Characterising Lithium-Ion Battery Degradation through the Identification and Tracking of Electrochemical Battery Model Parameters
Abstract
:1. Introduction
2. Model Formulation and Parameters
2.1. Pseudo Two-Dimensional Model Formulation
2.2. Pseudo Two-Dimensional Model Parameters
3. Method for Restricting the Number of Parameters for Identification
3.1. Expected Parameter Changes Resulting from Battery Degradation
3.2. Reducing the Number of Parameters Selected for Identification
4. Parameter Identification Process
4.1. Optimisation Strategy
4.2. Verifying the Non-Aged Refined Parameter Set for LiNiCoAlO2
5. Results and Discussions
5.1. Conditions for the Cell Ageing Experiment
5.2. Battery Ageing Characterisation
5.3. Battery Ageing Diagnostics Using Parameter Identification
5.4. Analysis of Model Extracted Results
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
BMS | Battery management system |
NCA | LiNiCoAlO2 |
PHEV | Plug-in hybrid electric vehicle |
P2D | Pseudo two-dimensional |
SEI | Solid electrolyte interphase |
SoC | State of charge |
SP | Single particle |
ΔSoC | Change in state of charge |
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Relation/Domain | Governing Equations | Boundary Conditions | |
---|---|---|---|
Conservation of charge | Electrolyte phase | ||
Solid Phase | |||
Conservation of lithium | Electrolyte phase | ||
Solid Phase | , | ||
Kinetics | Electrochemical reaction rate | ||
Overpotential |
Parameter | Symbol | Initial | Refined | Difference (%) |
---|---|---|---|---|
Thickness of negative electrode | L− (10−4 cm) | 149.9 | 153.1 | 2.1 |
Thickness of positive electrode | L+ (10−4 cm) | 134.0 | 129.8 | −3.2 |
Thickness of separator | Lsep (10−4 cm) | 25.0 | 27.5 | 9.1 |
Surface area of negative electrode, | A− (cm2) | 428.4 | 437.5 | 2.1 |
Surface area of positive electrode | A+ (cm2) | 389.61 | 377.4 | −3.2 |
Surface area of separator | Asep (cm2) | 448.35 | 493.2 | 9.1 |
Modal radius of negative electrode particle | Rs,− (10−4 cm) | 10.7 | 10.9 | 1.8 |
Modal radius of positive electrode particle | Rs,+ (10−4 cm) | 5.7 | 7.9 | 27.8 |
Active material volume fraction of negative electrode | εs,− | 0.3 | 0.31 | 3.2 |
Active material volume fraction of positive electrode | εs,+ | 0.3 | 0.49 | 38.8 |
Electrolyte phase volume fraction of negative electrode | εe,− | 0.595 | 0.595 | 0.0 |
Electrolyte phase volume fraction of positive electrode | εe,+ | 0.63 | 0.63 | 0.0 |
Volume fraction of separator in liquid phase | εe,sep | 0.5 | 0.45 | −11.1 |
Volume fraction of inactive material in negative electrode | εf,− | 0.105 | 0.04 | −162.5 |
Volume fraction of inactive material in positive electrode | εf,+ | 0.07 | 0.99 | 92.9 |
Maximum li-concentration in negative electrode | (10−3 mol·cm−3) | 30.6 † | 30.6 | 0.0 |
Maximum li-concentration in positive electrode | (10−3 mol·cm−3) | 51.6 † | 51.0 | −1.2 |
Average electrolyte concentration | ce,0 (10−3 mol·cm−3) | 1.2 * | 1.04 | −15.4 |
Stoichiometry of negative electrode at 0% SoC | x−,0 | 0.126 * | 0.126 | 0.0 |
Stoichiometry of positive electrode at 0% SoC | x+,0 | 0.936 * | 0.936 | 0.0 |
Stoichiometry of negative electrode at 100% SoC | x−,100 | 0.676 * | 0.676 | 0.0 |
Stoichiometry of positive electrode at 100% SoC | x+,100 | 0.442 * | 0.442 | 0.0 |
Diffusion coefficient of negative electrode in solid phase | Ds,− (10−12 cm2·s−1) | 1.14 | 1.14 | 0.0 |
Diffusion coefficient of positive electrode in solid phase | Ds,+ (10−12 cm2·s−1) | 3.7 * | 3.7 | 0.0 |
Diffusion coefficient in liquid phase | De (10−6 cm2·s−1) | 2.6 * | 2.6 | 0.0 |
Conductivity of negative electrode in solid phase | σs,− (S·cm−1) | 1.0 * | 1 | 0.0 |
Conductivity of positive electrode in solid phase | σs,+ (S·cm−1) | 1.0 † | 1 | 0.0 |
Charge transfer coefficient in negative electrode | ke,− (10−6 cm2.5·mol−0.5·s−1) | 5.03 | 5.03 | 0.0 |
Charge transfer coefficient in positive electrode | ke,+ (10−6 cm2.5·mol−0.5·s−1) | 2.33 | 2.33 | 0.0 |
Anodic charge transfer coefficient | αa | 0.5 | 0.5 | 0.0 |
Cathodic charge transfer coefficient | αc | 0.5 | 0.5 | 0.0 |
Li transference number | 0.36 | 0.36 | 0.0 | |
Electrolyte activity coefficient | 1.0 | 1 | 0.0 | |
Bruggeman porosity exponent | p | 1.5 | 1.5 | 0.0 |
Resistivity of film layers (including SEI) | - | 0.1 | 0.001 | −990 |
Resistivity of the current collector | Rf (Ω·cm2) | 20 | 10 | −100 |
Negative electrode potential, coefficients | - | - | - | |
Positive electrode potential, , coefficients | - | - | - |
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Uddin, K.; Perera, S.; Widanage, W.D.; Somerville, L.; Marco, J. Characterising Lithium-Ion Battery Degradation through the Identification and Tracking of Electrochemical Battery Model Parameters. Batteries 2016, 2, 13. https://doi.org/10.3390/batteries2020013
Uddin K, Perera S, Widanage WD, Somerville L, Marco J. Characterising Lithium-Ion Battery Degradation through the Identification and Tracking of Electrochemical Battery Model Parameters. Batteries. 2016; 2(2):13. https://doi.org/10.3390/batteries2020013
Chicago/Turabian StyleUddin, Kotub, Surak Perera, W. Dhammika Widanage, Limhi Somerville, and James Marco. 2016. "Characterising Lithium-Ion Battery Degradation through the Identification and Tracking of Electrochemical Battery Model Parameters" Batteries 2, no. 2: 13. https://doi.org/10.3390/batteries2020013