# Scale-Up of Physics-Based Models for Predicting Degradation of Large Lithium Ion Batteries

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Selection of Domain Models

#### 2.1. Cell Domain Models

#### 2.2. Comparisons of Lumped Cell and 3D Cell Models

^{2}.

## 3. Lumped Cell Model with Equivalent Resistances (LER Cell Model)

^{−1}m

^{−2}), V is the battery’s working voltage (V), $U$ is the open-circuit voltage (V), and ${\overline{j}}^{\u2033}$ is the average current density (A/m

^{2}) at the current collector. The DOD is obtained from the ratio of the discharged capacity to the cell total capacity.

^{2}for the 20-Ah and 60-Ah pouch cells, and 20-Ah cylindrical cell, respectively, compared to the lumped cell model. The increases of the internal resistance in the 3D cell models are relatively constant regardless of DOD changes in Figure 3c, while the internal resistances vary considerably from 2 mΩ·m

^{2}to 10 mΩ·m

^{2}depending on the DOD, as shown in Figure 3b. This implies that the relation between the internal resistance increments occurring in the cell domain and the electrochemical status, such as DOD, is relatively weak. Therefore, these internal resistance increments in the 3D cell model, $\Delta R$, can be applied to the LER cell model as the electrical resistances in the cell domain, ${R}_{CD,E}$.

^{2}) can be found using the sum of the calculated overpotentials and the average current density ${\overline{J}}^{\u2033}$ (A/m

^{2}) at the current collector.

^{2}in the 20-Ah and 60-Ah pouch cells and in the 20-Ah cylindrical cell, respectively. The calculated electrical resistance of the current collectors ${R}_{\mathrm{cc}}$ can be used as the electrical resistance in the LER cell model, ${R}_{CD,E}$, and almost coincides with the increase of the internal resistance in the 3D cell model, $\Delta R$, as calculated using a linear polarization expression. This also confirms that the additional internal resistance generated by the cell design of large LIBs is mostly the electrical resistance of the collector plate, and the resistance can be represented by a constant value regardless of the DOD. Thus, in the LER cell model, the output voltage ${V}_{LER}$ is calculated as follows with the output voltage ${V}_{L}$ (V) calculated in the lumped cell model, the electrical resistance ${R}_{CD,E}$ and the average current density ${\overline{J}}^{\u2033}$ (A/m

^{2}):

_{CD,T}, (K/W) of the cell domain.

^{−3}, 3.8 × 10

^{−3}, and 4.2 × 10

^{−1}for the 20-Ah and 60-Ah pouch cells and the 20-Ah cylindrical cell, respectively. In the LER cell model, the cell temperature is calculated using the conductive thermal resistance, ${R}_{CD,T}$, and the convective thermal resistance ${R}_{\mathrm{conv}}$ = hA

^{−1}, where the cooling condition is given with the convective heat transfer coefficient, h (W/m

^{2.}K), and the surface cooling area, A (m

^{2}):

