# Energy Consumption and Life Cycle Costs of Overhead Catenary Heavy-Duty Trucks for Long-Haul Transportation

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Methodology

#### 2.2. Modeling of Overhead Catenary Truck

#### 2.2.1. Route Model

_{OC}. The actual position is calculated by integrating the actual speed v

_{act}over simulation time and the signal’s reference speed v

_{ref}, slope, and maximum available catenary power P

_{OC}are provided to the following blocks.

#### 2.2.2. Driver Model

_{set}to meet the reference speed by accelerating or decelerating the vehicle. The set acceleration is shown in Figure 3. The value of the set acceleration varies depending on the actual velocity and corresponds to the acceleration of a 40 t diesel truck [10] multiplied by a factor 0.7, as it is assumed that the vehicle does not accelerate at full power at standard driving situation. The deceleration is assumed to be constant at 0.9 m/s

^{2}. Both the acceleration and the deceleration values were chosen to fit the typical acceleration and deceleration times of heavy-duty trucks on highways that can be observed.

#### 2.2.3. Driving Resistances Model

_{set}, the slope, and the actual velocity v

_{act}and calculates the set drivetrain power P

_{drive,set}to overcome the actual driving resistance. The actual driving resistance is the sum of air resistance, rolling resistance, slope resistance, and acceleration resistance. The driving resistances model is described in detail in the previous study [4].

#### 2.2.4. Drivetrain Model

_{OC}, the battery power P

_{bat}, the power P

_{drive}to overcome the driving resistances and the power P

_{aux}for auxiliary consumers, the following power balance at the direct current link results:

_{pan}is the pantograph efficiency, η

_{BC}is the efficiency of the battery converter, η

_{gearbox}is the gearbox efficiency, and η

_{mot&conv}is the efficiency of the electric motor and its converter. The pantograph efficiency η

_{pan}is set to 0.99 according to the measurement results of a prototype overhead catenary truck in the project ENUBA 2 [8]. The efficiency η

_{BC}of the battery converter is assumed in this study to 0.95. According to the gearbox efficiencies for heavy-duty trucks given in [13], the gearbox efficiency η

_{gearbox}is assumed as 0.94. The electric machine and the traction converter were implemented as an efficiency map [14]. Their efficiency η

_{mot&conv}depends on the shaft speed and torque. As the implemented three-phase permanent magnet electric motor has a nominal power of 188 kW, two these motors were implemented, providing a total power of 376 kW that is suitable for a heavy-duty truck. The auxiliary power P

_{aux}is assumed constant as 5 kW.

_{bat,set}using Equation (1), the set drivetrain power P

_{drive,set}to overcome the actual driving resistance, and the overhead catenary power P

_{OC}. Afterwards, the battery power P

_{bat,act}is simulated by a separate block that is described in the next subsection. Finally, the inverse drivetrain model calculates the actual available drivetrain power P

_{drive,act}to overcome the driving resistances.

#### 2.2.5. Battery Model

#### 2.3. Modeling of Life Cycle Costs

## 3. Calculation

#### 3.1. Dimensioning of Traction Battery

_{bat,dch}is connected to the battery capacity C

_{bat}via discharge current rate R

_{dch}according to the equation:

#### 3.2. Dimensioning of Catenary Power System

_{pan}provided to the pantograph in order to charge the battery and to cover the traction power, the following equation is used:

_{pan}is the pantograph efficiency of 0.99, S

_{bat}is the distance driven by battery, and S

_{oc}is the distance driven by the overhead catenary. For the battery charging efficiency η

_{bat,cha}the previous simulations showed an efficiency of 0.97. The first summand in this formula gives the average traction power and the second summand gives the required power to charge the battery during driving on a catenary section.

