# An Optimal Fast-Charging Strategy for Lithium-Ion Batteries via an Electrochemical–Thermal Model with Intercalation-Induced Stresses and Film Growth

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## Abstract

**:**

## 1. Introduction

## 2. Electrochemical–Thermal Model with Intercalation-Induced Stress and Film Growth

#### 2.1. SPM-Electrolyte-T Model

#### 2.2. Intercalation-Induced Stress

#### 2.3. Film Growth Model

## 3. Temperature Control Based on the Backstepping Technique

## 4. Problem Formulation

## 5. Simulation and Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BMS | Batteries management system |

DP | Dynamic optimization |

SoC | State of Charge |

CC-CV | Constant current-constant voltage |

CC | Constant current |

IC | Incremental capacity |

OCV | Open circuit voltage |

TTC | Time-to-charge |

EL | Energy losses |

TRI | Temperature rise index |

P2D | Pseudo-two dimensional |

MPC | Model predictive control |

CT-CV | Constant temperature-constant voltage |

LGR | Legendre-Gauss-Radau |

PID | Proportional-integral-derivative |

SPM | Single particle model |

PDE | Partial differential equation |

ODE | Ordinary differential equation |

UDDS | Urban Dynamometer Driving Schedule |

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Range | $\mathit{I}(\mathit{t})$ (C) | ${\mathit{t}}_{\mathit{f}}$ (min) | $\mathit{V}(\mathit{t})$ (V) | ${\mathit{\sigma}}_{\mathit{r},\mathbf{max}}^{-}(\mathit{t})$ (MPa) | $-{\mathit{\sigma}}_{\mathit{t},\mathbf{max}}^{-}(\mathit{t})$ (MPa) | $\partial {\dot{\mathit{\delta}}}_{\mathit{f}\mathit{i}\mathit{l}\mathit{m}}(\mathit{t})$ (μΩ/m^{2}/s) |
---|---|---|---|---|---|---|

Upper | 3 | 80 | 4.3 | 160 | 220 | 0.5 |

Lower | 0 | 15 | 2 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Chen, G.; Liu, Z.; Su, H.
An Optimal Fast-Charging Strategy for Lithium-Ion Batteries via an Electrochemical–Thermal Model with Intercalation-Induced Stresses and Film Growth. *Energies* **2020**, *13*, 2388.
https://doi.org/10.3390/en13092388

**AMA Style**

Chen G, Liu Z, Su H.
An Optimal Fast-Charging Strategy for Lithium-Ion Batteries via an Electrochemical–Thermal Model with Intercalation-Induced Stresses and Film Growth. *Energies*. 2020; 13(9):2388.
https://doi.org/10.3390/en13092388

**Chicago/Turabian Style**

Chen, Guangwei, Zhitao Liu, and Hongye Su.
2020. "An Optimal Fast-Charging Strategy for Lithium-Ion Batteries via an Electrochemical–Thermal Model with Intercalation-Induced Stresses and Film Growth" *Energies* 13, no. 9: 2388.
https://doi.org/10.3390/en13092388