pith. sign in

arxiv: 2303.09838 · v4 · pith:5SXWD4YQnew · submitted 2023-03-17 · ⚛️ physics.app-ph

A Computational Framework Integrating Physics-based Model and Equivalent Circuit Network Model to Simulate Li-ion Batteries

Han Yuan , Shen Li , Tao Zhu , Simon O'Kane , Carlos Garcia , Gregory Offer , Monica Marinescu This is my paper

Pith reviewed 2026-05-24 09:21 UTC · model grok-4.3

classification ⚛️ physics.app-ph
keywords Li-ion battery modelingDFN modeldistributed ECNthermal inhomogeneitypouch cell simulationvoltage prediction errorcomputational frameworkKokam SLPB75106100
0
0 comments X

The pith

Integrating a physics-based DFN model with a 3D-distributed ECN model produces faster battery simulations with roughly one-third the voltage error of a lumped DFN-thermal model at high C-rates or low temperatures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to overcome the trade-off between accuracy and speed in Li-ion battery modeling by linking a detailed electrochemical DFN model to a spatially distributed ECN model. DFN models capture internal processes well but become too slow when fully coupled to 3D thermal fields, while distributed ECN models run quickly yet depend on experiments that are distorted by internal temperature gradients. The framework extracts ECN parameters directly from the DFN solution so that spatial variations in electrochemistry, heat generation, and current flow are retained without new lab campaigns. Tests on a 7.5 Ah Kokam pouch cell show the integrated model cuts the largest prediction error to about one-third of the standard lumped approach at 3 C and 25 °C or at 1 C and 0 °C, with differences reaching 377 mV at 3 C and 5 °C. This matters for engineers who need reliable voltage and temperature forecasts to size cooling systems and set safe operating limits without prohibitive computation time.

Core claim

By integrating electrochemical DFN model and 3D distributed ECN model together, the computational framework can simulate the complicated interplay between electrochemistry, thermal process, and electricity within a cell fast and accurately. The largest predicting error of the framework at 3 C-rate & Tam = 25°C and at 1 C-rate & Tam = 0°C is approximately 1/3 of that for DFN model. At 3 C-rate & Tam = 5°C, the difference between these two can rise to 377 mV.

What carries the argument

The integration framework that extracts 3D-distributed ECN parameters from a DFN solution to embed spatial thermal inhomogeneity directly into the fast network model.

If this is right

  • The integrated model outperforms the lumped DFN-thermal model at low-temperature and high C-rate conditions.
  • Voltage prediction differences reach 377 mV at 3 C-rate and 5 °C ambient.
  • The framework captures the coupled electrochemistry-thermal-electricity behavior inside the cell without full 3D thermal solving at every step.
  • It provides a practical tool for battery design and control that runs faster than fully coupled physics models.
  • Parameter derivation from DFN avoids the resource cost and thermal-gradient errors of direct ECN experiments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same parameter-transfer step could be applied to other cell formats or chemistries to test whether the error reduction holds when internal gradients are larger.
  • The framework’s speed advantage might allow real-time control algorithms that adjust current limits based on predicted local temperatures rather than average cell temperature.
  • Extending the 3D ECN mesh to module or pack level would test whether the method scales without reintroducing the original computational bottleneck.
  • If the DFN-to-ECN mapping proves robust, it could reduce reliance on expensive thermal-chamber characterization rigs for new cell designs.

Load-bearing premise

The DFN-derived ECN parameters correctly embed spatial thermal effects even though they are not measured in separate experiments that themselves contain internal temperature gradients.

What would settle it

A set of discharge tests at 3 C and 0 °C on the same pouch cell where the integrated model’s voltage error exceeds that of the lumped DFN-thermal model by more than 50 mV.

