# Research on Braking Energy Regeneration for Hybrid Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model and Objective Function

#### 2.1. Vehicle System Model

- The torsional vibration of the engine and shaft and the effect of the clutch torsional damper on the system are neglected.
- The transverse vibration of the drive shaft and the driven shaft is neglected.
- Each component is a rigid inertial element without damping.
- The clearance of the kinematic pair is neglected.

#### 2.1.1. Engine Model

_{ed}represents the output torque of the engine, T

_{e}is the engine torque, T

_{ef}is the internal friction torque, J

_{e}is the inertia of the engine, and ω

_{e}is the engine angular velocity.

_{e}is the engine speed.

#### 2.1.2. Motor Model

_{md}. T

_{m}is the engine torque, and T

_{mf}is the internal friction torque of the engine. J

_{m}is the inertia moment of the engine; ω

_{m}is the motor angular velocity, where ω

_{m}= ω

_{e}.

#### 2.1.3. Battery Model

_{v}is the voltage of the battery; B

_{c}is the current of the battery; and B

_{s}is the SOC of the battery.

#### 2.1.4. Other Mathematical Model

_{td}should be expressed as (6). J

_{t1}is the inertia moment of the input of transmission; J

_{t2}is the inertia moment of the output of transmission; T

_{tf}is the internal friction torque of transmission; and ω

_{t}is the transmission output shaft angular velocity.

_{f1}is the inertia moment of the input of the final drive; J

_{f2}is the inertia moment of the output of the final drive; T

_{ff}internal friction torque of the final drive; T

_{fd}is the output torque of the final drive; and ω

_{f}is the final drive angular velocity.

_{D}is the air resistance coefficient; A is the frontal area; v is the velocity of the vehicle; J

_{v}is the inertia moment of the differential and wheel; $a$ is the vehicle acceleration; f is the friction coefficient of the pavement; and α is the slope angle.

_{T}is the mechanical efficiency of the transmission system; δ

_{i}is the rotational mass conversion factor in i gear.

#### 2.2. Objective Function

_{i}

_{,i−1}, the function is shown as (10):

_{b}is the downshifting acceleration; and t

_{br}is the shifting time. In this paper, t

_{br}is taken as 1.2 s, according to real vehicle experimental testing.

_{0}and the minimum regeneration speed in i − 1 gear is v

_{1}, the vehicle speed from v

_{1}to v

_{0}, the objective function of regeneration energy can be expressed as (12):

## 3. Solving Process of the Optimization Problem

_{s}, motor torque T

_{ms}, and vehicle weight m in the objective function are sampled. To avoid the dispersion and accumulation of the sampling points, Latin hypercube sampling is used, and the consequences are shown in Figure 8.

_{s}.

## 4. Optimization Results Analysis

_{ms}change during the braking process. If r < 1 at the beginning of braking, and with the changes in the acceleration as and motor torque T

_{ms}, the objective function shows that the vehicle should shift, and the velocity of the vehicle is under the optimum downshifting velocity. Under this condition, the braking regeneration of the vehicle may not achieve maximum values. Thus, more studies should be conducted on this condition.

_{s}, motor torque T

_{ms}, and vehicle velocity v are sampled to calculate rr. These variables are discretized, as shown below.

_{r}can be obtained. Therefore, if the vehicle velocity v is lower than the minimum vehicle velocity v

_{r}, there is no gear shifting. Moreover, if v > v

_{r}, the vehicle shifts gear, and the optimization of the objective function can be shown as (19):

## 5. Simulation and Validation of Optimization Results

#### 5.1. Model Validation

#### 5.2. Validation of Gear Shifting Strategy in Braking Process

#### 5.3. Validation of Gear Shifting Strategy under Different Braking Strengths

_{s}> 1.4 m/s

^{2}, the optimal strategy is the same as D gear, and there is no gear shifting in the braking process. Compared with L gear, the optimal strategy braking energy regeneration increases from 3.8% to 57.4%. When the acceleration a

_{s}< 0.6 m/s

^{2}, the optimal strategy is the same as L gear, and the vehicle should shift gear. Compared with D gear, the optimal strategy braking energy regeneration increases by approximately 5%. When the acceleration is 0.6 m/s