## 4. Results and Discussion

#### 4.1. Constant Current Discharge Simulation

#### 4.2. Power Profile Simulation

#### 4.3. Cycle Life Simulation

#### 4.4. Comparison of Calculation Times

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Zhang, L.J.; Peng, H.; Ning, Z.S.; Mu, Z.Q.; Sun, C.Y. Comparative Research on RC Equivalent Circuit Models for Lithium-Ion Batteries of Electric Vehicles. Appl. Sci.
**2017**, 7, 1002. [Google Scholar] [CrossRef][Green Version] - Zhang, X.; Lu, J.L.; Yuan, S.F.; Yang, J.; Zhou, X. A novel method for identification of lithium-ion battery equivalent circuit model parameters considering electrochemical properties. J. Power Sources
**2017**, 345, 21–29. [Google Scholar] [CrossRef] - Zhang, C.; Allafi, W.; Dinh, Q.; Ascencio, P.; Marco, J. Online estimation of battery equivalent circuit model parameters and state of charge using decoupled least squares technique. Energy
**2018**, 142, 678–688. [Google Scholar] [CrossRef] - Saleem, K.; Mehran, K.; Ali, Z. Online reduced complexity parameter estimation technique for equivalent circuit model of lithium-ion battery. Electr. Power Syst. Res.
**2020**, 185, 106356. [Google Scholar] [CrossRef] - Harris, S.J.; Harris, D.J.; Li, C. Failure statistics for commercial lithium ion batteries: A study of 24 pouch cells. J. Power Sources
**2017**, 342, 589–597. [Google Scholar] [CrossRef][Green Version] - Ma, Y.; Li, B.S.; Li, G.Y.; Zhang, J.X.; Chen, H. A Nonlinear Observer Approach of SOC Estimation Based on Hysteresis Model for Lithium-ion Battery. IEEE/CAA J. Autom.
**2017**, 4, 195–204. [Google Scholar] [CrossRef] - Xiong, R.; Tian, J.P.; Mu, H.; Wang, C. A systematic model-based degradation behavior recognition and health monitoring method for lithium-ion batteries. Appl. Energy
**2017**, 207, 372–383. [Google Scholar] [CrossRef] - Rodriguez, A.; Plett, G.L. Controls-oriented models of lithium-ion cells having blend electrodes. Part 2: Physics-based reduced-order models. J. Energy Storage
**2017**, 11, 219–236. [Google Scholar] [CrossRef] - Lai, X.; Zheng, Y.J.; Sun, T. A comparative study of different equivalent circuit models for estimating state-of-charge of lithium-ion batteries. Electrochim. Acta
**2018**, 259, 566–577. [Google Scholar] [CrossRef] - Deng, Z.W.; Deng, H.; Yang, L.; Cai, Y.S.; Zhao, X.W. Implementation of reduced-order physics-based model and multi parameters identification strategy for lithium-ion battery. Energy
**2017**, 138, 509–519. [Google Scholar] [CrossRef] - Bonkile, M.P.; Ramadesigan, V. Power management control strategy using physics-based battery models in standalone PV-battery hybrid systems. J. Energy Storage
**2019**, 23, 258–268. [Google Scholar] [CrossRef] - Fuller, T.F.; Doyle, M.; Newman, J. Simulation and Optimization of the Dual Lithium Ion Insertion Cell. J. Electrochem. Soc.
**1994**, 141, 1–10. [Google Scholar] [CrossRef][Green Version] - Doyle, M.; Newman, J.; Gozdz, A.S.; Schmutz, C.N.; Tarascon, J.M. Comparison of modeling predictions with experimental data from plastic lithium ion cells. J. Electrochem. Soc.
**1996**, 143, 1890–1903. [Google Scholar] [CrossRef] - Kwon, K.H.; Shin, C.B.; Kang, T.H.; Kim, C.S. A two-dimensional modeling of a lithium-polymer battery. J. Power Sources
**2006**, 163, 151–157. [Google Scholar] [CrossRef] - Kim, U.S.; Shin, C.B.; Kim, C.S. Modeling for the scale-up of a lithium-ion polymer battery. J. Power Sources
**2009**, 189, 841–846. [Google Scholar] [CrossRef] - Kim, G.H.; Smith, K.; Lee, K.J.; Santhanagopalan, S.; Pesaran, A. Multi-Domain Modeling of Lithium-Ion Batteries Encompassing Multi-Physics in Varied Length Scales. J. Electrochem. Soc.
