Numerical investigation of module-level inhomogeneous ageing in lithium-ion batteries from temperature gradients and electrical connection topologies

The distribution of current/voltage can be further regulated by optimising the electrical connection topology, considering a particular battery thermal management systems. This study numerically investigates a 4P6S battery module with two connection topologies: 1) a straight connection topology, where the sub-modules consist of parallel-connected cells that are serial connected in a linear configuration, and 2) a parallelogram connection topology, where the sub-modules are serial connected in a parallelogram configuration. We find that the straight topology is more advantageous, as it allows the temperature gradient to be distributed among the parallel-connected cells in the sub-modules, mitigating over(dis)charging. Consequently, it achieves a 0.8% higher effective capacity than the parallelogram topology at 1C discharge, along with a higher state of health at 80.15% compared to 80% for the parallelogram topology. Notably, the straight topology results in a maximum current maldistribution of 0.24C at 1C discharge, which is considered an acceptable trade-off.

Reviewer #2 (Remarks to the Author): The authors have developed 2D and 3D models to investigate the impact of serial and parallelogram design architecture on inhomogeneous aging at the module level.The physical baseline of the models is well explained; however, it is unclear what are the novel contributions of the work.The overall quality of the writing and manuscript structure is good.Further comments are listed below for the reviewed work.
• The abstract fails to introduce the straight and parallelogram design so that the results make sense.The authors should also rewrite the last two lines, especially because 'due to limiting the voltage range' is unclear.
• The authors are recommended to focus on BTMS only to provide the baseline study reasoning.At times, the discussion seems unnecessarily engaged in the thermal gradient, BTMS, etc. Otherwise, the title of the work should be rephrased.
• The topology type should be in a consistent format like αPβS; not 15p1s (and similar on page 3).
• In section 1, point 1 -the authors assume a literature-driven aging rate; however, this is cell-specific.Same comment for the point 2. Are these studies based on the same cell?How to justify the assumptions when the research topic is about inhomogeneous aging on the cell level?• Table A1 is mentioned to be taken from ref [32] in the text but the table itself refers to [45].The authors should use only one reference.
• The bottom views of Fig. 3d and 3e have no significance, thus, suggested to be removed.
• Typo in the text on page 11 and in Fig. 4c where the cold temperature is said to be 15°C, and 10°C.Only one value should be correct, this, unfortunately, creates confusion.
• The theoretical models' generated influential factor calculation is made and the numbers are mentioned in the text but no physical explanations are available for many cases.The authors are encouraged to dive deeper into the aging mechanism.
• The model-based results are not validated in physical measurement.This is a big shortcoming.The data from the literature must be verified with the specified test for the specified topologies.
• The novel contribution of the research seems also to require bigger motivation as most of the works are taken from different literature.
• The authors should also comment on additional module-level factors like cell-to-cell variation, pressure, electrical connection, vibration, etc. which are to be discussed as possible reasons behind inhomogeneous aging.
Reviewer #3 (Remarks to the Author): The authors investigate the unbalanced distributions among the cells with two study cases, the straight and parallelogram.The authors have done a very nice work and presented their results in a clear way.
Introduction main focus is the inhomogeneities from thermal management point of view, with the various cooling methods (air-liquid, which is also not SoA).More efforts should be placed on the effect of electrical connections/ bus bars/ materials/ soldering methods etc to align with the paper title.This is also contradicting with page 3 ("this study incorporates...under changing temperatures.)Assumption 2 and 3: elaborate more on this.Why such important parameters are not considered?What are the limitations of considering only the capacity fade during ageing (and only by SEI) and how relevant is this capacity fade to electrical topology and nonuniform heat distribution?Which other ageing mechanisms the uniformities can affect?Include a table with the parameters used for the electrical, thermal and ageing models and indicate their values and how they were obtained.This will increase the validity and reproducibility of the paper.
The thermal model is not clear and it needs improvements.How the surface temperature of the cells is derived?How did the thermal parameters are obtained?What is the reference temperature stated in the paper?
3D thermal model appears more as a TMS study instead of electrical connections/topology.What is the deference in the physics between the two models (straight and parallel)?How these two designs affect the heat generation of the cells or the conduction?More focus and explanations should be given on the electrical connections of the models.Do all the cells have the same parameters and states in both modules, i.e is a single cell extrapolated to the whole module?
Is the 3D module model is validated?What is the limitations here?Fig. 5c and 5f.Why the Vohmic increases for the 35degC, while it decreases for the 15degC?Please indicate the charge-discharge profile with respect to time.Section2.4,what is the natural convention (no cooling temperature behavior) of the cells/modules for both cases?How is the balancing of the BMS could affect the conclusions of this paper?What is the cost of each module with respect to the components used?

