# Energy Uncertainty Analysis of Electric Buses

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State-of-the-Art

## 3. Methods

#### 3.1. Buses and Routes

#### 3.2. Measurements

#### 3.2.1. Data Collection

#### 3.2.2. Discharge Cycles

#### 3.2.3. Charge Cycles

#### 3.3. Sensitivity Analysis with Multiple Linear Regression

#### 3.3.1. Background

#### 3.3.2. MLR with Correlated Inputs

#### 3.3.3. Normalization of Second-Order Effects

#### 3.4. Statistical Analysis

## 4. Results

#### 4.1. Operation Factors

#### 4.1.1. Temperature Factors

#### 4.1.2. Auxiliary Devices

#### 4.1.3. Route and Behavior Factors

#### 4.2. Energy Consumption Rate (ECR) on Discharges

#### 42.1. Output Analysis

^{2}to 0.7 m/s

^{2}. The reason for this setting was an earlier study of the same bus on the same route, where the driving behavior of BEBs was compared with diesel buses [51]. The BEBs were driven 10% faster and accelerated 10% faster than the diesel buses. The lowering of the acceleration limit had an opposite effect to what was expected. The average speed was increased by 4% and the average driving aggressiveness by 14%. Thus, it would seem that limiting the driver’s ability to accelerate could lead to unwanted frustration and actually increase recklessness rather than reduce it. However, the acceleration limit change did not have a notable effect on the ECR.

#### 4.2.2. Input Analysis

#### 4.3. Internal Resistance of the Battery (IRB) on Charges

#### 4.3.1. Output Analysis

#### 4.3.2. Input Analysis

## 5. Discussion

## 6. Conclusions

^{2}to 0.7 m/s

^{2}had no effect on energy consumption, yet it significantly increased driving aggressiveness.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The studied bus routes: E11, H23 and H55. Route E11 operates in the suburban city Espoo and the other two in the Finnish capital, Helsinki. The figure was produced with GPS Visualizer [29].

**Figure 2.**Operation factor data that were gathered from the battery electric buses (BEBs), using an Internet of Things (IoT) cloud server platform.

**Figure 3.**Raw current signal collected from the server compared with the corrected and normalized current signal.

**Figure 4.**Data parsing of charge cycles. The presented view shows a complete charge cycle. The start and end of a charging event is highlighted with a vertical line. The black line represents the battery current and the blue dashed line represents the battery voltage.

**Figure 5.**On the left, the parabolic relation between ambient temperature and energy consumption rate (ECR). On the right, the linear relation between battery temperature and internal resistance of the battery (IRB).

**Figure 6.**Auxiliary device power of E1 bus as a function of time. The measurement was done on 18 April 2016. The outside temperature on this cycle was 20.5 degrees Celsius on average.

**Figure 14.**The probability density functions of energy regeneration in the suburban (Espoo) and city (Helsinki) routes.

**Figure 17.**Sensitivity indices of the crucial operation factors affecting the variation in ECR. (

**a**) The partial variance decomposition is on the left, and (

**b**) the normalized second-order effects are on the right.

**Figure 19.**The average fast-charge resistance variation as a function of charges. The lines are the fourth-degree polynomial average internal resistances of the battery packs of the buses.

**Figure 20.**Sensitivity indices of the crucial operation factors affecting the variation in the IRB. (

**a**) The partial variance decomposition is on the left, and (

**b**) the normalized second-order effects are on the right.

Frame | Aluminum |
---|---|

Curb weight | 10,500 kg |

Gear-ratio | 4.88 |

Manufacturing year | 2015 |

Length | 12 m |

Dynamic radius of tire | 43 cm |

Battery manufacturer | Toshiba |

Battery chemistry | Lithium Titanate Oxide |

Battery capacity | 55 kWh, 80 Ah × 690 V |

Motor manufacturer | Visedo |

Motor | Max power 180 kW |

Charging system | 350 kW roof connected pantograph |

Diesel heater | 24 kW |

Heat pump | 5 kW |

Symbol | Factor | Range | Mean | Unit | Data |
---|---|---|---|---|---|

Discharges | |||||

t | Time | [13.0, 49.3] | 26.3 | min | total, measured |

Tb | Battery temperature | [−17.4, 48.5] | 24.1 | °C | mean, measured |

Ta | Ambient temperature | [−17.4, 28.7] | 10.8 | °C | mean, measured |

Pac | Air compressor power | [0.0, 2.0] | 0.44 | kW | mean, measured |

Pdc | DCDC converter power | [0.4, 5.9] | 1.9 | kW | mean, measured |

Php | Heat pump | [0.0, 3.46] | 0.81 | kW | mean, measured |

Pps | Power steering power | [0.1, 1.0] | 0.54 | kW | mean, measured |

SOC | Battery state-of-charge | [17.1, 99.5] | 70.4 | % | start, measured |

Bh | Battery age | [1, 4099] | 1739 | h | start, measured |

v | Average speed | [9.9, 44.9] | 21.2 | km/h | mean, measured |

Agg | Driving aggressiveness | [0.06, 0.31] | 0.17 | m/s^{2} | single, computed |

Dist | Distance | [6.7, 10.4] | 9.1 | km | total, computed |

Spk | Stops per kilometer | [0.1, 5.6] | 2.1 | 1/km | total, computed |

Idle | Idle time | [0.3, 58.0] | 22.0 | % | total, computed |

dir | Direction | [0, 1] | 0.5 | - | single, computed |

Charges | |||||

t | Time | [0.5, 9.1] | 3.8 | min | total, measured |

Tb | Battery temperature | [1.3, 47.6] | 24.9 | °C | mean, measured |

Ta | Ambient temperature | [−12.0, 28.0] | 11.1 | °C | mean, measured |

Ib | Battery Current | [218.8, 449.4] | 357.7 | A | mean, measured |

Vb | Battery Voltage | [402.4, 920.0] | 758.6 | V | mean, measured |

SOC | Battery State-of-Charge | [0.3, 77] | 50.1 | % | start, measured |

Helsinki vs. Espoo | |||||
---|---|---|---|---|---|

Metric | Ta | Pac | Pdc | Spk | Agg |

Mean | −25.6% | 36.4% | 42.0% | 29.6% | 5.7% |

St. dev. | −20.6% | 1.5% | 60.2% | 31.0% | −11.5% |

Metric | Pdc | Pps | Idle | Spk | Ta | v | Pac | Agg | Php | Tb | SOC |
---|---|---|---|---|---|---|---|---|---|---|---|

VIF | 2.31 | 2.71 | 5.37 | 6.87 | 2.05 | 9.88 | 1.7 | 2.47 | 1.54 | 1.53 | 1.11 |

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## Share and Cite

**MDPI and ACS Style**

Vepsäläinen, J.; Ritari, A.; Lajunen, A.; Kivekäs, K.; Tammi, K.
Energy Uncertainty Analysis of Electric Buses. *Energies* **2018**, *11*, 3267.
https://doi.org/10.3390/en11123267

**AMA Style**

Vepsäläinen J, Ritari A, Lajunen A, Kivekäs K, Tammi K.
Energy Uncertainty Analysis of Electric Buses. *Energies*. 2018; 11(12):3267.
https://doi.org/10.3390/en11123267

**Chicago/Turabian Style**

Vepsäläinen, Jari, Antti Ritari, Antti Lajunen, Klaus Kivekäs, and Kari Tammi.
2018. "Energy Uncertainty Analysis of Electric Buses" *Energies* 11, no. 12: 3267.
https://doi.org/10.3390/en11123267