**2011**, 158, A955–A969. [Google Scholar] [CrossRef] - Lee, K.J.; Smith, K.; Pesaran, A.; Kim, G.H. Three dimensional thermal-, electrical-, and electrochemical-coupled model for cylindrical wound large format lithium-ion batteries. J. Power Sources
**2013**, 241, 20–32. [Google Scholar] [CrossRef] - Smith, K.; Wang, C.Y. Solid-state diffusion limitations on pulse operation of a lithium ion cell for hybrid electric vehicles. J. Power Sources
**2006**, 161, 628–639. [Google Scholar] [CrossRef] - Cai, L.; White, R.E. Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations. J. Electrochem. Soc.
**2009**, 156, A154–A161. [Google Scholar] [CrossRef][Green Version] - Guo, M.; White, R.E. A distributed thermal model for a Li-ion electrode plate pair. J. Power Sources
**2013**, 221, 334–344. [Google Scholar] [CrossRef] - Rodriguez, A.; Plett, G.L.; Trimboli, M.S. Improved transfer functions modeling linearized lithium-ion battery-cell internal electrochemical variables. J. Energy Storage
**2018**, 20, 560–575. [Google Scholar] [CrossRef] - Jin, X.; Liu, C. Physics-based control-oriented reduced-order degradation model for LiNiMnCoO2—Graphite cell. Electrochim. Acta
**2019**, 312, 188–201. [Google Scholar] [CrossRef] - Li, Y.; Vilathgamuwa, M.; Farrell, T.; Choi, S.S.; Tran, N.T.; Teague, J. A physics-based distributed-parameter equivalent circuit model for lithium-ion batteries. Electrochim. Acta
**2019**, 299, 451–469. [Google Scholar] [CrossRef] - Yin, Y.L.; Hu, Y.; Choe, S.Y.; Cho, H.; Joe, W.T. New fast charging method of lithium-ion batteries based on a reduced order electrochemical model considering side reaction. J. Power Sources
**2019**, 423, 367–379. [Google Scholar] [CrossRef] - Yang, X.G.; Leng, Y.J.; Zhang, G.S.; Ge, S.H.; Wang, C.Y. Modeling of lithium plating induced aging of lithium-ion batteries: Transition from linear to nonlinear aging. J. Power Sources
**2017**, 360, 28–40. [Google Scholar] [CrossRef] - Safari, M.; Morcrette, M.; Teyssot, A.; Delacourt, C. Multimodal Physics-Based Aging Model for Life Prediction of Li-Ion Batteries. J. Electrochem. Soc.
**2009**, 156, A145–A153. [Google Scholar] [CrossRef] - Ramadass, P.; Haran, B.; Gomadam, P.M.; White, R.; Popov, B.N. Development of first principles capacity fade model for Li-ion cells. J. Electrochem. Soc.
**2004**, 151, A196–A203. [Google Scholar] [CrossRef] - Ning, G.; White, R.E.; Popov, B.N. A generalized cycle life model of rechargeable Li-ion batteries. Electrochim. Acta
**2006**, 51, 2012–2022. [Google Scholar] [CrossRef] - Kim, H.K.; Kim, C.J.; Kim, C.W.; Lee, K.J. Numerical analysis of accelerated degradation in large lithium-ion batteries. Comput. Chem. Eng.
**2018**, 112, 82–91. [Google Scholar] [CrossRef] - Kim, H.K.; Choi, J.H.; Lee, K.J. A Numerical Study of the Effects of Cell Formats on the Cycle Life of Lithium Ion Batteries. J. Electrochem. Soc.
**2019**, 166, A1769–A1778. [Google Scholar] [CrossRef] - Viswanathan, V.V.; Choi, D.; Wang, D.H.; Xu, W.; Towne, S.; Williford, R.E.; Zhang, J.G.; Liu, J.; Yang, Z.G. Effect of entropy change of lithium intercalation in cathodes and anodes on Li-ion battery thermal management. J. Power Sources
**2010**, 195, 3720–3729. [Google Scholar] [CrossRef] - MeCleary, D.A.H.; Meyers, J.P.; Kim, B. Three-Dimensional Modeling of Electrochemical Performance and Heat Generation of Spirally and Prismatically Wound Lithium-Ion Batteries. J. Electrochem. Soc.
**2013**, 160, A1931–A1943. [Google Scholar] [CrossRef] - Taheri, P.; Mansouri, A.; Yazdanpour, M.; Bahrami, M. Theoretical Analysis of Potential and Current Distributions in Planar Electrodes of Lithium-ion Batteries. Electrochim. Acta
**2014**, 133, 197–208. [Google Scholar] [CrossRef] - Zhao, W.; Luo, G.; Wang, C.Y. Effect of tab design on large-format Li-ion cell performance. J. Power Sources
**2014**, 257, 70–79. [Google Scholar] [CrossRef] - Conover, D.R.; Crawford, A.J.; Viswanathan, V.; Ferreira, S.R.; Schoenwald, D.A. Protocol for Uniformly Measuring and Expressing the Performance of Energy Storage Systems PNNL-22010 Rev. 1; Pacific Northwest National Laboratory: Richland, WA, USA, 2014. [Google Scholar]