General comments:
In my view, the -tle should be made more specific, and the abstract and conclusions should be re-wri:en, in order to highlight the key limita-ons of the study, i.e.: 1) it is a model-based and not an experimental study, 2) it is not a universal study, but a study case, providing just incremental insights, 3) focuses on cycling ageing with a CCCV profile, and disregards calendar ageing, 4) resistance interconnec-ons are not considered, and 5) the ageing model only considers capacity loss based on SEI layer growth.
Response: we have re-wri0en the abstract and conclusions to reflect these changes, and highlighted in red Page 1 and 23-24.Main changes include: 1) We have added "numerically invesFgated…" in Abstract and Conclusion to reflect this.The Ftle of the paper has also been changed to highlight that this is a numerical study.
2) This study demonstrates the interacFon between electrical connecFons, thermal management and ageing through the use of a representaFve test case, but is not a universal study.3) This paper focusses on inhomogeneous ageing under cycling because this is when the majority of inhomogeneiFes occur at the module/pack level.During steady state calendar ageing, there is minimal thermal gradient between cells, no current maldistribuFon and cell voltages are ideally balanced by the ba0ery management system.We have modified the manuscript to be0er indicate this and to highlight that SOH refers to cyclic only: -We changed 'inhomogeneous ageing' to 'inhomogeneous cycling ageing' in the manuscript.-We updated our assumpFon point 3 and 4 (highlighted in red on Page 8): "3.The temperature-related ageing rate varies under cycling or resFng condiFons, and increases at lower temperatures during cycling [41], but decreases at lower temperatures during calendar ageing [42].This study exclusively focuses on cyclic ageing due to cells experiencing the same calendar ageing rate when the temperature distribuFon is homogeneous and the cell is resFng.4. The ageing mechanism considered in this study is the SEI formaFon, which is the main ageing process in most graphite-based lithium-ion ba0eries [43].Lithium plaFng is not considered due to it mainly occurring in low temperature or high C-rate condiFons [43]."AddiFonally, in the Conclusion, we emphasise that the ageing profile is based on 'CC-CV' ageing results.
4) The resistance of interconnecFons were not considered to present an idealised case that isolates the influence of topology design only and not topology and resistance combined, we have modified the manuscript to be0er highlight this point in the following ways: We have added a discussion of interconnecFon resistance on Page 19: "It is worth noFng that, to isolate the variables, interconnecFon resistance is neglected in this study.However, the proposed 3D model can also assess interconnecFon resistance by sebng the connector's electrical conducFvity to its original material value.Nevertheless, the study of interconnecFon resistance can be case-sensiFve, as it depends on the selected material 's electrical properFes,geometry,and joining techniques [62].This study primarily focuses on exploring representaFve electrical connecFon topologies, and the influence of interconnecFon resistance is beyond the scope of this research.However, to be0er demonstrate the influence of interconnecFon resistance in this study, a sensiFvity analysis is conducted by comparing current distribuFon at 1C discharge using three different materials: steel, aluminium, and a hypotheFcal super-low resistance material (i.e. in this study).The current distribuFon can be found in Fig. S3 of the Supplementary InformaFon.The results indicate that current maldistribuFon decreases with increasing electrical conducFvity; however, the difference in current distribuFon between aluminium and the hypotheFcal super-low resistance material is negligible, jusFfying why we have opted to neglect interconnecFon resistance.This also underscores the reason why aluminium is one of the most used materials [63].Thus, when selecFng a material with high electrical conducFvity (e.g.aluminium), interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study." Note: Fig. S3 can be found at the end of this document.

In Conclusion, we added:
"To isolate variables, cell-to-cell variances caused by intrinsic factors (i.e.capacity, internal resistance) and extrinsic factors (i.e.interconnecFon resistance and welding resistance) are not considered."5) To reflect ageing, we updated our assumpFon point 4 (highlighted in red on Page 8): The ageing mechanism considered in this study is the SEI formaFon, which is the main ageing process in most graphite-based lithium-ion ba0eries [43].Lithium plaFng is not considered due to it mainly occurring in low temperature or high C-rate condiFons [43].
The geometric dimensions of the modules are not provided, and this means that the results cannot be reproduced without access to the original simula-on files.
Response: We have updated Fig. 3 (e-f) with geometric dimensions on Page 7: This is oversimplified.The interac-ons between current, SOC and temperature influence calendar and cycling ageing differently.For example, low temperatures decelerate calendar ageing.This also influences the op-mal opera-ng temperature, which is actually variable within a wide range of temperatures, as low as 10°C in the case of an applica-on with low Crates.
This issue is briefly commented later in methods, but in my view should be discussed here: "The temperature-related ageing rate varies under cycling or res-ng condi-ons and is higher at lower temperatures during cycling [28], but lower at lower temperatures during calendar ageing [29].This study focuses exclusively on cycling ageing."(Page 4, third paragraph).
Response: We have rewri0en the ageing review and discussed the ageing mechanism under cycling and calendar ageing, respecFvely.The revised content is highlighted in red on Page 2: "Cell ageing can be categorised into two types: calendar ageing and cycling ageing.Calendar ageing occurs predominantly when the ba0ery is not being used, while cycling ageing happens during charge or discharge, for example, when an EV is being charged or driven [1].The calendar ageing rate increases with a higher state of charge (SOC) and temperatures, while it decreases over Fme due to the formaFon of the solid electrolyte interphase (SEI) layer, which follows the inverse of the square root of Fme dependence [2].Conversely, the rate of cycling ageing is influenced by several factors: it increases with the C-rate, SOC, and higher temperatures, and also accelerates under lower temperatures due to lithium plaFng [2,3].
We have also updated ageing assumpFon in Point 4, and highlighted in red on Page 8: "The temperature-related ageing rate varies under cycling or resFng condiFons, and increases at lower temperatures during cycling [41], but decreases at lower temperatures during calendar ageing [42].This study exclusively focuses on cyclic ageing due to cells experiencing the same calendar ageing rate when the temperature distribuFon is homogeneous and the cell is resFng." 2. "To provide useable power outputs for EVs, cells are parallel/series-connected at module level, which can significantly reduce the cycling C-rate while mee-ng the same power requirements [4]." For the same number of cells, the C-rate is the same if the cells independent of the series parallel arrangement.
Response: Thank you for highlighFng this.We have removed this incorrect statement.
3. "Liquid cooling, as a prevalent BTMS, provides high cooling efficiency, improved maintainability, moderate power usage, quick thermal response, and adaptability to both cooling and prehea-ng condi-ons [6,7]." I assume that in comparison with forced air cooling, but the authors should clarify.There are different ways to implement liquid cooling, and also other means, e.g.immersion cooling.However, the later is not men-oned, and the former very briefly and not explicitly.I would recommend elabora-ng a bit more on that.Suggested to take a look to C. Roe et al. [R3] for ideas.
Response: We have rewri0en the BTMS review by comparing indirect liquid cooling to forced air cooling and direct cooling, respecFvely.The revised content is highlighted in red on Page 2: "An effecFve ba0ery thermal management system (BTMS) is crucial in EVs to maintain uniform temperature distribuFon within the ba0ery pack.Indirect liquid cooling has become the most prevalent BTMS in commercial EVs to date [7,8].This method offers a quicker thermal response, higher cooling efficiency, and adaptability to both cooling and preheaFng condiFons compared to forced air cooling [8,9].When compared to direct cooling (or immersion cooling), indirect cooling is favoured due to its easier implementaFon [10].Moreover, the liquid coolant (e.g.ethylene glycol/water) has a lower viscosity than dielectric liquids (e.g.mineral oil), allowing for a much higher flow rate with fixed pumping power [10,11]." 4. "For the temperature distribu-on regula-on, previous research has primarily focused on op-misa-on strategies of cell layouts [17,18], flow pa:erns [19,20], and BTMS geometries [21,22]." I would say that there has been a lot of work on other topics, such as ba:ery thermal modelling and parameteriza-on (thermal conduc-vity and heat capacity), cell temperature inhomogenei-es, prehea-ng and self-hea-ng methods, cell tab design, interconnec-on resistances, ba:ery mechanical design, ba:ery re-configura-on methods, or novel balancing methods that aim to control temperature.
Response: we have deleted "leading".
7. "Before the numerical simula-on, the following assump-ons have been made in this study as follows: 1. (…) 2. Cell ohmic resistance changes due to ageing is not considered, given that only a 5% increase was observed when the SOH decreased from 1 to 0.8 in Teliz et al.'s study [30]." The validity of this assump-on is not clear for me, since the data used for model parameteriza-on is apparently coming from other sources [32,36,37] and based on a specific Panasonic cell, while in [30] no cell is specified.S4 of the Supplementary InformaFon.The results show that the maximum temperature difference is 0.8 °C, indicaFng that the temperature distribuFon pa0ern is not significantly affected by the aging process."