read the original abstract

Battery models generally fall into two categories: physics-based models and ECM models. Physics-based Doyle-Fuller-Newman (DFN) models can accurately simulate the battery internal electrochemical processes, but to properly account for thermal effects requires a strong coupling between a DFN model and a 3D thermal model, which is computationally unaffordable. Distributed Equivalent Circuit Network (ECN) models can perform simulations with high speed and reasonable accuracy. However, these models rely heavily on the characterisation experiments for ECN parameter identification, which is resource-intensive and can lead to inaccurate parametrisation outcomes due to internal thermal inhomogeneity. To harness the strengths of both models, we propose a computational framework to integrate electrochemical DFN model and 3D distributed ECN model together. Using this framework, we simulate constant current discharge experiments of Kokam 7.5 Ah pouch cell (Model SLPB75106100) and compare the simulations with the commonly-used lumped DFN-thermal model. The computational model outperforms the lumped DFN model at low-temperature and/or high C-rate scenarios significantly. The largest predicting error of the framework at 3 C-rate &Tam = 25oC and at 1 C-rate &Tam = 0 oC is approximately 1/3 of that for DFN model. At 3 C-rate &Tam = 5oC, the difference between these two can rise to 377 mV. By integrating DFN and 3D-distributed ECN together, the computational framework can simulate the complicated interplay between electrochemistry, thermal process, and electricity within a cell fast and accurately. We anticipate this computational framework to be a valuable toolset to assist researchers and engineers in the design and control of Li-ion batteries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a computational framework integrating the Doyle-Fuller-Newman (DFN) physics-based electrochemical model with a 3D distributed Equivalent Circuit Network (ECN) model to simulate Li-ion battery discharge, capturing the interplay of electrochemistry, thermal processes, and electricity. It claims this hybrid approach is computationally faster than a fully coupled DFN-3D thermal model while delivering higher accuracy than the commonly used lumped DFN-thermal model for a Kokam 7.5 Ah pouch cell, with the largest predicting error reduced to approximately one-third of the DFN error at 3 C-rate & 25°C and at 1 C-rate & 0°C (and a 377 mV difference at 3 C-rate & 5°C).

Significance. If the central performance claims hold after proper validation, the framework could offer a practical compromise between accuracy and speed for spatially resolved battery simulations where full DFN-3D thermal coupling is prohibitive, with potential utility in battery design and control.

major comments (2)
  1. [Abstract] Abstract: The quantitative performance claims (predicting error reduced to ~1/3 of DFN, 377 mV difference) are presented without error bars, description of the validation dataset, number of test conditions, or how errors were computed; this is load-bearing for the central claim that the framework outperforms the lumped DFN model.
  2. [Abstract] Abstract (and method description): No derivation of the coupling equations or procedure for extracting distributed ECN parameters from DFN runs is supplied. Because full DFN+3D-thermal coupling is stated to be unaffordable, the extraction step almost certainly relies on DFN simulations at fixed uniform temperatures; parameters obtained this way cannot encode the self-consistent feedback in which local heating alters local current density and heat generation, creating an unquantified approximation error precisely in the high-C-rate/low-T regime where the largest accuracy gains are asserted.
minor comments (2)
  1. [Abstract] Abstract: Notation 'Tam = 25oC' and 'Tam = 0 oC' should be standardized (e.g., T_am = 25 °C) for clarity and consistency.
  2. [Abstract] Abstract: The phrase 'constant current discharge experiments' is used but the full range of C-rates and ambient temperatures actually simulated is not enumerated beyond the two highlighted cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment point-by-point below and will revise the manuscript to incorporate clarifications and additional details as needed.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The quantitative performance claims (predicting error reduced to ~1/3 of DFN, 377 mV difference) are presented without error bars, description of the validation dataset, number of test conditions, or how errors were computed; this is load-bearing for the central claim that the framework outperforms the lumped DFN model.

    Authors: We agree that the abstract would be strengthened by additional context on the validation. In the revised manuscript, we will expand the abstract to briefly describe the validation dataset (constant-current discharge experiments on the Kokam 7.5 Ah pouch cell), the test conditions (including 3 C-rate at 25°C, 1 C-rate at 0°C, and 3 C-rate at 5°C), and clarify that the predicting error is the maximum absolute voltage deviation from experimental measurements. The simulations are deterministic, so error bars do not apply, but we will specify the error metric. These details appear in the main text; we will make the abstract self-contained for the central claims. revision: yes

  2. Referee: [Abstract] Abstract (and method description): No derivation of the coupling equations or procedure for extracting distributed ECN parameters from DFN runs is supplied. Because full DFN+3D-thermal coupling is stated to be unaffordable, the extraction step almost certainly relies on DFN simulations at fixed uniform temperatures; parameters obtained this way cannot encode the self-consistent feedback in which local heating alters local current density and heat generation, creating an unquantified approximation error precisely in the high-C-rate/low-T regime where the largest accuracy gains are asserted.