_{pan}for the considered catenary configurations assuming a daily driving distance of 720 km (Section 3.4). For the continuous catenary configuration, the distance S

_{bat}driven with energy from battery is 40 km for the route sections apart the highway at the beginning and at the end of the daily route. The remaining distance of 680 km is driven with energy from catenary. Also, for the sectional catenary configuration, 40 km driving distance on route sections apart the highway is assumed. So, one third of the remaining 680 km distance is equipped with catenary. The resulting pantograph power for both catenary configurations using Equation (3) are stated in Table 3.

_{trucks}for trucks on highways and the substations number n

_{sub}per 100 km. According to [19], the average daily traffic intensity on a German highway is 8620 trucks per driving direction. Assuming that most trucks drive between 6 a.m. and 10 p.m. and disregarding the night traffic, the average hourly traffic intensity n

_{trucks}results in ca. 540 trucks per driving direction. The substations number n

_{sub}is given in [7] as 20 substations per 100 km highway at 1.5 kV catenary voltage with direct current. Using the average hourly traffic intensity n

_{trucks}, the substations number n

_{sub}per 100 km and the average speed v of 80 km/h, the trucks number n

_{trucks,sub}fed from one substation on both driving directions can be calculated:

_{trucks,sub}is 67.5 trucks that are fed from one substation. Taking the catenary line efficiency η

_{oc}of 0.95, the rectifier efficiency η

_{rect}of 0.98, the transformer efficiency η

_{tr}of 0.97 [8] and the calculated pantograph power P

_{pan}for the considered catenary configurations, the output power P

_{sub}and the electricity grid connection power P

_{con}of one substation can be calculated using the following equations:

#### 3.3. Calculation of Vehicle Weight

#### 3.4. Definition of Transportation Scenario

## 4. Results

#### 4.1. Truck Performance

#### 4.2. Life Cycle Costs

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Parameter | Value | Source |
---|---|---|

Overhead Catenary Truck | ||

Vehicle Body (w/o drivetrain) | 91,800 € | [3] |

Battery with HEa Cells | 300 €/kWh | [23] and own estimation |

Battery with HPa Cells | 400 €/kWh | [23] and own estimation |

Battery Price Development | −6.7%/a | [23] |

E-Machine | 27.5 €/kW | [3] |

Power Electronics | 35 €/kW | [3] |

Pantograph | 38,000 € | [3] |

Battery Electric Truck | ||

Vehicle Body (w/o drivetrain) | 91,800 € | [3] |

Battery with HEa Cells | 300 €/kWh | [23] and own estimation |

Battery Price Development | −6.7%/a | [23] |

E-Machine | 27.5 €/kW | [3] |

Power Electronics | 35 €/kW | [3] |

Diesel Truck | ||

Diesel Truck | 120,000 € | [3] |

Parameter | Value | Source |
---|---|---|

Electricity | ||

Electricity, net | 0.139 €/kWh | [27] |

Electricity Price Development | 5.3%/a | [27] |

Diesel Fuel | ||

Diesel Fuel, net | 0.949 €/L | [28,29] |

Diesel Fuel Price Development | 2.3%/a | [28] |

Parameter | Value | Source |
---|---|---|

Substation | ||

Rectifier | 80 €/kW | [30] |

Transformer | 45 €/kW | [30] |

Finishing Costs | 85,000 € | [30] |

Grid Connection | ||

Connection to Grid (assuming 2.5 km distance) | Fix: 25.9 €/kW, Var: 140 €/m | [6,30] |

Contribution towards Network | 60.44 €/kW | [30] |

Catenary | ||

Catenary incl. Pylons (per Direction) | 730 €/m | [8,17] |

Lifetimes | ||

Lifetime Transformer | 25 a | [30] |

Lifetime Power Electronics | 12 a | [30] |

**Table A4.**Cost parameters for charging station infrastructure. The source for the costs parameters in this table is private communication with manufacturers, who want to stay anonymous [30].

