# Simulation Study on Heat Generation Characteristics of Lithium-Ion Battery Aging Process

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## Abstract

**:**

## 1. Introduction

## 2. Experiments

_{0.8}Co

_{0.15}Al

_{0.05}) O

_{2}cathode material) was experimentally characterized. A NEWARE (CT4008-5V12A; Shenzhen, China) test system, 8-channel A-to-D converter, and a computer data logger were used to monitor the charge–discharge current and battery voltage. A real-time graph was created and stored on a computer. The battery was placed in a temperature control box for operating at different temperatures.

## 3. Model Development

#### 3.1. Model Assumptions and Calculation Domain

- (1)
- The intricate winding structure within the cell was disregarded and the cell was treated as a uniform cylinder.
- (2)
- Current collector effects on lithium-ion transport and heat transfer were disregarded.
- (3)
- The change in the entropic coefficient throughout the battery aging process was not taken into account.
- (4)
- Adverse effects during the operation were disregarded.

_{Cu}, L

_{n}, L

_{sep}, L

_{p,}and L

_{Al}denote the thickness of the negative collector (copper foil), negative electrode, separator, positive electrode, and positive collector (aluminum foil), respectively.

#### 3.2. Electrochemical Model

#### 3.2.1. Lithium-Ion Concentration Distribution

_{s}is the lithium-ion concentration in the solid phase, D

_{s,i}is the solid phase diffusivity, and r is the radius distance variable of the particle.

_{e,i}is the solution phase volume fraction, c

_{e}is the lithium-ion concentration in the solution phase, x is the distance variable through a cell component, t

^{+}is the transference number of Li-ion species dissolved in a solution, j

_{tot}is the total current density, and F is Faraday’s constant.

#### 3.2.2. Electric Potential Distribution

_{s}distribution can be derived.

_{e}is the solution phase potential, κ

^{eff}is the effective ionic conductivity of the electrolyte, ${\kappa}_{\mathrm{D}}^{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective ionic diffusion conductivity, R is the gas constant, and T is the cell temperature.

#### 3.2.3. Electrode Reaction Kinetics

_{int}of the lithium embedding and de-embedding reaction:

_{s,i}is the specific surface area, i

_{0,i}is the exchange current density, α

_{p,}and α

_{n}are the transfer coefficients for the positive and negative current, η

_{act,int}is the activation overpotential of the reaction, R

_{film}is the film resistance on the surface of the active material particles, U

_{eq,i}is the open-circuit voltage, and k

_{0,i}is the reaction rate constant.

_{i}, defined as the ratio of the lithium-ion concentration on the surface of the active material ${c}_{s,i}^{\mathrm{surf}}$ to its maximum lithium ion concentration ${c}_{s,i}^{\mathrm{max}}$.

#### 3.3. Aging Model

#### 3.3.1. Loss of Lithium-Ion Inventory (LLI)

_{2}CO

_{3}. In addition to the reaction kinetics, the diffusion of solvent molecules within the existing SEI limited the current density of the SEI growth reaction. Safari et al. [27] established a model for the SEI growth reaction, including diffusion constraints based on the Tafer formulation of the aforementioned process.

_{film}is the thickness of the film on the surface of the active particle, and D

_{EC}is the diffusion coefficient of EC in the film.

_{film}is as follows:

_{SEI}is the molar mass and ρ

_{SEI}is the density of the SEI.

#### 3.3.2. Loss of Active Material (LAM)

_{DVA_LAM}and the cumulative battery power throughput ψ after taking the logarithm, respectively. Therefore, after a linear fit, it can be converted into a power function to represent the relationship between the active material loss index and the cumulative battery power throughput, and the rate of change in the solid phase volume fraction as the active material loss rate can be expressed using the following equation:

#### 3.4. Thermal Model

_{batt}is the density of the cell, C

_{p,batt}is the heat capacity of the cell, λ

_{batt,r}, λ

_{batt,φ}, and λ

_{batt,z}are the radial, circumferential, and axial thermal conductivities of the cell, respectively, ${\dot{q}}_{\mathrm{batt}}$ is the average power of heat generation per unit volume of the cell, L

_{batt}is the total electrode thickness (including the collector), R

_{batt}is the outer diameter of the cell, l

_{batt}is the height of the cell, and A

_{c}is the area of the positive (both sides) that has an opposing negative.

_{cov}is the heat transfer coefficient and T

_{amb}is the ambient temperature.