^{2}< a

_{s}< 1.4 m/s

^{2}, compared with D gear, the optimal strategy braking energy regeneration increases by approximately 0.5% to 5.3%. Compared with L gear, the optimal strategy braking energy regeneration increases from approximately 0.4% to 1.8%. From the above results, the optimal strategy appears to have a better performance in braking energy regeneration under different braking strengths.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Berjoza, D.; Pirs, V.; Jurgena, I. Research into the regenerative braking of an electric car in urban driving. World Electr. Veh. J.
**2022**, 13, 202. [Google Scholar] [CrossRef] - Hu, X.; Johannesson, L.; Murgovski, N.; Egardt, B. Longevity-conscious dimensioning and power management of the hybrid energy storage system in a fuel cell hybrid electric bus. Appl. Energy
**2015**, 137, 913–924. [Google Scholar] [CrossRef] - Li, T.; Liu, H.; Zhang, Z.; Ding, D.-L. Shift scheduling strategy development for parallel hybrid construction vehicles. J. Cent. South Univ.
**2019**, 26, 587–603. [Google Scholar] [CrossRef] - Song, Q.; Ye, S.; Li, W. Research on AMT overall shift schedule for pure electric vehicles based on NSGA-II algorithm. Chin. J. Automot. Eng.
**2017**, 7, 44–51. [Google Scholar] - Ngo, V.; Hofman, T.; Steinbuch, M.; Serrarens, A. Effect of gear shift and engine start losses on energy management strategies for hybrid electric vehicles. Int. J. Powertrains
**2015**, 4, 141–162. [Google Scholar] [CrossRef] - Hua, Y. Research on Control Strategy for Double Synchronized Gear-Shift for Parallel Hybrid Electric Bus. Dalian University of Technology. 2014. Available online: https://kns.cnki.net/kcms2/article/abstract?v=3uoqIhG8C475KOm_zrgu4lQARvep2SAkVNKPvpjdBoadmPoNwLRuZyEhqbyUdN4bwC47MsOtZnyuqNqdK5mVILBfBvr8lzDA&uniplatform=NZKPT (accessed on 1 February 2023).
- Qin, D.; Ye, X.; Hu, M.; Chen, Q. Optimization of Control Strategy for Medium Hybrid Electric Vehicle with ISG at Drive Condition. J. Mech. Eng.
**2010**, 46, 86–92. [Google Scholar] [CrossRef] - Wang, W.; Wang, Q.; Zeng, X. Research on Gear-shift Schedules in the Braking Process of Parallel Hybrid Electric Bus. J. Jilin Univ.
**2009**, 39, 10–13. [Google Scholar] - Liu, W.; Chen, G.; Zong, C.; Li, C. Research on Electric Vehicle Braking Force Distribution for Maximizing Energy Regeneration. In Proceedings of the SAE 2016 World Congress and Exhibition, Detroit, MI, USA, 12–14 April 2016. [Google Scholar]
- Lu, J. Hill-Start Control Strategy of Heavy Off-Road Vehicles Equipped with AMT Based on Multi-Signal Integration; Beijing Institute of Technology: Beijing, China, 2014. [Google Scholar]
- Guo, H. Optimization Study on Control Strategy for the Cooperative Braking System in an Electric Vehicle with Independently Driven Front and Rear Axles; Beijing Institute of Technology: Beijing, China, 2014. [Google Scholar]
- Shen, W.; Hu, Y.; Yu, H. Shifting Process Control of AMT Based on Virtual Clutch Technology for Hybrid Electric Vehicle. J. Mech. Eng.
**2014**, 50, 108–117. [Google Scholar] [CrossRef] - Mehrdad, E.; Yinin, G.; Ali, E. Modern Electric, Hybrid Electric, and Fuel Cell Vehicles: Fundamentals Theory, and Design, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2010. [Google Scholar]
- Lai, Y.; Jiang, X.; Fang, L. Optimization Theory and Examples of Parameters by Isight; Beihang University Press: Beijing, China, 2012. [Google Scholar]
- Zhong, Y.; Chen, B.; Wang, Z. Principles and Methods of Multidisciplinary Design Optimization; Huazhong University of Science and Technology Press: Wuhan, China, 2007. [Google Scholar]
- Yu, Z. Automobile Theory; Machinery Industry Press: Beijing, China, 2019. [Google Scholar]

