# Exploration of Optimal Powertrain Design Using Realistic Load Profiles

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

- Powertrain weight;
- Powertrain efficiency;
- Load Point Shifting.

#### 2.1. Derivation of a Realistic Speed and Slope Profile

#### 2.2. Estimation of Passenger Occupancy

_{i}is the count of passengers boarding at stop i, z

_{j}is the count of passengers alighting at stop j, and x

_{ij}is the number of passengers on-board the vehicle. The inference model uses a Markov chain to calculate the alighting probability matrix P

_{ij}, using the transitional probability q

_{ij}, that a passenger will alight at stop i given that the passenger is in the vehicle at the i-1 stop, as shown in Equation (1). The probability q

_{j}is calculated in a Bayesian analysis by using a beta distribution to calculate the posterior probability, which is taken to be the posterior mean of the beta distribution, given by Equation (2). The alighting probability matrix is calculated by substituting the transitional probability into Equation (1) from which the trip O-D matrix is estimated using Equation (3).

#### 2.3. Vehicle Specification and Design Requirements

#### 2.4. Simulation Model for Vehicle Longitudinal Dynamics

#### 2.5. Energy Consumption Estimation

#### 2.6. Mass and Cost Estimation

#### 2.7. Optimization Framework

## 3. Results

#### 3.1. Effect of Powertrain Architecture Vatiation on the Total Cost

#### 3.2. Effects of Powertrain Architecture Variation on Vehicle Characteristics

#### 3.2.1. Rear Wheel Drive Powertrain Configuration

#### 3.2.2. All-Wheel Powertrain Configuration

#### 3.3. Load Point Shifting (Transmission and Motor)

#### 3.4. Effects of Motor Power Distribution

#### 3.5. Influence of Passenger Mass Variation and Occupancy

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Flow of passengers along the route [22].

**Figure 7.**Example of the motor power distribution between two 100 kW motors in first gear 7 (

**a**) Power request at front axle; 7 (

**b**) Power request at rear axle.

**Figure 8.**Variation of powertrain architectures. 8 (

**a**) Base version; 8 (

**b**) 2 Rear motors; 8 (

**c**) Booster, 1 Rear motor; 8 (

**d**) Booster, 2 Rear motors; 8 (

**e**) 2 Boosters, 1 Rear motor; 8 (

**f**) 4 motors.

**Figure 12.**Load point shifting by transmission (

**a**) v1 configuration with fixed gear (

**b**) 4 speed configuration (

**c**) v5 Booster configuration.

**Table 1.**Vehicle requirements and parameters [13].

Requirements | Value | Unit |

r1: Maximum speed | 80 | km/h |

r2: Gradeability | 20 | % |

Speed at gradeability | 30 | km/h |

Acceleration at gradeability | 1 | m/s^{2} |

r3: Maximum acceleration | 1.5 | m/s^{2} |

Speed at maximum acceleration | 30 | km/h |

r4: Range | 200 | Km |

Vehicle parameters | Value | Unit |

Gross vehicle weight | 6090 | Kg |

Curb weight | 3654 | Kg |

Front area | 7.1145 | m^{2} |

Drag coefficient | 0.4 | - |

Dynamic tire radius | 0.372 | m |

Rolling resistance | 0.011 | - |

Number of wheels | 4 | - |

Battery energy content | 120 | kWh |

HVAC energy demand | 3 | kW |

Other auxiliaries | 1.5 | kW |

Charging efficiency | 0.90 | - |

**Table 2.**Description of the symbols, their respective unit, and the value of the cost calculation [19].

Parameters | Symbols | Unit | Value |
---|---|---|---|

Costs of powertrain | ${C}_{PWT}$ | EUR | - |

Costs of battery | ${C}_{bat}$ | EUR | - |

Number of drive units | ${n}_{DU}$ | - | [1,2,3,4] |

Costs of inverter | ${C}_{inv}$ | EUR | - |

Costs of motor | ${C}_{mot}$ | EUR | - |

Costs of transmission | ${C}_{TM}$ | EUR | - |

Time of operation | ${t}_{op}$ | Y | - |

Energy consumption | ${E}_{cons}$ | kWh/km | - |

Distance | ${s}_{d}$ | km/day | 200 |

Days of operation | ${t}_{i}$ | - | 360 |

Costs of energy | ${c}_{kWh}$ | EUR/kWh | 0.13 |

Discount rate | ${d}_{i}$ | - | 0.05 |

Distance over lifetime | - | km | 579,600 |

Configurations | Motor Power in kW | No. of Motors | No. of Gears | |||
---|---|---|---|---|---|---|

