# Energy Management Strategy for P1 + P3 Plug-In Hybrid Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure of the P1 + P3 Plug-in Hybrid Powertrain System

#### 2.2. Rule-Based Energy Management Strategy

#### 2.2.1. Low- to Mid-Speed Phase

- Determining whether the vehicle operates in driving mode or regenerative braking mode based on the overall vehicle torque demand.
- Deciding whether to enter EM alone or extended-range mode and whether to engage energy recovery based on SOC status.
- Based on the maximum regenerative braking capability of the P3 motor, determining whether to engage in blended braking.

#### 2.2.2. High-Speed Phase

## 3. Modeling

#### 3.1. Engine Characteristic Model

#### 3.2. Drive Motor Characteristic Model

#### 3.3. Power Battery Pack Model

#### 3.4. Vehicle Dynamics Model

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 14.**Comparison of engine output torque between conventional vehicle and P1 + P3 du-al-motor configuration.

Operating Modes | Status of Key Components | ||||
---|---|---|---|---|---|

Engine | P1 Motor | P3 Motor | Power Battery | Clutch | |

EM alone | OFF | OFF | ON | discharged | disengaged |

Extended-range mode | ON | ON | ON | charged | engaged |

ICE alone | ON | OFF | OFF | idle | engaged |

Combined ICE-EM | ON | ON | OFF | discharged | engaged |

Power split | ON | ON | OFF | charged | engaged |

Regenerative braking | OFF | OFF | ON | charged | disengaged |

Operating Modes | Switching Logic | Torque Allocation | |
---|---|---|---|

Condition 1 | Condition 2 | ||

EM alone | $SOC>SO{C}_{min}$ | ${T}_{req}\le {T}_{P3\_max}$ | ${T}_{eng}=0$ |

${T}_{P1}=0$ | |||

${T}_{P3}={T}_{req}$ | |||

Extended-range mode | $SOC\le SO{C}_{min}$ | — | ${T}_{eng}={T}_{eng\_opt}$ |

${T}_{P1}={T}_{eng\_opt}$ | |||

${T}_{P3}={T}_{req}$ | |||

Regenerative braking | $SOC\le SO{C}_{max}$ | ${T}_{req}\le {T}_{P3\_max}$ | ${T}_{eng}=0$ |

${T}_{P1}=0$ | |||

${T}_{P3}={T}_{req}$ | |||

${T}_{req}>{T}_{P3gen\_max}$ | ${T}_{eng}=0$ | ||

${T}_{P1}=0$ | |||

${T}_{P3}={T}_{P3gen\_max}$ |

Operating Modes | Switching Logic | Torque Allocation | |
---|---|---|---|

Condition 1 | Condition 2 | ||

ICE alone | $0<SOC\le SO{C}_{min}$ | ${T}_{req}>{T}_{eng\_opt}$ | ${T}_{eng}=min({T}_{req},{T}_{engmax})$ |

${T}_{P1}=0$ | |||

${T}_{P3}=0$ | |||

Combined ICE-EM | $SOC>SO{C}_{min}$ | ${T}_{eng\_opt}<{T}_{req}\le {T}_{eng\_max}$ | ${T}_{eng}={T}_{eng\_opt}$ |

${T}_{P1}={T}_{req}$-${T}_{eng\_opt}$ | |||

${T}_{P3}=0$ | |||

$\begin{array}{c}{T}_{req}>{T}_{eng\_max}\\ {T}_{req}\le {T}_{cb1}\end{array}$ | ${T}_{eng}={T}_{req}-{T}_{P1\_max}$ | ||

${T}_{P1}={T}_{cb2}$ | |||

${T}_{P3}=0$ | |||

$\begin{array}{c}{T}_{req}>{T}_{eng\_max}\\ {T}_{req}>{T}_{cb1}\end{array}$ | ${T}_{eng}={T}_{req}-{T}_{P1\_max}$ | ||