    Authors: We acknowledge that the manuscript does not currently supply a derivation of the coupling equations or the parameter extraction procedure, and we will add this material (likely as a dedicated methods subsection or appendix) in the revision. The distributed ECN parameters are extracted from DFN simulations at multiple fixed uniform temperatures to obtain temperature-dependent circuit elements, which are then assigned spatially in the 3D network. The framework uses the 3D ECN to resolve spatial variations in temperature, current density, and heat generation during runtime, providing an approximation to the coupled physics that remains computationally tractable. We will explicitly derive the coupling equations, discuss the limitations of the uniform-temperature extraction step, and add analysis of the approximation error in the high-C-rate/low-T regime, including any supporting sensitivity checks. The reported accuracy gains are demonstrated empirically against both experimental data and the lumped DFN model. revision: yes

Circularity Check

0 steps flagged

No significant circularity; integration claims rest on independent simulation comparisons

full rationale

The paper describes a framework that extracts ECN parameters from DFN runs at fixed temperatures and inserts them into a 3D distributed ECN for coupled simulation, then reports lower voltage errors versus a lumped DFN-thermal model at high C-rate/low-T conditions. No quoted step shows a performance metric reducing to a fitted parameter by construction, nor any load-bearing self-citation or uniqueness theorem. The accuracy numbers are presented as outcomes of the integrated simulation, not as tautological re-statements of the extraction procedure. The derivation chain therefore remains self-contained against the external benchmark of the lumped model.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; free parameters, axioms, and invented entities cannot be enumerated because the coupling equations, parameter identification procedure, and any ad-hoc assumptions are not described.

pith-pipeline@v0.9.0 · 5868 in / 1200 out tokens · 32968 ms · 2026-05-24T09:21:19.298586+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [1]

    Energy Storage Systems in Electronics

    Osaka T, Datta M. Energy Storage Systems in Electronics. CRC Press; 2000. https://doi.org/10.1201/9781482296891

    work page doi:10.1201/9781482296891 2000

  2. [2]

    Post -lithium-ion battery cell production and its compatibility with lithium-ion cell production infrastructure

    Duffner F, Kronemeyer N, T übke J, Leker J, Winter M, Schmuch R. Post -lithium-ion battery cell production and its compatibility with lithium-ion cell production infrastructure. Nat Energy 2021;6:123–34. https://doi.org/10.1038/s41560-020-00748-8

    work page doi:10.1038/s41560-020-00748-8 2021

  3. [3]

    Restricted diffusion in binary solutions

    Newman J, Chapman TW. Restricted diffusion in binary solutions. AIChE J 1973;19:343 –8. https://doi.org/10.1002/aic.690190220

    work page doi:10.1002/aic.690190220 1973

  4. [4]

    Porous ‐electrode theory with battery applications

    Newman J, Tiedemann W. Porous ‐electrode theory with battery applications. AIChE J 1975;21:25–41. https://doi.org/10.1002/aic.690210103

    work page doi:10.1002/aic.690210103 1975

  5. [5]

    Theoretical Analysis of Current Distribution in Porous Electrodes

    Newman JS, Tobias CW. Theoretical Analysis of Current Distribution in Porous Electrodes. J Electrochem Soc 1962;109:1183. https://doi.org/10.1149/1.2425269

    work page doi:10.1149/1.2425269 1962

  6. [6]

    Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell

    Doyle M, Fuller TF, Newman J. Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell. J Electrochem Soc 1993;140:1526 –33. https://doi.org/10.1149/1.2221597

    work page doi:10.1149/1.2221597 1993

  7. [7]

    Simulation and Optimization of the Dual Lithium Ion Insertion Cell

    Fuller TF, Doyle M, Newman J. Simulation and Optimization of the Dual Lithium Ion Insertion Cell. J Electrochem Soc 1994;141:1–10. https://doi.org/10.1149/1.2054684

    work page doi:10.1149/1.2054684 1994

  8. [8]

    Development of Experimental Techniques for Parameterization of Multi-scale Lithium-ion Battery Models