Response
8. "Before the numerical simula-on, the following assump-ons have been made in this study as follows: 1. (…) 3. Interconnec-on resistance is not considered in this study due to the focus on inves-ga-ng the impact of electrical topologies on inhomogeneous ageing.In the 2D model, the connector resistance is neglected.In the 3D model, the electrical conduc-vity of connectors is manually set to an extremely high value of 1×1012 Sm−1 to minimise the voltage drop and ohmic hea-ng across the connectors." The validity of this assump-on is not clear for me, since in the series-parallel arrangement in the two packs considered is not the same, and therefore the interconnec-on resistances could play a role on inhomogeneous ageing, as shown in previous literature, e.g. in [16].
Response: The interconnecFon resistance is not considered in order to focus solely on the electrical connecFon topology, thereby represenFng a best-case scenario where interconnecFon resistance is minimal and only the effects of topology are considered.This approach helps demonstrate the level of inherent inhomogeneity that cannot be miFgated through the design of low-resistance bus bars and cell connecFons.We have run a sensiFvity analysis on interconnecFon resistance with different busbar resistance and show the impact the interconnecFon resistance is neglectable when adopFng high electric conducFvity materials, such as aluminium, or hypotheFcal super-low resistance material (i.e. in this study) We have added a discussion of interconnecFon resistance on Page 19: "It is worth noFng that, to isolate the variables, interconnecFon resistance is neglected in this study.However, the proposed 3D model can also assess interconnecFon resistance by sebng the connector's electrical conducFvity to its original material value.Nevertheless, the study of interconnecFon resistance can be case-sensiFve, as it depends on the selected material's electrical properFes, geometry, and joining techniques [62].This study primarily focuses on exploring representaFve electrical connecFon topologies, and the influence of interconnecFon resistance is beyond the scope of this research.However, to be0er demonstrate the influence of interconnecFon resistance in this study, a sensiFvity analysis is conducted by comparing current distribuFon at 1C discharge using three different materials: steel, aluminium, and a hypotheFcal super-low resistance material (i.e. in this study).The current distribuFon can be found in Fig. S3 of the Supplementary InformaFon.The results indicate that current maldistribuFon decreases with increasing electrical conducFvity; however, the difference in current distribuFon between aluminium and the hypotheFcal super-low resistance material is negligible.This also underscores the reason why aluminium is one of the most used materials [63].Thus, when selecFng a material with high electrical conducFvity (e.g.aluminium), interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study." Note: Fig. S3 can be found at the end of this document.
AddiFonally, we revised assumpFon 2 to make it clearer, highlighted in red on Page8: "Cell-to-cell variances due to extrinsic factors, such as interconnecFon resistance and welding techniques, are not accounted for in controlling the variables.This is to focus on the impact of connecFon topology on inhomogeneous ageing due to temperature gradients.Thus, interconnecFon resistance is neglected in the 2D model.In the 3D model, the electrical conducFvity of connectors is manually set to an extremely high value of 1 × 10 !"  #! to minimise the voltage drop and ohmic heaFng across the connectors.The influence of interconnecFon resistance is further discussed in SecFon 2.4." 9. "Before the numerical simula-on, the following assump-ons have been made in this study as follows: 1. (…) 4. Heat conduc-on is the only heat transfer mode considered in this simula-on." To ease understanding, the authors should clarify here if this means if what are the actual paths considered for heat transfer by conduc-on, e.g.: 1) cell-to-cell through the surface, 2) cell-to-cell through the busbar, 3) cell-to-cooling system, etc.I know the answer aoer reading the whole paper, but the authors should make clear here if they are assuming: 1) a lumped thermal cell model, i.e., if they use a volume averaged temperature, or a 2) 3D distributed thermal cell model, and reflect somewhere on what are the consequences of that in the results obtained.
Response: We have rewri0en the sentence to make our statement clearer.The revised content is highlighted in red on Page 8, point 6: "The heat transfer considered in this model is limited to heat convecFon (i.e.heat removed by the cooling liquid) and heat conducFon (i.e.heat transfer from the cells to the cooling pipe and between cells through the busbar).Heat transfer from cell to cell and from cell to ambient air is not considered.We note cells tend to have an insulaFon layer in ba0ery pack design to prevent thermal runaway propagaFon [44,45]." A diagram explaining how the 2D an" the'3D model interact would be useful too, to ease understanding.
Response: 2D model focuses on invesFgaFng the impact of temperature variaFons on cells with fixed temperature gradient at sub-module level.3D model focus on the inhomogeneous cycling ageing at module-level.To make the link between 2D and 3D model clearer, we updated the manuscript on Page 5, highlighted in red:  Also, to be0er illustrate the relaFonship between 2D and 3D models, we have reorganized the structure of 'SecFon 1 Method', by adding a subsecFon Ftled '1.1 Geometry Development' on Pages 6-8.
10. Regarding other possible assump-ons to be listed.
