“Full factorial design of experiments dataset for parallel-connected lithium-ion cells imbalanced performance investigation”

This paper shares an experimental dataset of lithium-ion battery parallel-connected modules. The campaign, conducted at the Stanford Energy Control Laboratory, employs a comprehensive full factorial Design of Experiment methodology on ladder-configured parallel strings. A total of 54 test conditions were investigated under various operating temperatures, cell-to-cell interconnection resistance, cell chemistry, and aging levels. The module-level testing procedure involved Constant Current Constant Voltage (CC-CV) charging and Constant Current (CC) discharge. Beyond monitoring total module current and voltage, Hall sensors and thermocouples were employed to measure the signals from each individual cell to quantify both current and temperature distribution within each tested module configuration. Additionally, the dataset contains cell characterization data for every cell (i.e. NCA Samsung INR21700-50E and NMC LG-Chem INR21700-M50T) used in the module-level experiments. This dataset provides valuable resources for developing battery physics-based, empirical, and data-driven models at single cell and module level. Ultimately, it contributes to advance our understanding of how cell-to-cell heterogeneity propagates within the module and how that affects the overall system performance.


a b s t r a c t
This paper shares an experimental dataset of lithium-ion battery parallel-connected modules.The campaign, conducted at the Stanford Energy Control Laboratory, employs a comprehensive full factorial Design of Experiment methodology on ladder-configured parallel strings.A total of 54 test conditions were investigated under various operating temperatures, cell-to-cell interconnection resistance, cell chemistry, and aging levels.The module-level testing procedure involved Constant Current Constant Voltage (CC-CV) charging and Constant Current (CC) discharge.Beyond monitoring total module current and voltage, Hall sensors and thermocouples were employed to measure the signals from each individual cell to quantify both current and temperature distribution within each tested module configuration.Additionally, the dataset contains cell characterization data for every cell (i.e.NCA Samsung INR21700-50E and NMC LG-Chem INR21700-M50T) used in the module-level experiments.This dataset provides valuable resources for developing battery

Value of the Data
• Single-cell characterization, in the form of galvanostatic discharge, HPPC test, and Multi-Sine profiles are performed on a total of 39 single cells at 23 °C.In particular, the experimental campaign includes two fresh batches consisting of 18 Samsung INR21700-50E and 19 LG-Chem INR21700-M50T cells, aimed at identifying out-of-manufacture cell-tocell variations.The third batch consists of one aged cell per chemistry type.• The testing campaign for the parallel-connected battery modules are designed adopting a comprehensive full factorial DoE methodology.A total of 54 module-level experiments are conducted, considering four distinct factors within the DoE approach.These factors encompass 3 levels of testing: temperature (10, 25 and 40 °C), cell-to-cell interconnection resistance (0, 1 and 3 m ) and cell chemistry (all NMC, all NCA and mixed NMC/NCA), as well as two levels of cell ageing (aged and unaged).• At the module level, the testing procedure consists of a CC-CV charging at a rate of C/3.
The cut-off current of 50 mA is reached when holding at a CV of 4.2 V. Subsequently, a CC discharge is conducted at a rate of 0.75C.Throughout each test, alongside monitoring the overall module current and voltage, the currents delivered by each individual cell within the module, as well as their respective temperatures, were measured.The aim is to quantify the impact of cell-to-cell variations on module operations across a wide range of usage scenarios.
• The dataset provides parallel-connected module data that can enable the development of battery physics-based, empirical, and data-driven pack-level modelling frameworks for the understanding of cell-to-cell heterogeneity propagation.It also allows statistical analysis based on the DoE factors.• To the best of the authors' knowledge, this is the first dataset (that is both peer-reviewed and within the public domain) including data on cells connected in parallel, where the current and temperature of each cell connected in parallel are measured under different operating conditions and applying DoE methodology.

