⚡ electrical engineering

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

This paper proposes a robust optimization framework that combines topology screening with a mixed-integer linear program to assemble heterogeneous second-life lithium-ion battery packs under parameter uncertainty, demonstrating significantly improved feasibility and reduced cell mismatch compared to traditional single-metric heuristics.

Original authors: Hassan Zahid Butt, Xingpeng Li

Published 2026-07-15

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CC BY 4.0

Original authors: Hassan Zahid Butt, Xingpeng Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a giant box of old, retired batteries from electric cars. They are all different: some are still strong, some are tired, some hold a lot of energy, and some leak it away quickly. You want to build a new, reliable power pack to keep a house running during a blackout. The problem? If you just grab a handful of these batteries and stick them together, the weak ones will drag down the strong ones, or the whole pack might fail exactly when you need it most.

This paper suggests a clever, computer-driven way to sort these "second-life" batteries so they work together perfectly, even if our measurements of them aren't 100% perfect.

The Problem: The "One-Size-Fits-All" Trap

The authors argue that the old way of doing things—sorting batteries by just one thing—is a recipe for disaster. They tested three simple sorting methods:

Sort by Capacity: Picking the biggest batteries first.
Sort by Resistance: Picking the ones that let electricity flow easiest.
Sort by Self-Discharge: Picking the ones that leak energy the slowest.

In their simulations, every single one of these simple methods failed on at least one type of battery inventory. Why? Because a battery pack is like a chain; it's only as strong as its weakest link. If you sort only by size, you might end up with a group of huge batteries that have terrible electrical resistance, causing them to overheat or fail. If you sort only by resistance, you might get a pack that can't hold enough energy to last the night. The paper explicitly rules out these single-metric sorting tricks as insufficient for building a reliable pack.

The Solution: The "Smart Matchmaker"

Instead of a simple list, the authors propose a two-step "Smart Matchmaker" system (a robust optimization framework).

Step 1: The Blueprint Check (Topology Screening)
Before picking specific batteries, the computer first figures out the best shape for the pack. It asks: "How many rows (series) and how many batteries side-by-side (parallel) do we need to hit our targets?"
For a backup system needing 10 kW of power and 10 kWh of energy, the computer calculated that a 16S2P configuration (16 rows of 2 batteries each) was the smallest, most efficient shape. It ruled out smaller shapes that couldn't deliver the power and larger ones that would waste cells.

Step 2: The Perfect Pairing (Robust Optimization)
Once the shape is set, the computer plays a high-stakes matching game. It doesn't just look at the "average" numbers of the batteries. It assumes the measurements might be slightly wrong (uncertainty).

The Analogy: Imagine you are packing a team for a relay race. You don't just pick the fastest runners; you pick a team where everyone's speed is guaranteed to be close enough, even if their stopwatches were slightly off.
The Math: The computer uses a "worst-case" scenario. It says, "Even if this battery's capacity is at the very bottom of its possible range, and that one's resistance is at the very top, will the pack still work?" If the answer is no, it rejects that combination.

The Results: A Safety Net

The authors ran this system on four different "virtual warehouses" of 100 batteries each, designed to be tricky (some had huge differences in size, others had huge differences in resistance, and some had very fuzzy measurements).

The Simple Sorters: In the simulations, the simple sorting methods failed to meet the requirements. For example, the "Capacity Sorter" built packs that were too weak on resistance (up to 32.9% mismatch, way over the 10% safety limit), while the "Resistance Sorter" built packs that didn't have enough energy (dropping below the 10 kWh requirement).
The Smart Matchmaker: The new method succeeded in every single case. It managed to reduce the "mismatch" (how different the batteries were from each other) by 76% to 87% compared to the best of the simple methods.

Crucially, the paper notes that this success was achieved while guaranteeing that the pack would still deliver 10 kWh of energy and stay within a 10% resistance difference, even when the measurements were at their worst possible error.

The Bottom Line

This paper doesn't claim to have solved the problem for real-world, messy factories yet. Instead, it shows through careful computer simulations that a complex, math-heavy approach is necessary. You can't just sort batteries by one number. You need a system that looks at the whole picture—energy, resistance, and measurement errors—all at once to build a battery pack that won't quit when the lights go out.

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

Problem Statement
The paper addresses the challenge of assembling second-life batteries (SLBs) from retired electric vehicle (EV) cells into reliable stationary energy storage packs. While the supply of retired EV batteries is growing rapidly, their reuse is hindered by significant heterogeneity in cell parameters—specifically capacity, DC internal resistance (DCIR), and self-discharge rates. This variation, which widens as cells age, leads to critical pack-level issues: resistance mismatches in parallel groups distort current sharing and accelerate degradation, while capacity and self-discharge variations along series strings limit usable energy and cause long-term state-of-charge (SOC) imbalance.