• Cell-to-cell differences are not considered, although they are well documented in the literature, e.g. in [R4].This assump-on could be fine, but this should be included in the list and the consequences of that in the results commented clearly.
• The ageing model only considers SEI growth, which might be fine too, but it should be highlighted and listed.
Response: we have added these two assumpFons in bullet point 1, and 4, and highlighted in red on Page 6-8: "1. Cell-to-cell variances due to intrinsic reasons, such as the cell capacity, internal resistance, and energy density, are not considered as this study focuses on the cell-to-cell variance in temperature-sensiFve electrochemical parameters due to temperature gradients (i.e.ohmic resistance, exchange current, and diffusion coefficient) [4,20].Therefore, cells are assumed to exhibit the same electrochemical properFes when they are at the same temperature.
4. The ageing mechanism considered in this study is the SEI formaFon, which is the main ageing process in most graphite-based lithium-ion ba0eries [43].Lithium plaFng is not considered due to it mainly occurring in low temperature or high C-rate condiFons [43]." 11. Regarding the thermal model parameteriza-on: heat capacity and thermal conduc-vi-es.
Considering the type of model-based study that the authors are presen-ng, careful parameteriza-on of the thermal model is mandatory.
The authors jus-fy the cell heat capacity parameter value of 750 J/kg-K based on [46], but: 1) in that reference a lower value is provided (727 J/kg-K), 2) this is not an appropriate reference, since it is an inves-ga-on based on a fake/surrogate cell, and not a real cell, and 3) in [46] it is men-oned a wide range of possible values for heat capacity found in the literature 800-1700 J/kg-K.Authors are encouraged to find a be:er reference to jus-fy the elec-on and change the value if needed.
Regarding the axial/radial thermal conduc-vi-es, the authors jus-fy the selec-on of the parameters based on reference [47], i.e.M. Al-Zareer "Numerical Study of Flow and Heat Transfer Performance of 3D-Printed Polymer-Based Ba:ery Thermal Management."Based on that thereference too, the heat capacity of the cell is 1400 J/(kg • K), which is contradictory with previous assump-ons.Moreover, in this reference, the author jus-fies the values of the heat capacity and thermal conduc-vi-es based on references: • T.F.Fuller, M. Doyle, J. Newman, "Simula-on and Op-miza-on of the Dual Lithium Ion Inser-on Cell", J. Electrochem.Soc., 141 (1) (1994), pp.1-9.
However, in none of these references there is data about thermal parameters.
The authors are suggested to take a look to [R5] to find references to jus-fy their selec-on of parameters.
Changing the values of these parameters necessarily means that the authors will have to repeat the simula-ons and re-write the results sec-on.The current parameters are not valid.
Response: Thank you for providing these useful references.We have reviewed them and updated the thermal properFes of the cell accordingly.All simulaFons have been rerun, and the simulaFon results have been updated to reflect these changes.
Table 1 shows the original thermal properFes and the updated thermal properFes of the cell.12.The key limita-ons and assump-ons, and their impact in the results, should be commented in the conclusions -or a discussion sec-on could be included in the paper.
Response: We have added discussions on the impacts of assumpFons in SecFon 2 Results and discussion: 1) We have added a discussion of interconnecFon resistance on Page 19: "It is worth noFng that, to isolate the variables, interconnecFon resistance is neglected in this study.However, the proposed 3D model can also assess interconnecFon resistance by sebng the connector's electrical conducFvity to its original material value.Nevertheless, the study of interconnecFon resistance can be case-sensiFve, as it depends on the selected material's electrical properFes, geometry, and joining techniques [62].This study primarily focuses on exploring representaFve electrical connecFon topologies, and the influence of interconnecFon resistance is beyond the scope of this research.However, to be0er demonstrate the influence of interconnecFon resistance in this study, a sensiFvity analysis is conducted by comparing current distribuFon at 1C discharge using three different materials: steel, aluminium, and a hypotheFcal super-low resistance material (i.e. in this study).The current distribuFon can be found in Fig. S3 of the Supplementary InformaFon.The results indicate that current maldistribuFon decreases with increasing electrical conducFvity; however, the difference in current distribuFon between aluminium and the hypotheFcal super-low resistance material is negligible.This also underscores the reason why aluminium is one of the most used materials [63].Thus, when selecFng a material with high electrical conducFvity (e.g.aluminium), interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study."Note: Fig. S3 can be found at the end of this document.
2) Discussion on ageing assumpFon, highlighted in red on Page 23: The ageing model only considers capacity loss due to SEI growth as it is the main ageing factor in most graphite-based lithium-ion ba0eries.Lithium plaFng is not considered, as it mainly occurs under high C-rate or low-temperature condiFons, where the C-rate is under 1C, and the temperature is above 25 °C in this study.Calendar ageing rate is not considered in this study as cells experience same ageing rate when the temperature distribuFon is homogeneous in their resFng condiFon at the same SOC.