**Figure 2.**Comparisons of output voltages and average temperatures between the 3D cell models and the lumped models of the (

**a**) 20-Ah pouch cell, (

**b**) 60-Ah pouch cell, and (

**c**) 20-Ah cylindrical cell.

**Figure 3.**(

**a**) Linear dependency of voltage and current at various DODs by 3D cell model (20-Ah pouch cell), (

**b**) Internal resistance vs. DOD for each type of cell, and (

**c**) difference of internal resistance between the lumped cell model and the 3D cell models.

**Figure 4.**Contours of the electric potentials in the 3D cell models at 5 min after 1 C discharge: (

**a**) 20-Ah pouch cell, (

**b**) 60-Ah pouch cell, and (

**c**) 20-Ah cylindrical cell, and (

**d**) the equivalent electrical resistance of current collectors at various DODs.

**Figure 6.**Output voltage and average temperature at constant current discharge conditions calculated by the LER cell and 3D cell models for (

**a**) 20-Ah pouch cell, (

**b**) 60-Ah pouch cell, and (

**c**) 20-Ah cylindrical cell.

**Figure 7.**Output voltage at the duty cycle condition of energy storage systems calculated by the LER cell, 3D cell, and lumped cell models for (

**a**) 20-Ah pouch cell, (

**b**) 60-Ah pouch cell, and (

**c**) 20-Ah cylindrical cell.

**Figure 8.**Comparisons of the LER cell, 3D cell, and lumped cell models: (

**a**) capacity retention of the 20-Ah pouch cell, (

**b**) 60-Ah pouch cell and 20-Ah cylindrical cell, and (

**c**) output voltages of the 60-Ah pouch cell and 20-Ah cylindrical cell at 973 and 746 cycles, respectively.

Governing Equations | Boundary Conditions | |
---|---|---|

1D Spherical Particle Model | ||

Li^{+} conservationin active material | $\frac{\partial {c}_{s}}{\partial t}=\frac{{D}_{s}}{{r}^{2}}\frac{\partial}{\partial r}\left({r}^{2}\frac{\partial {c}_{s}}{\partial r}\right)$$\left(1\right)$ | ${\frac{\partial {c}_{s}}{\partial r}|}_{r=0}=0$, ${\frac{\partial {c}_{s}}{\partial r}|}_{r={R}_{s}}=-\frac{{i}^{\u2033}}{{D}_{s}F}$ |

Charge transfer Kinetic (Butler–Volmer equation) | ${i}^{\u2033}={i}_{r}^{\u2033}+{i}_{\mathrm{para}}^{\u2033}$ (2) where ${i}_{r}^{\u2033}=F{k}_{i}{\left({c}_{e}\right)}^{{\alpha}_{a}}{\left({c}_{s,\mathrm{max}}-{c}_{s,e}\right)}^{{\alpha}_{a}}{\left({c}_{s,e}\right)}^{{\alpha}_{a}}\left\{\mathrm{exp}\left[\frac{{\alpha}_{a}F}{RT}\eta \right]-\mathrm{exp}\left[\frac{{\alpha}_{c}F}{RT}\eta \right]\right\},$ $\eta ={\varphi}_{s}-{\varphi}_{e}-{U}_{OCV}-{i}^{\u2033}{R}_{SEI}$ (negative electrode) and $\eta ={\varphi}_{s}-{\varphi}_{e}-{U}_{OCV}$ (positive electrode) | |

Aging mechanism (SEI layer growth) | ${i}_{\mathrm{para}}^{\u2033}=-{i}_{\mathrm{para},\mathrm{init}}^{\u2033}\mathrm{exp}\left[-\frac{{\alpha}_{c}F}{RT}{\eta}_{\mathrm{para}}\right]$, $({i}_{\mathrm{para},\mathrm{init}}^{\u2033}=F{k}_{0,SEI}{c}_{EC}^{s}$) (3) where ${\eta}_{\mathrm{para}}=\eta ={\varphi}_{s}-{\varphi}_{e}-{U}_{\mathrm{para}}-{i}^{\u2033}{R}_{SEI}$, $-{D}_{EC}\frac{\left({c}_{EC}^{s}-{c}_{EC}^{0}\right)}{{\delta}_{SEI}}=-\frac{{i}_{\mathrm{para}}^{\u2033}}{F}$, $\frac{\partial {\delta}_{SEI}}{\partial t}=\frac{{i}_{\mathrm{para}}^{\u2033}{M}_{SEI}}{{\rho}_{SEI}F}$, and ${R}_{SEI}=\frac{{\delta}_{SEI}}{{\kappa}_{SEI}}$ | |

