Performance Imbalances in Parallel-Connected Cells

Efficiently addressing performance imbalances in parallel-connected cells is crucial in the rapidly developing area of lithium-ion battery technology. This is especially important as the need for more durable and efficient batteries rises in industries such as electric vehicles (EVs) and renewable energy storage systems (ESS).

Written by: Gabriele Piombo, Visiting Scholar at the Department of Energy Science and Engineering, Stanford University, USA and EngD candidate at WMG, University of Warwick, Coventry, United Kingdom

cells in parallel

Parallel string performance imbalances are inevitable due to intrinsic cell-to-cell variations and suboptimal pack designs. Traditional methods often fall short in pinpointing the underlying causes of module imbalances. This is a result of to the intricate interplay among various factors, hindering the experimental setups’ capability to isolate these interactions.

A recent study leveraged explainable machine learning (XML) techniques, combined with a full factorial design of experiments (DoE), to provide new insights into the performance characteristics of lithium-ion battery modules. A robust experimental setup was employed to investigate the performance of a 1S4P module configuration. This involved analysing two batches of twenty new and four aged commercial NMC and NCA cells. The cells were individually characterised for internal resistance and capacity distributions. Then, a 54-condition full factorial DoE on modules was performed with the following parameters:

  • operating temperature (10, 25, 40°C)
  • interconnection resistance (0.1, 0.3, 1.0 mΩ)
  • cell chemistry (NMC, NCA)
  • ageing status

The modules were subjected to a full charge-discharge cycle at a rate of 3/4C.

The study utilized advanced data analytics, including multivariate linear models and XML techniques like SHAP (SHapley Additive exPlanations), Individual Conditional Expectation (ICE) plots, and Partial Dependence Plots (PDP), to explore and explain the influence of the different factors on module performance.

cells in parallel data analysis flow chart

The work highlighted several critical insights:

  • Interconnection Resistance: This emerged as the primary driver of performance heterogeneity within the modules, significantly impacting current and temperature distribution across the cells.
  • Cell-to-cell variations: In the first and middle phases of the discharge, the distributions of internal resistance and capacity impact the load imbalance across the cells, respectively.
  • Cell Chemistry and Ageing: Despite combining NMC and NCA cells is possible, mixing different cell chemistries and the inclusion of aged cells adversely affected the balanced performance of the module.
  • Temperature Effects: Higher operating temperatures exacerbated the thermal gradients within the modules, influencing the performance imbalance.

This research demonstrates that by integrating XML with traditional experimental methods, it is possible to offer more precise diagnoses and predictions of cells’ performance, paving the way for more reliable and efficient battery packs. This advancement paves the way for future research addressing the exploration of alternative cell chemistries and module configurations, as well as the development of new strategies to mitigate the effects of ageing on battery performance.

For a detailed exploration of the study’s methodology, results, and implications, we encourage you to read the full paper, “Unveiling the Performance Impact of Module Level Features on Parallel-Connected Lithium-Ion Cells via Explainable Machine Learning Techniques on a Full Factorial Design of Experiments”, Gabriele Piombo, Simone Fasolato, Robert Heymer, Dr Marc Hidalgo, Dr Mona Faraji Niri, Prof Simona Onori, and Prof James Marco, published in the Journal of Energy Storage, volume 84 [1].

To promote transparency and reproducibility, the dataset used in this study is made publicly available. The description of the experimental setup, data collection methods, and results are published in a separate paper in Data in Brief [2]. Researchers and practitioners are encouraged to explore this dataset to further advance the field of lithium-ion battery technology, particularly in the context of parallel-connected cells.


  1. Gabriele Piombo, Simone Fasolato, Robert Heymer, Marc Hidalgo, Mona Faraji Niri, Simona Onori, James Marco, Unveiling the performance impact of module level features on parallel-connected lithium-ion cells via explainable machine learning techniques on a full factorial design of experiments, Journal of Energy Storage, Volume 84, Part A, 2024, 110783
  2. Piombo G, Fasolato S, Heymer R, Hidalgo MF, Faraji Niri M, Raimondo DM, Marco J, Onori S. “Full factorial design of experiments dataset for parallel-connected lithium-ion cells imbalanced performance investigation“. Data Brief. 2024 Feb 22;53:110227

Leave a Comment