# Dual Closed-Loops Capacity Evolution Prediction for Energy Storage Batteries Integrated with Coupled Electrochemical Model

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## Abstract

**:**

## 1. Introduction

## 2. Reduced-Order Physical Degradation Model

#### 2.1. SEI Growth Sub-Model

#### 2.2. LAM Sub-Model

#### 2.3. Lithium Plating Sub-Model

#### 2.4. Coupling Principle for Sub-Models

## 3. Calibration and Verification

#### 3.1. Microgrid Operations Simplified for Accelerated Degradation

#### 3.2. Result Analysis and Model Verification

## 4. Dual Closed-Loops Capacity Prediction Framework

#### 4.1. The First Closed Loop: Mechanism Interpretation

#### 4.2. Second Closed Loop: Parameter Updating

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Degradation speeded-up tests simplified. (

**a**) Microgrid operations simplified equivalently; (

**b**) Current under different C-rates; (

**c**) SOC under different C-rates.

**Figure 4.**Calculation result of degradation model. (

**a**) Display of results between experiments and calculations; (

**b**) Relative error; (

**c**). Capacity loss brought by SEI growth sub-module; (

**d**) Capacity loss brought by LAM sub-module; (

**e**) Capacity loss brought by lithium plating sub-module.

**Figure 6.**Incremental capacity analysis. (

**a**) Incremental capacity evolution with up#1; (

**b**) Incremental capacity evolution with up#2; (

**c**). Incremental capacity evolution with up#3; (

**d**) Incremental capacity evolution with up#4; (

**e**) Incremental capacity evolution with up#5.

**Figure 7.**State estimation for capacity prediction. (

**a**) Evolution of ${a}_{n}$ updated; (

**b**) Evolution of ${b}_{n}$ updated; (

**c**). Evolution of ${c}_{n}$ updated; (

**d**) Evolution of ${d}_{n}$ updated.

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

$\lambda $ | 86,995 | ${\sigma}_{yield}$ | 787.41 $\mathrm{MPa}$ |

${k}_{SEI}$ | 15.55 ${\mathrm{s}}^{-1/2}$ | $m$ | 0.23 |

${E}_{SEI}$ | 27,219 $\mathrm{J}/\mathrm{mol}$ | ${k}_{Li}$ | 4.20 |

${k}_{LAM}$ | 1.61 | ${\phi}_{onset}$ | −5.5 $\mathrm{mV}$ |

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

$n$ | 1 | ${\delta}_{n}$ | 16.7 $\mathsf{\mu}\mathrm{m}$ | ${E}_{p}$ | 15 $\mathrm{Gpa}$ |

$F$ | 96,487 | ${\epsilon}_{s,n0}$ | 0.59 | ${E}_{s}$ | 0.5 $\mathrm{Gpa}$ |

$\alpha $ | 0.5 | ${\delta}_{SEI0}$ | 0.02 $\mathsf{\mu}\mathrm{m}$ | ${v}_{p}$ | 0.3 |

$R$ | 8.314 | ${R}_{SEI0}$ | 4 $\mathrm{m}\mathsf{\Omega}$ | ${v}_{s}$ | 0.2 |

${R}_{n}$ | 9 $\mathsf{\mu}\mathrm{m}$ | $M$ | 0.162 $\mathrm{kg}/\mathrm{mol}$ | ${c}_{p,max}$ | 31.92 $\mathrm{mol}/{\mathrm{dm}}^{3}$ |

${i}_{0}$ | 2 $\mathrm{A}/{\mathrm{m}}^{2}$ | $\rho $ | 1690 $\mathrm{kg}/{\mathrm{m}}^{3}$ | ${\mathsf{\Omega}}_{p}\left({c}_{p},max\right)$ | 3.1 ${\mathrm{cm}}^{3}/\mathrm{mol}$ |

$A$ | 1 ${\mathrm{m}}^{2}$ | ${\sigma}_{SEI}$ | 5 × 10^{−6} $\mathrm{S}/\mathrm{m}$ | ${U}_{SEI}^{ref}$ | 0.4 $\mathrm{V}$ |

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## Share and Cite

**MDPI and ACS Style**

Xu, B.; Sun, T.; Wang, S.; Wei, Y.; Han, X.; Zheng, Y.
Dual Closed-Loops Capacity Evolution Prediction for Energy Storage Batteries Integrated with Coupled Electrochemical Model. *World Electr. Veh. J.* **2021**, *12*, 109.
https://doi.org/10.3390/wevj12030109

**AMA Style**

Xu B, Sun T, Wang S, Wei Y, Han X, Zheng Y.
Dual Closed-Loops Capacity Evolution Prediction for Energy Storage Batteries Integrated with Coupled Electrochemical Model. *World Electric Vehicle Journal*. 2021; 12(3):109.
https://doi.org/10.3390/wevj12030109

**Chicago/Turabian Style**

Xu, Bowen, Tao Sun, Shuoqi Wang, Yifan Wei, Xuebing Han, and Yuejiu Zheng.
2021. "Dual Closed-Loops Capacity Evolution Prediction for Energy Storage Batteries Integrated with Coupled Electrochemical Model" *World Electric Vehicle Journal* 12, no. 3: 109.
https://doi.org/10.3390/wevj12030109