General comment:
The authors have developed 2D and 3D models to inves-gate the impact of serial and parallelogram connec-on topology architecture on inhomogeneous aging at the module level.
The physical baseline of the models is well explained; however, it is unclear what are the novel contribu-ons of the work.The overall quality of the wri-ng and manuscript structure is good.
Response: We have updated the manuscript to emphasise where the novelty in this work lies.The revised content is highlighted in red on Page 4: "These aforemenFoned studies underscore that, under idenFcal cooling condiFons, inhomogeneous ageing can be further managed by modifying electrical configuraFons.However, the limitaFons can be summarised as follows: 1. Most previous studies focus on parallel connecFons (nP1S), which may not adequately represent the current distribuFon at the module level.
2. Most previous studies rely on 2D models, which cannot fully capture real-Fme temperature changes or distribuFon throughout the enFre cycling process.In these studies, the temperature gradient is onen set to a constant value (e.g. a 5 °C increment in Liu et al.'s study [18]; a fixed gradient of 12.5 °C or 25 °C in Marlow et al.'s study [17]).

Most research has focussed on interconnecFon resistance and welding techniques
to opFmise module-level variances.To the best of the authors' knowledge, the cell-tocell variances caused by temperature gradients across different electrical connecFon topologies has not been reported.
Therefore, it is crucial to develop a 3D ba0ery module model that includes both parallel and series connecFons while considering real-Fme temperature changes.This will enable a comprehensive understanding of the different module-level inhomogeneous cycling ageing caused by different electrical connecFon topologies." Bullet comment: 1.The abstract fails to introduce the straight and parallelogram connec-on topology so that the results make sense.The authors should also rewrite the last two lines, especially because 'due to limi-ng the voltage range' is unclear.
Response: The reviewer makes a good point.We have added a descripFon to the straight and parallelogram connecFon topology, and highlighted in red on Page 1: "This study numerically invesFgates a 4P6S ba0ery module, comprising sub-modules with two different connecFon topologies: 1) a straight connecFon topology, the sub-modules consisFng of parallel-connected cells are serial connected in a linear configuraFon, and 2) a parallelogram connecFon topology, where the sub-modules are serial connected in a parallelogram configuraFon." We have re-wri0en the last part of the Abstract to make it clearer: "We find that the straight electrical connecFon topology is more advantageous.This topology allows the temperature gradient to be distributed among the parallel-connected cells in the sub-modules, miFgaFng the issue of over(dis)charging.Consequently, it results in a higher effecFve capacity increase of 0.8% than the parallelogram connecFon topology.AddiFonally, it exhibits a higher State of Health (SOH) of 80.15% when the parallelogram connecFon topology first reaches the end-of-life (80%).However, it is noteworthy that the straight connecFon topology results in increased current maldistribuFon within sub-modules, but it is considered an acceptable trade-off." 2. The authors are recommended to focus on BTMS only to provide the baseline study reasoning.At -mes, the discussion seems unnecessarily engaged in the thermal gradient, BTMS, etc. Otherwise, the -tle of the work should be rephrased.
Response: This study invesFgated the combined effects of different electrical connecFon topologies on inhomogeneous cycling ageing due to temperature gradient stemming from the BTMS.Thus, we feel the inclusion of thermal gradient and BTMS parts are important.However, we have changed the Ftle of the paper to make it clearer: "Numerical invesFgaFon of variance in module-level inhomogeneous cycling ageing due to temperature gradient across different electrical connecFon topologies" 3. The topology type should be in a consistent format like αPβS; not 15p1s (and similar on page3).
4. In sec-on 1, point 1 -the authors assume a literature-driven aging rate; however, this is cell specific.Same comment for the point 2. Are these studies based on the same cell?How to jus-fy the assump-ons when the research topic is about inhomogeneous aging on the cell level?
Response  S4 of the Supplementary InformaFon.The results show that the maximum temperature difference is 0.8 °C, indicaFng that the temperature distribuFon pa0ern is not significantly affected by the aging process." 3) We have added two new assumpFons on the cell-to-cell variance (point 1 and 2, on Page 6-8): "Point 1: Cell-to-cell variances due to intrinsic reasons, such as the cell capacity, internal resistance, and energy density, are not considered as this study focuses on the cell-to-cell variance in temperature-sensiFve electrochemical parameters due to temperature gradients (i.e.ohmic resistance, exchange current, and diffusion coefficient) [4,20].Therefore, cells are assumed to exhibit the same electrochemical properFes when they are at the same temperature.
Point 2: Cell-to-cell variances due to extrinsic factors, such as interconnecFon resistance and welding techniques, are not accounted for in controlling the variables.This is to focus on the impact of connecFon topology on inhomogeneous ageing due to temperature gradients.Thus, interconnecFon resistance is neglected in the 2D model.In the 3D model, the electrical conducFvity of connectors is manually set to an extremely high value of 1 × 10 !"  #! to minimise the voltage drop and ohmic heaFng across the connectors.The influence of interconnecFon resistance is further discussed in SecFon 2.4.The influence of interconnecFon resistance is further discussed in SecFon 2.4." We have also added a discussion of interconnecFon resistance on Page 19: "It is worth noFng that, to isolate the variables, interconnecFon resistance is neglected in this study.However, the proposed 3D model can also assess interconnecFon resistance by sebng the connector's electrical conducFvity to its original material value.Nevertheless, the study of interconnecFon resistance can be case-sensiFve, as it depends on the selected material's electrical properFes, geometry, and joining techniques [62].This study primarily focuses on exploring representaFve electrical connecFon topologies, and the influence of interconnecFon resistance is beyond the scope of this research.However, to be0er demonstrate the influence of interconnecFon resistance in this study, a sensiFvity analysis is conducted by comparing current distribuFon at 1C discharge using three different materials: steel, aluminium, and a hypotheFcal super-low resistance material (i.e. in this study).The current distribuFon can be found in Fig. S3 of the Supplementary InformaFon.The results indicate that current maldistribuFon decreases with increasing electrical conducFvity; however, the difference in current distribuFon between aluminium and the hypotheFcal super-low resistance material is negligible.This also underscores the reason why aluminium is one of the most used materials [63].Thus, when selecFng a material with high electrical conducFvity (e.g.aluminium), interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study." Note: Fig. S3 can be found at the end of this document.A1 is men-oned to be taken from ref [32] in the text but the table itself refers to [45].

Table
The authors should use only one reference.

Response: we have corrected the reference in Table A1 on Page 24 and highlighted it in red on
Page 25.
4. The bo:om views of Fig. 3d and 3e have no significance, thus, suggested to be removed.
Response: we have removed the bo0om views of Fig. 3d and 3e.
5. Typo in the text on page 11 and in Fig. 4c where the cold temperature is said to be 15°C, and 10°C.Only one value should be correct, this, unfortunately, creates confusion.
Response: we have corrected the "15°C" to "10°C" in the text, highlighted in red on Page 14.We have corrected the temperature from 15°C to 10°C in Fig. 4c, highlighted in red on Page 15.
6.The theore-cal models' generated influen-al factor calcula-on is made and the numbers are men-oned in the text but no physical explana-ons are available for many cases.The authors are encouraged to dive deeper into the aging mechanism.To reflect this, we have changed the Ftle to emphasis this is a numerical invesFgaFon on the module-level inhomogeneous ageing.

Response: we have rewri0en the ageing model by adding more physical explanaFons to each ageing factor (highlighted in red on
We have also added a discussion of interconnecFon resistance on Page 19: "It is worth noFng that, to isolate the variables, interconnecFon resistance is neglected in this study.However, the proposed 3D model can also assess interconnecFon resistance by sebng the connector's electrical conducFvity to its original material value.Nevertheless, the study of interconnecFon resistance can be case-sensiFve, as it depends on the selected material 's electrical properFes,geometry,and joining techniques [62].This study primarily focuses on exploring representaFve electrical connecFon topologies, and the influence of interconnecFon resistance is beyond the scope of this research.However, to be0er demonstrate the influence of interconnecFon resistance in this study, a sensiFvity analysis is conducted by comparing current distribuFon at 1C discharge using three different materials: steel, aluminium, and a hypotheFcal super-low resistance material (i.e. in this study).The current distribuFon can be found in Fig. S3 of the Supplementary InformaFon.The results indicate that current maldistribuFon decreases with increasing electrical conducFvity; however, the difference in current distribuFon between aluminium and the hypotheFcal super-low resistance material is negligible.This also underscores the reason why aluminium is one of the most used materials [63].Thus, when selecFng a material with high electrical conducFvity (e.g.aluminium), interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study." Note: Fig. S3 can be found at the end of this document.
8. The novel contribu-on of the research seems also to require bigger mo-va-on as most of the works are taken from different literature.
Response: We have summarised the research gap, and highlighted in red on Page 4: "1.Most previous studies focus on parallel connecFons (nP1S), which may not adequately represent the current distribuFon at the module level.
2. Most previous studies rely on 2D models, which cannot fully capture real-Fme temperature changes or distribuFon throughout the enFre cycling process.In these studies, the temperature gradient is onen arbitrarily set to a constant value (e.g. a 5 °C increment in Liu et al.'s study [18];fixed 12.5 °C or 25 °C gradient in Marlow et al.'s study [17]).