Background
The performed experimental campaign aimed to increase our level of understanding of the role of out-of-manufacture single-cell parameters distributions and module-level features on the uneven performance of parallel connected cells.Ultimately, the objective of this study is to inform about the mechanisms underlying the propagation of cell-to-cell variations, and how these variations ultimately influence the overall functioning of modules/packs.The dataset also encompasses standard characterisation test results for both unaged and aged batches of two distinct lithium-ion cell chemistries, offering an overview of the electrical properties distributions at the end of the manufacturing process.The developed dataset is associated with the publication in the Journal of Energy Storage [ 1 ] ( https://doi.org/10.1016/j.est.2024.110783), which adds value to this article by providing an in-depth analysis via Explainable Machine Learning (XML) techniques.As the implemented methodology rigorously relied on a Full-Factorial DoE, this dataset can support further development of battery physics-based, empirical, and data-driven models at single cell and module level.

Data Description
The dataset includes two complementary experimental campaigns.The first one is a single cells' characterisation campaign on all the 39 individual cells to identify sample properties and their out-of-manufacture distribution.The second one covers 0.75C CC discharge on four cells connected in parallel in a ladder configuration.To facilitate the reader's understanding of the testing procedures carried out in this study, a high-level visual flowchart of the steps involved in both campaigns is offered in Fig. 1 .Cell characterisation was performed before the module-level tests.The 39 cells included in the study are 19 new LGM50T Lithium-Nickel-Manganese-Cobalt-Oxide (LiNiMnCoO 2 ), 18 Samsung 50E Lithium Nickel-Cobalt-Aluminium Oxide Li(NiCoAl)O 2 , and one pre-aged cell for each chemistry.Both LG and Samsung cells implement Silicon-doped graphite (SiC) for the negative electrode.The technical specifications of the cells are included in Table 1 for completeness.
Understanding the cell-to-cell variability is a crucial step to enhance the interpretability of module level imbalance phenomena.This is related to the impact of differences in cells' properties have on the load and temperature distributions in parallel strings.Part of the experimental campaign is therefore focused on reference performance tests (RPT) on the cells' used in the Single-cell characterization (top) is performed before module-level testing (bottom) and consists of four phases: preinspection, namely visual investigation, weighting and sample labelling, identification of discharge capacity via the pseudo-OCV procedure, derivation of impedance via HPPC and MultiSine protocols, and conditioning for long-term storage.Module-level testing is grounded in the selected Full-Factorial DoE and consists of four phases: cells' selection and grouping, module assembly, test delivery, and data processing.Between the two campaigns, Hall-type current sensors are calibrated, and derived voltage-current maps are then leveraged to translate raw data into processed data.