    Chen C-H, Brosa Planella F, O’Regan K, Gastol D, Widanage WD, Kendrick E. Development of Experimental Techniques for Parameterization of Multi-scale Lithium-ion Battery Models. J Electrochem Soc 2020;167:080534. https://doi.org/10.1149/1945-7111/ab9050

    work page doi:10.1149/1945-7111/ab9050 2020

  9. [9]

    Parameterization of a Physico -Chemical Model of a Lithium -Ion Battery:II

    Ecker M, Käbitz S, Laresgoiti I, Sauer DU. Parameterization of a Physico -Chemical Model of a Lithium -Ion Battery:II. Model Validation To. J Electrochem Soc 2015;162:A1849 –57. https://doi.org/10.1149/2.0541509jes

    work page doi:10.1149/2.0541509jes 2015

  10. [10]

    Physical Modelling of the Slow Voltage Relaxation Phenomenon in Lithium -Ion Batteries

    Kirk TL, Please CP, Jon Chapman S. Physical Modelling of the Slow Voltage Relaxation Phenomenon in Lithium -Ion Batteries. J Electrochem Soc 2021;168:060554. https://doi.org/10.1149/1945-7111/ac0bf7

    work page doi:10.1149/1945-7111/ac0bf7 2021

  11. [11]

    A continuum of physics- 28 based lithium-ion battery models reviewed

    Brosa Planella F, Ai W, Boyce AM, Ghosh A, Korotkin I, Sahu S, et al. A continuum of physics- 28 based lithium-ion battery models reviewed. Prog Energy 2022;4. https://doi.org/10.1088/2516- 1083/ac7d31

    work page doi:10.1088/2516- 2022

  12. [12]

    Coupled thermal - electrochemical modelling of uneven heat generation in lithium -ion battery packs

    Wu B, Yufit V, Marinescu M, Offer GJ, Martinez -Botas RF, Brandon NP. Coupled thermal - electrochemical modelling of uneven heat generation in lithium -ion battery packs. J Power Sources 2013;243:544–54. https://doi.org/10.1016/j.jpowsour.2013.05.164

    work page doi:10.1016/j.jpowsour.2013.05.164 2013

  13. [13]

    Optimal cell tab design and cooling strategy for cylindrical lithium -ion batteries

    Li S, Kirkaldy N, Zhang C, Gopalakrishnan K, Amietszajew T, Diaz LB, et al. Optimal cell tab design and cooling strategy for cylindrical lithium -ion batteries. J Power Sources 2021;492:229594. https://doi.org/10.1016/j.jpowsour.2021.229594

    work page doi:10.1016/j.jpowsour.2021.229594 2021

  14. [14]

    Probing multiscale transport and inhomogeneity in a lithium -ion pouch cell using in situ neutron methods

    Zhou H, An K, Allu S, Pannala S, Li J, Bilheux HZ, et al. Probing multiscale transport and inhomogeneity in a lithium -ion pouch cell using in situ neutron methods. ACS Energy Lett 2016;1:981–6

    work page 2016

  15. [15]

    Visualization of inhomogeneous current distribution on ZrO 2 -coated LiCoO 2 thin -film electrodes using scanning electrochemical cell microscopy

    Inomata H, Takahashi Y, Takamatsu D, Kumatani A, Ida H, Shiku H, et al. Visualization of inhomogeneous current distribution on ZrO 2 -coated LiCoO 2 thin -film electrodes using scanning electrochemical cell microscopy. Chem Commun 2019;55:545–8

    work page 2019

  16. [16]

    Universal battery parameterization to yield a non - linear equivalent circuit valid for battery simulation at arbitrary load

    Barsoukov E, Kim JH, Yoon CO, Lee H. Universal battery parameterization to yield a non - linear equivalent circuit valid for battery simulation at arbitrary load. J Power Sources 1999;83:61–70

    work page 1999

  17. [17]

    Modeling of lithium ion cells - A simple equivalent -circuit model approach

    Liaw BY, Nagasubramanian G, Jungst RG, Doughty DH. Modeling of lithium ion cells - A simple equivalent -circuit model approach. Solid State Ionics 2004;175:835 –9. https://doi.org/10.1016/j.ssi.2004.09.049

    work page doi:10.1016/j.ssi.2004.09.049 2004

  18. [18]