1D Porous Electrode Model | ||

Li conservation in liquid phase | $\frac{\partial \left({\epsilon}_{e}{c}_{e}\right)}{\partial t}=\frac{\partial}{\partial x}\left({D}_{e}^{eff}\frac{\partial}{\partial x}{c}_{e}\right)+\frac{\left(1-{t}_{+}^{0}\right)}{F}{a}_{s}{i}_{r}^{\u2033}-\frac{{i}_{e}^{\u2033}}{F}\frac{\partial {t}_{+}^{0}}{\partial x}$ (4) | ${\frac{\partial {c}_{e}}{\partial x}|}_{x=0}=0,{\frac{\partial {c}_{e}}{\partial x}|}_{x={L}_{a}+{L}_{s}+{L}_{c}}=0$ |

Charge conservation in liquid phase | $\frac{\partial}{\partial x}\left({\kappa}^{eff}\frac{\partial}{\partial x}{\varphi}_{e}\right)+\frac{\partial}{\partial x}\left({\kappa}_{D}^{eff}\frac{\partial}{\partial x}\mathrm{ln}{c}_{e}\right)+{a}_{s}{i}_{r}^{\u2033}=0$ (5) where ${\kappa}_{D}^{eff}=-\frac{2{\kappa}^{eff}RT}{F}\left(1+\frac{\partial \mathrm{ln}{f}_{\pm}}{\partial \mathrm{ln}{c}_{e}}\right)\left(1-{t}_{+}^{0}\right)$ | ${\frac{\partial {\varphi}_{e}}{\partial x}|}_{x=0}=0$, ${\frac{\partial {\varphi}_{e}}{\partial x}|}_{x={L}_{a}+{L}_{s}+{L}_{c}}=0$ |

Charge conservation in solid phase | $\frac{\partial}{\partial x}\left({\sigma}^{\mathrm{eff}}\frac{\partial}{\partial x}{\varphi}_{s}\right)-{a}_{\mathrm{s}}{i}_{r}^{\u2033}=0$ (6) | ${\frac{\partial {\varphi}_{s}}{\partial x}|}_{x=0}={\mathsf{\Phi}}_{N}$, ${\frac{\partial {\varphi}_{s}}{\partial x}|}_{x={L}_{a}}=0$ ${\frac{\partial {\varphi}_{s}}{\partial x}|}_{x={L}_{a}+{L}_{s}}=0$, ${\frac{\partial {\varphi}_{s}}{\partial x}|}_{x={L}_{a}+{L}_{s}+{L}_{c}}={\mathsf{\Phi}}_{P}$ |

Particle Domain & Electrode Domain | Negative Electrode | Separator | Positive Electrode | |
---|---|---|---|---|

Particle radius, R_{s} (m) | 4 × 10^{−6 d} | - | 4 × 10^{−6 d} | |

Diffusivity, D_{s,a}, D_{s,c} (m^{2}/s) | 1.5 × 10^{−14 e} | - | 2.0 × 10^{−14 e} | |

Reaction rate constant k_{a}, k_{c} (m/s) | 4.8 × 10^{−11 e} | - | 5.5 × 10^{−11 e} | |

SEI layer molecular weight, ${M}_{SEI}$ (kg/mol) | 0.1 [27,28,29,30] | - | - | |

SEI layer density, ${\rho}_{SEI}$ (kg/m^{3}) | 2100 [27,28,29,30] | - | - | |

Equilibrium potential of parasitic reaction,${U}_{\mathrm{para}}$ (V) | 0.4 [27,29,30] | - | - | |

SEI layer conductivity, ${\kappa}_{SEI}$ (S/m) | 3.8 × 10^{−6 e} | - | - | |

Initial concentration of EC, ${C}_{EC}^{0}$ (mol/m^{3}) | 4541 [30] | - | - | |

Diffusivity of EC, ${D}_{EC}$ (mol/m^{3}) | 2.0 × 10^{−18} [30] | |||

Reaction rate for SEI layer, k0,SEI (m/s) | 1.1 × 10^{−15 e} | |||

Initial SEI layer resistance ($\mathsf{\Omega}\cdot {\mathrm{m}}^{2}$) | 0.001 | - | - | |

Electrode thickness, L_{a}, L_{s}, L_{c} (m) | 39 × 10^{−6 d} | 20 × 10^{−6 d} | 31 × 10^{−6 d} | |

Electrolyte diffusion coefficient, D_{e} (m^{2}/s) | - | 3 × 10^{−10 e} | - | |

Conductivity, ${\sigma}_{s,a}$,${\sigma}_{s,c}$ (S/m) | 100 [16] | - | 10 [16] | |