Most research has focussed on interconnecFon resistance and welding techniques to opFmise module-level variances. To the best of the authors' knowledge, the cell-to-cell variances caused by temperature gradients across different electrical connecFon topologies has not been reported.
Therefore, it is crucial to develop a 3D ba0ery module model that includes both parallel and series connecFons while considering real-Fme temperature changes.This will enable a comprehensive understanding of the different module-level inhomogeneous cycling ageing caused by different electrical connecFon topologies." 9. The authors should also comment on addi-onal module-level factors like cell-to-cell varia-on, pressure, electrical connec-on, vibra-on, etc. which are to be discussed as possible reasons behind inhomogeneous aging.

Response:
We have added more literature on other factors that could introduce inhomogeneous aging in IntroducFon.We have highlighted them in red on Page 3: "The unavoidable temperature gradient between cells can also lead to cell-to-cell variaFons, which can be categorised into three levels: parFcle level, cell level, and module level.At the parFcle level, defects or irregulariFes in electrode materials due to manufacturing techniques can lead to local inhomogeneiFes, impacFng the performance, durability, and safety of the ba0ery [12].However, parFcle-level inhomogeneiFes are typically intrinsic and difficult to control.Thus, most studies focus on the cell level and explore aspects such as surface temperature inhomogeneiFes [13,14], capacity variaFon [15], internal resistance variaFon [15], and mechanical stress variaFon [16].Compared cell-level study, research on module-level variaFons is relaFvely less explored.Previous cell-level studies have predominantly focused on current regulaFon regarding thermal gradients [17], interconnecFon resistance [18,19], and welding techniques [18].
From a thermal perspecFve, temperature gradients lead to variances in temperature-sensiFve electrochemical properFes among cells, such as internal ohmic resistance, charge exchange current, and diffusion coefficient [20].For example, ohmic resistance decreases with increasing temperature due to lithium ions migraFng faster through the electrolyte [21].The charge exchange current increases with temperature as electrodes become more reacFve [22].
1.The authors inves-gate the unbalanced distribu-ons among the cells with two study cases, the straight and parallelogram.The authors have done a very nice work and presented their results in a clear way.
Response: Thank you for your recogniFon for our work.
2. Introduc-on main focus is the inhomogenei-es from thermal management point of view, with the various cooling methods (air-liquid, which is also not SoA).More efforts should be placed on the effect of electrical connec-ons/ bus bars/ materials/ soldering methods etc to align with the paper -tle.This is also contradic-ng with page 3 ("this study incorporates...under changing temperatures.) Response: 1) We have added more literature on other effects that could introduce inhomogeneous ageing in IntroducFon.We have highlighted them in red on Page 3: "The unavoidable temperature gradient between cells can also lead to cell-to-cell variaFons, which can be categorised into three levels: parFcle level, cell level, and module level.At the parFcle level, defects or irregulariFes in electrode materials due to manufacturing techniques can lead to local inhomogeneiFes, impacFng the performance, durability, and safety of the ba0ery [12].However, parFcle-level inhomogeneiFes are typically intrinsic and difficult to control.Thus, most studies focus on the cell level and explore aspects such as surface temperature inhomogeneiFes [13,14], capacity variaFon [15], internal resistance variaFon [15], and mechanical stress variaFon [16].Compared cell-level study, research on module-level variaFons is relaFvely less explored.Previous cell-level studies have predominantly focused on current regulaFon regarding thermal gradients [17], interconnecFon resistance [18,19], and welding techniques [18].
From a thermal perspecFve, temperature gradients lead to variances in temperature-sensiFve electrochemical properFes among cells, such as internal ohmic resistance, charge exchange current, and diffusion coefficient [20].For example, ohmic resistance decreases with increasing temperature due to lithium ions migraFng faster through the electrolyte [21].The charge exchange current increases with temperature as electrodes become more reacFve [22].Similarly, the diffusion coefficient increases with temperature, enhancing the kineFcs of lithium ions [23,24].These variaFons lead to uneven distribuFon of temperature, current, and voltage, exacerbaFng inhomogeneous cycling ageing in the cells [10,25].Liu et al. [17] found that a thermal gradient of 25°C increased aging rate by 5.2%.Various approaches have been proposed to regulate temperature homogeneity within the module, such as cell tab opFmisaFon [26,27], low-temperature preheaFng/self-heaFng techniques [28], ba0ery mechanical design [29], reconfigurable ba0ery management systems [30], and novel balancing methods [31,32].From the perspecFve of the BTMS, various aspects such as cell layouts [33,34], flow pa0erns [35,36], and BTMS geometries [37,38] have been studied as means to improve homogeneity." 2) We have rewri0en the sentence to make our statement clearer (highlighted in red on Page 5): Original: This study incorporates both thermal and electrical configuraFons into the analysis to simulate in real-Fme the current and voltage distribuFons under changing temperatures.
Revised: It integrates thermal and electrochemical models to simulate real-Fme current, voltage and temperature distribuFons using a representaFve 3D ba0ery module (4P6S).
3. Assump-on 2 and 3: elaborate more on this.Why such important parameters are not considered?What are the limita-ons of considering only the capacity fade during ageing (and only by SEI) and how relevant is this capacity fade to electrical topology and nonuniform heat distribu-on?Which other ageing mechanisms the uniformi-es can affect?
Response: 1).The interconnecFon resistance is not considered in order to focus solely on the electrical connecFon topology, thereby represenFng a best-case scenario where interconnecFon resistance is minimal and only the effects of topology are considered.This approach helps demonstrate the level of inherent inhomogeneity that cannot be miFgated through the design of low-resistance bus bars and cell connecFons.We have rewri0en the assumpFons to make our statement clearer, and added a discussion on the influence of interconnecFon resistance, which can be found in the Supplementary Note 1.The revised assumpFons are highlighted in red on Page 6-8, Point 1 and 2: 1. Cell-to-cell variances due to intrinsic reasons, such as the cell capacity, internal resistance, and energy density, are not considered as this study focuses on the cell-tocell variance in temperature-sensiFve electrochemical parameters due to temperature gradients (i.e.ohmic resistance, exchange current, and diffusion coefficient) [4,20].Therefore, cells are assumed to exhibit same electrochemical properFes when they are at the same temperature.