    A Review of Li-ion Battery Equivalent Circuit Models ADOPTED Li-ion BATTERY EQUIVALENT 2016;17:311–6

    Zhang X, Zhang W, Lei G. A Review of Li-ion Battery Equivalent Circuit Models ADOPTED Li-ion BATTERY EQUIVALENT 2016;17:311–6

    work page 2016

  19. [19]

    How to Cool Lithium Ion Batteries: Optimising Cell Design using a Thermally Coupled Model

    Zhao Y, Diaz LB, Patel Y, Zhang T, Offer GJ. How to Cool Lithium Ion Batteries: Optimising Cell Design using a Thermally Coupled Model. J Electrochem Soc 2019;166:A2849 –59. https://doi.org/10.1149/2.0501913jes

    work page doi:10.1149/2.0501913jes 2019

  20. [20]

    Modeling the Effects of Thermal Gradients Induced by Tab and Surface Cooling on Lithium Ion Cell Performance

    Zhao Y, Patel Y, Zhang T, Offer GJ. Modeling the Effects of Thermal Gradients Induced by Tab and Surface Cooling on Lithium Ion Cell Performance. J Electrochem Soc 2018;165:A3169–78. https://doi.org/10.1149/2.0901813jes

    work page doi:10.1149/2.0901813jes 2018

  21. [21]

    How to enable large format 4680 cylindrical lithium -ion batteries

    Li S, Marzook MW, Zhang C, Offer GJ, Marinescu M. How to enable large format 4680 cylindrical lithium -ion batteries. Appl Energy 2023;349:121548. https://doi.org/10.1016/j.apenergy.2023.121548

    work page doi:10.1016/j.apenergy.2023.121548 2023

  22. [22]

    Hua X, Heckel C, Modrow N, Zhang C, Hales A, Holloway J, et al. The prismatic surface cell cooling coefficient: A novel cell design optimisation tool & thermal parameterization method for a 3D discretised electro-thermal equivalent-circuit model. ETransportation 2021;7:100099. https://doi.org/10.1016/j.etran.2020.100099

    work page doi:10.1016/j.etran.2020.100099 2021

  23. [23]

    Li S, Rawat SK, Zhu T, Offer GJ, Marinescu M. Python -based Equivalent Circuit Network (PyECN) Model -ling Framework for Lithium -ion Batteries: Next generation open -source battery modelling framework for Lithium -ion batteries. Engineering Archive; n.d. https://doi.org/https://doi.org/10.31224/2972

    work page doi:10.31224/2972

  24. [24]

    Von Srbik MT, Marinescu M, Martinez -Botas RF, Offer GJ. A physically meaningful equivalent circuit network model of a lithium -ion battery accounting for local electrochemical and thermal behaviour, variable double layer capacitance and degradation. J Power Sources 2016;325:171–84. https://doi.org/10.1016/j.jpowsour.2016.05.051

    work page doi:10.1016/j.jpowsour.2016.05.051 2016

  25. [25]

    Modelling inhomogeneous degradation in lithium-ion batteries : the effect of thermal gradients (Preprint)

    Li S, Zhang C, Zhao Y, Offer GJ, Marinescu M. Modelling inhomogeneous degradation in lithium-ion batteries : the effect of thermal gradients (Preprint). n.d. https://doi.org/10.13140/RG.2.2.21690.52164

    work page doi:10.13140/rg.2.2.21690.52164

  26. [26]

    Load-responsive model switching estimation for state of charge of lithium -ion batteries

    Tang X, Gao F, Zou C, Yao K, Hu W, Wik T. Load-responsive model switching estimation for state of charge of lithium -ion batteries. Appl Energy 2019;238:423 –34. https://doi.org/10.1016/j.apenergy.2019.01.057

    work page doi:10.1016/j.apenergy.2019.01.057 2019

  27. [27]

    Finding a better fit for lithium ion batteries: A simple, novel, load 29 dependent, modified equivalent circuit model and parameterization method

    Hua X, Zhang C, Offer G. Finding a better fit for lithium ion batteries: A simple, novel, load 29 dependent, modified equivalent circuit model and parameterization method. J Power Sources 2021;484:229117. https://doi.org/10.1016/j.jpowsour.2020.229117

    work page doi:10.1016/j.jpowsour.2020.229117 2021

  28. [28]