Porosity, ${\epsilon}_{i}$ | 0.397 ^{d} | 0.43 ^{d} | 0.404 ^{d} | |

Volume fraction AB, ${\epsilon}_{f,i}$ | 0.044 ^{d} | - | 0.042 ^{d} | |

Volume fraction PVDF, ${\epsilon}_{p,i}$ | 0.007 ^{d} | - | 0.064 ^{d} | |

Initial salt concentration, c_{e}, (mol/m^{3}) | 1200 ^{d} | |||

Transport number, ${t}_{+}^{0}$ | 0.363 [29,30] | |||

Faraday’s constant, F, (C/mol) | 96,450 | |||

Gas constant, R (J/mol·K) | 8.314 | |||

Cell domain | Pouch, 20-Ah | Pouch, 60-Ah | Cylindrical, 20-Ah | |

Dimension (mm) | 185 × 147 × 5.88 ^{d} | 278 × 195 × 8.85 ^{d} | 44(D) × 110(h) ^{d} | |

Mass density of jelly roll (kg/m^{3}) | 2580 ^{d} | |||

Specific heat of jelly roll (J/kg∙K) | 975 ^{d} | |||

Electric conductivity for Cu, ${\sigma}_{-}$ (S/m) | 59.6 × 10 ^{6} [16,17] | |||

Electric conductivity for Al, ${\sigma}_{+}$ (S/m) | 37.8 × 10 ^{6} [16,17] | |||

Thermal conductivity (W/m∙K) | x, y direction: 27 [16] z direction: 0.8 [16] | azimuthal direction, ${k}_{r}$:27 [17] transversal direction, ${k}_{t}$: 0.8 [17] | ||

Convective heat transfer coefficient, $h$ (W/m^{2}∙K) | 25 | |||

Initial temperature, ${T}_{\mathrm{init}}$(°C) | 25 | |||

Atmospheric temperature, ${T}_{\mathrm{amb}}$(°C) | 25 |

^{e}: estimated,

^{d}: design parameter.

Number of Nodes | Pouch (20-Ah) | Pouch (60-Ah) | Cylindrical | |

Lumped cell model | Particle domain | 15 | 15 | 15 |

Electrode domain | 25 | 25 | 25 | |

Cell domain | 1 | 1 | 1 | |

3D cell model | Particle domain | 15 | 15 | 15 |

Electrode domain | 25 | 25 | 25 | |

Cell domain | 3000 | 3000 | 15,000 | |

Calculation Time(1 C discharge) | Pouch (20-Ah) | Pouch (60-Ah) | Cylindrical | |

Lumped cell model | 1 CPU core | 6.6 s | 6.8 s | 6.6 s |

3D cell model | 1 CPU core | 1 h 53 min | 1 h 56 min | 7 h 20 min |

8 CPU core | 27 min | 28 min | 1 h 40 min |

Run Mode | Model | Pouch (20-Ah) | Pouch (60-Ah) | Cylindrical |
---|---|---|---|---|

Discharge (1CD) | 3D cell model | 27 min | 28 min | 1 h 40 min |

LER cell model | 7.59 s | 7.86 s | 6.84 s | |

PNNL cycle (300 min) | 3D cell model | 3 days | 3 days | 9 days |

LER cell model | 4 m 30 s | 4 m 28 s | 4 m 12 s | |

4CD4CC42CV (~80%) | 3D cell model | 6 days | 7 days | 22 days |

LER cell model | 35 min | 31 min | 24 min |

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**MDPI and ACS Style**

Kim, H.-K.; Lee, K.-J. Scale-Up of Physics-Based Models for Predicting Degradation of Large Lithium Ion Batteries. *Sustainability* **2020**, *12*, 8544.
https://doi.org/10.3390/su12208544

**AMA Style**

Kim H-K, Lee K-J. Scale-Up of Physics-Based Models for Predicting Degradation of Large Lithium Ion Batteries. *Sustainability*. 2020; 12(20):8544.
https://doi.org/10.3390/su12208544

**Chicago/Turabian Style**

Kim, Hong-Keun, and Kyu-Jin Lee. 2020. "Scale-Up of Physics-Based Models for Predicting Degradation of Large Lithium Ion Batteries" *Sustainability* 12, no. 20: 8544.
https://doi.org/10.3390/su12208544