# Parameter Matching Method of a Battery-Supercapacitor Hybrid Energy Storage System for Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. HESS Topology

## 3. Analysis of Six Typical Driving Cycles

## 4. HESS Parameter Matching Method and Optimization

#### 4.1. Energy Matching of Batteries

#### 4.2. Energy Matching of Supercapacitors

#### 4.3. Power Matching Method

#### 4.4. Optimization Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Velocity and power curves for six standard driving cycles. (

**a**) HL07. (

**b**) HWFET. (

**c**) UKBUS6. (

**d**) NYCC. (

**e**) INDIA-HWY-SAMPLE. (

**f**) WVUSUB.

Parameter | Values |
---|---|

Curb weight $M$ | 1845 kg |

Coefficient of air resistance ${C}_{D}$ | 0.36 |

Frontal area $A$ | 2.53 m² |

Rotating mass conversion factor $\delta $ | 1.03 |

Acceleration of gravity $g$ | 9.8 m/s² |

Rolling resistance coefficient $f$ | 0.025 |

Transmission efficiency $\eta $ | 0.9 |

Driving ranges $S$ | 300 km |

Maximum speed | 130 km/h |

Maximum grade $\alpha $ | 25% |

Rated busbar voltage ${U}_{\mathrm{m}}$ | 360 V |

Assisted acceleration time | 15 s |

0~50 km/h Acceleration time | ≤10 s |

Driving Cycles/ Parameters | Maximum Acceleration (m/s²) | Positive Peak Power (kW) | Positive Average Power (kW) | Negative Peak Power (kW) |
---|---|---|---|---|

HL07 | 3.576 | 135.822 | 45.816 | −38.403 |

HWFET | 1.431 | 53.606 | 24.790 | −52.259 |

UKBUS6 | 1.313 | 27.093 | 4.871 | −16.221 |

NYCC | 2.682 | 56.956 | 9.564 | −31.743 |

INDIA_HWY_SAMPLE | 2.121 | 55.345 | 16.845 | −33.525 |

WVUSUB | 1.295 | 41.270 | 11.179 | −48.049 |

${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}-\mathit{p}}$ | ${\mathit{C}}_{\mathit{B}\mathit{a}\mathit{t}-\mathit{c}\mathit{e}\mathit{l}\mathit{l}}\left(\mathbf{Ah}\right)$ | ${\mathit{N}}_{\mathbf{sc}-\mathit{p}}$ | ${\mathit{C}}_{\mathbf{sc}}\left(\mathbf{F}\right)$ |
---|---|---|---|

1 | ≥233.790 | 1 | ≥3658.198 |

2 | ≥116.900 | 2 | ≥1829.099 |

3 | ≥77.930 | 3 | ≥1219.399 |

4 | ≥58.450 | 4 | ≥914.549 |

5 | ≥46.760 | 5 | ≥731.639 |

6 | ≥38.965 | 6 | ≥609.699 |

7 | ≥33.400 | 7 | ≥522.599 |

8 | ≥29.220 | 8 | ≥457.275 |

9 | ≥25.970 | 9 | ≥406.466 |

10 | ≥23.380 | 10 | ≥365.820 |

${\mathit{C}}_{\mathit{B}\mathit{a}\mathit{t}-\mathit{c}\mathit{e}\mathit{l}\mathit{l}}\left(\mathbf{Ah}\right)$ | ${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}-\mathit{p}}$ | $\mathit{m}\left(\mathbf{kg}\right)$ | ${\mathit{\rho}}_{\mathbf{bat}}\left(\mathbf{Wh}/\mathbf{kg}\right)$ | ${\mathit{W}}_{\mathbf{bat}}\left(\$/\mathbf{Wh}\right)$ |
---|---|---|---|---|

25 | ≥9.352 | 0.585 | 170 | 0.430 |

35 | ≥6.680 | 1.080 | 135 | 0.430 |

60 | ≥3.900 | 1.850 | 130 | 0.430 |

100 | ≥2.338 | 3.050 | 115 | 0.430 |

${\mathit{C}}_{\mathit{s}\mathit{c}}\left(\mathbf{F}\right)$ | ${\mathit{\rho}}_{\mathit{E}\mathbf{sc}}\left(\mathbf{Wh}/\mathbf{kg}\right)$ | $\mathit{m}\left(\mathbf{kg}\right)$ | ${\mathit{\rho}}_{\mathbf{sc}}\left(\mathbf{W}/\mathbf{kg}\right)$ | ${\mathit{W}}_{\mathbf{sc}}\left(\$/\mathbf{Wh}\right)$ | ${\mathit{N}}_{\mathbf{sc}-\mathit{p}}$ |
---|---|---|---|---|---|

650 | 3.29 | 0.20 | 5400 | 11.55 | ≥6.173 |

1200 | 4.05 | 0.30 | 5000 | 11.55 | ≥4.444 |

1500 | 4.75 | 0.32 | 5800 | 11.55 | ≥3.592 |

2000 | 5.06 | 0.40 | 6200 | 11.55 | ≥2.688 |

3000 | 5.52 | 0.55 | 5400 | 11.55 | ≥2.245 |

${\mathit{C}}_{\mathit{B}\mathit{a}\mathit{t}-\mathit{c}\mathit{e}\mathit{l}\mathit{l}}\left(\mathbf{Ah}\right)$ | 25 | 35 | 60 | 100 |
---|---|---|---|---|

$\mathrm{min}{N}_{Bat-p}$ | 10 | 7 | 4 | 3 |

min weight (kg) | 585 | 756 | 740 | 915 |

min cost (k$) | 42.763 | 43.886 | 41.366 | 45.247 |

${\mathit{C}}_{\mathit{s}\mathit{c}}\left(\mathbf{F}\right)$ | 650 | 1200 | 1500 | 2000 | 3000 |
---|---|---|---|---|---|

$\mathrm{min}{N}_{\mathrm{sc}-p}$ | 7 | 5 | 4 | 3 | 3 |

min weight (kg) | 189.0 | 202.5 | 172.8 | 162.0 | 222.8 |

min cost (k$) | 7.181 | 9.472 | 9.480 | 9.468 | 14.201 |

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**MDPI and ACS Style**

Liu, F.; Wang, C.; Luo, Y.
Parameter Matching Method of a Battery-Supercapacitor Hybrid Energy Storage System for Electric Vehicles. *World Electr. Veh. J.* **2021**, *12*, 253.
https://doi.org/10.3390/wevj12040253

**AMA Style**

Liu F, Wang C, Luo Y.
Parameter Matching Method of a Battery-Supercapacitor Hybrid Energy Storage System for Electric Vehicles. *World Electric Vehicle Journal*. 2021; 12(4):253.
https://doi.org/10.3390/wevj12040253

**Chicago/Turabian Style**

Liu, Fengchen, Chun Wang, and Yunrong Luo.
2021. "Parameter Matching Method of a Battery-Supercapacitor Hybrid Energy Storage System for Electric Vehicles" *World Electric Vehicle Journal* 12, no. 4: 253.
https://doi.org/10.3390/wevj12040253