Manufacturer
LG Chem  To account for cells' internal properties dependency on SoC, the ohmic resistance measurements are performed at even intervals of 10 % by anticipating them with a constant current discharge profiles at a 1C rate (Step 9) followed by 60 minutes rest (Step 10).The ohmic resistance is sensed by means of two different protocols in Steps 11 and 12. First, HPPC current profiles are applied with a charge/discharge ratio of 0.75 and a duration of 10 s, as per automotive standards (Step 11) [4] .Then, MultiSine type dynamic current profiles are supplied following the procedure described in [ 5 , 6 ] with an α value of 0.6 and a pulse duration of 10 s (Step 12).A resting period of two minutes is imposed in Step 13 to allocate for cycle recursive management.Steps 9 to 13 are repeated until 2.5V is reached by applying multiple exit conditions.Last, a constant current constant voltage charge takes back the cells to 4.2V in Steps 14 and 15.The protocol ends when the supplied current goes below 50 mA.All the RPT are performed at a controlled thermal chamber temperature of 23 °C.
The module-level campaign aimed to enhance our level of understanding regarding the influence of various factors on the inconsistent performance of parallel connected cells.The considered factors can be referred, in part, to the single cell characterisation campaign, which provides valuable insights into the distribution of electrical properties.The remaining features refer to module-level characteristics, which serve as indicators of the influence exerted by design choices and operating conditions.A four-cells parallel string in a ladder configuration is tested, meaning the terminals of the module are connected on the same side.The experimental parameters encompass operating temperature, cell-to-cell interconnection resistance, chemistry (NCA, NMC, and mixed) and ageing status (Aged, and Unaged).The operating temperatures are 10 °C, 25 °C and 40 °C.The interconnection resistance levels are 0, 1 and 3 m , leveraging high-precision shunt resistors ( ±1 %) soldered to 3.3 mm thick and 25.4 mm deep copper bars with negligible electrical resistance.The influence of the shunt soldering is tested upon manufacture and deemed to be negligible, as reported in [1] .In this study, a "Mixed" chemistry configuration refers to a combination of two NMC and two NCA cells in the parallel string being tested.The NCA cells are always kept closest to the terminals to represent the worst-case scenario of load imbalance among cells, as their ohmic resistance is lower than the NMC ones.On the other hand, the "NMC" and "NCA" configurations represent modules with cells of equal chemistry.Finally, the "Unaged" configuration denotes the connection of four fresh cells, while "Aged" refers to the inclusion in position 4 of one aged cell of the same chemistry.The location of the aged cell is selected to ensure a worst-case scenario standpoint in the form of maximum load imbalance, due to its higher ohmic resistance and lower discharge capacity when compared to unaged cells.The mixed and aged case includes a test where both the chemistries are mixed and two aged cells are included in the string.The factors ranges are selected upon literature and expert's review following previously conducted group campaigns on series-connected cells [7] .To mitigate the evolution of the cells' characteristics over the experimental campaign, a randomized sampling methodology was developed.At each instance, four cells combination among the twenty in the batches are randomly selected and given a position (1)(2)(3)(4) in the module to ensure repetitive tests on the same cells are minimized.The Stat-Ease Design Expert 22.0.2software is employed to define the experimental design and entail the examination of all possible combinations of the factors and levels included resulting in a full-factorial DoE.The list of control variables is reported in Table 3 , resulting in a total of 54 testing points.
The module level test protocol consists of 8 consecutive steps, listed in Table 4 and illustrated in Fig. 2(a) .A cycle starts with a 90 min resting period (Step 1 ) to allow the cells to self-balance and reach equilibrium (thermal and electrochemical) before testing, eliminating potential interferences due to cells' initial states.Steps 2 and 3 comprise the charging phase of CC at C/3 up to 4.2V followed by a CV terminated when the module current (total supplied current) is lower than 200 mA.The module is then left to rest for 30 min (Step 4 ).Next, a 0.75C constant current discharge profile is applied until the terminal voltage reaches the lower limit of 2.5 V (Step 5 ).Self-balancing currents occur in the following one-hour rest phase (Step 6 ).The protocol is finalised by Steps 7 and 8 which are the repetition of Steps 2 and 3 (a C/3 CC phase up to 4.2 V followed by a CV phase terminated when the supplied current goes below 200 mA) from a lower SoC level.The described procedure is repeated for each of the 54 testing points reported in Table 5 .
Throughout each test, alongside monitoring the overall module current and voltage ( Fig. 2(a) ), the currents delivered by each individual cell within the module and their respective temperatures were measured.Fig. 2(b) -(d) and Fig. 2(c) -(e) provide examples of the current and thermal distribution within the tested module during Step 5 and 7 -8 , respectively.Note that the current measurements on individual cells are gathered by means of Hall sensors.The Hall sensors working principle consists of the voltage across the output pins being linearly proportional to the magnetic field generated by the current source.The sensed voltage signals need coherently to be translated into currents via a calibration procedure.To calibrate the Hall sensors, a stepwise constant current profile is imposed via known current levels covering the C-rates range (−2C to 2C) used in the experimental campaign.The resulting profile is included in Fig. 3 .

