# Advanced Methodology for the Optimal Sizing of the Energy Storage System in a Hybrid Electric Refuse Collector Vehicle Using Real Routes

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## Abstract

**:**

## 1. Introduction

## 2. Hybrid Electric Refuse Collector Vehicle

## 3. Energy Storage System

## 4. Optimal Sizing of the ESS

## 5. Validation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$RCV$ | Refuse collector vehicle |

$HEV$ | Hybrid electric vehicle |

$HE$–$RCV$ | Hybrid electric refuse collector vehicle |

$EM$ | Electric machine |

$ICE$ | Internal combustion engine |

$ESS$ | Energy storage system |

$ECM$ | Engine control module |

${F}_{t}$ | Traction force |

${F}_{a}$ | Aerodynamic resistance |

${F}_{r}$ | Rolling resistance |

${F}_{g}$ | Force caused by gravity |

${m}_{RCV}$ | RCV mass |

${m}_{vehicle}$ | Vehicle mass |

${m}_{d}$ | Dynamic vehicle mass |

${m}_{EM}$ | EM mass |

${m}_{ESS}$ | ESS mass |

${P}_{body}$ | Body power |

${P}_{ESS}$ | ESS power |

${P}_{in}$ | In power |

${P}_{out}$ | Out power |

$Li$–$Po$ | Lithium polymer battery |

${C}_{nom}$ | Nominal capacity |

${C}_{ESS}$ | ESS capacity |

${V}_{OC}$ | Open-circuit voltage |

$SOC$ | State of charge |

$eD$ | Energy density |

$lb$ | Lower bound |

$ub$ | Upper bound |

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**Figure 10.**Behaviour of the resistance ${R}_{0}$ for a Li-Po cell according to the ${V}_{OC}$ and ${V}_{L}$ identification.

**Figure 11.**Behaviour of the resistance ${R}_{1}$ for a Li-Po cell according to the ${V}_{OC}$ and ${V}_{L}^{{}^{\prime}}$ identification.

**Figure 12.**Behaviour of the capacitance ${C}_{1}$ for a Li-Po cell according to the ${V}_{OC}$, ${V}_{L}^{{}^{\prime}}$ identification and the ${R}_{1}$ value.

**Figure 15.**Optimal solution space with the multi-objective genetic algorithm and the particle swarm optimisation for the optimisation problem.

Parameters | Value |
---|---|

Manufacturing cost | 125–1300 US/kWh |

Energy density (eD) | 295–305 Wh/L |

Objectives | 2 ($Cost,\phantom{\rule{3.33333pt}{0ex}}dE$) |

Variables | 3 (${C}_{nom}$, ${V}_{nom}$, L) |

Population | 10 |

Crossover | 0.8 |

Tolerance | 1 × 10${}^{-9}$ |

Combustion engine | 200 kW |

Gears | 6 |

Gear ratios ($\gamma $) | 1 (4.59), 2 (2.25), 3 (1.54) |

4 (1.000), 5 (0.75), 6 (0.65) | |

Weight (${m}_{Vehicle}$) | |

(Empty/Full loaded) | 15,000/25,000 kg |

Frontal area (${A}_{f}$) | 7.5 m${}^{2}$ |

Drag coefficient (${C}_{d}$) | 0.6210 |

Rolling resistance (${C}_{r}$) | 0.009 |

Tire (Radius) | 315/80/R22.5 (0.5455 m) |

# | $\mathit{Cost}$ | $\mathit{eD}$ (Wh/L) | L (L) | ${\mathit{C}}_{\mathit{nom}}$ (Ah) | ${\mathit{N}}_{\mathit{s}}$ |
---|---|---|---|---|---|

1 | 1.300812 | −305.006906 | 0.144788 | 11.93545 | 440 |

2 | 0.123982 | −294.991340 | 0.115369 | 9.198045 | 571 |

3 | 0.927891 | −301.833114 | 0.142080 | 11.59035 | 453 |

4 | 1.300812 | −305.006906 | 0.144788 | 11.93545 | 440 |

5 | 0.241222 | −295.989126 | 0.115397 | 9.231446 | 569 |

6 | 0.677771 | −299.704430 | 0.127566 | 10.33298 | 508 |

7 | 1.180479 | −303.982803 | 0.137194 | 11.27155 | 466 |

8 | 1.019624 | −302.613820 | 0.142736 | 11.67404 | 450 |

9 | 0.851227 | −301.180651 | 0.131935 | 10.73951 | 489 |

10 | 0.123982 | −294.991340 | 0.115369 | 9.198045 | 571 |

# | ${\mathit{C}}_{\mathit{nom}}$ (Ah) | ${\mathit{N}}_{\mathit{s}}$ | Array Capacity (Wh) | Consumption (kg) |
---|---|---|---|---|

1 | 11.93545 | 440 | 19,430.92 | 19.64 |

2 | 9.198045 | 571 | 19,432.71 | 19.61 |

3 | 11.59035 | 453 | 19,426.60 | 19.61 |

4 | 11.93545 | 440 | 19,430.92 | 19.64 |

5 | 9.231446 | 569 | 19,434.96 | 19.03 |

6 | 10.33298 | 508 | 19,421.88 | 19.06 |

7 | 11.27155 | 466 | 19,434.42 | 20.00 |

8 | 11.67404 | 450 | 19,437.28 | 20.00 |

9 | 10.73951 | 489 | 19,431.00 | 19.47 |

10 | 9.198045 | 571 | 19,432.71 | 19.61 |

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**MDPI and ACS Style**

Cortez, E.; Moreno-Eguilaz, M.; Soriano, F.
Advanced Methodology for the Optimal Sizing of the Energy Storage System in a Hybrid Electric Refuse Collector Vehicle Using Real Routes. *Energies* **2018**, *11*, 3279.
https://doi.org/10.3390/en11123279

**AMA Style**

Cortez E, Moreno-Eguilaz M, Soriano F.
Advanced Methodology for the Optimal Sizing of the Energy Storage System in a Hybrid Electric Refuse Collector Vehicle Using Real Routes. *Energies*. 2018; 11(12):3279.
https://doi.org/10.3390/en11123279

**Chicago/Turabian Style**

Cortez, Ernest, Manuel Moreno-Eguilaz, and Francisco Soriano.
2018. "Advanced Methodology for the Optimal Sizing of the Energy Storage System in a Hybrid Electric Refuse Collector Vehicle Using Real Routes" *Energies* 11, no. 12: 3279.
https://doi.org/10.3390/en11123279