2. Cell-to-cell variances due to extrinsic factors, such as interconnecFon resistance and welding techniques, are not accounted for in controlling the variables.This study focuses on examining the impact of various electrical connecFon topologies on inhomogeneous ageing, which is a0ributed to the temperature gradient stemming from the BTMS.Thus, connector resistance is neglected in the 2D model.In the 3D model, the electrical conducFvity of connectors is manually set to an extremely high value of 1 × 10 !"  #! to minimise the voltage drop and ohmic heaFng across the connectors.The influence of interconnecFon resistance is further discussed in SecFon 2.4.
3) The thermal parameters of NCA/graphite Panasonic 18650 cell are obtained from Ref. [70][71].The thermal parameters of other materials (e.g.cooling water, aluminium cooling pipe, steel busbar) are obtained from COMSOL in-build materials.
4) The reference temperature is 25°C.We have emphasised this by adding: "The reference temperature of this study is 25 °C.",highlighted in red on Page 6.
6. 3D thermal model appears more as a TMS study instead of electrical connec-ons/topology.What is the deference in the physics between the two models (straight and parallel)?How these two designs affect the heat genera-on of the cells or the conduc-on?More focus and explana-ons should be given on the electrical connec-ons of the models.Do all the cells have the same parameters and states in both modules, i.e is a single cell extrapolated to the whole module?
Response: 1) What is the deference in the physics between the two models (straight and parallel? We added a 2D schemaFc diagrams of electrical connecFon: 2) How these two designs affect the heat generaFon of the cells or the conducFon?
We have added a comparison of "heat generaFon rate" in Fig. 7 e-f, and have also added a discussion on the influence of heat generaFon rate for these two designs, on Page 19-20: "Fig.7c illustrates the heat generaFon rate among cells during the 1C discharge phase.The heat generaFon rate of a cell depends on the current and temperature, as described Eq.23-29.It is observed that cells on the cooler side exhibit a higher heat generaFon rate due to experiencing greater overpotenFal.AddiFonally, a higher current maldistribuFon leads to a more pronounced heat generaFon rate gradient in the straight connecFon topology.However, the overall difference in heat generaFon between the two designs does not significantly influence the temperature distribuFon, as illustrated in Fig. 7a." 3) Do all the cells have the same parameters and states in both modules, i.e is a single cell extrapolated to the whole module?Cells have the same parameters if they experience the same temperature.However, when temperature changes, temperature-sensiFve electrochemical parameters also change, resulFng in different cell states.We updated AssumpFon Point 1 on Page 6 to reflect this: 1. "Cell-to-cell variances due to intrinsic reasons, such as the cell capacity, internal resistance, and energy density, are not considered as this study focuses on the cell-tocell variance in temperature-sensiFve electrochemical parameters due to temperature gradients (i.e.ohmic resistance, exchange current, and diffusion coefficient) [4,20].Therefore, cells are assumed to exhibit the same electrochemical properFes when they are at the same temperature." 7. Is the 3D module model is validated?What is the limita-ons here?
Response We have added charge-discharge profile to the Fig. 5, on Page 16: 9. , what is the natural conven-on (no cooling temperature behavior) of the cells/modules for both cases?
Response: The natural air convenFon is not considered in this model as it is not the main cooling mechanism, and the cells tend to have an insulaFon layer in ba0ery pack design to prevent thermal runaway propagaFon [53,54].We have updated AssumpFon Point 6 (Page 6) to make the heat transfer mechanism clearer: "Point 6.The heat transfer considered in this model is limited to heat convecFon (i.e.heat removed by the cooling liquid) and heat conducFon (i.e.heat transfer from the cells to the cooling pipe and between cells through the busbar).Heat transfer from cell to cell and from cell to ambient air is not considered.We note cells tend to have an insulaFon layer in ba0ery pack design to prevent thermal runaway propagaFon [44,45]." 10. How is the balancing of the BMS could affect the conclusions of this paper?What is the cost of each module with respect to the components used?
Response: 1) How is the balancing of the BMS could affect the conclusions of this paper?
We have added a discussion on the potenFal impact of BMS on acFve balancing, and highlighted in red on Page:23: "Current ba0ery management system (BMS) commonly esFmates the SOC of individual cells in series by measuring voltage or coulomb counFng.However, for individual cells connected in parallel (i.e. the sub-module), the BMS treats them as a single 'lumped' cell due to the lack of access to specific currents and temperatures of each cell [64].This approach prevents the BMS from differenFaFng the aging scenario within the sub-module.The BMS could a0empt to compensate for inhomogeneous aging by having series-connected cells at different voltages, but this would limit the operaFng capacity of the pack due to voltage limit constraints." 2) What is the cost of each module with respect to the components used?
Cost is not considered in this study due to it beyond the scope of this study.However, regarding the cost difference between the two designs, it primarily lies in the electrical connectors.We believe this will not significantly impact the overall cost.
1. Following the response to the general comment, the authors should look at the recently published paper if it has addressed some of the shortcomingshttps://doi.org/10.1038/s44172-023-00153-5 This reviewer is still not convinced with the responses to Points 7 and 8.The novel contribution is weak unless an experimental verification of the 3D outcome is demonstrated.The named concerns could be highlighted in case of significant deviation from the experimental study.
Response This work provides some numerical investigation on the cell-to-cell variance due to temperature gradient.The paper is well written.I have two main concerns: 1.The results of the numerical investigation are only valid if the model is correct and can be experimentally validated, which is unfortunately not the case in this work.
Response: The model has been validated at the cell level.Experimental validation at the module level can be challenging, as other factors mentioned in the manuscript (i.e., internal resistance, cell capacity variety, and energy density variety) are difficult to eliminate in the experiment.In this work, we focus solely on one facto, i.e. electrical connection topology.Thus, isolating this single factor and validating it via experimental work is difficult.
2. The lack of experimental validation also leads to the three highlights mentioned in the answer to Reviewer 2's 8th comment being unconvincing.Because these highlights are hard to be claimed when the model used in this work has not been validated.
To summarize, I really recommend the authors carry out further experimental validations of the whole model to convince the readers of the main conclusions of this work.
Response: We do recommend conducting future experimental work to analyse inhomogeneous aging, taking all these factors into consideration together.The revised content is highlighted in red on Page 21: "The future work will focus on module-level experimental validation to further examine the current maldistribution and inhomogeneous ageing within the proposed battery module."