#### 3.5. Solution Method

## 4. Model Parameterization and Validation

#### 4.1. Parameterization

#### 4.1.1. Basic Design Parameters

Parameters | Negative Electrode | Separator | Positive Electrode |
---|---|---|---|

L_{i}/m | 5 × 10^{−6} | - | 5 × 10^{−6} |

σ_{s,i}/S·m^{−1} | 6.3 × 10^{7} [6] | - | 3.8 × 10^{7} [6] |

L_{i}/m | 88 × 10^{−6} | 8 × 10^{−6} | 62 × 10^{−6} |

R_{i}/m | 9 × 10^{−6} | - | 5 × 10^{−6} |

ε_{s,i} | 0.71 | - | 0.703 |

ε_{e,i} | 0.21 | 0.45 | 0.19 |

c_{e,0}/mol·m^{−3} | 1200 [29] | 1200 [29] | 1200 [29] |

${c}_{s,i}^{\mathrm{max}}$/mol·m^{−3} | 34,507 [29] | - | 49,000 [29] |

α_{a,int}, α_{c,int} | 0.5 [6] | - | 0.5 [6] |

β | 1.5 | 1.5 | 1.7 |

${D}_{s,i}$/m^{2}·s^{−1} | 9 × 10^{−14} [30] | - | 1.5 × 10^{−14} [30] |

σ_{s,i}/S·m^{−1} | 100 [29] | - | 3.8 [29] |

i_{0,ref}/A·m^{2} | 0.75 | - | 2 |

E_{aD,i}/J·mol^{−1} | 48,000 | - | 22,000 |

E_{ak,i}/J·mol^{−1} | 36,000 | - | 30,000 |

t_{+} | 0.363 [6] | ||

T_{ref/}K | 298.15 | ||

R_{film,0}/Ω·m^{2} | 0.001 [28] | ||

A_{c}/m^{2} | 0.12 | ||

F/C.mol^{−1} | 96,487 | ||

R/J.(mol·K)^{−1} | 8.314 |

Parameters | Value |
---|---|

${c}_{\mathrm{EC}}^{0}$/mol·m^{−3} | 4500 [31] |

U_{eq, SEI}/V | 0.4 [28] |

α_{c, SEI} | 0.5 [28] |

E_{a,Dsei/}J·mol^{−1} | 30,000 |

E_{a,ksei/}J·mol^{−1} | 35,000 |

σ_{film}/S·m^{−1} | 5 × 10^{−6} [31] |

M_{SEI}/kg·mol^{−1} | 0.07388 |

ρ_{SEI}/kg·m^{−3} | 2110 [25] |

Parameters | Value |
---|---|

C_{p,batt}/J·kg^{−1}·K^{−1} | 880 |

λ_{batt,r}/W·m^{−1}·K^{−1} | 0.7 |

λ_{batt,φ}/W·m^{−1}·K^{−1} | 10.5 |

λ_{batt,z}/W·m^{−1}·K^{−1} | 10.5 |

ρ_{batt}/kg·m^{−3} | 2846 |

h_{cov}/W·m^{−2}·K^{−1} | 18 |

l_{batt}/m | 0.0700 |

R_{batt}/m | 0.0105 |

#### 4.1.2. Kinetic Parameters

_{e}and conductivity κ of lithium ions in the electrolyte could be calculated.

#### 4.1.3. Thermodynamic Parameters

#### 4.1.4. Active Material Loss Model Calibration

#### 4.2. Model Validation

## 5. Results and Discussion

#### 5.1. Changes in Heat Generation Power of Different Components during the Aging Process

#### 5.2. Effect of SEI Physical Parameters on Heat Generation during Aging

#### 5.2.1. Ion Conductivity

^{−5}S/m to 1 × 10

^{−6}S/m, and the SEI resistance tended to accelerate growth. In addition, when the ionic conductivity of the SEI was reduced with age, negative porosity decreased.

^{−5}S/m to 1 × 10

^{−4}S/m, there was no substantial increase in the SEI resistance and SEI heat generation at the conclusion of the cycle, showing that 1 × 10

^{−5}S/m was already a higher value for the SEI ionic conductivity.

^{−6}to 1 × 10

^{−5}S/m, the susceptibility to SEI resistance and cell heat production increased.

#### 5.2.2. Molar Volume

^{−6}to 1 × 10

^{−4}m

^{3}/mol had a substantial effect on the cell capacity’s decline and heat generation after aging.