Furthermore, the problem is compounded by measurement uncertainty inherent in the screening process. Diagnostic estimates often rely on test conditions that may not reflect real-world performance, and data traceability remains inconsistent. Consequently, a pack assembled based solely on nominal values may fail under realistic parameter deviations. The core problem is combinatorial: selecting cells, determining series-parallel topology, and assigning cells to specific positions must simultaneously satisfy application-level constraints (power, voltage, energy, and current limits) while minimizing parameter spread, all under bounded uncertainty.

Methodology
The authors propose a two-phase robust optimization framework, termed OASLB (Optimal Assembly of Second-Life Batteries), to solve the cell-to-pack assembly problem.

Phase 1: Topology Screening
Before optimization, the framework analytically screens series-parallel configurations to identify the minimum-cell topology that satisfies application requirements. It enumerates integer values for the number of series groups ( $N_s$ ) and parallel cells per group ( $N_p$ ) based on inverter voltage windows, power/current limits, and energy requirements. This stage reduces the dimensionality of the subsequent assignment problem by eliminating infeasible configurations and fixing the topology before optimization begins.
Phase 2: Robust Mixed-Integer Linear Programming (MILP)
For each candidate topology, a MILP model assigns individual cells to parallel-group positions along the series string.
- Objective Function: The model minimizes a normalized, weighted sum of three mismatch metrics: DCIR spread within parallel groups, capacity spread within parallel groups, and self-discharge imbalance across the series string.
- Hard Constraints: Unlike heuristic approaches, the model enforces application requirements (energy, power, voltage, current) as hard constraints.
- Robustness: To address screening uncertainty, the model treats capacity and DCIR as bounded intervals. It guarantees feasibility under worst-case parameter deviations by ensuring that even if all measurements deviate to their unfavorable edges, the pack still meets the energy floor, DCIR tolerance, and loaded-voltage limits.
- Symmetry Breaking: The model includes constraints to order groups by nominal minimum DCIR, eliminating redundant permutations and reducing solver runtime.

Key Contributions
The paper identifies three primary research gaps in existing literature and addresses them through the following contributions:

Unified Formulation: It integrates topology screening, cell selection, and cell-to-position assignment into a single formulation, moving beyond the separation of these steps found in previous works.
Application-Aware Constraints: The framework directly incorporates application-specific constraints (power capability, backup duration, voltage/current limits) as hard constraints within the optimization, rather than as post-hoc checks.
Robust Optimization: It introduces a robust formulation that incorporates bounded intervals for capacity and DCIR, guaranteeing worst-case feasibility rather than relying on nominal values.

Results
The framework was evaluated on four synthetic lithium-iron-phosphate (LFP) inventories (100 cells each) designed to stress different aspects of heterogeneity: DCIR dominance, capacity dominance, combined heterogeneity, and high measurement uncertainty. The target application was a 10 kW/10 kWh stationary backup system.

Feasibility: The robust OASLB method satisfied all feasibility requirements (energy floor, DCIR tolerance, and loaded-voltage) in every inventory case. In contrast, three single-metric sorting heuristics (sorting by capacity, DCIR, or self-discharge) each failed on at least one inventory. For instance, capacity sorting failed DCIR tolerance checks, while DCIR sorting failed energy requirements.
Objective Performance: Relative to the best-performing single-metric baseline on each inventory, the proposed method reduced the normalized mismatch objective by 76% to 87%.
Robustness vs. Determinism: When comparing the robust model to a deterministic version (ignoring uncertainty), the robust assembly guaranteed worst-case energy feasibility across all inventories with only a modest increase in the nominal mismatch objective (e.g., rising from 0.109 to 0.155 in the high-uncertainty D4 case).

Significance
The paper claims that its primary significance lies in demonstrating that jointly optimizing cell matching with application-level feasibility requirements, while explicitly accounting for measurement uncertainty, significantly improves the reliability of heterogeneous second-life pack assembly. The results suggest that single-metric sorting heuristics are insufficient for complex, coupled requirements and that robust optimization is necessary to ensure that nominally feasible designs do not fail under real-world screening deviations. The authors conclude that this approach effectively addresses cell heterogeneity and uncertainty as integral components of the assembly formulation, paving the way for more reliable repurposing of retired EV batteries. Future work is noted as focusing on validating the framework with field-measured inventories.

The Problem: The "One-Size-Fits-All" Trap

The Solution: The "Smart Matchmaker"

The Results: A Safety Net

The Bottom Line

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

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