Figure 8 Figure 9
Figure 8 The temperature, current, voltage, and SOC distribu8on of the module.(a) Temperature distribu8on for the straight and parallelogram connec8on topologies at 3214 s.(b) Current distribu8on for the straight and parallelogram connec8on topologies at 600 s and 3214 s.(c) SOC distribu8on for the straight and parallelogram connec8on topologies at 3214 s.(d) Cell voltage and electrical connectors poten8al distribu8on for the straight and parallelogram connec8on topologies at 3214s.We have updated Fig.9 (Page 22) with 3D SOH and temperature distribuFon included:

Figure 7
Figure 7 Comparisons of module-level temperature, current, heat genera8on rate, SOC, and voltage change for straight and parallelogram connec8on topologies under 1C discharge.(a) Temperature increases from 25 ℃ to a maximum of 34 ℃ and temperature difference between two topologies is negligible (< 0.62 °C).(b) Current change shows the straight connec8on topology exhibits higher maldistribu8on due to higher temperature gradient among cells within a sub-module due to higher temperature gradient among cells within a sub-module.(c) Heat genera8on rate change shows cells on the cool side have higher heat genera8on rate due to experiencing higher overpoten8al, and higher current maldistribu8on leads to higher heat genera8on rate gradient.(d) SOC change shows the straight connec8on topology exhibits a higher SOC gradient at the endof-discharge due to current maldistribu8on.(e) Voltage change shows the parallelogram connec8on topology exhibits a higher voltage maldistribu8on due to higher temperature gradient among sub-modules.

Table 1
Thermal property of 18650 cell The authors have implemented a 3D model in COMSOL, but the authors do not present any figure in the paper that shows actual 3D results of the temperature distribu-on with inhomogeneous cell temperatures.I would suggest including that, and not only 2D results plots (Fig.7 and 8).
Response: We added a new Fig.8 (Page 22) with 3D temperature distribuFon included: % : High SOC values (typically resulFng in high ba0ery voltage) accelerate capacity loss[58].%representstheresult of either a parasiFc electrochemical reducFon reacFon occurring on the negaFve electrode, or an oxidaFon reacFon occurring on the posiFve electrode.2.& : Ba0ery lifeFme is related to the amount of cycled equivalent full cycles.&representsthelinearrelaFon between the capacity fade and the number of full cycles.3.'():Ageinghistory defines how many Fmes the capacity loss rate will have been reduced when all capacity has been lost.'()representstherate of the capacity fade slowed down by the parasiFc reacFons, e.g. the formaFon of SEI.4.* : The cycling ageing rate increase in both higher and lower temperature[3].* is the ageing caused by temperature, described by an Arrhenius expression.7.The model-based results are not validated in physical measurement.This is a big shortcoming.The data from the literature must be verified with the specified test for the specified topologies.
:1.Response: The cell electrochemical and ageing model have been validated based on the experimental data.The ba0ery module model is not validated by experiment.However, it would be difficult to undertake a good experimental validaFon of the full 3D model as measuring current distribuFon in parallel is very difficult without interfering with the system under test (i.e.shunt resistors or hall effect sensors).AddiFonally, we only focus on the cell-tocell variance in temperature-sensiFve electrochemical parameters (i.e.ohmic resistance, exchange current, and diffusion coefficient) due to the temperature gradient stemming from the BTMS.Other factors, such as interconnectors resistance, cell level variances can be difficult to eliminate in experimental test.
83 in Raj et al.'s study.Thus, we neglect the ohmic resistance change for the simplificaFon purpose.We have added a further discussion in SecFon 2.4 to invesFgate the influence of internal resistance change.The revised assumpFon is highlighted in red on Page 6, point 5: "Cell ohmic resistance changes due to ageing are not considered for the simplificaFon purpose.The influence of internal resistance change is further discussed in SecFon 2.4."Include a table with the parameters used for the electrical, thermal and ageing models and indicate their values and how they were obtained.This will increase the validity and reproducibility of the paper.Response: A table of symbols and values used in ba0ery and ageing mode is added in Table A3, Page 25.A table of symbols and values used in thermal mode is in TableA4, Page 26.5.The thermal model is not clear and it needs improvements.How the surface temperature of the cells is derived?How did the thermal parameters are obtained?What is the reference temperature stated in the paper?
. Fig.5c and 5f.Why the Vohmic increases for the 35degC, while it decreases for the 15degC?Please indicate the charge-discharge profile with respect to -me./01 =  /01  +',, , we can see that  /01 is dependent on  /01 and  +',, .In a serial connecFon,  +',, is the same for every cell; thus,  /01 depends solely on  /01 .However, in a parallel connecFon, a cell with higher temperature will undergo a higher  +',, due to lower resistance.At the same Fme, /01 is lower.When these two factors are mulFplied, they result in the corresponding change in  /01 .2) Please indicate the charge-discharge profile with respect to Fme.
interconnecFon resistance is not the primary factor influencing the inhomogeneous ageing between the straight and parallelogram connecFon topologies for this study."Note:Fig.S3can be found at the end of this document.8

Reviewer #4 (Remarks to the Author):
: The model has been validated at the cell level.Experimental validation at the module level can be challenging, as other factors mentioned in the manuscript (i.e., internal resistance, cell capacity variety, and energy density variety) are difficult to eliminate in the experiment.In this work, we focus solely on one facto, i.e. electrical connection topology.Thus, isolating this single factor and validating it via experimental work is difficult.However,We do recommend conducting experimental work in the future to analyse inhomogeneous aging, taking all these factors into consideration together.The revised content is highlighted in red on Page 21: "The future work will focus on module-level experimental validation to further examine the current maldistribution and inhomogeneous ageing within the proposed battery module."Wealso reviewed the recommended reference, and cited the results from this work to support our conclusion.The revised content is highlighted in red on Page 20: "In this study, if the discharge stops when the first cell reaches the cut-off voltage, the parallelogram connection topology has an effective discharge capacity of 88.6%, while the straight connection topology has an effective discharge capacity of 89.4% at a 1C discharge, resulting in a 0.8% capacity difference.This find agrees with Marlow et al.'s study 12 that within parallel-connected cells, accessible capacity is reduced due to the end-of-discharge SOC deficit."