Parameter | Value |
---|---|

Charging Station | |

Power Electronics (Fast Charging Station) | 149,000 € |

Power Electronics (Slow Charging Station) | 9800 € |

Coupling Connection (Fast Charging Station) | 21,000 € |

Coupling Connection (Slow Charging Station) | 1400 € |

Finishing Costs (Fast Charging Station) | 85,000 € |

Finishing Costs (Slow Charging Station) | 10,000 € |

Transformer | 45 €/kW |

Grid Connection | |

Connection to Grid (assuming 2.5 km distance) | Fix: 25.9 €/kW, |

Var: 140 €/m, | |

Total: 609,000 € | |

Contribution towards Network | 60,44 €/kW |

Lifetimes | |

Lifetime Transformer | 25 a |

Lifetime Power Electronics | 12 a |

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**Figure 1.**Overview of the holistic model including the vehicle simulation model and the life cycle costs (LCC) model.

**Figure 7.**Weight breakdown of the main truck components for the overhead catenary trucks with different traction batteries and battery cells compared to diesel trucks and battery electric trucks.

**Figure 8.**Energy consumption for the overhead catenary trucks with different configurations of catenary and traction batteries compared to battery electric truck and diesel truck.

**Figure 9.**(

**a**) State of charge (SOC) and (

**b**) temperature of the traction battery during the daily transportation scenario for the overhead catenary trucks using the continuous and sectional catenary configurations.

**Figure 10.**Net present values for catenary infrastructure and charging infrastructure per one truck in the specified transportation scenario.

**Figure 11.**Life cycle costs of the considered overhead catenary trucks, battery electric trucks, and diesel trucks in the specified transportation scenario related to the total mileage.

**Table 1.**Technical data of cells contained in the electric cell model and assumed costs of battery pack containing the particular cell type.

Cell Id | Cell Type | Chemistry | Nominal Capacity | Nominal Voltage | Max. Charge Current Rate | Max. Discharge Current Rate | Number of Cycles (15 °C, 1 C) | Assumed Battery Pack Costs |
---|---|---|---|---|---|---|---|---|

Cell HEa | High Energy | Li(NiMnCo)O_{2} | 10 Ah | 3.6 V | 2 C | 2 C | 6500 Cycles | 300 €/kWh |

Cell HPa | High Power | Li(NiMnCo)O_{2} | 6 Ah | 3.6 V | 5 C | 20 C | 20,000 Cycles | 400 €/kWh |

Catenary Configuration | Battery Cells | Battery Capacity |
---|---|---|

Continuous Catenary | HEa | 190.5 kWh |

HPa | 96 kWh | |

Sectional Catenary | HEa | 190.5 kWh |

HPa | 120 kWh |

Catenary Configuration | Driving Distance S_{oc} with Catenary | Driving Distance S_{bat} without Catenary | Pantograph Power P_{pan} |
---|---|---|---|

Continuous Catenary | 680 km | 40 km | 155 kW |

Sectional Catenary | 230 km | 490 km | 480 kW |

Average Substation | Continuous Catenary | Sectional Catenary |
---|---|---|

Substation Output Power P_{sub} | 11.0 MW | 34.0 MW |

Transformer Output Power | 11.3 MW | 34.7 MW |

Grid Connection Power P_{con} | 11.6 MW | 35.7 MW |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mareev, I.; Sauer, D.U.
Energy Consumption and Life Cycle Costs of Overhead Catenary Heavy-Duty Trucks for Long-Haul Transportation. *Energies* **2018**, *11*, 3446.
https://doi.org/10.3390/en11123446

**AMA Style**

Mareev I, Sauer DU.
Energy Consumption and Life Cycle Costs of Overhead Catenary Heavy-Duty Trucks for Long-Haul Transportation. *Energies*. 2018; 11(12):3446.
https://doi.org/10.3390/en11123446

**Chicago/Turabian Style**

Mareev, Ivan, and Dirk Uwe Sauer.
2018. "Energy Consumption and Life Cycle Costs of Overhead Catenary Heavy-Duty Trucks for Long-Haul Transportation" *Energies* 11, no. 12: 3446.
https://doi.org/10.3390/en11123446