${T}_{P1}={T}_{P1\_max}$ | |||

${T}_{P3}=0$ | |||

Power split | $0<SOC\le SO{C}_{max}$ | $\begin{array}{c}{T}_{eng\_min}<{T}_{req}\le {T}_{eng\_opt}\\ {T}_{cb2}\le {T}_{P1gen\_max}\end{array}$ | ${T}_{eng}={T}_{eng\_opt}$ |

${T}_{P1}={T}_{cb2}$ | |||

${T}_{P3}=0$ | |||

$\begin{array}{c}{T}_{eng\_min}<{T}_{req}\le {T}_{eng\_opt}\\ {T}_{cb2}>{T}_{P1gen\_max}\end{array}$ | ${T}_{eng}={T}_{eng\_opt}-{T}_{P1gen\_max}$ | ||

${T}_{P1}={T}_{P1gen\_max}$ | |||

${T}_{P3}=0$ | |||

Regenerative braking | ${T}_{req}<0$ | ${T}_{eng}=0$ | |

${T}_{P1}=0$ | |||

${T}_{P3}=max({T}_{req},{T}_{P3gen\_max})$ |

Variable Names | Variable Descriptions |
---|---|

$SO{C}_{min}$ | Minimum SOC threshold value |

$SO{C}_{max}$ | Maximum SOC threshold value |

${T}_{req}$ | Vehicle wheel-end torque demand |

${T}_{eng\_max}$ | Engine maximum torque |

${T}_{eng\_min}$ | Engine minimum operating torque threshold value |

${T}_{eng\_opt}$ | Engine high-efficiency zone optimal torque |

${T}_{P1gen\_max}$ | P1 motor maximum regenerative torque |

${T}_{P1\_max}$ | P1 motor maximum drive torque |

${T}_{P3gen\_max}$ | P3 motor maximum regenerative torque |

${T}_{P3\_max}$ | P3 motor maximum drive torque |

Project | Parameters | Numerical |
---|---|---|

Vehicle | Curb weight | 2130 kg |

Total mass | 2545 kg | |

Frontal area | 2.26 m^{2} | |

Drag coefficient | 0.33 | |

Engine | Engine displacement | 1.5 L |

Engine power | 105 kW | |

P1 motor | Peak power | 47 kW |

Peak torque | 75 Nm | |

Maximum RPM | 11,000 rpm | |

P3 motor | Peak power | 300 kW |

Peak torque | 300 Nm | |

Maximum RPM | 14,500 rpm | |

Tires | Rolling radius | 287 mm |

Transmission | Gear ratio | 1:0.75 |

Power battery | Battery pack capacity | 11.52 kWh |

Battery pack rated voltage | 320 V |

Vehicle Models | Fuel Consumption Per Hundred Kilometers (L) | Fuel Efficiency Gain |
---|---|---|

Conventional vehicle | 10.00 | — |

P1 + P3 hybrid electric vehicle | 6.74 | 67.4% |

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## Share and Cite

**MDPI and ACS Style**

Zhang, B.; Shi, P.; Mou, X.; Li, H.; Zhao, Y.; Zheng, L.
Energy Management Strategy for P1 + P3 Plug-In Hybrid Electric Vehicles. *World Electr. Veh. J.* **2023**, *14*, 332.
https://doi.org/10.3390/wevj14120332

**AMA Style**

Zhang B, Shi P, Mou X, Li H, Zhao Y, Zheng L.
Energy Management Strategy for P1 + P3 Plug-In Hybrid Electric Vehicles. *World Electric Vehicle Journal*. 2023; 14(12):332.
https://doi.org/10.3390/wevj14120332

**Chicago/Turabian Style**

Zhang, Bo, Peilin Shi, Xiangli Mou, Hao Li, Yushuai Zhao, and Liaodong Zheng.
2023. "Energy Management Strategy for P1 + P3 Plug-In Hybrid Electric Vehicles" *World Electric Vehicle Journal* 14, no. 12: 332.
https://doi.org/10.3390/wevj14120332