    State -of-charge estimators considering temperature effect, hysteresis potential, and thermal evolution for LiFePO4 batteries

    Xie J, Ma J, Bai K. State -of-charge estimators considering temperature effect, hysteresis potential, and thermal evolution for LiFePO4 batteries. Int J Energy Res 2018;42:2710 –27. https://doi.org/10.1002/er.4060

    work page doi:10.1002/er.4060 2018

  29. [29]

    Python Battery Mathematical Modelling (PyBaMM)

    Sulzer V, Marquis SG, Timms R, Robinson M, Chapman SJ. Python Battery Mathematical Modelling (PyBaMM). J Open Res Softw 2021;9:1–8. https://doi.org/10.5334/JORS.309

    work page doi:10.5334/jors.309 2021

  30. [30]

    Parameterization of a Physico-Chemical Model of a Lithium -Ion Battery:I

    Ecker M, Tran TKD, Dechent P, K äbitz S, Warnecke A, Sauer DU. Parameterization of a Physico-Chemical Model of a Lithium -Ion Battery:I. Determination of Parameters. J Electrochem Soc 2015;162:A1836–48. https://doi.org/10.1149/2.0551509jes

    work page doi:10.1149/2.0551509jes 2015

  31. [31]

    Application -specific parameterization of reduced order equivalent circuit battery models for improved accuracy at dynamic load

    Waag W, K äbitz S, Sauer DU. Application -specific parameterization of reduced order equivalent circuit battery models for improved accuracy at dynamic load. Meas J Int Meas Confed 2013;46:4085–93. https://doi.org/10.1016/j.measurement.2013.07.025

    work page doi:10.1016/j.measurement.2013.07.025 2013

  32. [32]

    Nonlinear system identification: A user-oriented road map

    Schoukens J, Ljung L. Nonlinear system identification: A user-oriented road map. IEEE Control Syst Mag 2019;39:28–99

    work page 2019

  33. [33]

    Lithium -ion battery model parametrisation: BatPar an all -in-one toolkit for equivalent circuit models

    Zhu T, Tomlin R, Garcia C, Rawat S, Holland T, Offer G, et al. Lithium -ion battery model parametrisation: BatPar an all -in-one toolkit for equivalent circuit models. J Energy Storage 2024;92:112220. https://doi.org/10.1016/j.est.2024.112220

    work page doi:10.1016/j.est.2024.112220 2024

  34. [34]

    On Experiment Design for Parameter Estimation of Equivalent-Circuit Battery Models

    Beelen HPGJ, Bergveld HJ, Donkers MCF. On Experiment Design for Parameter Estimation of Equivalent-Circuit Battery Models. 2018 IEEE Conf Control Technol Appl CCTA 2018 2018:1526–31. https://doi.org/10.1109/CCTA.2018.8511529

    work page doi:10.1109/ccta.2018.8511529 2018

  35. [35]

    The Cell Cooling Coefficient: A Standard to Define Heat Rejection from Lithium -Ion Batteries

    Hales A, Diaz LB, Marzook MW, Zhao Y, Patel Y, Offer G. The Cell Cooling Coefficient: A Standard to Define Heat Rejection from Lithium -Ion Batteries. J Electrochem Soc 2019;166:A2383–95. https://doi.org/10.1149/2.0191912jes

    work page doi:10.1149/2.0191912jes 2019

  36. [37]

    Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods

    Brosa Planella F, Sheikh M, Widanage WD. Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods. Electrochim Acta 2021;388. https://doi.org/10.1016/j.electacta.2021.138524

    work page doi:10.1016/j.electacta.2021.138524 2021

  37. [38]

    Power and thermal characterization of a lithium -ion battery pack for hybrid-electric vehicles

    Smith K, Wang CY. Power and thermal characterization of a lithium -ion battery pack for hybrid-electric vehicles. J Power Sources 2006;160:662 –73. https://doi.org/10.1016/j.jpowsour.2006.01.038

    work page doi:10.1016/j.jpowsour.2006.01.038 2006

  38. [39]

    New method for parameter estimation of an electrochemical-thermal coupling model for LiCoO2 battery

