## 1 Introduction  
With the increasing global emphasis on decarbonization and sustainable energy solutions, lithium-ion batteries have emerged as the leading choice for energy storage in electric vehicles (EVs) due to their high energy density, long cycle life, and favorable performance characteristics [1, 2]. As the EV market continues to grow, the worldwide production and deployment of Li-ion batteries are expected to surge, resulting in a parallel increase in the number of batteries reaching their end of life [3, 4]. However, many of these batteries retain sufficient residual capacity and can be repurposed for less-demanding applications rather than being prematurely discarded. This concept of second-life usage provides both economic and environmental benefits by extending battery lifespans and reducing the environmental impact associated with battery manufacturing and disposal. Among various second-life applications, stationary energy storage systems (ESSs) have gained significant attention. Residential and commercial ESS solutions can buffer fluctuations in renewable energy sources and help to stabilize the power grid [5, 6, 7, 8, 9]. In particular, the demand for standardized battery module configurations is growing as it simplifies the integration process, lowers development costs, and ensures compatibility with existing battery management systems (BMSs). One widely adopted standard for residential ESSs is the 48 V module configuration, which provides a safe and modular building block [10, 11]. Despite its practical advantages, reassembling used cells into battery modules still faces challenges related to cell-to-cell variability, state of health (SOH) discrepancies, and capacity mismatches. These issues necessitate a robust and effective grouping or clustering strategy to ensure consistent module performance and prolonged operating life. In light of these challenges, there has been extensive research on methods to optimally regroup cells for second-life usage. Beyond simple heuristic or rule-based approaches, data-driven clustering and classification methods are increasingly being adopted to handle complex, multidimensional battery performance data [12]. For instance, Support Vector Clustering (SVC) leverages the kernel trick to capture non-linear relationships in the data, making it suitable for identifying tightly knit clusters even when the boundaries are not trivially separable. K-means, a classic and widely used partitioning algorithm, remains attractive due to its simplicity and computational efficiency [13]. However, K-means typically assumes spherical or near-spherical cluster shapes, which may not always align with battery performance data distributions [14, 15]. Gaussian Mixture Models (GMMs), on the other hand, offer a probabilistic framework that can model more flexible cluster geometries and allow for soft clustering [16, 17], which is when data points can belong to multiple clusters with varying degrees of membership. Despite their theoretical differences, there is a need to systematically compare these clustering methods under realistic operational scenarios, especially for second-life battery modules intended for residential ESS applications. In this work, we offer a theoretical comparison of three clustering algorithms--K-means, Gaussian Mixture Models (GMMs), and Support Vector Clustering (SVC)--by applying them directly to our 60-cell dataset to form four equal 15-cell modules. We then quantify how each method's cluster assignments affect voltage deviation and coulombic efficiency in 15s2p simulations, showing that GMMs' probabilistic grouping produces the most uniform performance across cells. By validating these approaches on real battery data, this comparative framework highlights the theoretical basis for choosing clustering techniques to optimize second-life module design.