# Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation

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## Abstract

**:**

## 1. Introduction

## 2. Modeling and EMR of the Studied Car

## 3. Inversion-Based Control of the Studied Car

## 4. Braking Strategy

#### 4.1. Distribution of Braking Forces Between Front and Rear Wheels

#### 4.2. RBS and FBS Contribution in the Rear Wheels

## 5. Results

#### 5.1. Studied Race Car and Driving Cycle

#### 5.2. Simulation Using the Proposed Braking Strategy

#### 5.3. Comparison of Different Braking Strategies

_{4}batteries is 100 Wh/kg [38]. The results are presented in Table 5.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**EMR elements. (

**a**) Source element; (

**b**) Conversion element; (

**c**) Accumulation element; (

**d**) Coupling element.

**Figure 11.**Braking forces distribution (

**a**) Electric differential effect on left and right wheels; (

**b**) Braking strategy effect in front and rear wheels.

Parameter | Value |
---|---|

Mass [kg] | 375.00 |

Width [m] | 1.35 |

Drag coefficient (${C}_{x}$) | 0.29 |

Downforce coefficient (${C}_{z}$) | 1.20 |

Front area [m^{2}] | 0.84 |

Wheel diameter [m] | 0.49 |

Rolling resistance coefficient (${C}_{rr}$) | 0.03 |

Wheelbase [m] | 1.46 |

La [m] | 0.7 |

Lb [m] | 0.76 |

Hg [m] | 0.34 |

Parameter | Value |
---|---|

Rated torque [Nm] | 47.70 |

Rated power [kW] | 17.02 |

Number of electric machines | 2 |

Total rated torque [Nm] | 94.50 |

Total rated power [kW] | 34.05 |

Rated angular speed (rpm) | 3000 |

Max. angular speed (rpm) | 6000 |

Gearbox ratio | 50/14 |

Traction mode | Rear wheel drive |

Parameter | Value |
---|---|

Rated cell voltage [V] | 3.20 |

Max. cell voltage [V] | 4.25 |

Min. cell voltage [V] | 2.50 |

Cells in series | 30.0 |

Parallel arrays | 1.0 |

Maximal charging current [A] | 80 |

Rated Capacity [Ah] | 90 |

Internal resistance [Ω] | 0.006 |

Test | Energy Recovered [Wh] |
---|---|

No RBS | 0.00 |

Proposed strategy | 1264.3 |

Ideal braking distribution | 922.34 |

Fixed distribution ${k}_{\alpha}=0.55$ | 1129.6 |

Fixed distribution ${k}_{\alpha}=0.75$ | 647.19 |

Test | Mass Reduction [kg] | Percentage of the Total Mass |
---|---|---|

No RBS | 0 | 0 |

Proposed strategy | 12.64 | 3.37 |

Ideal braking distribution | 9.22 | 2.46 |

Fixed distribution ${k}_{\alpha}=0.55$ | 11.29 | 3.01 |

Fixed distribution ${k}_{\alpha}=0.75$ | 6.47 | 1.72 |

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**MDPI and ACS Style**

Henao-Muñoz, A.C.; Pereirinha, P.; Bouscayrol, A.
Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation. *World Electr. Veh. J.* **2020**, *11*, 45.
https://doi.org/10.3390/wevj11020045

**AMA Style**

Henao-Muñoz AC, Pereirinha P, Bouscayrol A.
Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation. *World Electric Vehicle Journal*. 2020; 11(2):45.
https://doi.org/10.3390/wevj11020045

**Chicago/Turabian Style**

Henao-Muñoz, Andrés Camilo, Paulo Pereirinha, and Alain Bouscayrol.
2020. "Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation" *World Electric Vehicle Journal* 11, no. 2: 45.
https://doi.org/10.3390/wevj11020045