# Li-Ion Battery Lifetime Model’s Influence on the Economic Assessment of a Hybrid Electric Bus’s Operation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Scenario Overview

## 3. Modelling of the Onboard Dual ESS

#### 3.1. Electrical Modelling

_{SC}supercapacitor cells in series and the SC pack groups B

_{SC}strings in parallel, the equations describing the equivalent electrical model for the SC pack were implemented as follows:

_{BT}battery cells in series and the BT pack groups B

_{BT}strings in parallel, the equations for the equivalent electrical model of the BT pack were implemented as follows:

#### 3.2. Lifetime Modelling

^{6}cycles and a maximum lifetime of 10 years were implemented as the upper limit for the SC lifetime. On the contrary, the lifetime estimation of the Li-ion batteries was one of the core elements of the present study. Two different battery lifetime models were considered to evaluate their impact upon the ESS sizing and the determination of the optimal operation constraints: (i) a Wöhler-curve-based lifetime model and (ii) a semi-empirical lifetime model. These two different approaches represent different levels of complexity and experimental labour costs, but also are unequally accurate for prediction of BT lifetime under real operation conditions.

#### 3.2.1. Wöhler-Curve-Based Lifetime Model

#### 3.2.2. Semi-Empirical Lifetime Model

## 4. Rule-Based Energy Management Strategy

#### 4.1. Hybrid Driving Mode

- ${P}_{genset}\left(k\right)\text{}\left(\mathrm{kW}\right)$ the genset power target.
- ${P}_{BT\_dch}$ (kW) the BT power target during discharge.
- ${P}_{BT\_ch}\text{}\left(\mathrm{kW}\right)$ the BT power target during charge.
- ${V}_{nom\_BTcell}\text{}\left(\mathrm{V}\right)$ the nominal voltage of the BT cell.
- ${I}_{1C\_BTcell}\text{}\left(\mathrm{A}\right)$ the nominal current of the BT cell.
- ${C}_{rate}$ the C-rate limitation for the BT operation.
- ${p}_{dch}$ the ratio for BT pack discharging (${p}_{dch}\in \left[0\u20131\right]$) with different values for DM, SM, and Electric Mode (EM).
- ${p}_{ch}$ the ratio for charging the BT pack (${p}_{ch}\in \left[0\u20131\right]$).
- ${E}_{CB}\text{}(\mathrm{kWh})$ the energy dissipated in the crowbar.

- ${P}_{SC\_max\_ch}\text{}\left(\mathrm{kW}\right)$ is the maximum allowable power target for charging the SC pack (maximum power of the DC/DC).
- ${E}_{BT\_tr},{E}_{B{T}_{rg}}\left(\mathrm{kWh}\right)$ is the energy provided/stored in the BT pack during a traction and braking phase.
- ${E}_{SC\_tr},{E}_{S{C}_{rg}}\left(\mathrm{kWh}\right)$ is the energy provided/stored in the SC pack during a traction and braking phase.
- ${E}_{CB}\text{}\left(\mathrm{kWh}\right)$ is the energy dissipated in the crowbar.
- ${E}_{genset}\text{}\left(\mathrm{kWh}\right)$ is the energy provided by the genset.
- ${E}_{BT\_ch}\text{}\left(\mathrm{kWh}\right)$ is the energy provided by the genset to charge the BT pack.

#### 4.2. Full-Electric Driving Mode

## 5. Multi-Objective Optimisation Problem

#### Operation Cost of the Dual ESS

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Series Hybrid Electric Bus powertrain configuration. BT, battery; SC, supercapacitor; AC, alternating current; DC, direct current; EM, electric motor; T, transmission; ICE, internal combustion engine; EG, electric generator; CB, crowbar.

**Figure 4.**Number of cycles versus Depth of Discharge (DOD) curve considered for the Whöler curve [21].

**Figure 8.**Lifetime estimated for different battery and supercapacitor sizing values with the set of optimal operation constraints obtained with each of the two lifetime models considered. The lifetime is scaled in p.u. considering the maximum lifetime obtained for the Wöhler-based optimisation.

**Figure 9.**Comparison of the daily battery operation profile for the optimal solutions calculated: (

**a**) with the Wöhler-curve-based and (

**b**) semi-empirical lifetime models.

**Table 1.**Electrical parameters of the BT and SC base cells [15].

BT (LFP 2.3Ah 26650-Type) | SC (BCAP3000) | ||
---|---|---|---|

Nominal voltage | 3.3 V | Nominal voltage | 2.7 V |

Nominal capacity | 2.3 Ah | Nominal capacitance | 3000 F |

DC internal resistance | ${R}_{int}\left(SO{C}_{BT}\right)$ Ω | DC internal resistance | 0.29 mΩ |

Max C rate disch./ch. | 3.5/3.5 | - | - |

Gravimetric Energy Density | 108 Wh/kg | Gravimetric Energy Density | 6.0 Wh/kg |

Number of cells in series (pack) | 182 | Number of cells in series (pack) | 144 |

DC/DC converter rating | 50 kW | DC/DC converter rating | 150 kW |

Variable | Wöhler-Based Optimisation | Semi-Empirical-Based Optimisation |
---|---|---|

$SO{C}_{u\_ctrl}$(%) | 66 | 93 |

$SO{C}_{l\_ctrl}$(%) | 39 | 44 |

${P}_{genset\_1}$(kW) | 53 | 63 |

${P}_{genset\_2}$(kW) | 83 | 124 |

${p}_{dch\_DM}$(kW) | 78 | 71 |

${p}_{dch\_SM}$(kW) | 81 | 25 |

${p}_{dch\_AM}$(kW) | 21 | 30 |

${p}_{ch\_CM}$(kW) | 81 | 77 |

${B}_{BT}$(-) | 12 | 10 |

${B}_{SC}$(-) | 2 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Martinez-Laserna, E.; Herrera, V.I.; Gandiaga, I.; Milo, A.; Sarasketa-Zabala, E.; Gaztañaga, H.
Li-Ion Battery Lifetime Model’s Influence on the Economic Assessment of a Hybrid Electric Bus’s Operation. *World Electr. Veh. J.* **2018**, *9*, 28.
https://doi.org/10.3390/wevj9020028

**AMA Style**

Martinez-Laserna E, Herrera VI, Gandiaga I, Milo A, Sarasketa-Zabala E, Gaztañaga H.
Li-Ion Battery Lifetime Model’s Influence on the Economic Assessment of a Hybrid Electric Bus’s Operation. *World Electric Vehicle Journal*. 2018; 9(2):28.
https://doi.org/10.3390/wevj9020028

**Chicago/Turabian Style**

Martinez-Laserna, Egoitz, Victor I. Herrera, Iñigo Gandiaga, Aitor Milo, Elixabet Sarasketa-Zabala, and Haizea Gaztañaga.
2018. "Li-Ion Battery Lifetime Model’s Influence on the Economic Assessment of a Hybrid Electric Bus’s Operation" *World Electric Vehicle Journal* 9, no. 2: 28.
https://doi.org/10.3390/wevj9020028