# Comparisons of Energy Management Methods for a Parallel Plug-In Hybrid Electric Vehicle between the Convex Optimization and Dynamic Programming

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Vehicle Model Analysis and Simplification

#### 2.1. Engine Model

#### 2.2. Electric Machine and Gearbox Unit

_{eng}can be determined,

#### 2.3. Battery Pack Model

#### 2.4. Quadratic Static Equation

## 3. Optimization Methods

## 4. Simulation Validation and Results Analysis

#### 4.1. Simulation with Initial SOC of 0.9

#### 4.2. Simulation with Different Initial SOCs

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**The battery internal resistance and the open circuit voltage (OCV) curve with respect to state of charge (SOC).

**Figure 11.**(

**a**) The result based on dynamic programming (DP) when eight NEDC cycles are simulated; (

**b**) The result based on convex optimization and SA when eight NEDC cycles are simulated.

**Figure 13.**(

**a**) Engine efficiency comparison between the convex programming-based strategy and the strategy based on DP; (

**b**) Engine efficiency comparison between charging depleting–charging sustaining (CD/CS) strategy and the convex programming-based method.

**Figure 14.**Speed and driveline power demand for Urban Dynamometer Driving Schedule (UDDS) drive cycle.

Type | Parallel PHEV Value |
---|---|

Vehicle mass | 1720 kg |

Drive type | Front wheel drive |

Engine | Maximum power 65 kW |

Maximum speed 6000 rpm | |

Motor | Rated power 30 kW |

Peak power 70 kW |

Type | Parameter |
---|---|

Battery type | Lithium-ion battery |

Parallel number | 1 |

Serial number | 72 |

Minimum SOC | 0.2 |

Maximum SOC | 1 |

Initial SOC | 0.9 |

Termination SOC | 0.3 |

Capacity | 37 Ah |

Nominal voltage | 259.2 V |

**Table 3.**Results comparison with standard initial SOC. CD/CS: charging depleting–charging sustaining; DP: dynamic programming; HWFET: Highway Fuel Economy Driving Schedule; NEDC: New European Driving Cycle.

Drive Cycle | CD/CS Algorithm | DP Algorithm | Convex Algorithm | |||||
---|---|---|---|---|---|---|---|---|

F (kg) | Ending SOC | F (kg) | Ending SOC | Savings (%) | F (kg) | Ending SOC | Savings (%) | |

9 HWFET | 3.7004 | 0.2767 | 3.4980 | 0.3031 | 6.82 | 3.5030 | 0.2986 | 6.45 |

8 HWFET | 3.1666 | 0.2767 | 2.9817 | 0.3027 | 7.39 | 2.9934 | 0.2995 | 6.83 |

7 HWFET | 2.6328 | 0.2767 | 2.4719 | 0.3022 | 7.94 | 2.4768 | 0.2930 | 7.10 |

6 HWFET | 2.0990 | 0.2767 | 1.9655 | 0.3017 | 8.62 | 1.9656 | 0.2994 | 8.40 |

9 NEDC | 1.9803 | 0.2923 | 1.8449 | 0.3115 | 8.67 | 1.8486 | 0.3116 | 8.49 |

8 NEDC | 1.6325 | 0.2923 | 1.4687 | 0.2772 | 8.29 | 1.5187 | 0.3034 | 8.26 |

7 NEDC | 1.2847 | 0.2923 | 1.2059 | 0.3103 | 9.91 | 1.1910 | 0.3060 | 9.31 |

Drive Cycle | CPU Time (s) | |
---|---|---|

DP Algorithm | Convex Algorithm | |

9 HWFET | 170.5 | 3.1 |

8 HWFET | 151.9 | 2.8 |

7 HWFET | 133.1 | 2.5 |

6 HWFET | 114.5 | 2.5 |

9 NEDC | 227.9 | 7.0 |

8 NEDC | 189.9 | 5.5 |

7 NEDC | 176.7 | 4.2 |

Initial SOC | CD/CS Algorithm | DP Algorithm | Convex Algorithm | |||||
---|---|---|---|---|---|---|---|---|

F (kg) | Ending SOC | F (kg) | Ending SOC | Savings (%) | F (kg) | Ending SOC | Savings (%) | |

0.7 | 2.1871 | 0.2859 | 1.9729 | 0.2969 | 10.75 | 1.9758 | 0.2905 | 10.06 |

0.8 | 1.9988 | 0.2859 | 1.7842 | 0.2986 | 11.93 | 1.8108 | 0.2836 | 9.19 |

Initial SOC | Drive Cycle | CPU-Time (s) | |
---|---|---|---|

DP Algorithm | Convex Algorithm Optimization | ||

0.8 | 8 UDDS | 269.6 | 2.7 |

0.7 | 8 UDDS | 270.1 | 4.9 |

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**MDPI and ACS Style**

Xiao, R.; Liu, B.; Shen, J.; Guo, N.; Yan, W.; Chen, Z. Comparisons of Energy Management Methods for a Parallel Plug-In Hybrid Electric Vehicle between the Convex Optimization and Dynamic Programming. *Appl. Sci.* **2018**, *8*, 218.
https://doi.org/10.3390/app8020218

**AMA Style**

Xiao R, Liu B, Shen J, Guo N, Yan W, Chen Z. Comparisons of Energy Management Methods for a Parallel Plug-In Hybrid Electric Vehicle between the Convex Optimization and Dynamic Programming. *Applied Sciences*. 2018; 8(2):218.
https://doi.org/10.3390/app8020218

**Chicago/Turabian Style**

Xiao, Renxin, Baoshuai Liu, Jiangwei Shen, Ningyuan Guo, Wensheng Yan, and Zheng Chen. 2018. "Comparisons of Energy Management Methods for a Parallel Plug-In Hybrid Electric Vehicle between the Convex Optimization and Dynamic Programming" *Applied Sciences* 8, no. 2: 218.
https://doi.org/10.3390/app8020218