Front Axle | Rear Axle | Front Axle | Rear Axle | Front Axle | Rear Axle | |

v1: Base configuration | - | 240 | - | 1 | - | 1 |

v2: Base 2 speed | - | 240 | - | 1 | - | 2 |

v3: Base 4 speed | - | 240 | - | 1 | - | 4 |

v4: Two rear Motors | 120 | 120 | - | 2 | - | 4 |

v5: Booster, one rear motor | 90 | 150 | 1 | 1 | 1 | 1 |

v6: Booster, two rear motors | 90 | 150 | 1 | 2 | 4 | 1 |

v7: Tow boosters, one rear motor | 130 | 110 | 2 | 1 | 1 | 4 |

v8: Four motors | 120 | 120 | 2 | 2 | 4 | 1 |

Motor Topology/Power in kW | Number of Gears | Total Power in kW | Energy Cost (EUR) | Total Cost (EUR) | ||
---|---|---|---|---|---|---|

Front Axle | Rear Axle | Front Axle | Rear Axle | |||

Motor 1 | Motor 1 | |||||

Mean occupancy with passenger variation | ||||||

75 | 160 | 1 | 1 | 235 | 31,911.23 | 51,670.23 |

75 | 165 | 1 | 1 | 235 | 31,858.17 | 51,700.54 |

70 | 165 | 1 | 1 | 235 | 32,134.14 | 51,892.35 |

70 | 170 | 1 | 1 | 240 | 32,091.00 | 51,918.94 |

80 | 155 | 1 | 1 | 235 | 32,255.39 | 52,015.09 |

Mean occupancy with a constant number of passengers | ||||||

75 | 160 | 1 | 1 | 235 | 31,995.56 | 51,798.77 |

75 | 165 | 1 | 1 | 240 | 32,039.77 | 51,837.93 |

70 | 165 | 1 | 1 | 235 | 32,133.39 | 51,891.60 |

70 | 170 | 1 | 1 | 240 | 32,133.04 | 51,960.98 |

80 | 155 | 1 | 1 | 235 | 32,253.09 | 52,012.79 |

High occupancy with a constant number of passengers | ||||||

80 | 160 | 1 | 1 | 240 | 35,487.74 | 55,317.20 |

75 | 160 | 1 | 1 | 235 | 35,766.88 | 55,525.90 |

75 | 165 | 1 | 1 | 240 | 35,741.38 | 55,583.75 |

70 | 165 | 1 | 1 | 235 | 35,903.43 | 55,661.63 |

70 | 170 | 1 | 1 | 240 | 36,017.28 | 55,845.21 |

High occupancy with passenger variation | ||||||

90 | 145 | 1 | 1 | 235 | 35,438.75 | 55,199.58 |

90 | 150 | 1 | 1 | 240 | 35,367.71 | 55,214.49 |

85 | 150 | 1 | 1 | 235 | 35,462.29 | 55,238.75 |

80 | 155 | 1 | 1 | 235 | 35,543.55 | 55,303.25 |

95 | 140 | 1 | 1 | 235 | 35,575.27 | 55,332.06 |

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## Share and Cite

**MDPI and ACS Style**

Pathak, A.; Sethuraman, G.; Krapf, S.; Ongel, A.; Lienkamp, M.
Exploration of Optimal Powertrain Design Using Realistic Load Profiles. *World Electr. Veh. J.* **2019**, *10*, 56.
https://doi.org/10.3390/wevj10030056

**AMA Style**

Pathak A, Sethuraman G, Krapf S, Ongel A, Lienkamp M.
Exploration of Optimal Powertrain Design Using Realistic Load Profiles. *World Electric Vehicle Journal*. 2019; 10(3):56.
https://doi.org/10.3390/wevj10030056

**Chicago/Turabian Style**

Pathak, Aditya, Ganesh Sethuraman, Sebastian Krapf, Aybike Ongel, and Markus Lienkamp.
2019. "Exploration of Optimal Powertrain Design Using Realistic Load Profiles" *World Electric Vehicle Journal* 10, no. 3: 56.
https://doi.org/10.3390/wevj10030056