life batteries. A topology-screening stage first identifies minimum-cell series-parallel configurations satisfying inverter and energy requirements, reducing the dimensionality of the subsequent assignment problem. For each candidate topology, a mixed-integer linear program selects cells and assigns them along the series string, enforcing power, voltage, and energy requirements as hard constraints while minimizing a normalized, weighted sum of DCIR spread, capacity spread, and self-discharge imbalance. Additionally, measurement uncertainty in capacity and DCIR is modeled as bounded intervals to guarantee feasibility under worst-case parameter deviations. The framework is evaluated on four heterogeneous inventories for a 10 kW/10 kWh stationary backup application. The proposed method satisfies all feasibility requirements in every case, while single-metric sorting heuristics each fail on at least one inventory. Relative to the best single-metric baseline by objective value, it reduces the normalized mismatch objective by 76-87%, demonstrating that jointly optimizing cell matching with application-level feasibility requirements improves heterogeneous second-life pack assembly under screening uncertainty.