#### 5.3. Effect of Aging Mode on the Change in Heat Generation during Battery Aging

## 6. Conclusions

- (1)
- As the battery ages, its overall heat generation power at the same operating current grows dramatically. This is mostly due to the heat generation power increase in the SEI and the ohmic heat of the negative electrolyte.
- (2)
- The SEI ionic conductivity falls below 1 × 10
^{−5}S/m, the SEI resistance and heat generation power grow exponentially, and the negative electrolyte ohmic heat diminishes quickly. The increase in the SEI molar volume causes both the SEI heat generation power and the negative electrolyte ohmic heat to rise. Therefore, in the battery manufacturing process, reasonable formation technology should be adopted to improve the ion conductivity of the SEI and accelerate the lithium-ion mass transfer on the electrode surface and, at the same time, improve the compactness of the SEI to inhibit the decrease in electrode porosity caused by volume growth. - (3)
- Compared with the occurrence of both LLI and LAM, when only LLI occurred in the cell, the SEI film was thicker, and the negative porosity lower when the same capacity declined, so the SEI heat generation and the negative electrolyte ohmic heat could be greater. Simultaneously, the maximum amount of lithium embedded in the positive and negative electrodes continued to diminish throughout the course of the cycle, as did the polarized thermal power at the conclusion of battery charging and discharging. Consequently, when just LLI occurred, the maximum temperature rise during the operation at the same capacity decline was greater than when both LLI and LAM occurred, and the temperature rise rate at the end of discharge was lower due to the narrower window of positive and negative lithium de-embedding.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Intrinsic cell structure [22] and model calculation domain.

**Figure 3.**Thermodynamic parameters at different SOC: (

**a**) open-circuit voltages and (

**b**) the entropic coefficient.

**Figure 4.**Validation of new battery discharge voltage and surface temperature rises under different conditions.

**Figure 6.**Validation of battery capacity under different conditions of cycle aging at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 7.**Validation of surface temperature rise of aging cells during discharge at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 8.**Variation in heat generation power for different components during cyclic aging at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 9.**Variation in SEI resistance and negative porosity during cyclic aging at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 10.**Simulation results of capacity decline when using different SEI ionic conductivities at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 11.**Simulation results of the SEI resistance and negative porosity of the cell after aging when using different SEI ionic conductivities.

**Figure 12.**Simulation results of the heat generation rate during the discharge process of the cell after aging when using different SEI ionic conductivities. (

**a**) SEI growth heat and (

**b**) negative electrolyte ohmic heat.

**Figure 13.**Simulation results of maximum surface temperature rise during the discharging process of the cell after aging when using different SEI ionic conductivities.

**Figure 14.**Simulation results of capacity loss when using different SEI molar volumes at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 15.**Simulation results of SEI film resistance and anode porosity of cells after aging when using different SEI film molar volumes.

**Figure 16.**Simulation results of SEI and negative electrolyte ohmic heat generation rates during the discharge process of cells after aging when using different SEI film molar volumes. (

**a**) SEI growth heat and (

**b**) negative electrolyte ohmic heat.

**Figure 17.**The maximum surface temperature rises during the discharging process of the cell after aging when using different SEI film molar volumes.

**Figure 18.**Comparison of the main heat generation items during the discharging process when the cell ages to EOL under different aging modes at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 19.**Variations in SEI film resistance and anode porosity under different aging modes at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 20.**Variations in electrode SOC during the aging process when only LLI occurred in the cell at (

**a**) 23 °C and (

**b**) 40 °C.

**Figure 21.**The comparison of the surface temperature rises during the discharging process when the cell ages to EOL under different aging modes at (

**a**) 23 °C and (

**b**) 40 °C.

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**MDPI and ACS Style**

Huang, R.; Xu, Y.; Wu, Q.; Chen, J.; Chen, F.; Yu, X.
Simulation Study on Heat Generation Characteristics of Lithium-Ion Battery Aging Process. *Electronics* **2023**, *12*, 1444.
https://doi.org/10.3390/electronics12061444

**AMA Style**

Huang R, Xu Y, Wu Q, Chen J, Chen F, Yu X.
Simulation Study on Heat Generation Characteristics of Lithium-Ion Battery Aging Process. *Electronics*. 2023; 12(6):1444.
https://doi.org/10.3390/electronics12061444

**Chicago/Turabian Style**

Huang, Rui, Yidan Xu, Qichao Wu, Junxuan Chen, Fenfang Chen, and Xiaoli Yu.
2023. "Simulation Study on Heat Generation Characteristics of Lithium-Ion Battery Aging Process" *Electronics* 12, no. 6: 1444.
https://doi.org/10.3390/electronics12061444