Dataset structure
The root folder containing all the files is named "Parallel-connected module experimental campaign" and is divided into the three sub-folders: 1. Single-cell characterisation 2. Hall sensor calibration 3. Module level experiments An exhaustive description of each sub-folder is offered below, and schematically depicted in Fig. 4 , to improve the dataset understanding and utilisation.
1. Single-cell characterisation This folder contains the individual cells' RPT campaign results including the data gathered from the NMC and NCA unaged and aged batches.Each of the "Aged_cells", "NMC_cells" and "NCA_cells" sub-folders contain two folders named Pseudo OCV and HPPC-MS.These locations store the discharge Pseudo-OCV tests and HPPC-MultiSine results, respectively.The data was converted to the MATLAB format (.mat) and is named following the convention "Test-Type_CellName" where TestType can be either "OCVDis" or "HPPC_MultiSine" depending on the relevant test profile."CellName" refers to the series and number given to each cell.NMC, NCA cells belong to the "P", "F" series, respectively.NMC aged cell is coded as "Y1", NCA one as "GS3".
The .mat files contain double type arrays sensing: The "HPPC_MultiSine" .matfiles also include two additional signals facilitating data handling via flags, namely: • StepIndex: Flag indicating the step number reached in the test protocol [-] The Pseudo-OCV sampling time was set to 10[s].The HPPC and MultiSine profiles are logged at a 1[s] sampling intervals in all phases apart from the pulses, where they are set to 0.1[s].

Hall sensors calibration
This folder reports the data gathered while calibrating the voltage-current relationship used to derive the maps translating the raw to processed data in the module-level experimental campaign.A total of 8 Excel spreadsheets (.xlsx) logged files were converted to MATLAB (.mat) format to reduce storage space and are included following the naming convention "SensorNumber"_Calibration.To double the testing speed, a total of two twin modules as the one depicted in Fig. 5 were manufactured.Each module has four possible cell locations.Module number 1 (M1) includes locations 1-4, while module number two (M2) 5-8.Locations 1 and 5 are the closest to the module terminals, while 4 and 8 the furthest.Each sensor is logically allocated to a location and given the respective "SensorNumber".The .mat files include a "Data" table, with headers referring to: This folder includes the data of the 54 test points module-level experimental campaign performed.To facilitate readability and usage, the data were allocated to sub-folders referring to the 4 features included in Table 3 .The specific order of features is: chemistry, ageing, interconnection resistance and operating temperature, as reported in Fig. 4 .The last sub-folder in the directory coherently includes individual test data named following the convention: • "ModuleNumber_": refers to which module was used to perform the test (M1, M2).
Both the "raw" and "processed" data are reported with respective main sub-folders.The raw data are saved as Excel spreadsheets with .xlsxtype and refer to the data directly obtained from the MITS Pro software.The column headers refer to the sensed signal as follows: • Date_Time: Logged testing time in "day/month/year hour:minutes:seconds" format.To allow for a fast data analysis, the raw data are converted to .mattype files and reported as "processed".The data included were neither filtered nor resampled.Both raw and processed data share the same structure with the exception of the Hall sensors and power supply voltages ("Aux_Voltage_1-5") which are converted to current profiles (Current(A)_"CellNumber") leveraging the data included in the "Hall sensors calibration" folder.A schematic comparison of the data included in the raw and processed table data is offered in Fig. 5 .The processed table therefore results in 15 columns, with a new header indicated as: The "Data_processed" files contain an additional field indicated as "Cells_name".The "Cells_name" field can be used to identify which cells were allocated to the individual tests and is composed by a table with four columns mapping the relative position in the module (headers) with the code of the cell taken from the "Single-cell characterisation" folder.