    Li J, Wang L, Lyu C, Wang H, Liu X. New method for parameter estimation of an electrochemical-thermal coupling model for LiCoO2 battery. J Power Sources 2016;307:220 –

    work page 2016

  39. [40]

    https://doi.org/10.1016/j.jpowsour.2015.12.058

    work page doi:10.1016/j.jpowsour.2015.12.058 2015

  40. [41]

    Surface Cooling Causes Accelerated Degradation Compared to Tab Cooling for Lithium -Ion Pouch Cells

    Hunt IA, Zhao Y, Patel Y, Offer J. Surface Cooling Causes Accelerated Degradation Compared to Tab Cooling for Lithium -Ion Pouch Cells. J Electrochem Soc 2016;163:A1846 –52. https://doi.org/10.1149/2.0361609jes

    work page doi:10.1149/2.0361609jes 2016

  41. [42]

    The Surface Cell Cooling Coefficient: A Standard to Define Heat Rejection from Lithium Ion Battery Pouch Cells

    Hales A, Marzook MW, Bravo Diaz L, Patel Y, Offer G. The Surface Cell Cooling Coefficient: A Standard to Define Heat Rejection from Lithium Ion Battery Pouch Cells. J Electrochem Soc 2020;167:020524. https://doi.org/10.1149/1945-7111/ab6985

    work page doi:10.1149/1945-7111/ab6985 2020

  42. [43]

    Modeling Electrode Heterogeneity in Lithium -Ion Batteries: Unimodal and Bimodal Particle-Size Distributions

    Kirk TL, Evans J, Please CP, Chapman SJ. Modeling Electrode Heterogeneity in Lithium -Ion Batteries: Unimodal and Bimodal Particle-Size Distributions. SIAM J Appl Math 2022;82:625–

    work page 2022

  43. [44]

    https://doi.org/10.1137/20M1344305S

    work page doi:10.1137/20m1344305s

  44. [45]

    Foundations of heat transfer

    Incropera FP, DeWitt DP, Bergman TL, Lavine AS, Incropera FP. Foundations of heat transfer. Wiley Textbooks; 2012

    work page 2012

  45. [46]

    Effect of internal heat generation on the applicability of different lumped models with unsteady one -dimensional conduction

    Abbasi Souraki B, Assareh N, Omidi M. Effect of internal heat generation on the applicability of different lumped models with unsteady one -dimensional conduction. Heat Transf Res 2014;45:767–93. https://doi.org/10.1615/HeatTransRes.2014006552. 30

    work page doi:10.1615/heattransres.2014006552 2014

  46. [47]

    Development of electrochemical -thermal modelling for large -format Li -ion battery

    Hou M, Hu Y, Zhang J, Cao H, Wang Z. Development of electrochemical -thermal modelling for large -format Li -ion battery. Electrochim Acta 2020;347:136280. https://doi.org/10.1016/j.electacta.2020.136280

    work page doi:10.1016/j.electacta.2020.136280 2020

  47. [48]

    Thermal runaway propagation model for designing a safer battery pack with 25Ah LiNixCoyMnzO2 large format lithium ion battery

    Feng X, He X, Ouyang M, Lu L, Wu P, Kulp C, et al. Thermal runaway propagation model for designing a safer battery pack with 25Ah LiNixCoyMnzO2 large format lithium ion battery. Appl Energy 2015;154:74–91. https://doi.org/10.1016/j.apenergy.2015.04.118

    work page doi:10.1016/j.apenergy.2015.04.118 2015

  48. [49]

    Large format lithium ion pouch cell full thermal characterisation for improved electric vehicle thermal management

    Grandjean T, Barai A, Hosseinzadeh E, Guo Y, McGordon A, Marco J. Large format lithium ion pouch cell full thermal characterisation for improved electric vehicle thermal management. J Power Sources 2017;359:215–25. https://doi.org/10.1016/j.jpowsour.2017.05.016

    work page doi:10.1016/j.jpowsour.2017.05.016 2017

  49. [50]

    Quantitative characterisation of the layered structure within lithium -ion batteries using ultrasonic resonance

    Huang M, Kirkaldy N, Zhao Y, Patel Y, Cegla F, Lan B. Quantitative characterisation of the layered structure within lithium -ion batteries using ultrasonic resonance. J Energy Storage 2022;50:104585. https://doi.org/10.1016/j.est.2022.104585

    work page doi:10.1016/j.est.2022.104585 2022