# Regenerative Braking Strategy of Dual-Motor EV Considering Energy Recovery and Brake Stability

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model of a Dual-Motor EV Regenerative Braking System

#### 2.1. Dual-Motor EV System Configuration

#### 2.2. Motor Model

_{m}

_{1}and τ

_{m}

_{2}denote the time constants of the first-order system; T

_{m}

_{1,}T

_{m}

_{2}denote the actual output torque

#### 2.3. Power Battery Loss Model

_{o}denotes the battery terminal voltage; R

_{c}and R

_{c_dis}denote the battery equivalent resistance and the battery discharge resistance, respectively; and P

_{m}denotes the total generated power of the motor.

#### 2.4. Vehicle Braking Model

_{xb_f}and F

_{xb_r}denote the ground braking force of the front wheel and the rear wheel, respectively; F

_{w}and F

_{f}denote the wind resistance and the rolling resistance of the vehicle; C

_{d}and f

_{v}indicate the wind resistance coefficient and the rolling resistance coefficient; and A

_{v}is expressed as the equivalent wind resistance area.

_{f}and J

_{r}denote the equivalent rotational inertia of the front and rear wheels, respectively; R

_{v}indicates the wheel radius; ω

_{f}and ω

_{r}represent the front and rear wheel rotational speeds; T

_{bF_h}and T

_{bR_h}represent the hydraulic braking force of the front and rear wheels. T

_{bF_m}is the regenerative braking torque applied to the wheel end by the dual motor, expressed as follows:

_{m}

_{1}and T

_{m}

_{2}denote the output torque of motor 1 and motor 2; i

_{m}

_{2}and i

_{0}denote the output reduction ratio of motor 2 and the final drive ratio, respectively; and i

_{g}

_{1}and i

_{g}

_{2}represent the corresponding reduction ratios of motor 1 and motor 2 in the current operating mode of the coupling mechanism.

## 3. Regenerative Braking Strategy for Dual-Motor EV

#### 3.1. Energy Recovery-Dominated Regenerative Braking Torque Distribution (RBD) Rule

_{bF}and F

_{bR}denote the front wheel braking torque and the rear wheel braking torque, respectively.

#### 3.2. Regenerative Braking Torque Optimisation Incorporating Energy Recovery and Braking Stability

_{w}denotes wheel end rotational speed; η

_{1}and η

_{2}denote the generation efficiency of motor 1 and motor 2, respectively; v

_{t}and v

_{0}represent the current vehicle speed and the initial braking speed; and P

_{los}denotes the loss of power for battery charging.

_{If}and T

_{Ir}represent the front and rear wheel braking torques corresponding to when the braking force distribution curve is on the ideal distribution curve, respectively.

_{1}and w

_{2}denote the corresponding weighting factors.

_{1}will be increased. Conversely, at high speeds or high braking intensities the focus is on braking stability and the weighting factor w

_{1}will be reduced, w

_{2}increased. When braking under normal operating conditions, the weighting coefficients are taken to be 0.5, respectively, in order to take into account the effects of both braking energy recovery and braking stability.

- (1)
- Initialization

- (2)
- Calculation of the fitness

_{I}), and determine whether it satisfies the termination condition of the genetic algorithm; if it does, then output the optimal solution, otherwise continue to evolutionary operations.

- (3)
- Evolutionary operations

## 4. Results Verification

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Vehicle speed-braking intensity-braking torque distribution maps. (

**a**) Motor 1 braking torque. (

**b**) Motor 2 braking torque. (

**c**) Front wheel hydraulic braking torque. (

**d**) Rear wheel hydraulic braking torque.

**Figure 10.**Comparative graph of the different braking torque distribution strategies. (

**a**) Motor 1 braking torque. (

**b**) Motor 2 braking torque. (

**c**) Front wheel hydraulic braking torque. (

**d**) Rear wheel hydraulic braking torque.

**Figure 11.**Comparative graphs of motor efficiency under the different strategies. (

**a**) Motor 1 efficiency. (

**b**) Motor 2 efficiency.

**Figure 12.**Comparative graphs of energy recovery and stability under the different strategies. (

**a**) Cumulative energy recovery. (

**b**) Stability coefficient.

Components | Description |
---|---|

Transmission | Reduction ratios (i_{1}, i_{2}): 2.11/1.31 |

Final drive ratio (i_{0}): 3.91 | |

Reduction ratio of the motor 2 end (i_{m}_{2}): 1.72 | |

Motor | Type: Permanent magnet synchronous motor (PMSM) |

Maximum power: 55 kW (M1); 75 kW (M2) | |

Battery | Type: NiMH |

Voltage: 387 V | |

Capacity: 25 kW·h | |

Vehicle | Internal resistance: 0.015 Ω |

Vehicle mass: 1570 kg | |

Frontal area of vehicle: 1.26 m^{2}; Aerodynamic drag: 0.35 | |

Tire rolling resistance coefficient: 0.018 | |

Drive wheel radius: 0.3 m |

Braking Intensity | Vehicle Speed [km/h] | Distribution Strategy | ε-RMS | Change Rate | Recovered Energy [KJ] | Change Rate |
---|---|---|---|---|---|---|

0.2 | v = 60 | R-RBD | 0.482 | −2.7% | 30.43 | 8.3% |

GA-RBD | 0.469 | 32.96 | ||||

v = 75 | R-RBD | 0.473 | −3.8% | 34.63 | 10.2% | |

GA-RBD | 0.455 | 38.16 | ||||

v = 90 | R-RBD | 0.452 | −4.3% | 42.09 | 13.1% | |

GA-RBD | 0.433 | 47.60 | ||||

0.4 | v = 60 | R-RBD | 0.331 | −2.9% | 21.32 | 11.5% |

GA-RBD | 0.321 | 23.77 | ||||

v = 75 | R-RBD | 0.321 | −3.1% | 21.12 | 14.2% | |

GA-RBD | 0.311 | 24.12 | ||||

v = 90 | R-RBD | 0.311 | −3.4% | 19.71 | 18.1% | |

GA-RBD | 0.300 | 23.28 | ||||

0.6 | v = 60 | R-RBD | 0.150 | −4.6% | 8.29 | 13.5% |

GA-RBD | 0.143 | 9.08 | ||||

v = 75 | R-RBD | 0.140 | −5.0% | 11.01 | 16.2% | |

GA-RBD | 0.133 | 12.79 | ||||

v = 90 | R-RBD | 0.128 | −5.4% | 13.71 | 20.2% | |

GA-RBD | 0.121 | 16.48 |

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**MDPI and ACS Style**

Wu, T.; Wang, F.; Ye, P.
Regenerative Braking Strategy of Dual-Motor EV Considering Energy Recovery and Brake Stability. *World Electr. Veh. J.* **2023**, *14*, 19.
https://doi.org/10.3390/wevj14010019

**AMA Style**

Wu T, Wang F, Ye P.
Regenerative Braking Strategy of Dual-Motor EV Considering Energy Recovery and Brake Stability. *World Electric Vehicle Journal*. 2023; 14(1):19.
https://doi.org/10.3390/wevj14010019

**Chicago/Turabian Style**

Wu, Tonglie, Feng Wang, and Peng Ye.
2023. "Regenerative Braking Strategy of Dual-Motor EV Considering Energy Recovery and Brake Stability" *World Electric Vehicle Journal* 14, no. 1: 19.
https://doi.org/10.3390/wevj14010019