Component | Specification | Value | Unit |
---|---|---|---|

Engine | Type | Natural gas | - |

Rated power/speed | 140/2500 | kW/rpm | |

Maximum torque/speed | 650/1500 | Nm/rpm | |

Motor | Type | Permanent magnet | - |

Rated power/speed | 26/2600 | kW/rpm | |

Maximum torque/speed | 420/1000 | Nm/rpm | |

Battery | Voltage | 360 | V |

Capacity | 8 | Ah | |

Transmission | Gear ratio | 7.05/4.13/2.52/1.59/ 1.00/0.78/R6.75 | - |

Coefficients | Scaled | Normalized | |
---|---|---|---|

Constant | 82.54907361 | ||

n_{m} | 0.007776876 | 3.796131489 | 31.01952404 |

T_{m} | 0.022894698 | −1.328832684 | −10.8583587 |

${n}_{\mathrm{m}}^{2}$ | −2.07 × 10^{−6} | −1.49752163 | −12.23677534 |

${T}_{\mathrm{m}}^{2}$ | −9.83 × 10^{−5} | −3.873657126 | −31.65301326 |

T_{m} − n_{m} | 1.03× 10^{−5} | 1.741735007 | 14.23232865 |

Major Component | Main Parameter | Parameter Value |
---|---|---|

Engine | Output volume (L) | 6.5 |

Rated power/rotational speed (Kw/rpm) | 140/2500 | |

Maximum torque/rotational speed (Nm/rpm) | 650/1500 | |

Clutch | Type | Single-piece dry-type diaphragm spring clutch |

Motor | Type | Permanent magnet synchronous motor |

Voltage (V) | 340 | |

Rated power/rotational speed (Kw/rpm) | 26/2600 | |

Maximum torque/rotational speed (Nm/rpm) | 420/1000 | |

Battery | Type | Aluminum–plastic film manganese oxide lithium-ion power battery |

Voltage (V) | 360 | |

Capacity | 8Ah | |

Transmission | Manipulation mode | AMT |

Speed ratio of each gear | 7.05/4.13/2.52/1.59/1.00/0.78/R6.75 |

Acceleration (m/s ^{2}) | Regeneration Energy | Acceleration (m/s ^{2}) | Regeneration Energy | ||||
---|---|---|---|---|---|---|---|

D | Optimal Strategy | L | D | Optimal Strategy | L | ||

−0.4 | 0.1229 | 0.1229 | 0.1229 | −1.2 | 0.0426 | 0.0439 | 0.0430 |

−0.5 | 0.0974 | 0.1022 | 0.1022 | −1.3 | 0.0389 | 0.0391 | 0.0388 |

−0.6 | 0.0802 | 0.0843 | 0.0843 | −1.4 | 0.0359 | 0.0359 | 0.0352 |

−0.7 | 0.0719 | 0.0758 | 0.0755 | −1.5 | 0.0332 | 0.0332 | 0.0320 |

−0.8 | 0.0657 | 0.0691 | 0.0687 | −1.6 | 0.0314 | 0.0314 | 0.0299 |

−0.9 | 0.0556 | 0.0581 | 0.0561 | −2 | 0.0264 | 0.0264 | 0.0241 |

−1.0 | 0.0496 | 0.0515 | 0.0509 | −3 | 0.0166 | 0.0166 | 0.0125 |

−1.1 | 0.0470 | 0.0498 | 0.0480 | −4 | 0.0121 | 0.0121 | 0.0077 |

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## Share and Cite

**MDPI and ACS Style**

Xu, M.; Peng, J.; Ren, X.; Yang, X.; Hu, Y.
Research on Braking Energy Regeneration for Hybrid Electric Vehicles. *Machines* **2023**, *11*, 347.
https://doi.org/10.3390/machines11030347

**AMA Style**

Xu M, Peng J, Ren X, Yang X, Hu Y.
Research on Braking Energy Regeneration for Hybrid Electric Vehicles. *Machines*. 2023; 11(3):347.
https://doi.org/10.3390/machines11030347

**Chicago/Turabian Style**

Xu, Mengtian, Jianxin Peng, Xiaochen Ren, Xuekun Yang, and Yuhui Hu.
2023. "Research on Braking Energy Regeneration for Hybrid Electric Vehicles" *Machines* 11, no. 3: 347.
https://doi.org/10.3390/machines11030347