Experimental Design, Materials and Methods
The equipment available at the Stanford Energy Control Lab [8] and employed in the experimental campaign is shown in Fig. 6 .The module cycling tests are designed with the MITS Pro software 1 , which allows to define protocols, i.e., the sequence of steps to be followed to perform an experiment.To supply the battery module with the desired current profile and collect sensor data (i.e.module voltage, hall sensor voltages, and cell surface temperatures), the Arbin LBT22013 3 is employed in conjunction with the Data Acquisition System (DAQ) 2 .During testing, each battery module 5 is tested within the Amerex IC500R thermal chamber 4 and is instrumented with 5 T-type thermocouples placed to measure the surface temperatures at the centre of each cell, as well as the ambient temperature.Besides, four Honeywell SS495A Hall sensors are installed in each module to measure parallel paths currents.Hall-principle-based instruments were compared and selected over standard shunt resistors as the latter require a compromise between signal accuracy and influence on module's current distribution to be made.The larger the shunt resistance, the larger the voltage drop and hence signal-to-noise ratio.Nevertheless, the larger resistance mitigates the cell-to-cell ohmic resistance heterogeneity impact on current distribution, influencing the test results.Hall sensors operate via an external 5V circuit and hence do not present this limitation, despite requiring some measures to ensure an adequate setup accuracy.The Hall sensors are mechanically inserted and glued into ferrite rings to improve the signal-to-noise ratio and increase the reading scale.To prevent operators' influence on sensor measurements, the ferrite rings are fixed around the current carrying connector at the negative terminal of each cell.In this way, the modules preparation does not require moving the sensors at each testing occurrence.Shielded cables are used to enclose signals and terminals legs are soldered and insulated to mechanically stabilize them and avoid shorts during operation.A 1mF capacitor is soldered across the 5V power supply to stabilize the input signal and mitigate its impact on readings.The raw data of each test is exported in Excel spreadsheets (.xlsx) file format.For more information about the setup the reader is referred to [9] .The Stat-Ease Design Expert software version 22.0.2 is used to develop the experimental design, factors levels and tests order.

Fig. 1 .
Fig. 1.A visual flowchart of the implemented experimental procedures, selected steps, and design of experiments.Single-cell characterization (top) is performed before module-level testing (bottom) and consists of four phases: preinspection, namely visual investigation, weighting and sample labelling, identification of discharge capacity via the pseudo-OCV procedure, derivation of impedance via HPPC and MultiSine protocols, and conditioning for long-term storage.Module-level testing is grounded in the selected Full-Factorial DoE and consists of four phases: cells' selection and grouping, module assembly, test delivery, and data processing.Between the two campaigns, Hall-type current sensors are calibrated, and derived voltage-current maps are then leveraged to translate raw data into processed data.

Fig. 2 .
Fig. 2. Cycling module-level testing protocol.(a) Terminal voltage (grey line) and total current (orange line) profiles across the 8 steps of the testing protocol listed in Table 3 .(b and c) Distribution of the supplied current across the four parallel connected cells (red-scale lines) and module terminal voltage (grey line) during the constant-current discharge (Step 5 ) and CCCV charging (Steps 7 -8 ) phases.(d,e) Distribution of the individual cells' surface temperatures during the constant-current discharge (Step 5 ) and CCCV charging (Steps 7 -8 ) phases.

Fig. 3 .
Fig. 3. a) Hall sensors supplied-current ramp (grey line) to response voltage profile (red dashed line).b) Example of a resulting linear regression line (continuous grey) used to map the gathered voltage-current data (red crosses).

Fig. 3 (
Fig.3 (a)  shows the correspondence between the supplied current and the sensed voltage.In Fig.3 (b), the linearity of the signal in the evaluated range is confirmed.The regression lines angular coefficients and biases are then derived to map each Hall sensor voltage to the actual current measurement.In total, 8 Hall sensors (i.e.four Hall sensors for each of the two manufactured module test benches) are calibrated and assigned to a specific string position before running the module-level campaign.

•Fig. 5 .
Fig. 5. Comparison between module-level raw and processed data, where the signal names are highlighted.

Table 2
Single cells characterisation campaign test protocol.
current profiles with a C/20 rate until 2.5V limit is reached, obtaining Pseudo-Open Circuit Voltage (OCV) curves.Cells are then left resting for a period of 30 min (Step 5).The CC-CV charging procedure is repeated in Steps 6 and 7 up to 100 % SoC, followed by a 30 minutes rest in Step 8.

Table 3
List of the control variables included in the DoE campaign.

Table 4
Module level campaign test protocol.

Table 5
Module-level campaign experimental design including tests' order, factors' specifications, cells' position allocation in the module and links to the dataset repository files.